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",[88,1029,1031,1060],{"className":1030},[91],[88,1032,1034],{"className":1033},[95],[97,1035,1036],{"xmlns":99},[101,1037,1038,1058],{},[104,1039,1040,1042,1056],{},[107,1041,110],{"stretchy":109},[112,1043,1044,1046,1048],{},[115,1045,117],{},[115,1047,120],{},[104,1049,1050,1052,1054],{},[115,1051,125],{},[107,1053,129],{"separator":128},[131,1055,133],{},[107,1057,136],{"stretchy":109},[138,1059,141],{"encoding":140},[88,1061,1063],{"className":1062,"ariaHidden":128},[145],[88,1064,1066,1069,1072,1132],{"className":1065},[149],[88,1067],{"className":1068,"style":154},[153],[88,1070,110],{"className":1071},[158],[88,1073,1075,1078],{"className":1074},[162],[88,1076,117],{"className":1077},[162,166],[88,1079,1081],{"className":1080},[170],[88,1082,1084,1124],{"className":1083},[174,175],[88,1085,1087,1121],{"className":1086},[179],[88,1088,1090,1101],{"className":1089,"style":184},[183],[88,1091,1092,1095],{"style":187},[88,1093],{"className":1094,"style":192},[191],[88,1096,1098],{"className":1097},[196,197,198,199],[88,1099,120],{"className":1100},[162,166,199],[88,1102,1103,1106],{"style":205},[88,1104],{"className":1105,"style":192},[191],[88,1107,1109],{"className":1108},[196,197,198,199],[88,1110,1112,1115,1118],{"className":1111},[162,199],[88,1113,125],{"className":1114,"style":218},[162,166,199],[88,1116,129],{"className":1117},[222,199],[88,1119,133],{"className":1120},[162,199],[88,1122,230],{"className":1123},[229],[88,1125,1127],{"className":1126},[179],[88,1128,1130],{"className":1129,"style":237},[183],[88,1131],{},[88,1133,136],{"className":1134},[243],[88,1136,1138,1167],{"className":1137},[91],[88,1139,1141],{"className":1140},[95],[97,1142,1143],{"xmlns":99},[101,1144,1145,1165],{},[104,1146,1147,1149,1163],{},[107,1148,110],{"stretchy":109},[112,1150,1151,1153,1155],{},[115,1152,117],{},[115,1154,120],{},[104,1156,1157,1159,1161],{},[115,1158,495],{},[107,1160,129],{"separator":128},[499,1162,501],{},[107,1164,136],{"stretchy":109},[138,1166,506],{"encoding":140},[88,1168,1170],{"className":1169,"ariaHidden":128},[145],[88,1171,1173,1176,1179,1242],{"className":1172},[149],[88,1174],{"className":1175,"style":516},[153],[88,1177,110],{"className":1178},[158],[88,1180,1182,1185],{"className":1181},[162],[88,1183,117],{"className":1184},[162,166],[88,1186,1188],{"className":1187},[170],[88,1189,1191,1234],{"className":1190},[174,175],[88,1192,1194,1231],{"className":1193},[179],[88,1195,1197,1208],{"className":1196,"style":538},[183],[88,1198,1199,1202],{"style":187},[88,1200],{"className":1201,"style":192},[191],[88,1203,1205],{"className":1204},[196,197,198,199],[88,1206,120],{"className":1207},[162,166,199],[88,1209,1210,1213],{"style":205},[88,1211],{"className":1212,"style":192},[191],[88,1214,1216],{"className":1215},[196,197,198,199],[88,1217,1219,1222,1225],{"className":1218},[162,199],[88,1220,495],{"className":1221,"style":564},[162,166,199],[88,1223,129],{"className":1224},[222,199],[88,1226,1228],{"className":1227},[162,571,199],[88,1229,501],{"className":1230},[162,575,199],[88,1232,230],{"className":1233},[229],[88,1235,1237],{"className":1236},[179],[88,1238,1240],{"className":1239,"style":237},[183],[88,1241],{},[88,1243,136],{"className":1244},[243],".",[1247,1248,1249],"h3",{"id":1249},"表达形式一",[56,1251,1252,1253,1282,1283,1311,1312,1340,1341,1369,1370,1468,1469,1570,1571,1599],{},"对于多元两相体系，包含",[88,1254,1256,1270],{"className":1255},[91],[88,1257,1259],{"className":1258},[95],[97,1260,1261],{"xmlns":99},[101,1262,1263,1268],{},[104,1264,1265],{},[115,1266,1267],{},"n",[138,1269,1267],{"encoding":140},[88,1271,1273],{"className":1272,"ariaHidden":128},[145],[88,1274,1276,1279],{"className":1275},[149],[88,1277],{"className":1278,"style":271},[153],[88,1280,1267],{"className":1281},[162,166],"个组元，以及",[88,1284,1286,1299],{"className":1285},[91],[88,1287,1289],{"className":1288},[95],[97,1290,1291],{"xmlns":99},[101,1292,1293,1297],{},[104,1294,1295],{},[115,1296,125],{},[138,1298,261],{"encoding":140},[88,1300,1302],{"className":1301,"ariaHidden":128},[145],[88,1303,1305,1308],{"className":1304},[149],[88,1306],{"className":1307,"style":271},[153],[88,1309,125],{"className":1310,"style":218},[162,166],"和",[88,1313,1315,1328],{"className":1314},[91],[88,1316,1318],{"className":1317},[95],[97,1319,1320],{"xmlns":99},[101,1321,1322,1326],{},[104,1323,1324],{},[115,1325,495],{},[138,1327,606],{"encoding":140},[88,1329,1331],{"className":1330,"ariaHidