[{"data":1,"prerenderedAt":16500},["ShallowReactive",2],{"navigation":3,"\u002Fblog\u002Fchemical-potential-and-diffusion-potential":46,"\u002Fblog\u002Fchemical-potential-and-diffusion-potential-surround":16496},[4],{"title":5,"path":6,"stem":7,"children":8,"page":45},"Blog","\u002Fblog","blog",[9,13,17,21,25,29,33,37,41],{"title":10,"path":11,"stem":12},"吉布斯自由能、化学势与扩散势","\u002Fblog\u002Fchemical-potential-and-diffusion-potential","blog\u002Fchemical-potential-and-diffusion-potential",{"title":14,"path":15,"stem":16},"Deploying Nuxt Static Sites with Nginx","\u002Fblog\u002Fdeploying-nuxt-static-site-with-nginx","blog\u002Fdeploying-nuxt-static-site-with-nginx",{"title":18,"path":19,"stem":20},"相变驱动力计算","\u002Fblog\u002Fphase-transformation-driving-force","blog\u002Fphase-transformation-driving-force",{"title":22,"path":23,"stem":24},"Python 环境配置完全指南：Conda 与国内镜像源","\u002Fblog\u002Fpython-environment-setup-guide","blog\u002Fpython-environment-setup-guide",{"title":26,"path":27,"stem":28},"Rust 编译与配置指南","\u002Fblog\u002Frust-compilation-and-configuration","blog\u002Frust-compilation-and-configuration",{"title":30,"path":31,"stem":32},"SSH Key Authentication Setup Guide","\u002Fblog\u002Fssh-key-authentication-setup","blog\u002Fssh-key-authentication-setup",{"title":34,"path":35,"stem":36},"Tauri + Rust 技术栈与编译说明","\u002Fblog\u002Ftauri-rust-tech-stack-and-build","blog\u002Ftauri-rust-tech-stack-and-build",{"title":38,"path":39,"stem":40},"Complete Guide to Utoipa Integration with Axum","\u002Fblog\u002Futoipa-integration-with-axum","blog\u002Futoipa-integration-with-axum",{"title":42,"path":43,"stem":44},"Rust: Code Once, Build Anywhere","\u002Fblog\u002Fwhy-rust-priority","blog\u002Fwhy-rust-priority",false,{"id":47,"title":10,"author":48,"body":52,"date":16487,"description":16488,"extension":16489,"image":16490,"meta":16491,"minRead":16492,"navigation":16493,"path":11,"seo":16494,"stem":12,"__hash__":16495},"blog\u002Fblog\u002Fchemical-potential-and-diffusion-potential.md",{"name":49,"avatar":50},"Jing Zhong",{"src":51,"alt":49},"https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002Fme.jpg",{"type":53,"value":54,"toc":16476},"minimark",[55,60,64,70,75,215,503,506,823,1131,1163,1454,1597,1600,1914,1917,2669,2672,3069,3239,3242,3947,3950,4992,4995,5551,5555,5663,5971,5973,6344,6347,6674,6704,6972,7113,7115,7481,7484,8205,8288,8290,8682,8846,8848,9546,9548,10580,10582,11122,11126,11132,11681,11685,12224,12228,12231,12236,12239,12570,12631,12943,12948,12951,13341,13343,13666,13669,13672,14243,14246,14750,14753,14994,14997,15286,15318,15868,15871,16131,16134,16459,16462,16466],[56,57,59],"h2",{"id":58},"the-partial-gibbs-energy-and-the-gibbs-energy","The partial Gibbs energy and the Gibbs energy",[61,62,63],"p",{},"The partial Gibbs energy, or the chemical potential, is the partial quantity of the Gibbs energy, which means that it is independent of the amount of substance. Generally speaking, the Gibbs energy can be described as a function of temperature, pressure and compositions of components, and thus the chemical potential can be derived from such a mathematical formula. Sometimes, one might feel confused that there exist several different formulas of chemical potential with respect to the Gibbs energy. In this post, two different formulas are to be discussed, respectively.",[61,65,66],{},[67,68,69],"em",{},"In the following derivation, the temperature and pressure are assumed as constant.",[71,72,74],"h3",{"id":73},"for-gibbs-energy-with-independent-composition","For Gibbs energy with independent composition",[61,76,77,78,123,124,184,185,214],{},"In this context, the Gibbs energy is a function of the solute components, denoted as 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",[79,186,188,201],{"className":187},[82],[79,189,191],{"className":190},[86],[88,192,193],{"xmlns":90},[92,194,195,199],{},[95,196,197],{},[137,198,139],{},[102,200,139],{"encoding":104},[79,202,204],{"className":203,"ariaHidden":109},[108],[79,205,207,211],{"className":206},[113],[79,208],{"className":209,"style":210},[117],"height:0.4306em;",[79,212,139],{"className":213},[122,162],"-th component is regarded as the solvent.",[61,216,217,252],{},[79,218,220,290],{"className":219},[82],[79,221,223],{"className":222},[86],[88,224,225],{"xmlns":90},[92,226,227,287],{},[95,228,229,232,235,238,242,250,253,260,262,266,268,270,272,284],{},[137,230,231],{},"G",[141,233,234],{},"=",[137,236,237],{},"f",[141,239,241],{"stretchy":240},"false","(",[243,244,245,248],"msub",{},[137,246,247],{},"n",[98,249,100],{},[141,251,252],{"separator":109},",",[243,254,255,257],{},[137,256,247],{},[98,258,259],{},"2",[141,261,252],{"separator":109},[137,263,265],{"mathvariant":264},"normal",".",[137,267,265],{"mathvariant":264},[137,269,265],{"mathvariant":264},[141,271,252],{"separator":109},[243,273,274,276],{},[137,275,247],{},[95,277,278,280,282],{},[137,279,139],{},[141,281,143],{},[98,283,100],{},[141,285,286],{"stretchy":240},")",[102,288,289],{"encoding":104},"G = f(n_1, n_2, ..., n_{m-1})",[79,291,293,314],{"className":292,"ariaHidden":109},[108],[79,294,296,300,303,307,311],{"className":295},[113],[79,297],{"className":298,"style":299},[117],"height:0.6833em;",[79,301,231],{"className":302},[122,162],[79,304],{"className":305,"style":306},[166],"margin-right:0.2778em;",[79,308,234],{"className":309},[310],"mrel",[79,312],{"className":313,"style":306},[166],[79,315,317,321,325,329,385,389,393,433,436,439,443,446,449,499],{"className":316},[113],[79,318],{"className":319,"style":320},[117],"height:1em;vertical-align:-0.25em;",[79,322,237],{"className":323,"style":324},[122,162],"margin-right:0.1076em;",[79,326,241],{"className":327},[328],"mopen",[79,330,332,335],{"className":331},[122],[79,333,247],{"className":334},[122,162],[79,336,339],{"className":337},[338],"msupsub",[79,340,344,376],{"className":341},[342,343],"vlist-t","vlist-t2",[79,345,348,371],{"className":346},[347],"vlist-r",[79,349,353],{"className":350,"style":352},[351],"vlist","height:0.3011em;",[79,354,356,361],{"style":355},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[79,357],{"className":358,"style":360},[359],"pstrut","height:2.7em;",[79,362,368],{"className":363},[364,365,366,367],"sizing","reset-size6","size3","mtight",[79,369,100],{"className":370},[122,367],[79,372,375],{"className":373},[374],"vlist-s","​",[79,377,379],{"className":378},[347],[79,380,383],{"className":381,"style":382},[351],"height:0.15em;",[79,384],{},[79,386,252],{"className":387},[388],"mpunct",[79,390],{"className":391,"style":392},[166],"margin-right:0.1667em;",[79,394,396,399],{"className":395},[122],[79,397,247],{"className":398},[122,162],[79,400,402],{"className":401},[338],[79,403,405,425],{"className":404},[342,343],[79,406,408,422],{"className":407},[347],[79,409,411],{"className":410,"style":352},[351],[79,412,413,416],{"style":355},[79,414],{"className":415,"style":360},[359],[79,417,419],{"className":418},[364,365,366,367],[79,420,259],{"className":421},[122,367],[79,423,375],{"className":424},[374],[79,426,428],{"className":427},[347],[79,429,431],{"className":430,"style":382},[351],[79,432],{},[79,434,252],{"className":435},[388],[79,437],{"className":438,"style":392},[166],[79,440,442],{"className":441},[122],"...",[79,444,252],{"className":445},[388],[79,447],{"className":448,"style":392},[166],[79,450,452,455],{"className":451},[122],[79,453,247],{"className":454},[122,162],[79,456,458],{"className":457},[338],[79,459,461,490],{"className":460},[342,343],[79,462,464,487],{"className":463},[347],[79,465,467],{"className":466,"style":352},[351],[79,468,469,472],{"style":355},[79,470],{"className":471,"style":360},[359],[79,473,475],{"className":474},[364,365,366,367],[79,476,478,481,484],{"className":477},[122,367],[79,479,139],{"className":480},[122,162,367],[79,482,143],{"className":483},[171,367],[79,485,100],{"className":486},[122,367],[79,488,375],{"className":489},[374],[79,491,493],{"className":492},[347],[79,494,497],{"className":495,"style":496},[351],"height:0.2083em;",[79,498],{},[79,500,286],{"className":501},[502],"mclose",[61,504,505],{},"or",[61,507,508,252],{},[79,509,511,580],{"className":510},[82],[79,512,514],{"className":513},[86],[88,515,516],{"xmlns":90},[92,517,518,577],{},[95,519,520,522,524,527,530,536,538,545,547,553,555,557,559,561,563,575],{},[137,521,231],{},[141,523,234],{},[137,525,526],{},"N",[141,528,529],{},"⋅",[243,531,532,534],{},[137,533,231],{},[137,535,139],{},[141,537,241],{"stretchy":240},[243,539,540,543],{},[137,541,542],{},"x",[98,544,100],{},[141,546,252],{"separator":109},[243,548,549,551],{},[137,550,542],{},[98,552,259],{},[141,554,252],{"separator":109},[137,556,265],{"mathvariant":264},[137,558,265],{"mathvariant":264},[137,560,265],{"mathvariant":264},[141,562,252],{"separator":109},[243,564,565,567],{},[137,566,542],{},[95,568,569,571,573],{},[137,570,139],{},[141,572,143],{},[98,574,100],{},[141,576,286],{"stretchy":240},[102,578,579],{"encoding":104},"G = N \\cdot G_m(x_1, x_2, ..., x_{m-1})",[79,581,583,601,620],{"className":582,"ariaHidden":109},[108],[79,584,586,589,592,595,598],{"className":585},[113],[79,587],{"className":588,"style":299},[117],[79,590,231],{"className":591},[122,162],[79,593],{"className":594,"style":306},[166],[79,596,234],{"className":597},[310],[79,599],{"className":600,"style":306},[166],[79,602,604,607,611,614,617],{"className":603},[113],[79,605],{"className":606,"style":299},[117],[79,608,526],{"className":609,"style":610},[122,162],"margin-right:0.109em;",[79,612],{"className":613,"style":167},[166],[79,615,529],{"className":616},[171],[79,618],{"className":619,"style":167},[166],[79,621,623,626,667,670,710,713,716,756,759,762,765,768,771,820],{"className":622},[113],[79,624],{"className":625,"style":320},[117],[79,627,629,632],{"className":628},[122],[79,630,231],{"className":631},[122,162],[79,633,635],{"className":634},[338],[79,636,638,659],{"className":637},[342,343],[79,639,641,656],{"className":640},[347],[79,642,645],{"className":643,"style":644},[351],"height:0.1514em;",[79,646,647,650],{"style":355},[79,648],{"className":649,"style":360},[359],[79,651,653],{"className":652},[364,365,366,367],[79,654,139],{"className":655},[122,162,367],[79,657,375],{"className":658},[374],[79,660,662],{"className":661},[347],[79,663,665],{"className":664,"style":382},[351],[79,666],{},[79,668,241],{"className":669},[328],[79,671,673,676],{"className":672},[122],[79,674,542],{"className":675},[122,162],[79,677,679],{"className":678},[338],[79,680,682,702],{"className":681},[342,343],[79,683,685,699],{"className":684},[347],[79,686,688],{"className":687,"style":352},[351],[79,689,690,693],{"style":355},[79,691],{"className":692,"style":360},[359],[79,694,696],{"className":695},[364,365,366,367],[79,697,100],{"className":698},[122,367],[79,700,375],{"className":701},[374],[79,703,705],{"className":704},[347],[79,706,708],{"className":707,"style":382},[351],[79,709],{},[79,711,252],{"className":712},[388],[79,714],{"className":715,"style":392},[166],[79,717,719,722],{"className":718},[122],[79,720,542],{"className":721},[122,162],[79,723,725],{"className":724},[338],[79,726,728,748],{"className":727},[342,343],[79,729,731,745],{"className":730},[347],[79,732,734],{"className":733,"style":352},[351],[79,735,736,739],{"style":355},[79,737],{"className":738,"style":360},[359],[79,740,742],{"className":741},[364,365,366,367],[79,743,259],{"className":744},[122,367],[79,746,375],{"className":747},[374],[79,749,751],{"className":750},[347],[79,752,754],{"className":753,"style":382},[351],[79,755],{},[79,757,252],{"className":758},[388],[79,760],{"className":761,"style":392},[166],[79,763,442],{"className":764},[122],[79,766,252],{"className":767},[388],[79,769],{"className":770,"style":392},[166],[79,772,774,777],{"className":773},[122],[79,775,542],{"className":776},[122,162],[79,778,780],{"className":779},[338],[79,781,783,812],{"className":782},[342,343],[79,784,786,809],{"className":785},[347],[79,787,789],{"className":788,"style":352},[351],[79,790,791,794],{"style":355},[79,792],{"className":793,"style":360},[359],[79,795,797],{"className":796},[364,365,366,367],[79,798,800,803,806],{"className":799},[122,367],[79,801,139],{"className":802},[122,162,367],[79,804,143],{"className":805},[171,367],[79,807,100],{"className":808},[122,367],[79,810,375],{"className":811},[374],[79,813,815],{"className":814},[347],[79,816,818],{"className":817,"style":496},[351],[79,819],{},[79,821,286],{"className":822},[502],[61,824,825,826,854,855,926,927,1000,1001,1030,1031,1101,1102,1130],{},"where ",[79,827,829,842],{"className":828},[82],[79,830,832],{"className":831},[86],[88,833,834],{"xmlns":90},[92,835,836,840],{},[95,837,838],{},[137,839,526],{},[102,841,526],{"encoding":104},[79,843,845],{"className":844,"ariaHidden":109},[108],[79,846,848,851],{"className":847},[113],[79,849],{"className":850,"style":299},[117],[79,852,526],{"className":853,"style":610},[122,162]," is the total amount of all the substances, ",[79,856,858,876],{"className":857},[82],[79,859,861],{"className":860},[86],[88,862,863],{"xmlns":90},[92,864,865,873],{},[95,866,867],{},[243,868,869,871],{},[137,870,231],{},[137,872,139],{},[102,874,875],{"encoding":104},"G_m",[79,877,879],{"className":878,"ariaHidden":109},[108],[79,880,882,886],{"className":881},[113],[79,883],{"className":884,"style":885},[117],"height:0.8333em;vertical-align:-0.15em;",[79,887,889,892],{"className":888},[122],[79,890,231],{"className":891},[122,162],[79,893,895],{"className":894},[338],[79,896,898,918],{"className":897},[342,343],[79,899,901,915],{"className":900},[347],[79,902,904],{"className":903,"style":644},[351],[79,905,906,909],{"style":355},[79,907],{"className":908,"style":360},[359],[79,910,912],{"className":911},[364,365,366,367],[79,913,139],{"className":914},[122,162,367],[79,916,375],{"className":917},[374],[79,919,921],{"className":920},[347],[79,922,924],{"className":923,"style":382},[351],[79,925],{}," is the mole Gibbs energy, ",[79,928,930,949],{"className":929},[82],[79,931,933],{"className":932},[86],[88,934,935],{"xmlns":90},[92,936,937,946],{},[95,938,939],{},[243,940,941,943],{},[137,942,247],{},[137,944,945],{},"i",[102,947,948],{"encoding":104},"n_i",[79,950,952],{"className":951,"ariaHidden":109},[108],[79,953,955,959],{"className":954},[113],[79,956],{"className":957,"style":958},[117],"height:0.5806em;vertical-align:-0.15em;",[79,960,962,965],{"className":961},[122],[79,963,247],{"className":964},[122,162],[79,966,968],{"className":967},[338],[79,969,971,992],{"className":970},[342,343],[79,972,974,989],{"className":973},[347],[79,975,978],{"className":976,"style":977},[351],"height:0.3117em;",[79,979,980,983],{"style":355},[79,981],{"className":982,"style":360},[359],[79,984,986],{"className":985},[364,365,366,367],[79,987,945],{"className":988},[122,162,367],[79,990,375],{"className":991},[374],[79,993,995],{"className":994},[347],[79,996,998],{"className":997,"style":382},[351],[79,999],{}," is the amount of the ",[79,1002,1004,1017],{"className":1003},[82],[79,1005,1007],{"className":1006},[86],[88,1008,1009],{"xmlns":90},[92,1010,1011,1015],{},[95,1012,1013],{},[137,1014,945],{},[102,1016,945],{"encoding":104},[79,1018,1020],{"className":1019,"ariaHidden":109},[108],[79,1021,1023,1027],{"className":1022},[113],[79,1024],{"className":1025,"style":1026},[117],"height:0.6595em;",[79,1028,945],{"className":1029},[122,162],"-th component and ",[79,1032,1034,1052],{"className":1033},[82],[79,1035,1037],{"className":1036},[86],[88,1038,1039],{"xmlns":90},[92,1040,1041,1049],{},[95,1042,1043],{},[243,1044,1045,1047],{},[137,1046,542],{},[137,1048,945],{},[102,1050,1051],{"encoding":104},"x_i",[79,1053,1055],{"className":1054,"ariaHidden":109},[108],[79,1056,1058,1061],{"className":1057},[113],[79,1059],{"className":1060,"style":958},[117],[79,1062,1064,1067],{"className":1063},[122],[79,1065,542],{"className":1066},[122,162],[79,1068,1070],{"className":1069},[338],[79,1071,1073,1093],{"className":1072},[342,343],[79,1074,1076,1090],{"className":1075},[347],[79,1077,1079],{"className":1078,"style":977},[351],[79,1080,1081,1084],{"style":355},[79,1082],{"className":1083,"style":360},[359],[79,1085,1087],{"className":1086},[364,365,366,367],[79,1088,945],{"className":1089},[122,162,367],[79,1091,375],{"className":1092},[374],[79,1094,1096],{"className":1095},[347],[79,1097,1099],{"className":1098,"style":382},[351],[79,1100],{}," is the mole fraction of the ",[79,1103,1105,1118],{"className":1104},[82],[79,1106,1108],{"className":1107},[86],[88,1109,1110],{"xmlns":90},[92,1111,1112,1116],{},[95,1113,1114],{},[137,1115,945],{},[102,1117,945],{"encoding":104},[79,1119,1121],{"className":1120,"ariaHidden":109},[108],[79,1122,1124,1127],{"className":1123},[113],[79,1125],{"className":1126,"style":1026},[117],[79,1128,945],{"className":1129},[122,162],"-th component.",[61,1132,1133,1134,1162],{},"The chemical potential of the ",[79,1135,1137,1150],{"className":1136},[82],[79,1138,1140],{"className":1139},[86],[88,1141,1142],{"xmlns":90},[92,1143,1144,1148],{},[95,1145,1146],{},[137,1147,945],{},[102,1149,945],{"encoding":104},[79,1151,1153],{"className":1152,"ariaHidden":109},[108],[79,1154,1156,1159],{"className":1155},[113],[79,1157],{"className":1158,"style":1026},[117],[79,1160,945],{"className":1161},[122,162],"-th component, is the partial quantity of the Gibbs energy and that is",[61,1164,1165],{},[79,1166,1168,1217],{"className":1167},[82],[79,1169,1171],{"className":1170},[86],[88,1172,1173],{"xmlns":90},[92,1174,1175,1214],{},[95,1176,1177,1184,1186,1212],{},[243,1178,1179,1182],{},[137,1180,1181],{},"μ",[137,1183,945],{},[141,1185,234],{},[1187,1188,1189,1202],"mfrac",{},[95,1190,1191,1194,1196],{},[137,1192,1193],{"mathvariant":264},"∂",[137,1195,526],{},[243,1197,1198,1200],{},[137,1199,231],{},[137,1201,139],{},[95,1203,1204,1206],{},[137,1205,1193],{"mathvariant":264},[243,1207,1208,1210],{},[137,1209,247],{},[137,1211,945],{},[137,1213,265],{"mathvariant":264},[102,1215,1216],{"encoding":104},"\\mu_i = \\frac{\\partial N G_m}{\\partial n_i}.",[79,1218,1220,1276],{"className":1219,"ariaHidden":109},[108],[79,1221,1223,1227,1267,1270,1273],{"className":1222},[113],[79,1224],{"className":1225,"style":1226},[117],"height:0.625em;vertical-align:-0.1944em;",[79,1228,1230,1233],{"className":1229},[122],[79,1231,1181],{"className":1232},[122,162],[79,1234,1236],{"className":1235},[338],[79,1237,1239,1259],{"className":1238},[342,343],[79,1240,1242,1256],{"className":1241},[347],[79,1243,1245],{"className":1244,"style":977},[351],[79,1246,1247,1250],{"style":355},[79,1248],{"className":1249,"style":360},[359],[79,1251,1253],{"className":1252},[364,365,366,367],[79,1254,945],{"className":1255},[122,162,367],[79,1257,375],{"className":1258},[374],[79,1260,1262],{"className":1261},[347],[79,1263,1265],{"className":1264,"style":382},[351],[79,1266],{},[79,1268],{"className":1269,"style":306},[166],[79,1271,234],{"className":1272},[310],[79,1274],{"className":1275,"style":306},[166],[79,1277,1279,1283,1451],{"className":1278},[113],[79,1280],{"className":1281,"style":1282},[117],"height:1.3413em;vertical-align:-0.4451em;",[79,1284,1286,1290,1448],{"className":1285},[122],[79,1287],{"className":1288},[328,1289],"nulldelimiter",[79,1291,1293],{"className":1292},[1187],[79,1294,1296,1439],{"className":1295},[342,343],[79,1297,1299,1436],{"className":1298},[347],[79,1300,1303,1366,1377],{"className":1301,"style":1302},[351],"height:0.8962em;",[79,1304,1306,1310],{"style":1305},"top:-2.655em;",[79,1307],{"className":1308,"style":1309},[359],"height:3em;",[79,1311,1313],{"className":1312},[364,365,366,367],[79,1314,1316,1320],{"className":1315},[122,367],[79,1317,1193],{"className":1318,"style":1319},[122,367],"margin-right:0.0556em;",[79,1321,1323,1326],{"className":1322},[122,367],[79,1324,247],{"className":1325},[122,162,367],[79,1327,1329],{"className":1328},[338],[79,1330,1332,1357],{"className":1331},[342,343],[79,1333,1335,1354],{"className":1334},[347],[79,1336,1339],{"className":1337,"style":1338},[351],"height:0.3281em;",[79,1340,1342,1346],{"style":1341},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[79,1343],{"className":1344,"style":1345},[359],"height:2.5em;",[79,1347,1351],{"className":1348},[364,1349,1350,367],"reset-size3","size1",[79,1352,945],{"className":1353},[122,162,367],[79,1355,375],{"className":1356},[374],[79,1358,1360],{"className":1359},[347],[79,1361,1364],{"className":1362,"style":1363},[351],"height:0.143em;",[79,1365],{},[79,1367,1369,1372],{"style":1368},"top:-3.23em;",[79,1370],{"className":1371,"style":1309},[359],[79,1373],{"className":1374,"style":1376},[1375],"frac-line","border-bottom-width:0.04em;",[79,1378,1380,1383],{"style":1379},"top:-3.4101em;",[79,1381],{"className":1382,"style":1309},[359],[79,1384,1386],{"className":1385},[364,365,366,367],[79,1387,1389,1392,1395],{"className":1388},[122,367],[79,1390,1193],{"className":1391,"style":1319},[122,367],[79,1393,526],{"className":1394,"style":610},[122,162,367],[79,1396,1398,1401],{"className":1397},[122,367],[79,1399,231],{"className":1400},[122,162,367],[79,1402,1404],{"className":1403},[338],[79,1405,1407,1428],{"className":1406},[342,343],[79,1408,1410,1425],{"className":1409},[347],[79,1411,1414],{"className":1412,"style":1413},[351],"height:0.1645em;",[79,1415,1416,1419],{"style":1341},[79,1417],{"className":1418,"style":1345},[359],[79,1420,1422],{"className":1421},[364,1349,1350,367],[79,1423,139],{"className":1424},[122,162,367],[79,1426,375],{"className":1427},[374],[79,1429,1431],{"className":1430},[347],[79,1432,1434],{"className":1433,"style":1363},[351],[79,1435],{},[79,1437,375],{"className":1438},[374],[79,1440,1442],{"className":1441},[347],[79,1443,1446],{"className":1444,"style":1445},[351],"height:0.4451em;",[79,1447],{},[79,1449],{"className":1450},[502,1289],[79,1452,265],{"className":1453},[122],[61,1455,1456,1457,1526,1527,1596],{},"In CALPHAD method and other physical models, the mole fraction or the composition is the most common state variable for the fraction of the components. And thus, we have a motivation to substitute the amount, i.e., ",[79,1458,1460,1477],{"className":1459},[82],[79,1461,1463],{"className":1462},[86],[88,1464,1465],{"xmlns":90},[92,1466,1467,1475],{},[95,1468,1469],{},[243,1470,1471,1473],{},[137,1472,247],{},[137,1474,945],{},[102,1476,948],{"encoding":104},[79,1478,1480],{"className":1479,"ariaHidden":109},[108],[79,1481,1483,1486],{"className":1482},[113],[79,1484],{"className":1485,"style":958},[117],[79,1487,1489,1492],{"className":1488},[122],[79,1490,247],{"className":1491},[122,162],[79,1493,1495],{"className":1494},[338],[79,1496,1498,1518],{"className":1497},[342,343],[79,1499,1501,1515],{"className":1500},[347],[79,1502,1504],{"className":1503,"style":977},[351],[79,1505,1506,1509],{"style":355},[79,1507],{"className":1508,"style":360},[359],[79,1510,1512],{"className":1511},[364,365,366,367],[79,1513,945],{"className":1514},[122,162,367],[79,1516,375],{"className":1517},[374],[79,1519,1521],{"className":1520},[347],[79,1522,1524],{"className":1523,"style":382},[351],[79,1525],{}," into fraction, i.e., ",[79,1528,1530,1547],{"className":1529},[82],[79,1531,1533],{"className":1532},[86],[88,1534,1535],{"xmlns":90},[92,1536,1537,1545],{},[95,1538,1539],{},[243,1540,1541,1543],{},[137,1542,542],{},[137,1544,945],{},[102,1546,1051],{"encoding":104},[79,1548,1550],{"className":1549,"ariaHidden":109},[108],[79,1551,1553,1556],{"className":1552},[113],[79,1554],{"className":1555,"style":958},[117],[79,1557,1559,1562],{"className":1558},[122],[79,1560,542],{"className":1561},[122,162],[79,1563,1565],{"className":1564},[338],[79,1566,1568,1588],{"className":1567},[342,343],[79,1569,1571,1585],{"className":1570},[347],[79,1572,1574],{"className":1573,"style":977},[351],[79,1575,1576,1579],{"style":355},[79,1577],{"className":1578,"style":360},[359],[79,1580,1582],{"className":1581},[364,365,366,367],[79,1583,945],{"className":1584},[122,162,367],[79,1586,375],{"className":1587},[374],[79,1589,1591],{"className":1590},[347],[79,1592,1594],{"className":1593,"style":382},[351],[79,1595],{},", where chain rule of derivatives should be adopted.",[61,1598,1599],{},"As",[61,1601,1602],{},[79,1603,1605,1672],{"className":1604},[82],[79,1606,1608],{"className":1607},[86],[88,1609,1610],{"xmlns":90},[92,1611,1612,1669],{},[95,1613,1614,1620,1622,1624,1626,1629,1631,1637,1639,1645,1647,1649,1651,1653,1655,1667],{},[243,1615,1616,1618],{},[137,1617,247],{},[137,1619,945],{},[141,1621,234],{},[137,1623,526],{},[141,1625,529],{},[137,1627,1628],{},"g",[141,1630,241],{"stretchy":240},[243,1632,1633,1635],{},[137,1634,542],{},[98,1636,100],{},[141,1638,252],{"separator":109},[243,1640,1641,1643],{},[137,1642,542],{},[98,1644,259],{},[141,1646,252],{"separator":109},[137,1648,265],{"mathvariant":264},[137,1650,265],{"mathvariant":264},[137,1652,265],{"mathvariant":264},[141,1654,252],{"separator":109},[243,1656,1657,1659],{},[137,1658,542],{},[95,1660,1661,1663,1665],{},[137,1662,139],{},[141,1664,143],{},[98,1666,100],{},[141,1668,286],{"stretchy":240},[102,1670,1671],{"encoding":104},"n_i = N \\cdot g(x_1, x_2, ..., x_{m-1})",[79,1673,1675,1730,1748],{"className":1674,"ariaHidden":109},[108],[79,1676,1678,1681,1721,1724,1727],{"className":1677},[113],[79,1679],{"className":1680,"style":958},[117],[79,1682,1684,1687],{"className":1683},[122],[79,1685,247],{"className":1686},[122,162],[79,1688,1690],{"className":1689},[338],[79,1691,1693,1713],{"className":1692},[342,343],[79,1694,1696,1710],{"className":1695},[347],[79,1697,1699],{"className":1698,"style":977},[351],[79,1700,1701,1704],{"style":355},[79,1702],{"className":1703,"style":360},[359],[79,1705,1707],{"className":1706},[364,365,366,367],[79,1708,945],{"className":1709},[122,162,367],[79,1711,375],{"className":1712},[374],[79,1714,1716],{"className":1715},[347],[79,1717,1719],{"className":1718,"style":382},[351],[79,1720],{},[79,1722],{"className":1723,"style":306},[166],[79,1725,234],{"className":1726},[310],[79,1728],{"className":1729,"style":306},[166],[79,1731,1733,1736,1739,1742,1745],{"className":1732},[113],[79,1734],{"className":1735,"style":299},[117],[79,1737,526],{"className":1738,"style":610},[122,162],[79,1740],{"className":1741,"style":167},[166],[79,1743,529],{"className":1744},[171],[79,1746],{"className":1747,"style":167},[166],[79,1749,1751,1754,1758,1761,1801,1804,1807,1847,1850,1853,1856,1859,1862,1911],{"className":1750},[113],[79,1752],{"className":1753,"style":320},[117],[79,1755,1628],{"className":1756,"style":1757},[122,162],"margin-right:0.0359em;",[79,1759,241],{"className":1760},[328],[79,1762,1764,1767],{"className":1763},[122],[79,1765,542],{"className":1766},[122,162],[79,1768,1770],{"className":1769},[338],[79,1771,1773,1793],{"className":1772},[342,343],[79,1774,1776,1790],{"className":1775},[347],[79,1777,1779],{"className":1778,"style":352},[351],[79,1780,1781,1784],{"style":355},[79,1782],{"className":1783,"style":360},[359],[79,1785,1787],{"className":1786},[364,365,366,367],[79,1788,100],{"className":1789},[122,367],[79,1791,375],{"className":1792},[374],[79,1794,1796],{"className":1795},[347],[79,1797,1799],{"className":1798,"style":382},[351],[79,1800],{},[79,1802,252],{"className":1803},[388],[79,1805],{"className":1806,"style":392},[166],[79,1808,1810,1813],{"className":1809},[122],[79,1811,542],{"className":1812},[122,162],[79,1814,1816],{"className":1815},[338],[79,1817,1819,1839],{"className":1818},[342,343],[79,1820,1822,1836],{"className":1821},[347],[79,1823,1825],{"className":1824,"style":352},[351],[79,1826,1827,1830],{"style":355},[79,1828],{"className":1829,"style":360},[359],[79,1831,1833],{"className":1832},[364,365,366,367],[79,1834,259],{"className":1835},[122,367],[79,1837,375],{"className":1838},[374],[79,1840,1842],{"className":1841},[347],[79,1843,1845],{"className":1844,"style":382},[351],[79,1846],{},[79,1848,252],{"className":1849},[388],[79,1851],{"className":1852,"style":392},[166],[79,1854,442],{"className":1855},[122],[79,1857,252],{"className":1858},[388],[79,1860],{"className":1861,"style":392},[166],[79,1863,1865,1868],{"className":1864},[122],[79,1866,542],{"className":1867},[122,162],[79,1869,1871],{"className":1870},[338],[79,1872,1874,1903],{"className":1873},[342,343],[79,1875,1877,1900],{"className":1876},[347],[79,1878,1880],{"className":1879,"style":352},[351],[79,1881,1882,1885],{"style":355},[79,1883],{"className":1884,"style":360},[359],[79,1886,1888],{"className":1887},[364,365,366,367],[79,1889,1891,1894,1897],{"className":1890},[122,367],[79,1892,139],{"className":1893},[122,162,367],[79,1895,143],{"className":1896},[171,367],[79,1898,100],{"className":1899},[122,367],[79,1901,375],{"className":1902},[374],[79,1904,1906],{"className":1905},[347],[79,1907,1909],{"className":1908,"style":496},[351],[79,1910],{},[79,1912,286],{"className":1913},[502],[61,1915,1916],{},", we can obtain",[61,1918,1919],{},[79,1920,1922,2042],{"className":1921},[82],[79,1923,1925],{"className":1924},[86],[88,1926,1927],{"xmlns":90},[92,1928,1929,2039],{},[95,1930,1931,1937,1939,1945,1963,1966,1968,1995,2017],{},[243,1932,1933,1935],{},[137,1934,1181],{},[137,1936,945],{},[141,1938,234],{},[243,1940,1941,1943],{},[137,1942,231],{},[137,1944,139],{},[1187,1946,1947,1953],{},[95,1948,1949,1951],{},[137,1950,1193],{"mathvariant":264},[137,1952,526],{},[95,1954,1955,1957],{},[137,1956,1193],{"mathvariant":264},[243,1958,1959,1961],{},[137,1960,247],{},[137,1962,945],{},[141,1964,1965],{},"+",[137,1967,526],{},[1969,1970,1971,1974,1983],"msubsup",{},[141,1972,1973],{},"∑",[95,1975,1976,1979,1981],{},[137,1977,1978],{},"j",[141,1980,234],{},[98,1982,100],{},[95,1984,1985,1987,1989,1991,1993],{},[137,1986,1978],{},[141,1988,234],{},[137,1990,139],{},[141,1992,143],{},[98,1994,100],{},[1187,1996,1997,2007],{},[95,1998,1999,2001],{},[137,2000,1193],{"mathvariant":264},[243,2002,2003,2005],{},[137,2004,231],{},[137,2006,139],{},[95,2008,2009,2011],{},[137,2010,1193],{"mathvariant":264},[243,2012,2013,2015],{},[137,2014,542],{},[137,2016,1978],{},[1187,2018,2019,2029],{},[95,2020,2021,2023],{},[137,2022,1193],{"mathvariant":264},[243,2024,2025,2027],{},[137,2026,542],{},[137,2028,1978],{},[95,2030,2031,2033],{},[137,2032,1193],{"mathvariant":264},[243,2034,2035,2037],{},[137,2036,247],{},[137,2038,945],{},[102,2040,2041],{"encoding":104},"\\mu_i = G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j}\\frac{\\partial x_j }{\\partial n_i}",[79,2043,2045,2100,2269],{"className":2044,"ariaHidden":109},[108],[79,2046,2048,2051,2091,2094,2097],{"className":2047},[113],[79,2049],{"className":2050,"style":1226},[117],[79,2052,2054,2057],{"className":2053},[122],[79,2055,1181],{"className":2056},[122,162],[79,2058,2060],{"className":2059},[338],[79,2061,2063,2083],{"className":2062},[342,343],[79,2064,2066,2080],{"className":2065},[347],[79,2067,2069],{"className":2068,"style":977},[351],[79,2070,2071,2074],{"style":355},[79,2072],{"className":2073,"style":360},[359],[79,2075,2077],{"className":2076},[364,365,366,367],[79,2078,945],{"className":2079},[122,162,367],[79,2081,375],{"className":2082},[374],[79,2084,2086],{"className":2085},[347],[79,2087,2089],{"className":2088,"style":382},[351],[79,2090],{},[79,2092],{"className":2093,"style":306},[166],[79,2095,234],{"className":2096},[310],[79,2098],{"className":2099,"style":306},[166],[79,2101,2103,2107,2147,2260,2263,2266],{"className":2102},[113],[79,2104],{"className":2105,"style":2106},[117],"height:1.3252em;vertical-align:-0.4451em;",[79,2108,2110,2113],{"className":2109},[122],[79,2111,231],{"className":2112},[122,162],[79,2114,2116],{"className":2115},[338],[79,2117,2119,2139],{"className":2118},[342,343],[79,2120,2122,2136],{"className":2121},[347],[79,2123,2125],{"className":2124,"style":644},[351],[79,2126,2127,2130],{"style":355},[79,2128],{"className":2129,"style":360},[359],[79,2131,2133],{"className":2132},[364,365,366,367],[79,2134,139],{"className":2135},[122,162,367],[79,2137,375],{"className":2138},[374],[79,2140,2142],{"className":2141},[347],[79,2143,2145],{"className":2144,"style":382},[351],[79,2146],{},[79,2148,2150,2153,2257],{"className":2149},[122],[79,2151],{"className":2152},[328,1289],[79,2154,2156],{"className":2155},[1187],[79,2157,2159,2249],{"className":2158},[342,343],[79,2160,2162,2246],{"className":2161},[347],[79,2163,2166,2220,2228],{"className":2164,"style":2165},[351],"height:0.8801em;",[79,2167,2168,2171],{"style":1305},[79,2169],{"className":2170,"style":1309},[359],[79,2172,2174],{"className":2173},[364,365,366,367],[79,2175,2177,2180],{"className":2176},[122,367],[79,2178,1193],{"className":2179,"style":1319},[122,367],[79,2181,2183,2186],{"className":2182},[122,367],[79,2184,247],{"className":2185},[122,162,367],[79,2187,2189],{"className":2188},[338],[79,2190,2192,2212],{"className":2191},[342,343],[79,2193,2195,2209],{"className":2194},[347],[79,2196,2198],{"className":2197,"style":1338},[351],[79,2199,2200,2203],{"style":1341},[79,2201],{"className":2202,"style":1345},[359],[79,2204,2206],{"className":2205},[364,1349,1350,367],[79,2207,945],{"className":2208},[122,162,367],[79,2210,375],{"className":2211},[374],[79,2213,2215],{"className":2214},[347],[79,2216,2218],{"className":2217,"style":1363},[351],[79,2219],{},[79,2221,2222,2225],{"style":1368},[79,2223],{"className":2224,"style":1309},[359],[79,2226],{"className":2227,"style":1376},[1375],[79,2229,2231,2234],{"style":2230},"top:-3.394em;",[79,2232],{"className":2233,"style":1309},[359],[79,2235,2237],{"className":2236},[364,365,366,367],[79,2238,2240,2243],{"className":2239},[122,367],[79,2241,1193],{"className":2242,"style":1319},[122,367],[79,2244,526],{"className":2245,"style":610},[122,162,367],[79,2247,375],{"className":2248},[374],[79,2250,2252],{"className":2251},[347],[79,2253,2255],{"className":2254,"style":1445},[351],[79,2256],{},[79,2258],{"className":2259},[502,1289],[79,2261],{"className":2262,"style":167},[166],[79,2264,1965],{"className":2265},[171],[79,2267],{"className":2268,"style":167},[166],[79,2270,2272,2276,2279,2282,2366,2369,2519],{"className":2271},[113],[79,2273],{"className":2274,"style":2275},[117],"height:1.5357em;vertical-align:-0.5423em;",[79,2277,526],{"className":2278,"style":610},[122,162],[79,2280],{"className":2281,"style":392},[166],[79,2283,2286,2292],{"className":2284},[2285],"mop",[79,2287,1973],{"className":2288,"style":2291},[2285,2289,2290],"op-symbol","small-op","position:relative;top:0em;",[79,2293,2295],{"className":2294},[338],[79,2296,2298,2357],{"className":2297},[342,343],[79,2299,2301,2354],{"className":2300},[347],[79,2302,2305,2327],{"className":2303,"style":2304},[351],"height:0.9646em;",[79,2306,2308,2311],{"style":2307},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[79,2309],{"className":2310,"style":360},[359],[79,2312,2314],{"className":2313},[364,365,366,367],[79,2315,2317,2321,2324],{"className":2316},[122,367],[79,2318,1978],{"className":2319,"style":2320},[122,162,367],"margin-right:0.0572em;",[79,2322,234],{"className":2323},[310,367],[79,2325,100],{"className":2326},[122,367],[79,2328,2330,2333],{"style":2329},"top:-3.2029em;margin-right:0.05em;",[79,2331],{"className":2332,"style":360},[359],[79,2334,2336],{"className":2335},[364,365,366,367],[79,2337,2339,2342,2345,2348,2351],{"className":2338},[122,367],[79,2340,1978],{"className":2341,"style":2320},[122,162,367],[79,2343,234],{"className":2344},[310,367],[79,2346,139],{"className":2347},[122,162,367],[79,2349,143],{"className":2350},[171,367],[79,2352,100],{"className":2353},[122,367],[79,2355,375],{"className":2356},[374],[79,2358,2360],{"className":2359},[347],[79,2361,2364],{"className":2362,"style":2363},[351],"height:0.4358em;",[79,2365],{},[79,2367],{"className":2368,"style":392},[166],[79,2370,2372,2375,2516],{"className":2371},[122],[79,2373],{"className":2374},[328,1289],[79,2376,2378],{"className":2377},[1187],[79,2379,2381,2507],{"className":2380},[342,343],[79,2382,2384,2504],{"className":2383},[347],[79,2385,2387,2442,2450],{"className":2386,"style":1302},[351],[79,2388,2389,2392],{"style":1305},[79,2390],{"className":2391,"style":1309},[359],[79,2393,2395],{"className":2394},[364,365,366,367],[79,2396,2398,2401],{"className":2397},[122,367],[79,2399,1193],{"className":2400,"style":1319},[122,367],[79,2402,2404,2407],{"className":2403},[122,367],[79,2405,542],{"className":2406},[122,162,367],[79,2408,2410],{"className":2409},[338],[79,2411,2413,2433],{"className":2412},[342,343],[79,2414,2416,2430],{"className":2415},[347],[79,2417,2419],{"className":2418,"style":1338},[351],[79,2420,2421,2424],{"style":1341},[79,2422],{"className":2423,"style":1345},[359],[79,2425,2427],{"className":2426},[364,1349,1350,367],[79,2428,1978],{"className":2429,"style":2320},[122,162,367],[79,2431,375],{"className":2432},[374],[79,2434,2436],{"className":2435},[347],[79,2437,2440],{"className":2438,"style":2439},[351],"height:0.2819em;",[79,2441],{},[79,2443,2444,2447],{"style":1368},[79,2445],{"className":2446,"style":1309},[359],[79,2448],{"className":2449,"style":1376},[1375],[79,2451,2452,2455],{"style":1379},[79,2453],{"className":2454,"style":1309},[359],[79,2456,2458],{"className":2457},[364,365,366,367],[79,2459,2461,2464],{"className":2460},[122,367],[79,2462,1193],{"className":2463,"style":1319},[122,367],[79,2465,2467,2470],{"className":2466},[122,367],[79,2468,231],{"className":2469},[122,162,367],[79,2471,2473],{"className":2472},[338],[79,2474,2476,2496],{"className":2475},[342,343],[79,2477,2479,2493],{"className":2478},[347],[79,2480,2482],{"className":2481,"style":1413},[351],[79,2483,2484,2487],{"style":1341},[79,2485],{"className":2486,"style":1345},[359],[79,2488,2490],{"className":2489},[364,1349,1350,367],[79,2491,139],{"className":2492},[122,162,367],[79,2494,375],{"className":2495},[374],[79,2497,2499],{"className":2498},[347],[79,2500,2502],{"className":2501,"style":1363},[351],[79,2503],{},[79,2505,375],{"className":2506},[374],[79,2508,2510],{"className":2509},[347],[79,2511,2514],{"className":2512,"style":2513},[351],"height:0.5423em;",[79,2515],{},[79,2517],{"className":2518},[502,1289],[79,2520,2522,2525,2666],{"className":2521},[122],[79,2523],{"className":2524},[328,1289],[79,2526,2528],{"className":2527},[1187],[79,2529,2531,2658],{"className":2530},[342,343],[79,2532,2534,2655],{"className":2533},[347],[79,2535,2538,2592,2600],{"className":2536,"style":2537},[351],"height:0.9934em;",[79,2539,2540,2543],{"style":1305},[79,2541],{"className":2542,"style":1309},[359],[79,2544,2546],{"className":2545},[364,365,366,367],[79,2547,2549,2552],{"className":2548},[122,367],[79,2550,1193],{"className":2551,"style":1319},[122,367],[79,2553,2555,2558],{"className":2554},[122,367],[79,2556,247],{"className":2557},[122,162,367],[79,2559,2561],{"className":2560},[338],[79,2562,2564,2584],{"className":2563},[342,343],[79,2565,2567,2581],{"className":2566},[347],[79,2568,2570],{"className":2569,"style":1338},[351],[79,2571,2572,2575],{"style":1341},[79,2573],{"className":2574,"style":1345},[359],[79,2576,2578],{"className":2577},[364,1349,1350,367],[79,2579,945],{"className":2580},[122,162,367],[79,2582,375],{"className":2583},[374],[79,2585,2587],{"className":2586},[347],[79,2588,2590],{"className":2589,"style":1363},[351],[79,2591],{},[79,2593,2594,2597],{"style":1368},[79,2595],{"className":2596,"style":1309},[359],[79,2598],{"className":2599,"style":1376},[1375],[79,2601,2603,2606],{"style":2602},"top:-3.5073em;",[79,2604],{"className":2605,"style":1309},[359],[79,2607,2609],{"className":2608},[364,365,366,367],[79,2610,2612,2615],{"className":2611},[122,367],[79,2613,1193],{"className":2614,"style":1319},[122,367],[79,2616,2618,2621],{"className":2617},[122,367],[79,2619,542],{"className":2620},[122,162,367],[79,2622,2624],{"className":2623},[338],[79,2625,2627,2647],{"className":2626},[342,343],[79,2628,2630,2644],{"className":2629},[347],[79,2631,2633],{"className":2632,"style":1338},[351],[79,2634,2635,2638],{"style":1341},[79,2636],{"className":2637,"style":1345},[359],[79,2639,2641],{"className":2640},[364,1349,1350,367],[79,2642,1978],{"className":2643,"style":2320},[122,162,367],[79,2645,375],{"className":2646},[374],[79,2648,2650],{"className":2649},[347],[79,2651,2653],{"className":2652,"style":2439},[351],[79,2654],{},[79,2656,375],{"className":2657},[374],[79,2659,2661],{"className":2660},[347],[79,2662,2664],{"className":2663,"style":1445},[351],[79,2665],{},[79,2667],{"className":2668},[502,1289],[61,2670,2671],{},"Take the last part from the equation above and we have",[61,2673,2674],{},[79,2675,2677,2740],{"className":2676},[82],[79,2678,2680],{"className":2679},[86],[88,2681,2682],{"xmlns":90},[92,2683,2684,2737],{},[95,2685,2686,2708,2710],{},[1187,2687,2688,2698],{},[95,2689,2690,2692],{},[137,2691,1193],{"mathvariant":264},[243,2693,2694,2696],{},[137,2695,542],{},[137,2697,1978],{},[95,2699,2700,2702],{},[137,2701,1193],{"mathvariant":264},[243,2703,2704,2706],{},[137,2705,247],{},[137,2707,945],{},[141,2709,234],{},[1187,2711,2712,2727],{},[95,2713,2714,2716,2722,2725],{},[137,2715,1193],{"mathvariant":264},[243,2717,2718,2720],{},[137,2719,247],{},[137,2721,1978],{},[137,2723,2724],{"mathvariant":264},"\u002F",[137,2726,526],{},[95,2728,2729,2731],{},[137,2730,1193],{"mathvariant":264},[243,2732,2733,2735],{},[137,2734,247],{},[137,2736,945],{},[102,2738,2739],{"encoding":104},"\\frac{\\partial x_j }{\\partial n_i} = \\frac{\\partial n_j \u002F N }{\\partial n_i}",[79,2741,2743,2907],{"className":2742,"ariaHidden":109},[108],[79,2744,2746,2750,2898,2901,2904],{"className":2745},[113],[79,2747],{"className":2748,"style":2749},[117],"height:1.4385em;vertical-align:-0.4451em;",[79,2751,2753,2756,2895],{"className":2752},[122],[79,2754],{"className":2755},[328,1289],[79,2757,2759],{"className":2758},[1187],[79,2760,2762,2887],{"className":2761},[342,343],[79,2763,2765,2884],{"className":2764},[347],[79,2766,2768,2822,2830],{"className":2767,"style":2537},[351],[79,2769,2770,2773],{"style":1305},[79,2771],{"className":2772,"style":1309},[359],[79,2774,2776],{"className":2775},[364,365,366,367],[79,2777,2779,2782],{"className":2778},[122,367],[79,2780,1193],{"className":2781,"style":1319},[122,367],[79,2783,2785,2788],{"className":2784},[122,367],[79,2786,247],{"className":2787},[122,162,367],[79,2789,2791],{"className":2790},[338],[79,2792,2794,2814],{"className":2793},[342,343],[79,2795,2797,2811],{"className":2796},[347],[79,2798,2800],{"className":2799,"style":1338},[351],[79,2801,2802,2805],{"style":1341},[79,2803],{"className":2804,"style":1345},[359],[79,2806,2808],{"className":2807},[364,1349,1350,367],[79,2809,945],{"className":2810},[122,162,367],[79,2812,375],{"className":2813},[374],[79,2815,2817],{"className":2816},[347],[79,2818,2820],{"className":2819,"style":1363},[351],[79,2821],{},[79,2823,2824,2827],{"style":1368},[79,2825],{"className":2826,"style":1309},[359],[79,2828],{"className":2829,"style":1376},[1375],[79,2831,2832,2835],{"style":2602},[79,2833],{"className":2834,"style":1309},[359],[79,2836,2838],{"className":2837},[364,365,366,367],[79,2839,2841,2844],{"className":2840},[122,367],[79,2842,1193],{"className":2843,"style":1319},[122,367],[79,2845,2847,2850],{"className":2846},[122,367],[79,2848,542],{"className":2849},[122,162,367],[79,2851,2853],{"className":2852},[338],[79,2854,2856,2876],{"className":2855},[342,343],[79,2857,2859,2873],{"className":2858},[347],[79,2860,2862],{"className":2861,"style":1338},[351],[79,2863,2864,2867],{"style":1341},[79,2865],{"className":2866,"style":1345},[359],[79,2868,2870],{"className":2869},[364,1349,1350,367],[79,2871,1978],{"className":2872,"style":2320},[122,162,367],[79,2874,375],{"className":2875},[374],[79,2877,2879],{"className":2878},[347],[79,2880,2882],{"className":2881,"style":2439},[351],[79,2883],{},[79,2885,375],{"className":2886},[374],[79,2888,2890],{"className":2889},[347],[79,2891,2893],{"className":2892,"style":1445},[351],[79,2894],{},[79,2896],{"className":2897},[502,1289],[79,2899],{"className":2900,"style":306},[166],[79,2902,234],{"className":2903},[310],[79,2905],{"className":2906,"style":306},[166],[79,2908,2910,2914],{"className":2909},[113],[79,2911],{"className":2912,"style":2913},[117],"height:1.4774em;vertical-align:-0.4451em;",[79,2915,2917,2920,3066],{"className":2916},[122],[79,2918],{"className":2919},[328,1289],[79,2921,2923],{"className":2922},[1187],[79,2924,2926,3058],{"className":2925},[342,343],[79,2927,2929,3055],{"className":2928},[347],[79,2930,2933,2987,2995],{"className":2931,"style":2932},[351],"height:1.0323em;",[79,2934,2935,2938],{"style":1305},[79,2936],{"className":2937,"style":1309},[359],[79,2939,2941],{"className":2940},[364,365,366,367],[79,2942,2944,2947],{"className":2943},[122,367],[79,2945,1193],{"className":2946,"style":1319},[122,367],[79,2948,2950,2953],{"className":2949},[122,367],[79,2951,247],{"className":2952},[122,162,367],[79,2954,2956],{"className":2955},[338],[79,2957,2959,2979],{"className":2958},[342,343],[79,2960,2962,2976],{"className":2961},[347],[79,2963,2965],{"className":2964,"style":1338},[351],[79,2966,2967,2970],{"style":1341},[79,2968],{"className":2969,"style":1345},[359],[79,2971,2973],{"className":2972},[364,1349,1350,367],[79,2974,945],{"className":2975},[122,162,367],[79,2977,375],{"className":2978},[374],[79,2980,2982],{"className":2981},[347],[79,2983,2985],{"className":2984,"style":1363},[351],[79,2986],{},[79,2988,2989,2992],{"style":1368},[79,2990],{"className":2991,"style":1309},[359],[79,2993],{"className":2994,"style":1376},[1375],[79,2996,2997,3000],{"style":2602},[79,2998],{"className":2999,"style":1309},[359],[79,3001,3003],{"className":3002},[364,365,366,367],[79,3004,3006,3009,3049,3052],{"className":3005},[122,367],[79,3007,1193],{"className":3008,"style":1319},[122,367],[79,3010,3012,3015],{"className":3011},[122,367],[79,3013,247],{"className":3014},[122,162,367],[79,3016,3018],{"className":3017},[338],[79,3019,3021,3041],{"className":3020},[342,343],[79,3022,3024,3038],{"className":3023},[347],[79,3025,3027],{"className":3026,"style":1338},[351],[79,3028,3029,3032],{"style":1341},[79,3030],{"className":3031,"style":1345},[359],[79,3033,3035],{"className":3034},[364,1349,1350,367],[79,3036,1978],{"className":3037,"style":2320},[122,162,367],[79,3039,375],{"className":3040},[374],[79,3042,3044],{"className":3043},[347],[79,3045,3047],{"className":3046,"style":2439},[351],[79,3048],{},[79,3050,2724],{"className":3051},[122,367],[79,3053,526],{"className":3054,"style":610},[122,162,367],[79,3056,375],{"className":3057},[374],[79,3059,3061],{"className":3060},[347],[79,3062,3064],{"className":3063,"style":1445},[351],[79,3065],{},[79,3067],{"className":3068},[502,1289],[61,3070,3071,3075,3076,3145,3146,3238],{},[3072,3073,3074],"strong",{},"Note"," One should keep in mind that we should not substitute ",[79,3077,3079,3096],{"className":3078},[82],[79,3080,3082],{"className":3081},[86],[88,3083,3084],{"xmlns":90},[92,3085,3086,3094],{},[95,3087,3088],{},[243,3089,3090,3092],{},[137,3091,247],{},[137,3093,945],{},[102,3095,948],{"encoding":104},[79,3097,3099],{"className":3098,"ariaHidden":109},[108],[79,3100,3102,3105],{"className":3101},[113],[79,3103],{"className":3104,"style":958},[117],[79,3106,3108,3111],{"className":3107},[122],[79,3109,247],{"className":3110},[122,162],[79,3112,3114],{"className":3113},[338],[79,3115,3117,3137],{"className":3116},[342,343],[79,3118,3120,3134],{"className":3119},[347],[79,3121,3123],{"className":3122,"style":977},[351],[79,3124,3125,3128],{"style":355},[79,3126],{"className":3127,"style":360},[359],[79,3129,3131],{"className":3130},[364,365,366,367],[79,3132,945],{"className":3133},[122,162,367],[79,3135,375],{"className":3136},[374],[79,3138,3140],{"className":3139},[347],[79,3141,3143],{"className":3142,"style":382},[351],[79,3144],{}," as ",[79,3147,3149,3171],{"className":3148},[82],[79,3150,3152],{"className":3151},[86],[88,3153,3154],{"xmlns":90},[92,3155,3156,3168],{},[95,3157,3158,3160,3162],{},[137,3159,526],{},[141,3161,529],{},[243,3163,3164,3166],{},[137,3165,542],{},[137,3167,945],{},[102,3169,3170],{"encoding":104},"N\\cdot x_i",[79,3172,3174,3192],{"className":3173,"ariaHidden":109},[108],[79,3175,3177,3180,3183,3186,3189],{"className":3176},[113],[79,3178],{"className":3179,"style":299},[117],[79,3181,526],{"className":3182,"style":610},[122,162],[79,3184],{"className":3185,"style":167},[166],[79,3187,529],{"className":3188},[171],[79,3190],{"className":3191,"style":167},[166],[79,3193,3195,3198],{"className":3194},[113],[79,3196],{"className":3197,"style":958},[117],[79,3199,3201,3204],{"className":3200},[122],[79,3202,542],{"className":3203},[122,162],[79,3205,3207],{"className":3206},[338],[79,3208,3210,3230],{"className":3209},[342,343],[79,3211,3213,3227],{"className":3212},[347],[79,3214,3216],{"className":3215,"style":977},[351],[79,3217,3218,3221],{"style":355},[79,3219],{"className":3220,"style":360},[359],[79,3222,3224],{"className":3223},[364,365,366,367],[79,3225,945],{"className":3226},[122,162,367],[79,3228,375],{"className":3229},[374],[79,3231,3233],{"className":3232},[347],[79,3234,3236],{"className":3235,"style":382},[351],[79,3237],{},", as there is no way to calculate the derivative with respect to fraction number.",[61,3240,3241],{},"Furthermore,",[61,3243,3244],{},[79,3245,3247,3350],{"className":3246},[82],[79,3248,3250],{"className":3249},[86],[88,3251,3252],{"xmlns":90},[92,3253,3254,3347],{},[95,3255,3256,3278,3280,3291,3293,3295,3317,3319,3325,3343,3345],{},[1187,3257,3258,3268],{},[95,3259,3260,3262],{},[137,3261,1193],{"mathvariant":264},[243,3263,3264,3266],{},[137,3265,542],{},[137,3267,1978],{},[95,3269,3270,3272],{},[137,3271,1193],{"mathvariant":264},[243,3273,3274,3276],{},[137,3275,247],{},[137,3277,945],{},[141,3279,234],{},[1187,3281,3282,3284],{},[98,3283,100],{},[3285,3286,3287,3289],"msup",{},[137,3288,526],{},[98,3290,259],{},[141,3292,241],{"stretchy":240},[137,3294,526],{},[1187,3296,3297,3307],{},[95,3298,3299,3301],{},[137,3300,1193],{"mathvariant":264},[243,3302,3303,3305],{},[137,3304,247],{},[137,3306,1978],{},[95,3308,3309,3311],{},[137,3310,1193],{"mathvariant":264},[243,3312,3313,3315],{},[137,3314,247],{},[137,3316,945],{},[141,3318,143],{},[243,3320,3321,3323],{},[137,3322,247],{},[137,3324,1978],{},[1187,3326,3327,3333],{},[95,3328,3329,3331],{},[137,3330,1193],{"mathvariant":264},[137,3332,526],{},[95,3334,3335,3337],{},[137,3336,1193],{"mathvariant":264},[243,3338,3339,3341],{},[137,3340,247],{},[137,3342,945],{},[141,3344,286],{"stretchy":240},[137,3346,265],{"mathvariant":264},[102,3348,3349],{"encoding":104},"\\frac{\\partial x_j }{\\partial n_i} = \\frac{1}{N^2} (N\\frac{\\partial n_j}{\\partial n_i} - n_j\\frac{\\partial N}{\\partial n_i}).",[79,3351,3353,3516,3783],{"className":3352,"ariaHidden":109},[108],[79,3354,3356,3359,3507,3510,3513],{"className":3355},[113],[79,3357],{"className":3358,"style":2749},[117],[79,3360,3362,3365,3504],{"className":3361},[122],[79,3363],{"className":3364},[328,1289],[79,3366,3368],{"className":3367},[1187],[79,3369,3371,3496],{"className":3370},[342,343],[79,3372,3374,3493],{"className":3373},[347],[79,3375,3377,3431,3439],{"className":3376,"style":2537},[351],[79,3378,3379,3382],{"style":1305},[79,3380],{"className":3381,"style":1309},[359],[79,3383,3385],{"className":3384},[364,365,366,367],[79,3386,3388,3391],{"className":3387},[122,367],[79,3389,1193],{"className":3390,"style":1319},[122,367],[79,3392,3394,3397],{"className":3393},[122,367],[79,3395,247],{"className":3396},[122,162,367],[79,3398,3400],{"className":3399},[338],[79,3401,3403,3423],{"className":3402},[342,343],[79,3404,3406,3420],{"className":3405},[347],[79,3407,3409],{"className":3408,"style":1338},[351],[79,3410,3411,3414],{"style":1341},[79,3412],{"className":3413,"style":1345},[359],[79,3415,3417],{"className":3416},[364,1349,1350,367],[79,3418,945],{"className":3419},[122,162,367],[79,3421,375],{"className":3422},[374],[79,3424,3426],{"className":3425},[347],[79,3427,3429],{"className":3428,"style":1363},[351],[79,3430],{},[79,3432,3433,3436],{"style":1368},[79,3434],{"className":3435,"style":1309},[359],[79,3437],{"className":3438,"style":1376},[1375],[79,3440,3441,3444],{"style":2602},[79,3442],{"className":3443,"style":1309},[359],[79,3445,3447],{"className":3446},[364,365,366,367],[79,3448,3450,3453],{"className":3449},[122,367],[79,3451,1193],{"className":3452,"style":1319},[122,367],[79,3454,3456,3459],{"className":3455},[122,367],[79,3457,542],{"className":3458},[122,162,367],[79,3460,3462],{"className":3461},[338],[79,3463,3465,3485],{"className":3464},[342,343],[79,3466,3468,3482],{"className":3467},[347],[79,3469,3471],{"className":3470,"style":1338},[351],[79,3472,3473,3476],{"style":1341},[79,3474],{"className":3475,"style":1345},[359],[79,3477,3479],{"className":3478},[364,1349,1350,367],[79,3480,1978],{"className":3481,"style":2320},[122,162,367],[79,3483,375],{"className":3484},[374],[79,3486,3488],{"className":3487},[347],[79,3489,3491],{"className":3490,"style":2439},[351],[79,3492],{},[79,3494,375],{"className":3495},[374],[79,3497,3499],{"className":3498},[347],[79,3500,3502],{"className":3501,"style":1445},[351],[79,3503],{},[79,3505],{"className":3506},[502,1289],[79,3508],{"className":3509,"style":306},[166],[79,3511,234],{"className":3512},[310],[79,3514],{"className":3515,"style":306},[166],[79,3517,3519,3522,3620,3623,3626,3774,3777,3780],{"className":3518},[113],[79,3520],{"className":3521,"style":2749},[117],[79,3523,3525,3528,3617],{"className":3524},[122],[79,3526],{"className":3527},[328,1289],[79,3529,3531],{"className":3530},[1187],[79,3532,3534,3608],{"className":3533},[342,343],[79,3535,3537,3605],{"className":3536},[347],[79,3538,3541,3583,3591],{"className":3539,"style":3540},[351],"height:0.8451em;",[79,3542,3543,3546],{"style":1305},[79,3544],{"className":3545,"style":1309},[359],[79,3547,3549],{"className":3548},[364,365,366,367],[79,3550,3552],{"className":3551},[122,367],[79,3553,3555,3558],{"className":3554},[122,367],[79,3556,526],{"className":3557,"style":610},[122,162,367],[79,3559,3561],{"className":3560},[338],[79,3562,3564],{"className":3563},[342],[79,3565,3567],{"className":3566},[347],[79,3568,3571],{"className":3569,"style":3570},[351],"height:0.7463em;",[79,3572,3574,3577],{"style":3573},"top:-2.786em;margin-right:0.0714em;",[79,3575],{"className":3576,"style":1345},[359],[79,3578,3580],{"className":3579},[364,1349,1350,367],[79,3581,259],{"className":3582},[122,367],[79,3584,3585,3588],{"style":1368},[79,3586],{"className":3587,"style":1309},[359],[79,3589],{"className":3590,"style":1376},[1375],[79,3592,3593,3596],{"style":2230},[79,3594],{"className":3595,"style":1309},[359],[79,3597,3599],{"className":3598},[364,365,366,367],[79,3600,3602],{"className":3601},[122,367],[79,3603,100],{"className":3604},[122,367],[79,3606,375],{"className":3607},[374],[79,3609,3611],{"className":3610},[347],[79,3612,3615],{"className":3613,"style":3614},[351],"height:0.345em;",[79,3616],{},[79,3618],{"className":3619},[502,1289],[79,3621,241],{"className":3622},[328],[79,3624,526],{"className":3625,"style":610},[122,162],[79,3627,3629,3632,3771],{"className":3628},[122],[79,3630],{"className":3631},[328,1289],[79,3633,3635],{"className":3634},[1187],[79,3636,3638,3763],{"className":3637},[342,343],[79,3639,3641,3760],{"className":3640},[347],[79,3642,3644,3698,3706],{"className":3643,"style":2537},[351],[79,3645,3646,3649],{"style":1305},[79,3647],{"className":3648,"style":1309},[359],[79,3650,3652],{"className":3651},[364,365,366,367],[79,3653,3655,3658],{"className":3654},[122,367],[79,3656,1193],{"className":3657,"style":1319},[122,367],[79,3659,3661,3664],{"className":3660},[122,367],[79,3662,247],{"className":3663},[122,162,367],[79,3665,3667],{"className":3666},[338],[79,3668,3670,3690],{"className":3669},[342,343],[79,3671,3673,3687],{"className":3672},[347],[79,3674,3676],{"className":3675,"style":1338},[351],[79,3677,3678,3681],{"style":1341},[79,3679],{"className":3680,"style":1345},[359],[79,3682,3684],{"className":3683},[364,1349,1350,367],[79,3685,945],{"className":3686},[122,162,367],[79,3688,375],{"className":3689},[374],[79,3691,3693],{"className":3692},[347],[79,3694,3696],{"className":3695,"style":1363},[351],[79,3697],{},[79,3699,3700,3703],{"style":1368},[79,3701],{"className":3702,"style":1309},[359],[79,3704],{"className":3705,"style":1376},[1375],[79,3707,3708,3711],{"style":2602},[79,3709],{"className":3710,"style":1309},[359],[79,3712,3714],{"className":3713},[364,365,366,367],[79,3715,3717,3720],{"className":3716},[122,367],[79,3718,1193],{"className":3719,"style":1319},[122,367],[79,3721,3723,3726],{"className":3722},[122,367],[79,3724,247],{"className":3725},[122,162,367],[79,3727,3729],{"className":3728},[338],[79,3730,3732,3752],{"className":3731},[342,343],[79,3733,3735,3749],{"className":3734},[347],[79,3736,3738],{"className":3737,"style":1338},[351],[79,3739,3740,3743],{"style":1341},[79,3741],{"className":3742,"style":1345},[359],[79,3744,3746],{"className":3745},[364,1349,1350,367],[79,3747,1978],{"className":3748,"style":2320},[122,162,367],[79,3750,375],{"className":3751},[374],[79,3753,3755],{"className":3754},[347],[79,3756,3758],{"className":3757,"style":2439},[351],[79,3759],{},[79,3761,375],{"className":3762},[374],[79,3764,3766],{"className":3765},[347],[79,3767,3769],{"className":3768,"style":1445},[351],[79,3770],{},[79,3772],{"className":3773},[502,1289],[79,3775],{"className":3776,"style":167},[166],[79,3778,143],{"className":3779},[171],[79,3781],{"className":3782,"style":167},[166],[79,3784,3786,3789,3830,3941,3944],{"className":3785},[113],[79,3787],{"className":3788,"style":2106},[117],[79,3790,3792,3795],{"className":3791},[122],[79,3793,247],{"className":3794},[122,162],[79,3796,3798],{"className":3797},[338],[79,3799,3801,3821],{"className":3800},[342,343],[79,3802,3804,3818],{"className":3803},[347],[79,3805,3807],{"className":3806,"style":977},[351],[79,3808,3809,3812],{"style":355},[79,3810],{"className":3811,"style":360},[359],[79,3813,3815],{"className":3814},[364,365,366,367],[79,3816,1978],{"className":3817,"style":2320},[122,162,367],[79,3819,375],{"className":3820},[374],[79,3822,3824],{"className":3823},[347],[79,3825,3828],{"className":3826,"style":3827},[351],"height:0.2861em;",[79,3829],{},[79,3831,3833,3836,3938],{"className":3832},[122],[79,3834],{"className":3835},[328,1289],[79,3837,3839],{"className":3838},[1187],[79,3840,3842,3930],{"className":3841},[342,343],[79,3843,3845,3927],{"className":3844},[347],[79,3846,3848,3902,3910],{"className":3847,"style":2165},[351],[79,3849,3850,3853],{"style":1305},[79,3851],{"className":3852,"style":1309},[359],[79,3854,3856],{"className":3855},[364,365,366,367],[79,3857,3859,3862],{"className":3858},[122,367],[79,3860,1193],{"className":3861,"style":1319},[122,367],[79,3863,3865,3868],{"className":3864},[122,367],[79,3866,247],{"className":3867},[122,162,367],[79,3869,3871],{"className":3870},[338],[79,3872,3874,3894],{"className":3873},[342,343],[79,3875,3877,3891],{"className":3876},[347],[79,3878,3880],{"className":3879,"style":1338},[351],[79,3881,3882,3885],{"style":1341},[79,3883],{"className":3884,"style":1345},[359],[79,3886,3888],{"className":3887},[364,1349,1350,367],[79,3889,945],{"className":3890},[122,162,367],[79,3892,375],{"className":3893},[374],[79,3895,3897],{"className":3896},[347],[79,3898,3900],{"className":3899,"style":1363},[351],[79,3901],{},[79,3903,3904,3907],{"style":1368},[79,3905],{"className":3906,"style":1309},[359],[79,3908],{"className":3909,"style":1376},[1375],[79,3911,3912,3915],{"style":2230},[79,3913],{"className":3914,"style":1309},[359],[79,3916,3918],{"className":3917},[364,365,366,367],[79,3919,3921,3924],{"className":3920},[122,367],[79,3922,1193],{"className":3923,"style":1319},[122,367],[79,3925,526],{"className":3926,"style":610},[122,162,367],[79,3928,375],{"className":3929},[374],[79,3931,3933],{"className":3932},[347],[79,3934,3936],{"className":3935,"style":1445},[351],[79,3937],{},[79,3939],{"className":3940},[502,1289],[79,3942,286],{"className":3943},[502],[79,3945,265],{"className":3946},[122],[61,3948,3949],{},"Put this result back into the original equation,",[61,3951,3952],{},[79,3953,3955,4113],{"className":3954},[82],[79,3956,3958],{"className":3957},[86],[88,3959,3960],{"xmlns":90},[92,3961,3962,4110],{},[95,3963,3964,3970,3972,3978,3996,3998,4000,4024,4046,4056,4058,4060,4082,4084,4090,4108],{},[243,3965,3966,3968],{},[137,3967,1181],{},[137,3969,945],{},[141,3971,234],{},[243,3973,3974,3976],{},[137,3975,231],{},[137,3977,139],{},[1187,3979,3980,3986],{},[95,3981,3982,3984],{},[137,3983,1193],{"mathvariant":264},[137,3985,526],{},[95,3987,3988,3990],{},[137,3989,1193],{"mathvariant":264},[243,3991,3992,3994],{},[137,3993,247],{},[137,3995,945],{},[141,3997,1965],{},[137,3999,526],{},[1969,4001,4002,4004,4012],{},[141,4003,1973],{},[95,4005,4006,4008,4010],{},[137,4007,1978],{},[141,4009,234],{},[98,4011,100],{},[95,4013,4014,4016,4018,4020,4022],{},[137,4015,1978],{},[141,4017,234],{},[137,4019,139],{},[141,4021,143],{},[98,4023,100],{},[1187,4025,4026,4036],{},[95,4027,4028,4030],{},[137,4029,1193],{"mathvariant":264},[243,4031,4032,4034],{},[137,4033,231],{},[137,4035,139],{},[95,4037,4038,4040],{},[137,4039,1193],{"mathvariant":264},[243,4041,4042,4044],{},[137,4043,542],{},[137,4045,1978],{},[1187,4047,4048,4050],{},[98,4049,100],{},[3285,4051,4052,4054],{},[137,4053,526],{},[98,4055,259],{},[141,4057,241],{"stretchy":240},[137,4059,526],{},[1187,4061,4062,4072],{},[95,4063,4064,4066],{},[137,4065,1193],{"mathvariant":264},[243,4067,4068,4070],{},[137,4069,247],{},[137,4071,1978],{},[95,4073,4074,4076],{},[137,4075,1193],{"mathvariant":264},[243,4077,4078,4080],{},[137,4079,247],{},[137,4081,945],{},[141,4083,143],{},[243,4085,4086,4088],{},[137,4087,247],{},[137,4089,1978],{},[1187,4091,4092,4098],{},[95,4093,4094,4096],{},[137,4095,1193],{"mathvariant":264},[137,4097,526],{},[95,4099,4100,4102],{},[137,4101,1193],{"mathvariant":264},[243,4103,4104,4106],{},[137,4105,247],{},[137,4107,945],{},[141,4109,286],{"stretchy":240},[102,4111,4112],{"encoding":104},"\\mu_i = G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j}\\frac{1}{N^2} (N\\frac{\\partial n_j}{\\partial n_i} - n_j\\frac{\\partial N}{\\partial 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the equation above,",[61,4996,4997],{},[79,4998,5000,5097],{"className":4999},[82],[79,5001,5003],{"className":5002},[86],[88,5004,5005],{"xmlns":90},[92,5006,5007,5094],{},[95,5008,5009,5015,5017,5023,5025,5049,5071,5073,5084,5086,5092],{},[243,5010,5011,5013],{},[137,5012,1181],{},[137,5014,945],{},[141,5016,234],{},[243,5018,5019,5021],{},[137,5020,231],{},[137,5022,139],{},[141,5024,1965],{},[1969,5026,5027,5029,5037],{},[141,5028,1973],{},[95,5030,5031,5033,5035],{},[137,5032,1978],{},[141,5034,234],{},[98,5036,100],{},[95,5038,5039,5041,5043,5045,5047],{},[137,5040,1978],{},[141,5042,234],{},[137,5044,139],{},[141,5046,143],{},[98,5048,100],{},[1187,5050,5051,5061],{},[95,5052,5053,5055],{},[137,5054,1193],{"mathvariant":264},[243,5056,5057,5059],{},[137,5058,231],{},[137,5060,139],{},[95,5062,5063,5065],{},[137,5064,1193],{"mathvariant":264},[243,5066,5067,5069],{},[137,5068,542],{},[137,5070,1978],{},[141,5072,241],{"stretchy":240},[243,5074,5075,5078],{},[137,5076,5077],{},"δ",[95,5079,5080,5082],{},[137,5081,945],{},[137,5083,1978],{},[141,5085,143],{},[243,5087,5088,5090],{},[137,5089,542],{},[137,5091,1978],{},[141,5093,286],{"stretchy":240},[102,5095,5096],{"encoding":104},"\\mu_i = G_m  + \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j} (\\delta_{ij} - x_j)",[79,5098,5100,5155,5210,5501],{"className":5099,"ariaHidden":109},[108],[79,5101,5103,5106,5146,5149,5152],{"className":5102},[113],[79,5104],{"className":5105,"style":1226},[117],[79,5107,5109,5112],{"className":5108},[122],[79,5110,1181],{"className":5111},[122,162],[79,5113,5115],{"className":5114},[338],[79,5116,5118,5138],{"className":5117},[342,343],[79,5119,5121,5135],{"className":5120},[347],[79,5122,5124],{"className":5123,"style":977},[351],[79,5125,5126,5129],{"style":355},[79,5127],{"className":5128,"style":360},[359],[79,5130,5132],{"className":5131},[364,365,366,367],[79,5133,945],{"className":5134},[122,162,367],[79,5136,375],{"className":5137},[374],[79,5139,5141],{"className":5140},[347],[79,5142,5144],{"className":5143,"style":382},[351],[79,5145],{},[79,5147],{"className":5148,"style":306},[166],[79,5150,234],{"className":5151},[310],[79,5153],{"className":5154,"style":306},[166],[79,5156,5158,5161,5201,5204,5207],{"className":5157},[113],[79,5159],{"className":5160,"style":885},[117],[79,5162,5164,5167],{"className":5163},[122],[79,5165,231],{"className":5166},[122,162],[79,5168,5170],{"className":5169},[338],[79,5171,5173,5193],{"className":5172},[342,343],[79,5174,5176,5190],{"className":5175},[347],[79,5177,5179],{"className":5178,"style":644},[351],[79,5180,5181,5184],{"style":355},[79,5182],{"className":5183,"style":360},[359],[79,5185,5187],{"className":5186},[364,365,366,367],[79,5188,139],{"className":5189},[122,162,367],[79,5191,375],{"className":5192},[374],[79,5194,5196],{"className":5195},[347],[79,5197,5199],{"className":5198,"style":382},[351],[79,5200],{},[79,5202],{"className":5203,"style":167},[166],[79,5205,1965],{"className":5206},[171],[79,5208],{"className":5209,"style":167},[166],[79,5211,5213,5217,5292,5295,5443,5446,5492,5495,5498],{"className":5212},[113],[79,5214],{"className":5215,"style":5216},[117],"height:1.5069em;vertical-align:-0.5423em;",[79,5218,5220,5223],{"className":5219},[2285],[79,5221,1973],{"className":5222,"style":2291},[2285,2289,2290],[79,5224,5226],{"className":5225},[338],[79,5227,5229,5284],{"className":5228},[342,343],[79,5230,5232,5281],{"className":5231},[347],[79,5233,5235,5255],{"className":5234,"style":2304},[351],[79,5236,5237,5240],{"style":2307},[79,5238],{"className":5239,"style":360},[359],[79,5241,5243],{"className":5242},[364,365,366,367],[79,5244,5246,5249,5252],{"className":5245},[122,367],[79,5247,1978],{"className":5248,"style":2320},[122,162,367],[79,5250,234],{"className":5251},[310,367],[79,5253,100],{"className":5254},[122,367],[79,5256,5257,5260],{"style":2329},[79,5258],{"className":5259,"style":360},[359],[79,5261,5263],{"className":5262},[364,365,366,367],[79,5264,5266,5269,5272,5275,5278],{"className":5265},[122,367],[79,5267,1978],{"className":5268,"style":2320},[122,162,367],[79,5270,234],{"className":5271},[310,367],[79,5273,139],{"className":5274},[122,162,367],[79,5276,143],{"className":5277},[171,367],[79,5279,100],{"className":5280},[122,367],[79,5282,375],{"className":5283},[374],[79,5285,5287],{"className":5286},[347],[79,5288,5290],{"className":5289,"style":2363},[351],[79,5291],{},[79,5293],{"className":5294,"style":392},[166],[79,5296,5298,5301,5440],{"className":5297},[122],[79,5299],{"className":5300},[328,1289],[79,5302,5304],{"className":5303},[1187],[79,5305,5307,5432],{"className":5306},[342,343],[79,5308,5310,5429],{"className":5309},[347],[79,5311,5313,5367,5375],{"className":5312,"style":1302},[351],[79,5314,5315,5318],{"style":1305},[79,5316],{"className":5317,"style":1309},[359],[79,5319,5321],{"className":5320},[364,365,366,367],[79,5322,5324,5327],{"className":5323},[122,367],[79,5325,1193],{"className":5326,"style":1319},[122,367],[79,5328,5330,5333],{"className":5329},[122,367],[79,5331,542],{"className":5332},[122,162,367],[79,5334,5336],{"className":5335},[338],[79,5337,5339,5359],{"className":5338},[342,343],[79,5340,5342,5356],{"className":5341},[347],[79,5343,5345],{"className":5344,"style":1338},[351],[79,5346,5347,5350],{"style":1341},[79,5348],{"className":5349,"style":1345},[359],[79,5351,5353],{"className":5352},[364,1349,1350,367],[79,5354,1978],{"className":5355,"style":2320},[122,162,367],[79,5357,375],{"className":5358},[374],[79,5360,5362],{"className":5361},[347],[79,5363,5365],{"className":5364,"style":2439},[351],[79,5366],{},[79,5368,5369,5372],{"style":1368},[79,5370],{"className":5371,"style":1309},[359],[79,5373],{"className":5374,"style":1376},[1375],[79,5376,5377,5380],{"style":1379},[79,5378],{"className":5379,"style":1309},[359],[79,5381,5383],{"className":5382},[364,365,366,367],[79,5384,5386,5389],{"className":5385},[122,367],[79,5387,1193],{"className":5388,"style":1319},[122,367],[79,5390,5392,5395],{"className":5391},[122,367],[79,5393,231],{"className":5394},[122,162,367],[79,5396,5398],{"className":5397},[338],[79,5399,5401,5421],{"className":5400},[342,343],[79,5402,5404,5418],{"className":5403},[347],[79,5405,5407],{"className":5406,"style":1413},[3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Gibbs energy with dependent composition",[61,5556,77,5557,123,5585,184,5635,214],{},[79,5558,5560,5573],{"className":5559},[82],[79,5561,5563],{"className":5562},[86],[88,5564,5565],{"xmlns":90},[92,5566,5567,5571],{},[95,5568,5569],{},[98,5570,100],{},[102,5572,100],{"encoding":104},[79,5574,5576],{"className":5575,"ariaHidden":109},[108],[79,5577,5579,5582],{"className":5578},[113],[79,5580],{"className":5581,"style":118},[117],[79,5583,100],{"className":5584},[122],[79,5586,5588,5605],{"className":5587},[82],[79,5589,5591],{"className":5590},[86],[88,5592,5593],{"xmlns":90},[92,5594,5595,5603],{},[95,5596,5597,5599,5601],{},[137,5598,139],{},[141,5600,143],{},[98,5602,100],{},[102,5604,148],{"encoding":104},[79,5606,5608,5626],{"className":5607,"ariaHidden":109},[108],[79,5609,5611,5614,5617,5620,5623],{"className":5610},[113],[79,5612],{"className":5613,"style":158},[117],[79,5615,139],{"className":5616},[122,162],[79,5618],{"className":5619,"style":167},[166],[79,5621,143],{"className":5622},[171],[79,5624],{"className":5625,"style":167},[166],[79,5627,5629,5632],{"className":5628},[113],[79,5630],{"className":5631,"style":118},[117],[79,5633,100],{"className":5634},[122],[79,5636,5638,5651],{"className":5637},[82],[79,5639,5641],{"className":5640},[86],[88,5642,5643],{"xmlns":90},[92,5644,5645,5649],{},[95,5646,5647],{},[137,5648,139],{},[102,5650,139],{"encoding":104},[79,5652,5654],{"className":5653,"ariaHidden":109},[108],[79,5655,5657,5660],{"className":5656},[113],[79,5658],{"className":5659,"style":210},[117],[79,5661,139],{"className":5662},[122,162],[61,5664,5665],{},[79,5666,5668,5736],{"className":5667},[82],[79,5669,5671],{"className":5670},[86],[88,5672,5673],{"xmlns":90},[92,5674,5675,5733],{},[95,5676,5677,5679,5681,5683,5685,5691,5693,5699,5701,5703,5705,5707,5709,5721,5723,5729,5731],{},[137,5678,231],{},[141,5680,234],{},[137,5682,237],{},[141,5684,241],{"stretchy":240},[243,5686,5687,5689],{},[137,5688,247],{},[98,5690,100],{},[141,5692,252],{"separator":109},[243,5694,5695,5697],{},[137,5696,247],{},[98,5698,259],{},[141,5700,252],{"separator":109},[137,5702,265],{"mathvariant":264},[137,5704,265],{"mathvariant":264},[137,5706,265],{"mathvariant":264},[141,5708,252],{"separator":109},[243,5710,5711,5713],{},[137,5712,247],{},[95,5714,5715,5717,5719],{},[137,5716,139],{},[141,5718,143],{},[98,5720,100],{},[141,5722,252],{"separator":109},[243,5724,5725,5727],{},[137,5726,247],{},[137,5728,139],{},[141,5730,286],{"stretchy":240},[141,5732,252],{"separator":109},[102,5734,5735],{"encoding":104},"G = f(n_1, n_2, ..., n_{m-1}, 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the spirit of the CALPHAD method and other physical models, the mole fraction or the composition is the most common state variable for the fraction of the components. And thus, we have a motivation to substitute the amount, i.e., 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= N \\cdot g(x_1, x_2, ..., x_{m-1}, x_m)",[79,7195,7197,7252,7270],{"className":7196,"ariaHidden":109},[108],[79,7198,7200,7203,7243,7246,7249],{"className":7199},[113],[79,7201],{"className":7202,"style":958},[117],[79,7204,7206,7209],{"className":7205},[122],[79,7207,247],{"className":7208},[122,162],[79,7210,7212],{"className":7211},[338],[79,7213,7215,7235],{"className":7214},[342,343],[79,7216,7218,7232],{"className":7217},[347],[79,7219,7221],{"className":7220,"style":977},[351],[79,7222,7223,7226],{"style":355},[79,7224],{"className":7225,"style":360},[359],[79,7227,7229],{"className":7228},[364,365,366,367],[79,7230,945],{"className":7231},[122,162,367],[79,7233,375],{"className":7234},[374],[79,7236,7238],{"className":7237},[347],[79,7239,7241],{"className":7240,"style":382},[351],[79,7242],{},[79,7244],{"className":7245,"style":306},[166],[79,7247,234],{"className":7248},[310],[79,7250],{"className":7251,"style":306},[166],[79,7253,7255,7258,7261,7264,7267],{"className":7254},[113],[79,7256],{"className":7257,"style":299},[117],[79,7259,526],{"className":7260,"style":610},[122,162],[79,7262],{"className":7263,"style":167},[166],[79,7265,529],{"className":7266},[171],[79,7268],{"className":7269,"style":167},[166],[79,7271,7273,7276,7279,7282,7322,7325,7328,7368,7371,7374,7377,7380,7383,7432,7435,7438,7478],{"className":7272},[113],[79,7274],{"className":7275,"style":320},[117],[79,7277,1628],{"className":7278,"style":1757},[122,162],[79,7280,241],{"className":7281},[328],[79,7283,7285,7288],{"className":7284},[122],[79,7286,542],{"className":7287},[122,162],[79,7289,7291],{"className":7290},[338],[79,7292,7294,7314],{"className":7293},[342,343],[79,7295,7297,7311],{"className":7296},[347],[79,7298,7300],{"className":7299,"style":352},[351],[79,7301,7302,7305],{"style":355},[79,7303],{"className":7304,"style":360},[359],[79,7306,7308],{"className":7307},[364,365,366,367],[79,7309,100],{"className":7310},[122,367],[79,7312,375],{"className":7313},[374],[79,7315,7317],{"className":7316},[347],[79,7318,7320],{"className":7319,"style":382},[351],[79,7321],{},[79,7323,252],{"className":7324},[388],[79,7326],{"className":7327,"style":392},[166],[79,7329,7331,7334],{"className":7330},[122],[79,7332,542],{"className":7333},[122,162],[79,7335,7337],{"className":7336},[338],[79,7338,7340,7360],{"className":7339},[342,343],[79,7341,7343,7357],{"className":7342},[347],[79,7344,7346],{"className":7345,"style":352},[351],[79,7347,7348,7351],{"style":355},[79,7349],{"className":7350,"style":360},[359],[79,7352,7354],{"className":7353},[364,365,366,367],[79,7355,259],{"className":7356},[122,367],[79,7358,375],{"className":7359},[374],[79,7361,7363],{"className":7362},[347],[79,7364,7366],{"className":7365,"style":382},[351],[79,7367],{},[79,7369,252],{"className":7370},[388],[79,7372],{"className":7373,"style":392},[166],[79,7375,442],{"className":7376},[122],[79,7378,252],{"className":7379},[388],[79,7381],{"className":7382,"style":392},[166],[79,7384,7386,7389],{"className":7385},[122],[79,7387,542],{"className":7388},[122,162],[79,7390,7392],{"className":7391},[338],[79,7393,7395,7424],{"className":7394},[342,343],[79,7396,7398,7421],{"className":7397},[347],[79,7399,7401],{"className":7400,"style":352},[351],[79,7402,7403,7406],{"style":355},[79,7404],{"className":7405,"style":360},[359],[79,7407,7409],{"className":7408},[364,365,366,367],[79,7410,7412,7415,7418],{"className":7411},[122,367],[79,7413,139],{"className":7414},[122,162,367],[79,7416,143],{"className":7417},[171,367],[79,7419,100],{"className":7420},[122,367],[79,7422,375],{"className":7423},[374],[79,7425,7427],{"className":7426},[347],[79,7428,7430],{"className":7429,"style":496},[351],[79,7431],{},[79,7433,252],{"className":7434},[388],[79,7436],{"className":7437,"style":392},[166],[79,7439,7441,7444],{"className":7440},[122],[79,7442,542],{"className":7443},[122,162],[79,7445,7447],{"className":7446},[338],[79,7448,7450,7470],{"className":7449},[342,343],[79,7451,7453,7467],{"className":7452},[347],[79,7454,7456],{"className":7455,"style":644},[351],[79,7457,7458,7461],{"style":355},[79,7459],{"className":7460,"style":360},[359],[79,7462,7464],{"className":7463},[364,365,366,367],[79,7465,139],{"className":7466},[122,162,367],[79,7468,375],{"className":7469},[374],[79,7471,7473],{"className":7472},[347],[79,7474,7476],{"className":7475,"style":382},[351],[79,7477],{},[79,7479,286],{"className":7480},[502],[61,7482,7483],{},"with the previous constraint, and we can 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= G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m}\\frac{\\partial G_m }{\\partial x_j}\\frac{\\partial x_j }{\\partial 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between the chemical potential and the diffusion potential",[61,12229,12230],{},"Diffusion potential is one of the most important variables in phase-field modeling. Mathematically, it should be defined as the partial derivative of the mole Gibbs energy.",[61,12232,12233,12235],{},[3072,12234,3074],{}," partial derivative of the mole Gibbs energy and the partial quantity of the Gibbs energy are two completely different things.",[61,12237,12238],{},"Considering that the mole Gibbs energy is described with those independent composition variables,",[61,12240,12241],{},[79,12242,12244,12310],{"className":12243},[82],[79,12245,12247],{"className":12246},[86],[88,12248,12249],{"xmlns":90},[92,12250,12251,12307],{},[95,12252,12253,12259,12261,12267,12269,12275,12277,12283,12285,12287,12289,12291,12293,12305],{},[243,12254,12255,12257],{},[137,12256,231],{},[137,12258,139],{},[141,12260,234],{},[243,12262,12263,12265],{},[137,12264,231],{},[137,12266,139],{},[141,12268,241],{"stretchy":240},[243,12270,12271,12273],{},[137,12272,542],{},[98,12274,100],{},[141,12276,252],{"separator":109},[243,12278,12279,12281],{},[137,12280,542],{},[98,12282,259],{},[141,12284,252],{"separator":109},[137,12286,265],{"mathvariant":264},[137,12288,265],{"mathvariant":264},[137,12290,265],{"mathvariant":264},[141,12292,252],{"separator":109},[243,12294,12295,12297],{},[137,12296,542],{},[95,12298,12299,12301,12303],{},[137,12300,139],{},[141,12302,143],{},[98,12304,100],{},[141,12306,286],{"stretchy":240},[102,12308,12309],{"encoding":104},"G_m = G_m(x_1, x_2, ..., x_{m-1})",[79,12311,12313,12368],{"className":12312,"ariaHidden":109},[108],[79,12314,12316,12319,12359,12362,12365],{"className":12315},[113],[79,12317],{"className":12318,"style":885},[117],[79,12320,12322,12325],{"className":12321},[122],[79,12323,231],{"className":12324},[122,162],[79,12326,12328],{"className":12327},[338],[79,12329,12331,12351],{"className":12330},[342,343],[79,12332,12334,12348],{"className":12333},[347],[79,12335,12337],{"className":12336,"style":644},[351],[79,12338,12339,12342],{"style":355},[79,12340],{"className":12341,"style":360},[359],[79,12343,12345],{"className":12344},[364,365,366,367],[79,12346,139],{"className":12347},[122,162,367],[79,12349,375],{"className":12350},[374],[79,12352,12354],{"className":12353},[347],[79,12355,12357],{"className":12356,"style":382},[351],[79,12358],{},[79,12360],{"className":12361,"style":306},[166],[79,12363,234],{"className":12364},[310],[79,12366],{"className":12367,"style":306},[166],[79,12369,12371,12374,12414,12417,12457,12460,12463,12503,12506,12509,12512,12515,12518,12567],{"className":12370},[113],[79,12372],{"className":12373,"style":320},[117],[79,12375,12377,12380],{"className":12376},[122],[79,12378,231],{"className":12379},[122,162],[79,12381,12383],{"className":12382},[338],[79,12384,12386,12406],{"className":12385},[342,343],[79,12387,12389,12403],{"className":12388},[347],[79,12390,12392],{"className":12391,"style":644},[351],[79,12393,12394,12397],{"style":355},[79,12395],{"className":12396,"style":360},[359],[79,12398,12400],{"className":12399},[364,365,366,367],[79,12401,139],{"className":12402},[122,162,367],[79,12404,375],{"className":12405},[374],[79,12407,12409],{"className":12408},[347],[79,12410,12412],{"className":12411,"style":382},[351],[79,12413],{},[79,12415,241],{"className":12416},[328],[79,12418,12420,12423],{"className":12419},[122],[79,12421,542],{"className":12422},[122,162],[79,12424,12426],{"className":12425},[338],[79,12427,12429,12449],{"className":12428},[342,343],[79,12430,12432,12446],{"className":12431},[347],[79,12433,12435],{"className":12434,"style":352},[351],[79,12436,12437,12440],{"style":355},[79,12438],{"className":12439,"style":360},[359],[79,12441,12443],{"className":12442},[364,365,366,367],[79,12444,100],{"className":12445},[122,367],[79,12447,375],{"className":12448},[374],[79,12450,12452],{"className":12451},[347],[79,12453,12455],{"className":12454,"style":382},[351],[79,12456],{},[79,12458,252],{"className":12459},[388],[79,12461],{"className":12462,"style":392},[166],[79,12464,12466,12469],{"className":12465},[122],[79,12467,542],{"className":12468},[122,162],[79,12470,12472],{"className":12471},[338],[79,12473,12475,12495],{"className":12474},[342,343],[79,12476,12478,12492],{"className":12477},[347],[79,12479,12481],{"className":12480,"style":352},[351],[79,12482,12483,12486],{"style":355},[79,12484],{"className":12485,"style":360},[359],[79,12487,12489],{"className":12488},[364,365,366,367],[79,12490,259],{"className":12491},[122,367],[79,12493,375],{"className":12494},[374],[79,12496,12498],{"className":12497},[347],[79,12499,12501],{"className":12500,"style":382},[351],[79,12502],{},[79,12504,252],{"className":12505},[388],[79,12507],{"className":12508,"style":392},[166],[79,12510,442],{"className":12511},[122],[79,12513,252],{"className":12514},[388],[79,12516],{"className":12517,"style":392},[166],[79,12519,12521,12524],{"className":12520},[122],[79,12522,542],{"className":12523},[122,162],[79,12525,12527],{"className":12526},[338],[79,12528,12530,12559],{"className":12529},[342,343],[79,12531,12533,12556],{"className":12532},[347],[79,12534,12536],{"className":12535,"style":352},[351],[79,12537,12538,12541],{"style":355},[79,12539],{"className":12540,"style":360},[359],[79,12542,12544],{"className":12543},[364,365,366,367],[79,12545,12547,12550,12553],{"className":12546},[122,367],[79,12548,139],{"className":12549},[122,162,367],[79,12551,143],{"className":12552},[171,367],[79,12554,100],{"className":12555},[122,367],[79,12557,375],{"className":12558},[374],[79,12560,12562],{"className":12561},[347],[79,12563,12565],{"className":12564,"style":496},[351],[79,12566],{},[79,12568,286],{"className":12569},[502],[61,12571,12572,12573,12601,12602,12630],{},"the diffusion potential of the ",[79,12574,12576,12589],{"className":12575},[82],[79,12577,12579],{"className":12578},[86],[88,12580,12581],{"xmlns":90},[92,12582,12583,12587],{},[95,12584,12585],{},[137,12586,945],{},[102,12588,945],{"encoding":104},[79,12590,12592],{"className":12591,"ariaHidden":109},[108],[79,12593,12595,12598],{"className":12594},[113],[79,12596],{"className":12597,"style":1026},[117],[79,12599,945],{"className":12600},[122,162],"-th component with respect to ",[79,12603,12605,12618],{"className":12604},[82],[79,12606,12608],{"className":12607},[86],[88,12609,12610],{"xmlns":90},[92,12611,12612,12616],{},[95,12613,12614],{},[137,12615,139],{},[102,12617,139],{"encoding":104},[79,12619,12621],{"className":12620,"ariaHidden":109},[108],[79,12622,12624,12627],{"className":12623},[113],[79,12625],{"className":12626,"style":210},[117],[79,12628,139],{"className":12629},[122,162],"-th component is",[61,12632,12633],{},[79,12634,12636,12684],{"className":12635},[82],[79,12637,12639],{"className":12638},[86],[88,12640,12641],{"xmlns":90},[92,12642,12643,12681],{},[95,12644,12645,12657,12659],{},[243,12646,12647,12655],{},[12648,12649,12650,12652],"mover",{"accent":109},[137,12651,1181],{},[141,12653,12654],{},"~",[137,12656,945],{},[141,12658,234],{},[1187,12660,12661,12671],{},[95,12662,12663,12665],{},[137,12664,1193],{"mathvariant":264},[243,12666,12667,12669],{},[137,12668,231],{},[137,12670,139],{},[95,12672,12673,12675],{},[137,12674,1193],{"mathvariant":264},[243,12676,12677,12679],{},[137,12678,542],{},[137,12680,945],{},[102,12682,12683],{"encoding":104},"\\tilde \\mu_i = \\frac{\\partial G_m}{\\partial x_i}",[79,12685,12687,12789],{"className":12686,"ariaHidden":109},[108],[79,12688,12690,12694,12780,12783,12786],{"className":12689},[113],[79,12691],{"className":12692,"style":12693},[117],"height:0.8623em;vertical-align:-0.1944em;",[79,12695,12697,12746],{"className":12696},[122],[79,12698,12701],{"className":12699},[122,12700],"accent",[79,12702,12704,12737],{"className":12703},[342,343],[79,12705,12707,12734],{"className":12706},[347],[79,12708,12711,12720],{"className":12709,"style":12710},[351],"height:0.6679em;",[79,12712,12714,12717],{"style":12713},"top:-3em;",[79,12715],{"className":12716,"style":1309},[359],[79,12718,1181],{"className":12719},[122,162],[79,12721,12723,12726],{"style":12722},"top:-3.35em;",[79,12724],{"className":12725,"style":1309},[359],[79,12727,12731],{"className":12728,"style":12730},[12729],"accent-body","left:-0.2222em;",[79,12732,12654],{"className":12733},[122],[79,12735,375],{"className":12736},[374],[79,12738,12740],{"className":12739},[347],[79,12741,12744],{"className":12742,"style":12743},[351],"height:0.1944em;",[79,12745],{},[79,12747,12749],{"className":12748},[338],[79,12750,12752,12772],{"className":12751},[342,343],[79,12753,12755,12769],{"className":12754},[347],[79,12756,12758],{"className":12757,"style":977},[351],[79,12759,12760,12763],{"style":355},[79,12761],{"className":12762,"style":360},[359],[79,12764,12766],{"className":12765},[364,365,366,367],[79,12767,945],{"className":12768},[122,162,367],[79,12770,375],{"className":12771},[374],[79,12773,12775],{"className":12774},[347],[79,12776,12778],{"className":12777,"style":382},[351],[79,12779],{},[79,12781],{"className":12782,"style":306},[166],[79,12784,234],{"className":12785},[310],[79,12787],{"className":12788,"style":306},[166],[79,12790,12792,12795],{"className":12791},[113],[79,12793],{"className":12794,"style":1282},[117],[79,12796,12798,12801,12940],{"className":12797},[122],[79,12799],{"className":12800},[328,1289],[79,12802,12804],{"className":12803},[1187],[79,12805,12807,12932],{"className":12806},[342,343],[79,12808,12810,12929],{"className":12809},[347],[79,12811,12813,12867,12875],{"className":12812,"style":1302},[351],[79,12814,12815,12818],{"style":1305},[79,12816],{"className":12817,"style":1309},[359],[79,12819,12821],{"className":12820},[364,365,366,367],[79,12822,12824,12827],{"className":12823},[122,367],[79,12825,1193],{"className":12826,"style":1319},[122,367],[79,12828,12830,12833],{"className":12829},[122,367],[79,12831,542],{"className":12832},[122,162,367],[79,12834,12836],{"className":12835},[338],[79,12837,12839,12859],{"className":12838},[342,343],[79,12840,12842,12856],{"className":12841},[347],[79,12843,12845],{"className":12844,"style":1338},[351],[79,12846,12847,12850],{"style":1341},[79,12848],{"className":12849,"style":1345},[359],[79,12851,12853],{"className":12852},[364,1349,1350,367],[79,12854,945],{"className":12855},[122,162,367],[79,12857,375],{"className":12858},[374],[79,12860,12862],{"className":12861},[347],[79,12863,12865],{"className":12864,"style":1363},[351],[79,12866],{},[79,12868,12869,12872],{"style":1368},[79,12870],{"className":12871,"style":1309},[359],[79,12873],{"className":12874,"style":1376},[1375],[79,12876,12877,12880],{"style":1379},[79,12878],{"className":12879,"style":1309},[359],[79,12881,12883],{"className":12882},[364,365,366,367],[79,12884,12886,12889],{"className":12885},[122,367],[79,12887,1193],{"className":12888,"style":1319},[122,367],[79,12890,12892,12895],{"className":12891},[122,367],[79,12893,231],{"className":12894},[122,162,367],[79,12896,12898],{"className":12897},[338],[79,12899,12901,12921],{"className":12900},[342,343],[79,12902,12904,12918],{"className":12903},[347],[79,12905,12907],{"className":12906,"style":1413},[351],[79,12908,12909,12912],{"style":1341},[79,12910],{"className":12911,"style":1345},[359],[79,12913,12915],{"className":12914},[364,1349,1350,367],[79,12916,139],{"className":12917},[122,162,367],[79,12919,375],{"className":12920},[374],[79,12922,12924],{"className":12923},[347],[79,12925,12927],{"className":12926,"style":1363},[351],[79,12928],{},[79,12930,375],{"className":12931},[374],[79,12933,12935],{"className":12934},[347],[79,12936,12938],{"className":12937,"style":1445},[351],[79,12939],{},[79,12941],{"className":12942},[502,1289],[61,12944,12945,12947],{},[3072,12946,3074],{}," I am writing this to tell that, diffusion potential, is state variable of the solute, which means that a solvent component always exists in this context.",[61,12949,12950],{},"The equation above is really convenient when you have a description of the mole Gibbs energy related to compositions of the solute components. However, CALPHAD technique has adopted the second strategy to demonstrate the relationship between the mole Gibbs energy and composition, which is",[61,12952,12953],{},[79,12954,12956,13032],{"className":12955},[82],[79,12957,12959],{"className":12958},[86],[88,12960,12961],{"xmlns":90},[92,12962,12963,13029],{},[95,12964,12965,12971,12973,12979,12981,12987,12989,12995,12997,12999,13001,13003,13005,13017,13019,13025,13027],{},[243,12966,12967,12969],{},[137,12968,231],{},[137,12970,139],{},[141,12972,234],{},[243,12974,12975,12977],{},[137,12976,231],{},[137,12978,139],{},[141,12980,241],{"stretchy":240},[243,12982,12983,12985],{},[137,12984,542],{},[98,12986,100],{},[141,12988,252],{"separator":109},[243,12990,12991,12993],{},[137,12992,542],{},[98,12994,259],{},[141,12996,252],{"separator":109},[137,12998,265],{"mathvariant":264},[137,13000,265],{"mathvariant":264},[137,13002,265],{"mathvariant":264},[141,13004,252],{"separator":109},[243,13006,13007,13009],{},[137,13008,542],{},[95,13010,13011,13013,13015],{},[137,13012,139],{},[141,13014,143],{},[98,13016,100],{},[141,13018,252],{"separator":109},[243,13020,13021,13023],{},[137,13022,542],{},[137,13024,139],{},[141,13026,286],{"stretchy":240},[141,13028,252],{"separator":109},[102,13030,13031],{"encoding":104},"G_m = G_m(x_1, x_2, ..., x_{m-1}, x_m),",[79,13033,13035,13090],{"className":13034,"ariaHidden":109},[108],[79,13036,13038,13041,13081,13084,13087],{"className":13037},[113],[79,13039],{"className":13040,"style":885},[117],[79,13042,13044,13047],{"className":13043},[122],[79,13045,231],{"className":13046},[122,162],[79,13048,13050],{"className":13049},[338],[79,13051,13053,13073],{"className":13052},[342,343],[79,13054,13056,13070],{"className":13055},[347],[79,13057,13059],{"className":13058,"style":644},[351],[79,13060,13061,13064],{"style":355},[79,13062],{"className":13063,"style":360},[359],[79,13065,13067],{"className":13066},[364,365,366,367],[79,13068,139],{"className":13069},[122,162,367],[79,13071,375],{"className":13072},[374],[79,13074,13076],{"className":13075},[347],[79,13077,13079],{"className":13078,"style":382},[351],[79,13080],{},[79,13082],{"className":13083,"style":306},[166],[79,13085,234],{"className":13086},[310],[79,13088],{"className":13089,"style":306},[166],[79,13091,13093,13096,13136,13139,13179,13182,13185,13225,13228,13231,13234,13237,13240,13289,13292,13295,13335,13338],{"className":13092},[113],[79,13094],{"className":13095,"style":320},[117],[79,13097,13099,13102],{"className":13098},[122],[79,13100,231],{"className":13101},[122,162],[79,13103,13105],{"className":13104},[338],[79,13106,13108,13128],{"className":13107},[342,343],[79,13109,13111,13125],{"className":13110},[347],[79,13112,13114],{"className":13113,"style":644},[351],[79,13115,13116,13119],{"style":355},[79,13117],{"className":13118,"style":360},[359],[79,13120,13122],{"className":13121},[364,365,366,367],[79,13123,139],{"className":13124},[122,162,367],[79,13126,375],{"className":13127},[374],[79,13129,13131],{"className":13130},[347],[79,13132,13134],{"className":13133,"style":382},[351],[79,13135],{},[79,13137,241],{"className":13138},[328],[79,13140,13142,13145],{"className":13141},[122],[79,13143,542],{"className":13144},[122,162],[79,13146,13148],{"className":13147},[338],[79,13149,13151,13171],{"className":13150},[342,343],[79,13152,13154,13168],{"className":13153},[347],[79,13155,13157],{"className":13156,"style":352},[351],[79,13158,13159,13162],{"style":355},[79,13160],{"className":13161,"style":360},[359],[79,13163,13165],{"className":13164},[364,365,366,367],[79,13166,100],{"className":13167},[122,367],[79,13169,375],{"className":13170},[374],[79,13172,13174],{"className":13173},[347],[79,13175,13177],{"className":13176,"style":382},[351],[79,13178],{},[79,13180,252],{"className":13181},[388],[79,13183],{"className":13184,"style":392},[166],[79,13186,13188,13191],{"className":13187},[122],[79,13189,542],{"className":13190},[122,162],[79,13192,13194],{"className":13193},[338],[79,13195,13197,13217],{"className":13196},[342,343],[79,13198,13200,13214],{"className":13199},[347],[79,13201,13203],{"className":13202,"style":352},[351],[79,13204,13205,13208],{"style":355},[79,13206],{"className":13207,"style":360},[359],[79,13209,13211],{"className":13210},[364,365,366,367],[79,13212,259],{"className":13213},[122,367],[79,13215,375],{"className":13216},[374],[79,13218,13220],{"className":13219},[347],[79,13221,13223],{"className":13222,"style":382},[351],[79,13224],{},[79,13226,252],{"className":13227},[388],[79,13229],{"className":13230,"style":392},[166],[79,13232,442],{"className":13233},[122],[79,13235,252],{"className":13236},[388],[79,13238],{"className":13239,"style":392},[166],[79,13241,13243,13246],{"className":13242},[122],[79,13244,542],{"className":13245},[122,162],[79,13247,13249],{"className":13248},[338],[79,13250,13252,13281],{"className":13251},[342,343],[79,13253,13255,13278],{"className":13254},[347],[79,13256,13258],{"className":13257,"style":352},[351],[79,13259,13260,13263],{"style":355},[79,13261],{"className":13262,"style":360},[359],[79,13264,13266],{"className":13265},[364,365,366,367],[79,13267,13269,13272,13275],{"className":13268},[122,367],[79,13270,139],{"className":13271},[122,162,367],[79,13273,143],{"className":13274},[171,367],[79,13276,100],{"className":13277},[122,367],[79,13279,375],{"className":13280},[374],[79,13282,13284],{"className":13283},[347],[79,13285,13287],{"className":13286,"style":496},[351],[79,13288],{},[79,13290,252],{"className":13291},[388],[79,13293],{"className":13294,"style":392},[166],[79,13296,13298,13301],{"className":13297},[122],[79,13299,542],{"className":13300},[122,162],[79,13302,13304],{"className":13303},[338],[79,13305,13307,13327],{"className":13306},[342,343],[79,13308,13310,13324],{"className":13309},[347],[79,13311,13313],{"className":13312,"style":644},[351],[79,13314,13315,13318],{"style":355},[79,13316],{"className":13317,"style":360},[359],[79,13319,13321],{"className":13320},[364,365,366,367],[79,13322,139],{"className":13323},[122,162,367],[79,13325,375],{"className":13326},[374],[79,13328,13330],{"className":13329},[347],[79,13331,13333],{"className":13332,"style":382},[351],[79,13334],{},[79,13336,286],{"className":13337},[502],[79,13339,252],{"className":13340},[388],[61,13342,6346],{},[61,13344,13345],{},[79,13346,13348,13407],{"className":13347},[82],[79,13349,13351],{"className":13350},[86],[88,13352,13353],{"xmlns":90},[92,13354,13355,13405],{},[95,13356,13357,13363,13365,13371,13373,13375,13377,13379,13381,13393,13395,13401,13403],{},[243,13358,13359,13361],{},[137,13360,542],{},[98,13362,100],{},[141,13364,1965],{},[243,13366,13367,13369],{},[137,13368,542],{},[98,13370,259],{},[141,13372,1965],{},[137,13374,265],{"mathvariant":264},[137,13376,265],{"mathvariant":264},[137,13378,265],{"mathvariant":264},[141,13380,1965],{},[243,13382,13383,13385],{},[137,13384,542],{},[95,13386,13387,13389,13391],{},[137,13388,139],{},[141,13390,143],{},[98,13392,100],{},[141,13394,1965],{},[243,13396,13397,13399],{},[137,13398,542],{},[137,13400,139],{},[141,13402,234],{},[98,13404,6409],{},[102,13406,6412],{"encoding":104},[79,13408,13410,13465,13520,13538,13602,13657],{"className":13409,"ariaHidden":109},[108],[79,13411,13413,13416,13456,13459,13462],{"className":13412},[113],[79,13414],{"className":13415,"style":6422},[117],[79,13417,13419,13422],{"className":13418},[122],[79,13420,542],{"className":13421},[122,162],[79,13423,13425],{"className":13424},[338],[79,13426,13428,13448],{"className":13427},[342,343],[79,13429,13431,13445],{"className":13430},[347],[79,13432,13434],{"className":13433,"style":352},[351],[79,13435,13436,13439],{"style":355},[79,13437],{"className":13438,"style":360},[359],[79,13440,13442],{"className":13441},[364,365,366,367],[79,13443,100],{"className":13444},[122,367],[79,13446,375],{"className":13447},[374],[79,13449,13451],{"className":13450},[347],[79,13452,13454],{"className":13453,"style":382},[351],[79,13455],{},[79,13457],{"className":13458,"style":167},[166],[79,13460,1965],{"className":13461},[171],[79,13463],{"className":13464,"style":167},[166],[79,13466,13468,13471,13511,13514,13517],{"className":13467},[113],[79,13469],{"className":13470,"style":6422},[117],[79,13472,13474,13477],{"className":13473},[122],[79,13475,542],{"className":13476},[122,162],[79,13478,13480],{"className":13479},[338],[79,13481,13483,13503],{"className":13482},[342,343],[79,13484,13486,13500],{"className":13485},[347],[79,13487,13489],{"className":13488,"style":352},[351],[79,13490,13491,13494],{"style":355},[79,13492],{"className":13493,"style":360},[359],[79,13495,13497],{"className":13496},[364,365,366,367],[79,13498,259],{"className":13499},[122,367],[79,13501,375],{"className":13502},[374],[79,13504,13506],{"className":13505},[347],[79,13507,13509],{"className":13508,"style":382},[351],[79,13510],{},[79,13512],{"className":13513,"style":167},[166],[79,13515,1965],{"className":13516},[171],[79,13518],{"className":13519,"style":167},[166],[79,13521,13523,13526,13529,13532,13535],{"className":13522},[113],[79,13524],{"className":13525,"style":158},[117],[79,13527,442],{"className":13528},[122],[79,13530],{"className":13531,"style":167},[166],[79,13533,1965],{"className":13534},[171],[79,13536],{"className":13537,"style":167},[166],[79,13539,13541,13544,13593,13596,13599],{"className":13540},[113],[79,13542],{"className":13543,"style":6551},[117],[79,13545,13547,13550],{"className":13546},[122],[79,13548,542],{"className":13549},[122,162],[79,13551,13553],{"className":13552},[338],[79,13554,13556,13585],{"className":13555},[342,343],[79,13557,13559,13582],{"className":13558},[347],[79,13560,13562],{"className":13561,"style":352},[351],[79,13563,13564,13567],{"style":355},[79,13565],{"className":13566,"style":360},[359],[79,13568,13570],{"className":13569},[364,365,366,367],[79,13571,13573,13576,13579],{"className":13572},[122,367],[79,13574,139],{"className":13575},[122,162,367],[79,13577,143],{"className":13578},[171,367],[79,13580,100],{"className":13581},[122,367],[79,13583,375],{"className":13584},[374],[79,13586,13588],{"className":13587},[347],[79,13589,13591],{"className":13590,"style":496},[351],[79,13592],{},[79,13594],{"className":13595,"style":167},[166],[79,13597,1965],{"className":13598},[171],[79,13600],{"className":13601,"style":167},[166],[79,13603,13605,13608,13648,13651,13654],{"className":13604},[113],[79,13606],{"className":13607,"style":958},[117],[79,13609,13611,13614],{"className":13610},[122],[79,13612,542],{"className":13613},[122,162],[79,13615,13617],{"className":13616},[338],[79,13618,13620,13640],{"className":13619},[342,343],[79,13621,13623,13637],{"className":13622},[347],[79,13624,13626],{"className":13625,"style":644},[351],[79,13627,13628,13631],{"style":355},[79,13629],{"className":13630,"style":360},[359],[79,13632,13634],{"className":13633},[364,365,366,367],[79,13635,139],{"className":13636},[122,162,367],[79,13638,375],{"className":13639},[374],[79,13641,13643],{"className":13642},[347],[79,13644,13646],{"className":13645,"style":382},[351],[79,13647],{},[79,13649],{"className":13650,"style":306},[166],[79,13652,234],{"className":13653},[310],[79,13655],{"className":13656,"style":306},[166],[79,13658,13660,13663],{"className":13659},[113],[79,13661],{"className":13662,"style":118},[117],[79,13664,6409],{"className":13665},[122],[61,13667,13668],{},"Obviously, there is no straight-forward way to compute the derivative of such a formula of the Gibbs energy, as a constraint has been imposed on the function.",[61,13670,13671],{},"Fortunately, we have another definition of the mole Gibbs energy,",[61,13673,13674],{},[79,13675,13677,13771],{"className":13676},[82],[79,13678,13680],{"className":13679},[86],[88,13681,13682],{"xmlns":90},[92,13683,13684,13768],{},[95,13685,13686,13692,13694,13700,13706,13708,13714,13720,13722,13724,13726,13728,13730,13742,13754,13756,13762],{},[243,13687,13688,13690],{},[137,13689,231],{},[137,13691,139],{},[141,13693,234],{},[243,13695,13696,13698],{},[137,13697,542],{},[98,13699,100],{},[243,13701,13702,13704],{},[137,13703,1181],{},[98,13705,100],{},[141,13707,1965],{},[243,13709,13710,13712],{},[137,13711,542],{},[98,13713,259],{},[243,13715,13716,13718],{},[137,13717,1181],{},[98,13719,259],{},[141,13721,1965],{},[137,13723,265],{"mathvariant":264},[137,13725,265],{"mathvariant":264},[137,13727,265],{"mathvariant":264},[141,13729,1965],{},[243,13731,13732,13734],{},[137,13733,542],{},[95,13735,13736,13738,13740],{},[137,13737,139],{},[141,13739,143],{},[98,13741,100],{},[243,13743,13744,13746],{},[137,13745,1181],{},[95,13747,13748,13750,13752],{},[137,13749,139],{},[141,13751,143],{},[98,13753,100],{},[141,13755,1965],{},[243,13757,13758,13760],{},[137,13759,542],{},[137,13761,139],{},[243,13763,13764,13766],{},[137,13765,1181],{},[137,13767,139],{},[102,13769,13770],{"encoding":104},"G_m = x_1 \\mu_1 + x_2 \\mu_2 + ... + x_{m-1} \\mu_{m-1} + x_{m} \\mu_{m}",[79,13772,13774,13829,13925,14020,14038,14151],{"className":13773,"ariaHidden":109},[108],[79,13775,13777,13780,13820,13823,13826],{"className":13776},[113],[79,13778],{"className":13779,"style":885},[117],[79,13781,13783,13786],{"className":13782},[122],[79,13784,231],{"className":13785},[122,162],[79,13787,13789],{"className":13788},[338],[79,13790,13792,13812],{"className":13791},[342,343],[79,13793,13795,13809],{"className":13794},[347],[79,13796,13798],{"className":13797,"style":644},[351],[79,13799,13800,13803],{"style":355},[79,13801],{"className":13802,"style":360},[359],[79,13804,13806],{"className":13805},[364,365,366,367],[79,13807,139],{"className":13808},[122,162,367],[79,13810,375],{"className":13811},[374],[79,13813,13815],{"className":13814},[347],[79,13816,13818],{"className":13817,"style":382},[351],[79,13819],{},[79,13821],{"className":13822,"style":306},[166],[79,13824,234],{"className":13825},[310],[79,13827],{"className":13828,"style":306},[166],[79,13830,13832,13836,13876,13916,13919,13922],{"className":13831},[113],[79,13833],{"className":13834,"style":13835},[117],"height:0.7778em;vertical-align:-0.1944em;",[79,13837,13839,13842],{"className":13838},[122],[79,13840,542],{"className":13841},[122,162],[79,13843,13845],{"className":13844},[338],[79,13846,13848,13868],{"className":13847},[342,343],[79,13849,13851,13865],{"className":13850},[347],[79,13852,13854],{"className":13853,"style":352},[351],[79,13855,13856,13859],{"style":355},[79,13857],{"className":13858,"style":360},[359],[79,13860,13862],{"className":13861},[364,365,366,367],[79,13863,100],{"className":13864},[122,367],[79,13866,375],{"className":13867},[374],[79,13869,13871],{"className":13870},[347],[79,13872,13874],{"className":13873,"style":382},[351],[79,13875],{},[79,13877,13879,13882],{"className":13878},[122],[79,13880,1181],{"className":13881},[122,162],[79,13883,13885],{"className":13884},[338],[79,13886,13888,13908],{"className":13887},[342,343],[79,13889,13891,13905],{"className":13890},[347],[79,13892,13894],{"className":13893,"style":352},[351],[79,13895,13896,13899],{"style":355},[79,13897],{"className":13898,"style":360},[359],[79,13900,13902],{"className":13901},[364,365,366,367],[79,13903,100],{"className":13904},[122,367],[79,13906,375],{"className":13907},[374],[79,13909,13911],{"className":13910},[347],[79,13912,13914],{"className":13913,"style":382},[351],[79,13915],{},[79,13917],{"className":13918,"style":167},[166],[79,13920,1965],{"className":13921},[171],[79,13923],{"className":13924,"style":167},[166],[79,13926,13928,13931,13971,14011,14014,14017],{"className":13927},[113],[79,13929],{"className":13930,"style":13835},[117],[79,13932,13934,13937],{"className":13933},[122],[79,13935,542],{"className":13936},[122,162],[79,13938,13940],{"className":13939},[338],[79,13941,13943,13963],{"className":13942},[342,343],[79,13944,13946,13960],{"className":13945},[347],[79,13947,13949],{"className":13948,"style":352},[351],[79,13950,13951,13954],{"style":355},[79,13952],{"className":13953,"style":360},[359],[79,13955,13957],{"className":13956},[364,365,366,367],[79,13958,259],{"className":13959},[122,367],[79,13961,375],{"className":13962},[374],[79,13964,13966],{"className":13965},[347],[79,13967,13969],{"className":13968,"style":382},[351],[79,13970],{},[79,13972,13974,13977],{"className":13973},[122],[79,13975,1181],{"className":13976},[122,162],[79,13978,13980],{"className":13979},[338],[79,13981,13983,14003],{"className":13982},[342,343],[79,13984,13986,14000],{"className":13985},[347],[79,13987,13989],{"className":13988,"style":352},[351],[79,13990,13991,13994],{"style":355},[79,13992],{"className":13993,"style":360},[359],[79,13995,13997],{"className":13996},[364,365,366,367],[79,13998,259],{"className":13999},[122,367],[79,14001,375],{"className":14002},[374],[79,14004,14006],{"className":14005},[347],[79,14007,14009],{"className":14008,"style":382},[351],[79,14010],{},[79,14012],{"className":14013,"style":167},[166],[79,14015,1965],{"className":14016},[171],[79,14018],{"className":14019,"style":167},[166],[79,14021,14023,14026,14029,14032,14035],{"className":14022},[113],[79,14024],{"className":14025,"style":158},[117],[79,14027,442],{"className":14028},[122],[79,14030],{"className":14031,"style":167},[166],[79,14033,1965],{"className":14034},[171],[79,14036],{"className":14037,"style":167},[166],[79,14039,14041,14044,14093,14142,14145,14148],{"className":14040},[113],[79,14042],{"className":14043,"style":6551},[117],[79,14045,14047,14050],{"className":14046},[122],[79,14048,542],{"className":14049},[122,162],[79,14051,14053],{"className":14052},[338],[79,14054,14056,14085],{"className":14055},[342,343],[79,14057,14059,14082],{"className":14058},[347],[79,14060,14062],{"className":14061,"style":352},[351],[79,14063,14064,14067],{"style":355},[79,14065],{"className":14066,"style":360},[359],[79,14068,14070],{"className":14069},[364,365,366,367],[79,14071,14073,14076,14079],{"className":14072},[122,367],[79,14074,139],{"className":14075},[122,162,367],[79,14077,143],{"className":14078},[171,367],[79,14080,100],{"className":14081},[122,367],[79,14083,375],{"className":14084},[374],[79,14086,14088],{"className":14087},[347],[79,14089,14091],{"className":14090,"style":496},[351],[79,14092],{},[79,14094,14096,14099],{"className":14095},[122],[79,14097,1181],{"className":14098},[122,162],[79,14100,14102],{"className":14101},[338],[79,14103,14105,14134],{"className":14104},[342,343],[79,14106,14108,14131],{"className":14107},[347],[79,14109,14111],{"className":14110,"style":352},[351],[79,14112,14113,14116],{"style":355},[79,14114],{"className":14115,"style":360},[359],[79,14117,14119],{"className":14118},[364,365,366,367],[79,14120,14122,14125,14128],{"className":14121},[122,367],[79,14123,139],{"className":14124},[122,162,367],[79,14126,143],{"className":14127},[171,367],[79,14129,100],{"className":14130},[122,367],[79,14132,375],{"className":14133},[374],[79,14135,14137],{"className":14136},[347],[79,14138,14140],{"className":14139,"style":496},[351],[79,14141],{},[79,14143],{"className":14144,"style":167},[166],[79,14146,1965],{"className":14147},[171],[79,14149],{"className":14150,"style":167},[166],[79,14152,14154,14157,14200],{"className":14153},[113],[79,14155],{"className":14156,"style":1226},[117],[79,14158,14160,14163],{"className":14159},[122],[79,14161,542],{"className":14162},[122,162],[79,14164,14166],{"className":14165},[338],[79,14167,14169,14192],{"className":14168},[342,343],[79,14170,14172,14189],{"className":14171},[347],[79,14173,14175],{"className":14174,"style":644},[351],[79,14176,14177,14180],{"style":355},[79,14178],{"className":14179,"style":360},[359],[79,14181,14183],{"className":14182},[364,365,366,367],[79,14184,14186],{"className":14185},[122,367],[79,14187,139],{"className":14188},[122,162,367],[79,14190,375],{"className":14191},[374],[79,14193,14195],{"className":14194},[347],[79,14196,14198],{"className":14197,"style":382},[351],[79,14199],{},[79,14201,14203,14206],{"className":14202},[122],[79,14204,1181],{"className":14205},[122,162],[79,14207,14209],{"className":14208},[338],[79,14210,14212,14235],{"className":14211},[342,343],[79,14213,14215,14232],{"className":14214},[347],[79,14216,14218],{"className":14217,"style":644},[351],[79,14219,14220,14223],{"style":355},[79,14221],{"className":14222,"style":360},[359],[79,14224,14226],{"className":14225},[364,365,366,367],[79,14227,14229],{"className":14228},[122,367],[79,14230,139],{"className":14231},[122,162,367],[79,14233,375],{"className":14234},[374],[79,14236,14238],{"className":14237},[347],[79,14239,14241],{"className":14240,"style":382},[351],[79,14242],{},[61,14244,14245],{},"Apply the rule of total derivative to the equation above",[61,14247,14248],{},[79,14249,14251,14345],{"className":14250},[82],[79,14252,14254],{"className":14253},[86],[88,14255,14256],{"xmlns":90},[92,14257,14258,14342],{},[95,14259,14260,14264,14270,14272,14292,14294,14300,14306,14308,14328,14334,14336],{},[14261,14262,14263],"mtext",{},"d",[243,14265,14266,14268],{},[137,14267,231],{},[137,14269,139],{},[141,14271,234],{},[1969,14273,14274,14276,14284],{},[141,14275,1973],{},[95,14277,14278,14280,14282],{},[137,14279,1978],{},[141,14281,234],{},[98,14283,100],{},[95,14285,14286,14288,14290],{},[137,14287,1978],{},[141,14289,234],{},[137,14291,139],{},[14261,14293,14263],{},[243,14295,14296,14298],{},[137,14297,542],{},[137,14299,1978],{},[243,14301,14302,14304],{},[137,14303,1181],{},[137,14305,1978],{},[141,14307,1965],{},[1969,14309,14310,14312,14320],{},[141,14311,1973],{},[95,14313,14314,14316,14318],{},[137,14315,1978],{},[141,14317,234],{},[98,14319,100],{},[95,14321,14322,14324,14326],{},[137,14323,1978],{},[141,14325,234],{},[137,14327,139],{},[243,14329,14330,14332],{},[137,14331,542],{},[137,14333,1978],{},[14261,14335,14263],{},[243,14337,14338,14340],{},[137,14339,1181],{},[137,14341,1978],{},[102,14343,14344],{"encoding":104},"\\textrm{d}G_m = \\sum_{j=1}^{j=m} \\textrm{d}x_j \\mu_j + \\sum_{j=1}^{j=m} x_j \\textrm{d} \\mu_j",[79,14346,14348,14412,14586],{"className":14347,"ariaHidden":109},[108],[79,14349,14351,14355,14363,14403,14406,14409],{"className":14350},[113],[79,14352],{"className":14353,"style":14354},[117],"height:0.8444em;vertical-align:-0.15em;",[79,14356,14359],{"className":14357},[122,14358],"text",[79,14360,14263],{"className":14361},[122,14362],"textrm",[79,14364,14366,14369],{"className":14365},[122],[79,14367,231],{"className":14368},[122,162],[79,14370,14372],{"className":14371},[338],[79,14373,14375,14395],{"className":14374},[342,343],[79,14376,14378,14392],{"className":14377},[347],[79,14379,14381],{"className":14380,"style":644},[351],[79,14382,14383,14386],{"style":355},[79,14384],{"className":14385,"style":360},[359],[79,14387,14389],{"className":14388},[364,365,366,367],[79,14390,139],{"className":14391},[122,162,367],[79,14393,375],{"className":14394},[374],[79,14396,14398],{"className":14397},[347],[79,14399,14401],{"className":14400,"style":382},[351],[79,14402],{},[79,14404],{"className":14405,"style":306},[166],[79,14407,234],{"className":14408},[310],[79,14410],{"className":14411,"style":306},[166],[79,14413,14415,14419,14488,14491,14497,14537,14577,14580,14583],{"className":14414},[113],[79,14416],{"className":14417,"style":14418},[117],"height:1.4004em;vertical-align:-0.4358em;",[79,14420,14422,14425],{"className":14421},[2285],[79,14423,1973],{"className":14424,"style":2291},[2285,2289,2290],[79,14426,14428],{"className":14427},[338],[79,14429,14431,14480],{"className":14430},[342,343],[79,14432,14434,14477],{"className":14433},[347],[79,14435,14437,14457],{"className":14436,"style":2304},[351],[79,14438,14439,14442],{"style":2307},[79,14440],{"className":14441,"style":360},[359],[79,14443,14445],{"className":14444},[364,365,366,367],[79,14446,14448,14451,14454],{"className":14447},[122,367],[79,14449,1978],{"className":14450,"style":2320},[122,162,367],[79,14452,234],{"className":14453},[310,367],[79,14455,100],{"className":14456},[122,367],[79,14458,14459,14462],{"style":2329},[79,14460],{"className":14461,"style":360},[359],[79,14463,14465],{"className":14464},[364,365,366,367],[79,14466,14468,14471,14474],{"className":14467},[122,367],[79,14469,1978],{"className":14470,"style":2320},[122,162,367],[79,14472,234],{"className":14473},[310,367],[79,14475,139],{"className":14476},[122,162,367],[79,14478,375],{"className":14479},[374],[79,14481,14483],{"className":14482},[347],[79,14484,14486],{"className":14485,"style":2363},[351],[79,14487],{},[79,14489],{"className":14490,"style":392},[166],[79,14492,14494],{"className":14493},[122,14358],[79,14495,14263],{"className":14496},[122,14362],[79,14498,14500,14503],{"className":14499},[122],[79,14501,542],{"className":14502},[122,162],[79,14504,14506],{"className":14505},[338],[79,14507,14509,14529],{"className":14508},[342,343],[79,14510,14512,14526],{"className":14511},[347],[79,14513,14515],{"className":14514,"style":977},[351],[79,14516,14517,14520],{"style":355},[79,14518],{"className":14519,"style":360},[359],[79,14521,14523],{"className":14522},[364,365,366,367],[79,14524,1978],{"className":14525,"style":2320},[122,162,367],[79,14527,375],{"className":14528},[374],[79,14530,14532],{"className":14531},[347],[79,14533,14535],{"className":14534,"style":3827},[351],[79,14536],{},[79,14538,14540,14543],{"className":14539},[122],[79,14541,1181],{"className":14542},[122,162],[79,14544,14546],{"className":14545},[338],[79,14547,14549,14569],{"className":14548},[342,343],[79,14550,14552,14566],{"className":14551},[347],[79,14553,14555],{"className":14554,"style":977},[351],[79,14556,14557,14560],{"style":355},[79,14558],{"className":14559,"style":360},[359],[79,14561,14563],{"className":14562},[364,365,366,367],[79,14564,1978],{"className":14565,"style":2320},[122,162,367],[79,14567,375],{"className":14568},[374],[79,14570,14572],{"className":14571},[347],[79,14573,14575],{"className":14574,"style":3827},[351],[79,14576],{},[79,14578],{"className":14579,"style":167},[166],[79,14581,1965],{"className":14582},[171],[79,14584],{"className":14585,"style":167},[166],[79,14587,14589,14592,14661,14664,14704,14710],{"className":14588},[113],[79,14590],{"className":14591,"style":14418},[117],[79,14593,14595,14598],{"className":14594},[2285],[79,14596,1973],{"className":14597,"style":2291},[2285,2289,2290],[79,14599,14601],{"className":14600},[338],[79,14602,14604,14653],{"className":14603},[342,343],[79,14605,14607,14650],{"className":14606},[347],[79,14608,14610,14630],{"className":14609,"style":2304},[351],[79,14611,14612,14615],{"style":2307},[79,14613],{"className":14614,"style":360},[359],[79,14616,14618],{"className":14617},[364,365,366,367],[79,14619,14621,14624,14627],{"className":14620},[122,367],[79,14622,1978],{"className":14623,"style":2320},[122,162,367],[79,14625,234],{"className":14626},[310,367],[79,14628,100],{"className":14629},[122,367],[79,14631,14632,14635],{"style":2329},[79,14633],{"className":14634,"style":360},[359],[79,14636,14638],{"className":14637},[364,365,366,367],[79,14639,14641,14644,14647],{"className":14640},[122,367],[79,14642,1978],{"className":14643,"style":2320},[122,162,367],[79,14645,234],{"className":14646},[310,367],[79,14648,139],{"className":14649},[122,162,367],[79,14651,375],{"className":14652},[374],[79,14654,14656],{"className":14655},[347],[79,14657,14659],{"className":14658,"style":2363},[351],[79,14660],{},[79,14662],{"className":14663,"style":392},[166],[79,14665,14667,14670],{"className":14666},[122],[79,14668,542],{"className":14669},[122,162],[79,14671,14673],{"className":14672},[338],[79,14674,14676,14696],{"className":14675},[342,343],[79,14677,14679,14693],{"className":14678},[347],[79,14680,14682],{"className":14681,"style":977},[351],[79,14683,14684,14687],{"style":355},[79,14685],{"className":14686,"style":360},[359],[79,14688,14690],{"className":14689},[364,365,366,367],[79,14691,1978],{"className":14692,"style":2320},[122,162,367],[79,14694,375],{"className":14695},[374],[79,14697,14699],{"className":14698},[347],[79,14700,14702],{"className":14701,"style":3827},[351],[79,14703],{},[79,14705,14707],{"className":14706},[122,14358],[79,14708,14263],{"className":14709},[122,14362],[79,14711,14713,14716],{"className":14712},[122],[79,14714,1181],{"className":14715},[122,162],[79,14717,14719],{"className":14718},[338],[79,14720,14722,14742],{"className":14721},[342,343],[79,14723,14725,14739],{"className":14724},[347],[79,14726,14728],{"className":14727,"style":977},[351],[79,14729,14730,14733],{"style":355},[79,14731],{"className":14732,"style":360},[359],[79,14734,14736],{"className":14735},[364,365,366,367],[79,14737,1978],{"className":14738,"style":2320},[122,162,367],[79,14740,375],{"className":14741},[374],[79,14743,14745],{"className":14744},[347],[79,14746,14748],{"className":14747,"style":3827},[351],[79,14749],{},[61,14751,14752],{},"According to Gibbs-Duhem equation, we have",[61,14754,14755],{},[79,14756,14758,14809],{"className":14757},[82],[79,14759,14761],{"className":14760},[86],[88,14762,14763],{"xmlns":90},[92,14764,14765,14806],{},[95,14766,14767,14787,14793,14795,14801,14803],{},[1969,14768,14769,14771,14779],{},[141,14770,1973],{},[95,14772,14773,14775,14777],{},[137,14774,1978],{},[141,14776,234],{},[98,14778,100],{},[95,14780,14781,14783,14785],{},[137,14782,1978],{},[141,14784,234],{},[137,14786,139],{},[243,14788,14789,14791],{},[137,14790,542],{},[137,14792,1978],{},[14261,14794,14263],{},[243,14796,14797,14799],{},[137,14798,1181],{},[137,14800,1978],{},[141,14802,234],{},[98,14804,14805],{},"0",[102,14807,14808],{"encoding":104},"\\sum_{j=1}^{j=m} x_j \\textrm{d} \\mu_j = 0",[79,14810,14812,14985],{"className":14811,"ariaHidden":109},[108],[79,14813,14815,14818,14887,14890,14930,14936,14976,14979,14982],{"className":14814},[113],[79,14816],{"className":14817,"style":14418},[117],[79,14819,14821,14824],{"className":14820},[2285],[79,14822,1973],{"className":14823,"style":2291},[2285,2289,2290],[79,14825,14827],{"className":14826},[338],[79,14828,14830,14879],{"className":14829},[342,343],[79,14831,14833,14876],{"className":14832},[347],[79,14834,14836,14856],{"className":14835,"style":2304},[351],[79,14837,14838,14841],{"style":2307},[79,14839],{"className":14840,"style":360},[359],[79,14842,14844],{"className":14843},[364,365,366,367],[79,14845,14847,14850,14853],{"className":14846},[122,367],[79,14848,1978],{"className":14849,"style":2320},[122,162,367],[79,14851,234],{"className":14852},[310,367],[79,14854,100],{"className":14855},[122,367],[79,14857,14858,14861],{"style":2329},[79,14859],{"className":14860,"style":360},[359],[79,14862,14864],{"className":14863},[364,365,366,367],[79,14865,14867,14870,14873],{"className":14866},[122,367],[79,14868,1978],{"className":14869,"style":2320},[122,162,367],[79,14871,234],{"className":14872},[310,367],[79,14874,139],{"className":14875},[122,162,367],[79,14877,375],{"className":14878},[374],[79,14880,14882],{"className":14881},[347],[79,14883,14885],{"className":14884,"style":2363},[351],[79,14886],{},[79,14888],{"className":14889,"style":392},[166],[79,14891,14893,14896],{"className":14892},[122],[79,14894,542],{"className":14895},[122,162],[79,14897,14899],{"className":14898},[338],[79,14900,14902,14922],{"className":14901},[342,343],[79,14903,14905,14919],{"className":14904},[347],[79,14906,14908],{"className":14907,"style":977},[351],[79,14909,14910,14913],{"style":355},[79,14911],{"className":14912,"style":360},[359],[79,14914,14916],{"className":14915},[364,365,366,367],[79,14917,1978],{"className":14918,"style":2320},[122,162,367],[79,14920,375],{"className":14921},[374],[79,14923,14925],{"className":14924},[347],[79,14926,14928],{"className":14927,"style":3827},[351],[79,14929],{},[79,14931,14933],{"className":14932},[122,14358],[79,14934,14263],{"className":14935},[122,14362],[79,14937,14939,14942],{"className":14938},[122],[79,14940,1181],{"className":14941},[122,162],[79,14943,14945],{"className":14944},[338],[79,14946,14948,14968],{"className":14947},[342,343],[79,14949,14951,14965],{"className":14950},[347],[79,14952,14954],{"className":14953,"style":977},[351],[79,14955,14956,14959],{"style":355},[79,14957],{"className":14958,"style":360},[359],[79,14960,14962],{"className":14961},[364,365,366,367],[79,14963,1978],{"className":14964,"style":2320},[122,162,367],[79,14966,375],{"className":14967},[374],[79,14969,14971],{"className":14970},[347],[79,14972,14974],{"className":14973,"style":3827},[351],[79,14975],{},[79,14977],{"className":14978,"style":306},[166],[79,14980,234],{"className":14981},[310],[79,14983],{"className":14984,"style":306},[166],[79,14986,14988,14991],{"className":14987},[113],[79,14989],{"className":14990,"style":118},[117],[79,14992,14805],{"className":14993},[122],[61,14995,14996],{},"and thus",[61,14998,14999],{},[79,15000,15002,15058],{"className":15001},[82],[79,15003,15005],{"className":15004},[86],[88,15006,15007],{"xmlns":90},[92,15008,15009,15055],{},[95,15010,15011,15013,15019,15021,15041,15043,15049],{},[14261,15012,14263],{},[243,15014,15015,15017],{},[137,15016,231],{},[137,15018,139],{},[141,15020,234],{},[1969,15022,15023,15025,15033],{},[141,15024,1973],{},[95,15026,15027,15029,15031],{},[137,15028,1978],{},[141,15030,234],{},[98,15032,100],{},[95,15034,15035,15037,15039],{},[137,15036,1978],{},[141,15038,234],{},[137,15040,139],{},[14261,15042,14263],{},[243,15044,15045,15047],{},[137,15046,542],{},[137,15048,1978],{},[243,15050,15051,15053],{},[137,15052,1181],{},[137,15054,1978],{},[102,15056,15057],{"encoding":104},"\\textrm{d}G_m = \\sum_{j=1}^{j=m} \\textrm{d}x_j \\mu_j",[79,15059,15061,15122],{"className":15060,"ariaHidden":109},[108],[79,15062,15064,15067,15073,15113,15116,15119],{"className":15063},[113],[79,15065],{"className":15066,"style":14354},[117],[79,15068,15070],{"className":15069},[122,14358],[79,15071,14263],{"className":15072},[122,14362],[79,15074,15076,15079],{"className":15075},[122],[79,15077,231],{"className":15078},[122,162],[79,15080,15082],{"className":15081},[338],[79,15083,15085,15105],{"className":15084},[342,343],[79,15086,15088,15102],{"className":15087},[347],[79,15089,15091],{"className":15090,"style":644},[351],[79,15092,15093,15096],{"style":355},[79,15094],{"className":15095,"style":360},[359],[79,15097,15099],{"className":15098},[364,365,366,367],[79,15100,139],{"className":15101},[122,162,367],[79,15103,375],{"className":15104},[374],[79,15106,15108],{"className":15107},[347],[79,15109,15111],{"className":15110,"style":382},[351],[79,15112],{},[79,15114],{"className":15115,"style":306},[166],[79,15117,234],{"className":15118},[310],[79,15120],{"className":15121,"style":306},[166],[79,15123,15125,15128,15197,15200,15206,15246],{"className":15124},[113],[79,15126],{"className":15127,"style":14418},[117],[79,15129,15131,15134],{"className":15130},[2285],[79,15132,1973],{"className":15133,"style":2291},[2285,2289,2290],[79,15135,15137],{"className":15136},[338],[79,15138,15140,15189],{"className":15139},[342,343],[79,15141,15143,15186],{"className":15142},[347],[79,15144,15146,15166],{"className":15145,"style":2304},[351],[79,15147,15148,15151],{"style":2307},[79,15149],{"className":15150,"style":360},[359],[79,15152,15154],{"className":15153},[364,365,366,367],[79,15155,15157,15160,15163],{"className":15156},[122,367],[79,15158,1978],{"className":15159,"style":2320},[122,162,367],[79,15161,234],{"className":15162},[310,367],[79,15164,100],{"className":15165},[122,367],[79,15167,15168,15171],{"style":2329},[79,15169],{"className":15170,"style":360},[359],[79,15172,15174],{"className":15173},[364,365,366,367],[79,15175,15177,15180,15183],{"className":15176},[122,367],[79,15178,1978],{"className":15179,"style":2320},[122,162,367],[79,15181,234],{"className":15182},[310,367],[79,15184,139],{"className":15185},[122,162,367],[79,15187,375],{"className":15188},[374],[79,15190,15192],{"className":15191},[347],[79,15193,15195],{"className":15194,"style":2363},[351],[79,15196],{},[79,15198],{"className":15199,"style":392},[166],[79,15201,15203],{"className":15202},[122,14358],[79,15204,14263],{"className":15205},[122,14362],[79,15207,15209,15212],{"className":15208},[122],[79,15210,542],{"className":15211},[122,162],[79,15213,15215],{"className":15214},[338],[79,15216,15218,15238],{"className":15217},[342,343],[79,15219,15221,15235],{"className":15220},[347],[79,15222,15224],{"className":15223,"style":977},[351],[79,15225,15226,15229],{"style":355},[79,15227],{"className":15228,"style":360},[359],[79,15230,15232],{"className":15231},[364,365,366,367],[79,15233,1978],{"className":15234,"style":2320},[122,162,367],[79,15236,375],{"className":15237},[374],[79,15239,15241],{"className":15240},[347],[79,15242,15244],{"className":15243,"style":3827},[351],[79,15245],{},[79,15247,15249,15252],{"className":15248},[122],[79,15250,1181],{"className":15251},[122,162],[79,15253,15255],{"className":15254},[338],[79,15256,15258,15278],{"className":15257},[342,343],[79,15259,15261,15275],{"className":15260},[347],[79,15262,15264],{"className":15263,"style":977},[351],[79,15265,15266,15269],{"style":355},[79,15267],{"className":15268,"style":360},[359],[79,15270,15272],{"className":15271},[364,365,366,367],[79,15273,1978],{"className":15274,"style":2320},[122,162,367],[79,15276,375],{"className":15277},[374],[79,15279,15281],{"className":15280},[347],[79,15282,15284],{"className":15283,"style":3827},[351],[79,15285],{},[61,15287,15288,15289,15317],{},"Supposing that the ",[79,15290,15292,15305],{"className":15291},[82],[79,15293,15295],{"className":15294},[86],[88,15296,15297],{"xmlns":90},[92,15298,15299,15303],{},[95,15300,15301],{},[137,15302,139],{},[102,15304,139],{"encoding":104},[79,15306,15308],{"className":15307,"ariaHidden":109},[108],[79,15309,15311,15314],{"className":15310},[113],[79,15312],{"className":15313,"style":210},[117],[79,15315,139],{"className":15316},[122,162],"-th is the solvent component, the composition of the solvent can be substituted with those of the solutes,",[61,15319,15320],{},[79,15321,15323,15431],{"className":15322},[82],[79,15324,15326],{"className":15325},[86],[88,15327,15328],{"xmlns":90},[92,15329,15330,15428],{},[95,15331,15332,15334,15340,15342,15366,15368,15374,15380,15382,15384,15386,15388,15390,15414,15420,15422],{},[14261,15333,14263],{},[243,15335,15336,15338],{},[137,15337,231],{},[137,15339,139],{},[141,15341,234],{},[1969,15343,15344,15346,15354],{},[141,15345,1973],{},[95,15347,15348,15350,15352],{},[137,15349,1978],{},[141,15351,234],{},[98,15353,100],{},[95,15355,15356,15358,15360,15362,15364],{},[137,15357,1978],{},[141,15359,234],{},[137,15361,139],{},[141,15363,143],{},[98,15365,100],{},[14261,15367,14263],{},[243,15369,15370,15372],{},[137,15371,542],{},[137,15373,1978],{},[243,15375,15376,15378],{},[137,15377,1181],{},[137,15379,1978],{},[141,15381,1965],{},[14261,15383,14263],{},[141,15385,241],{"stretchy":240},[98,15387,100],{},[141,15389,143],{},[1969,15391,15392,15394,15402],{},[141,15393,1973],{},[95,15395,15396,15398,15400],{},[137,15397,1978],{},[141,15399,234],{},[98,15401,100],{},[95,15403,15404,15406,15408,15410,15412],{},[137,15405,1978],{},[141,15407,234],{},[137,15409,139],{},[141,15411,143],{},[98,15413,100],{},[243,15415,15416,15418],{},[137,15417,542],{},[137,15419,1978],{},[141,15421,286],{"stretchy":240},[243,15423,15424,15426],{},[137,15425,1181],{},[137,15427,139],{},[102,15429,15430],{"encoding":104},"\\textrm{d}G_m = \\sum_{j=1}^{j=m-1} \\textrm{d}x_j \\mu_j + \\textrm{d} (1 - \\sum_{j=1}^{j=m-1} x_j) \\mu_m",[79,15432,15434,15495,15674,15701],{"className":15433,"ariaHidden":109},[108],[79,15435,15437,15440,15446,15486,15489,15492],{"className":15436},[113],[79,15438],{"className":15439,"style":14354},[117],[79,15441,15443],{"className":15442},[122,14358],[79,15444,14263],{"className":15445},[122,14362],[79,15447,15449,15452],{"className":15448},[122],[79,15450,231],{"className":15451},[122,162],[79,15453,15455],{"className":15454},[338],[79,15456,15458,15478],{"className":15457},[342,343],[79,15459,15461,15475],{"className":15460},[347],[79,15462,15464],{"className":15463,"style":644},[351],[79,15465,15466,15469],{"style":355},[79,15467],{"className":15468,"style":360},[359],[79,15470,15472],{"className":15471},[364,365,366,367],[79,15473,139],{"className":15474},[122,162,367],[79,15476,375],{"className":15477},[374],[79,15479,15481],{"className":15480},[347],[79,15482,15484],{"className":15483,"style":382},[351],[79,15485],{},[79,15487],{"className":15488,"style":306},[166],[79,15490,234],{"className":15491},[310],[79,15493],{"className":15494,"style":306},[166],[79,15496,15498,15501,15576,15579,15585,15625,15665,15668,15671],{"className":15497},[113],[79,15499],{"className":15500,"style":14418},[117],[79,15502,15504,15507],{"className":15503},[2285],[79,15505,1973],{"className":15506,"style":2291},[2285,2289,2290],[79,15508,15510],{"className":15509},[338],[79,15511,15513,15568],{"className":15512},[342,343],[79,15514,15516,15565],{"className":15515},[347],[79,15517,15519,15539],{"className":15518,"style":2304},[351],[79,15520,15521,15524],{"style":2307},[79,15522],{"className":15523,"style":360},[359],[79,15525,15527],{"className":15526},[364,365,366,367],[79,15528,15530,15533,15536],{"className":15529},[122,367],[79,15531,1978],{"className":15532,"style":2320},[122,162,367],[79,15534,234],{"className":15535},[310,367],[79,15537,100],{"className":15538},[122,367],[79,15540,15541,15544],{"style":2329},[79,15542],{"className":15543,"style":360},[359],[79,15545,15547],{"className":15546},[364,365,366,367],[79,15548,15550,15553,15556,15559,15562],{"className":15549},[122,367],[79,15551,1978],{"className":15552,"style":2320},[122,162,367],[79,15554,234],{"className":15555},[310,367],[79,15557,139],{"className":15558},[122,162,367],[79,15560,143],{"className":15561},[171,367],[79,15563,100],{"className":15564},[122,367],[79,15566,375],{"className":15567},[374],[79,15569,15571],{"className":15570},[347],[79,15572,15574],{"className":15573,"style":2363},[351],[79,15575],{},[79,15577],{"className":15578,"style":392},[166],[79,15580,15582],{"className":15581},[122,14358],[79,15583,14263],{"className":15584},[122,14362],[79,15586,15588,15591],{"className":15587},[122],[79,15589,542],{"className":15590},[122,162],[79,15592,15594],{"className":15593},[338],[79,15595,15597,15617],{"className":15596},[342,343],[79,15598,15600,15614],{"className":15599},[347],[79,15601,15603],{"className":15602,"style":977},[351],[79,15604,15605,15608],{"style":355},[79,15606],{"className":15607,"style":360},[359],[79,15609,15611],{"className":15610},[364,365,366,367],[79,15612,1978],{"className":15613,"style":2320},[122,162,367],[79,15615,375],{"className":15616},[374],[79,15618,15620],{"className":15619},[347],[79,15621,15623],{"className":15622,"style":3827},[351],[79,15624],{},[79,15626,15628,15631],{"className":15627},[122],[79,15629,1181],{"className":15630},[122,162],[79,15632,15634],{"className":15633},[338],[79,15635,15637,15657],{"className":15636},[342,343],[79,15638,15640,15654],{"className":15639},[347],[79,15641,15643],{"className":15642,"style":977},[351],[79,15644,15645,15648],{"style":355},[79,15646],{"className":15647,"style":360},[359],[79,15649,15651],{"className":15650},[364,365,366,367],[79,15652,1978],{"className":15653,"style":2320},[122,162,367],[79,15655,375],{"className":15656},[374],[79,15658,15660],{"className":15659},[347],[79,15661,15663],{"className":15662,"style":3827},[351],[79,15664],{},[79,15666],{"className":15667,"style":167},[166],[79,15669,1965],{"className":15670},[171],[79,15672],{"className":15673,"style":167},[166],[79,15675,15677,15680,15686,15689,15692,15695,15698],{"className":15676},[113],[79,15678],{"className":15679,"style":320},[117],[79,15681,15683],{"className":15682},[122,14358],[79,15684,14263],{"className":15685},[122,14362],[79,15687,241],{"className":15688},[328],[79,15690,100],{"className":15691},[122],[79,15693],{"className":15694,"style":167},[166],[79,15696,143],{"className":15697},[171],[79,15699],{"className":15700,"style":167},[166],[79,15702,15704,15707,15782,15785,15825,15828],{"className":15703},[113],[79,15705],{"className":15706,"style":14418},[117],[79,15708,15710,15713],{"className":15709},[2285],[79,15711,1973],{"className":15712,"style":2291},[2285,2289,2290],[79,15714,15716],{"className":15715},[338],[79,15717,15719,15774],{"className":15718},[342,343],[79,15720,15722,15771],{"className":15721},[347],[79,15723,15725,15745],{"className":15724,"style":2304},[351],[79,15726,15727,15730],{"style":2307},[79,15728],{"className":15729,"style":360},[359],[79,15731,15733],{"className":15732},[364,365,366,367],[79,15734,15736,15739,15742],{"className":15735},[122,367],[79,15737,1978],{"className":15738,"style":2320},[122,162,367],[79,15740,234],{"className":15741},[310,367],[79,15743,100],{"className":15744},[122,367],[79,15746,15747,15750],{"style":2329},[79,15748],{"className":15749,"style":360},[359],[79,15751,15753],{"className":15752},[364,365,366,367],[79,15754,15756,15759,15762,15765,15768],{"className":15755},[122,367],[79,15757,1978],{"className":15758,"style":2320},[122,162,367],[79,15760,234],{"className":15761},[310,367],[79,15763,139],{"className":15764},[122,162,367],[79,15766,143],{"className":15767},[171,367],[79,15769,100],{"className":15770},[122,367],[79,15772,375],{"className":15773},[374],[79,15775,15777],{"className":15776},[347],[79,15778,15780],{"className":15779,"style":2363},[351],[79,15781],{},[79,15783],{"className":15784,"style":392},[166],[79,15786,15788,15791],{"className":15787},[122],[79,15789,542],{"className":15790},[122,162],[79,15792,15794],{"className":15793},[338],[79,15795,15797,15817],{"className":15796},[342,343],[79,15798,15800,15814],{"className":15799},[347],[79,15801,15803],{"className":15802,"style":977},[351],[79,15804,15805,15808],{"style":355},[79,15806],{"className":15807,"style":360},[359],[79,15809,15811],{"className":15810},[364,365,366,367],[79,15812,1978],{"className":15813,"style":2320},[122,162,367],[79,15815,375],{"className":15816},[374],[79,15818,15820],{"className":15819},[347],[79,15821,15823],{"className":15822,"style":3827},[351],[79,15824],{},[79,15826,286],{"className":15827},[502],[79,15829,15831,15834],{"className":15830},[122],[79,15832,1181],{"className":15833},[122,162],[79,15835,15837],{"className":15836},[338],[79,15838,15840,15860],{"className":15839},[342,343],[79,15841,15843,15857],{"className":15842},[347],[79,15844,15846],{"className":15845,"style":644},[351],[79,15847,15848,15851],{"style":355},[79,15849],{"className":15850,"style":360},[359],[79,15852,15854],{"className":15853},[364,365,366,367],[79,15855,139],{"className":15856},[122,162,367],[79,15858,375],{"className":15859},[374],[79,15861,15863],{"className":15862},[347],[79,15864,15866],{"className":15865,"style":382},[351],[79,15867],{},[61,15869,15870],{},"because",[61,15872,15873],{},[79,15874,15876,15930],{"className":15875},[82],[79,15877,15879],{"className":15878},[86],[88,15880,15881],{"xmlns":90},[92,15882,15883,15927],{},[95,15884,15885,15891,15893,15895,15897,15921],{},[243,15886,15887,15889],{},[137,15888,542],{},[137,15890,139],{},[141,15892,234],{},[98,15894,100],{},[141,15896,143],{},[1969,15898,15899,15901,15909],{},[141,15900,1973],{},[95,15902,15903,15905,15907],{},[137,15904,1978],{},[141,15906,234],{},[98,15908,100],{},[95,15910,15911,15913,15915,15917,15919],{},[137,15912,1978],{},[141,15914,234],{},[137,15916,139],{},[141,15918,143],{},[98,15920,100],{},[243,15922,15923,15925],{},[137,15924,542],{},[137,15926,1978],{},[102,15928,15929],{"encoding":104},"x_m = 1 - \\sum_{j=1}^{j=m-1} x_j",[79,15931,15933,15988,16007],{"className":15932,"ariaHidden":109},[108],[79,15934,15936,15939,15979,15982,15985],{"className":15935},[113],[79,15937],{"className":15938,"style":958},[117],[79,15940,15942,15945],{"className":15941},[122],[79,15943,542],{"className":15944},[122,162],[79,15946,15948],{"className":15947},[338],[79,15949,15951,15971],{"className":15950},[342,343],[79,15952,15954,15968],{"className":15953},[347],[79,15955,15957],{"className":15956,"style":644},[351],[79,15958,15959,15962],{"style":355},[79,15960],{"className":15961,"style":360},[359],[79,15963,15965],{"className":15964},[364,365,366,367],[79,15966,139],{"className":15967},[122,162,367],[79,15969,375],{"className":15970},[374],[79,15972,15974],{"className":15973},[347],[79,15975,15977],{"className":15976,"style":382},[351],[79,15978],{},[79,15980],{"className":15981,"style":306},[166],[79,15983,234],{"className":15984},[310],[79,15986],{"className":15987,"style":306},[166],[79,15989,15991,15995,15998,16001,16004],{"className":15990},[113],[79,15992],{"className":15993,"style":15994},[117],"height:0.7278em;vertical-align:-0.0833em;",[79,15996,100],{"className":15997},[122],[79,15999],{"className":16000,"style":167},[166],[79,16002,143],{"className":16003},[171],[79,16005],{"className":16006,"style":167},[166],[79,16008,16010,16013,16088,16091],{"className":16009},[113],[79,16011],{"className":16012,"style":14418},[117],[79,16014,16016,16019],{"className":16015},[2285],[79,16017,1973],{"className":16018,"style":2291},[2285,2289,2290],[79,16020,16022],{"className":16021},[338],[79,16023,16025,16080],{"className":16024},[342,343],[79,16026,16028,16077],{"className":16027},[347],[79,16029,16031,16051],{"className":16030,"style":2304},[351],[79,16032,16033,16036],{"style":2307},[79,16034],{"className":16035,"style":360},[359],[79,16037,16039],{"className":16038},[364,365,366,367],[79,16040,16042,16045,16048],{"className":16041},[122,367],[79,16043,1978],{"className":16044,"style":2320},[122,162,367],[79,16046,234],{"className":16047},[310,367],[79,16049,100],{"className":16050},[122,367],[79,16052,16053,16056],{"style":2329},[79,16054],{"className":16055,"style":360},[359],[79,16057,16059],{"className":16058},[364,365,366,367],[79,16060,16062,16065,16068,16071,16074],{"className":16061},[122,367],[79,16063,1978],{"className":16064,"style":2320},[122,162,367],[79,16066,234],{"className":16067},[310,367],[79,16069,139],{"className":16070},[122,162,367],[79,16072,143],{"className":16073},[171,367],[79,16075,100],{"className":16076},[122,367],[79,16078,375],{"className":16079},[374],[79,16081,16083],{"className":16082},[347],[79,16084,16086],{"className":16085,"style":2363},[351],[79,16087],{},[79,16089],{"className":16090,"style":392},[166],[79,16092,16094,16097],{"className":16093},[122],[79,16095,542],{"className":16096},[122,162],[79,16098,16100],{"className":16099},[338],[79,16101,16103,16123],{"className":16102},[342,343],[79,16104,16106,16120],{"className":16105},[347],[79,16107,16109],{"className":16108,"style":977},[351],[79,16110,16111,16114],{"style":355},[79,16112],{"className":16113,"style":360},[359],[79,16115,16117],{"className":16116},[364,365,366,367],[79,16118,1978],{"className":16119,"style":2320},[122,162,367],[79,16121,375],{"className":16122},[374],[79,16124,16126],{"className":16125},[347],[79,16127,16129],{"className":16128,"style":3827},[351],[79,16130],{},[61,16132,16133],{},"Consequently, all the composition variables in the equation above become independent, and we know",[61,16135,16136],{},[79,16137,16139,16189],{"className":16138},[82],[79,16140,16142],{"className":16141},[86],[88,16143,16144],{"xmlns":90},[92,16145,16146,16186],{},[95,16147,16148,16170,16172,16178,16180],{},[1187,16149,16150,16160],{},[95,16151,16152,16154],{},[137,16153,1193],{"mathvariant":264},[243,16155,16156,16158],{},[137,16157,231],{},[137,16159,139],{},[95,16161,16162,16164],{},[137,16163,1193],{"mathvariant":264},[243,16165,16166,16168],{},[137,16167,542],{},[137,16169,945],{},[141,16171,234],{},[243,16173,16174,16176],{},[137,16175,1181],{},[137,16177,945],{},[141,16179,143],{},[243,16181,16182,16184],{},[137,16183,1181],{},[137,16185,139],{},[102,16187,16188],{"encoding":104},"\\frac{\\partial G_m}{\\partial x_i} = \\mu_i - \\mu_{m}",[79,16190,16192,16355,16410],{"className":16191,"ariaHidden":109},[108],[79,16193,16195,16198,16346,16349,16352],{"className":16194},[113],[79,16196],{"className":16197,"style":1282},[117],[79,16199,16201,16204,16343],{"className":16200},[122],[79,16202],{"className":16203},[328,1289],[79,16205,16207],{"className":16206},[1187],[79,16208,16210,16335],{"className":16209},[342,343],[79,16211,16213,16332],{"className":16212},[347],[79,16214,16216,16270,16278],{"className":16215,"style":1302},[351],[79,16217,16218,16221],{"style":1305},[79,16219],{"className":16220,"style":1309},[359],[79,16222,16224],{"className":16223},[364,365,366,367],[79,16225,16227,16230],{"className":16226},[122,367],[79,16228,1193],{"className":16229,"style":1319},[122,367],[79,16231,16233,16236],{"className":16232},[122,367],[79,16234,542],{"className":16235},[122,162,367],[79,16237,16239],{"className":16238},[338],[79,16240,16242,16262],{"className":16241},[342,343],[79,16243,16245,16259],{"className":16244},[347],[79,16246,16248],{"className":16247,"style":1338},[351],[79,16249,16250,16253],{"style":1341},[79,16251],{"className":16252,"style":1345},[359],[79,16254,16256],{"className":16255},[364,1349,1350,367],[79,16257,945],{"className":16258},[122,162,367],[79,16260,375],{"className":16261},[374],[79,16263,16265],{"className":16264},[347],[79,16266,16268],{"className":16267,"style":1363},[351],[79,16269],{},[79,16271,16272,16275],{"style":1368},[79,16273],{"className":16274,"style":1309},[359],[79,16276],{"className":16277,"style":1376},[1375],[79,16279,16280,16283],{"style":1379},[79,16281],{"className":16282,"style":1309},[359],[79,16284,16286],{"className":16285},[364,365,366,367],[79,16287,16289,16292],{"className":16288},[122,367],[79,16290,1193],{"className":16291,"style":1319},[122,367],[79,16293,16295,16298],{"className":16294},[122,367],[79,16296,231],{"className":16297},[122,162,367],[79,16299,16301],{"className":16300},[338],[79,16302,16304,16324],{"className":16303},[342,343],[79,16305,16307,16321],{"className":16306},[347],[79,16308,16310],{"className":16309,"style":1413},[351],[79,16311,16312,16315],{"style":1341},[79,16313],{"className":16314,"style":1345},[359],[79,16316,16318],{"className":16317},[364,1349,1350,367],[79,16319,139],{"className":16320},[122,162,367],[79,16322,375],{"className":16323},[374],[79,16325,16327],{"className":16326},[347],[79,16328,16330],{"className":16329,"style":1363},[351],[79,16331],{},[79,16333,375],{"className":16334},[374],[79,16336,16338],{"className":16337},[347],[79,16339,16341],{"className":16340,"style":1445},[351],[79,16342],{},[79,16344],{"className":16345},[502,1289],[79,16347],{"className":16348,"style":306},[166],[79,16350,234],{"className":16351},[310],[79,16353],{"className":16354,"style":306},[166],[79,16356,16358,16361,16401,16404,16407],{"className":16357},[113],[79,16359],{"className":16360,"style":13835},[117],[79,16362,16364,16367],{"className":16363},[122],[79,16365,1181],{"className":16366},[122,162],[79,16368,16370],{"className":16369},[338],[79,16371,16373,16393],{"className":16372},[342,343],[79,16374,16376,16390],{"className":16375},[347],[79,16377,16379],{"className":16378,"style":977},[351],[79,16380,16381,16384],{"style":355},[79,16382],{"className":16383,"style":360},[359],[79,16385,16387],{"className":16386},[364,365,366,367],[79,16388,945],{"className":16389},[122,162,367],[79,16391,375],{"className":16392},[374],[79,16394,16396],{"className":16395},[347],[79,16397,16399],{"className":16398,"style":382},[351],[79,16400],{},[79,16402],{"className":16403,"style":167},[166],[79,16405,143],{"className":16406},[171],[79,16408],{"className":16409,"style":167},[166],[79,16411,16413,16416],{"className":16412},[113],[79,16414],{"className":16415,"style":1226},[117],[79,16417,16419,16422],{"className":16418},[122],[79,16420,1181],{"className":16421},[122,162],[79,16423,16425],{"className":16424},[338],[79,16426,16428,16451],{"className":16427},[342,343],[79,16429,16431,16448],{"className":16430},[347],[79,16432,16434],{"className":16433,"style":644},[351],[79,16435,16436,16439],{"style":355},[79,16437],{"className":16438,"style":360},[359],[79,16440,16442],{"className":16441},[364,365,366,367],[79,16443,16445],{"className":16444},[122,367],[79,16446,139],{"className":16447},[122,162,367],[79,16449,375],{"className":16450},[374],[79,16452,16454],{"className":16453},[347],[79,16455,16457],{"className":16456,"style":382},[351],[79,16458],{},[61,16460,16461],{},"according to the properties of the total derivative.",[71,16463,16465],{"id":16464},"计算理想固溶体的吉布斯自由能化学势和扩散势","计算理想固溶体的吉布斯自由能、化学势和扩散势",[16467,16468,16472],"pre",{"className":16469,"code":16471,"language":14358},[16470],"language-text","void func_compenstate_multicomponent(const double *x, double *f, int cnum)\n{\n    double T = x[cnum-1]; \u002F\u002F the last element is temperature\n    double vars[cnum];\n    double v = 0;\n    for (int i = 0; i \u003C cnum-1; i++)\n    {\n        vars[i] = x[i] \u003C 1.0e-6 ? 1.0e-6 : (x[i] > 1.0 - 1.0e-6 ? 1.0 - 1.0e-6 : x[i]);\n        v += vars[i];\n    }\n    vars[cnum-1] = 1.0 - v;\n\n    double gm = 0;\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        gm += vars[ci] * log(vars[ci]);\n    }\n    gm = 8.31451 * T * gm;\n    f[0] = gm;\n\n    double partial_gm[cnum];\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        partial_gm[ci] = 8.31451 * T * (log(vars[ci]) + 1);\n    }\n\n    double sum_partial_gm = 0;\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        sum_partial_gm += partial_gm[ci] * vars[ci];\n    }\n\n    double mus[cnum];\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        mus[ci] = gm + partial_gm[ci] - sum_partial_gm;\n    }\n\n    for (int ci=0; ci\u003Ccnum-1; ci++)\n    {\n        f[ci+1] = mus[ci] - mus[cnum-1];\n    }\n}\n\nvoid func_compenstate_quaternary(const double *x, double *f)\n{\n    func_compenstate_multicomponent(x, f, 4);\n}\n",[16473,16474,16471],"code",{"__ignoreMap":16475},"",{"title":16475,"searchDepth":16477,"depth":16477,"links":16478},2,[16479],{"id":58,"depth":16477,"text":59,"children":16480},[16481,16483,16484,16485,16486],{"id":73,"depth":16482,"text":74},3,{"id":5553,"depth":16482,"text":5554},{"id":11124,"depth":16482,"text":11125},{"id":12226,"depth":16482,"text":12227},{"id":16464,"depth":16482,"text":16465},"2026-09-05","从偏摩尔量的定义出发，推导独立成分与约束成分变量下化学势的两种公式，并阐明化学势与相场模拟中扩散势的关系。","md","\u002Fblog\u002Fchemical-potential.svg",{},9,true,{"title":10,"description":16488},"iT6owxaYKsgqZJ6_RKSJtr8_KDhaWfw-k1CPG9t7rlk",[16497,16498],null,{"title":14,"path":15,"stem":16,"description":16499,"children":-1},"Learn how to generate static sites with Nuxt 3 and deploy them to Nginx, handling routing, caching, and avoiding common pitfalls like redirect loops.",1792686186191]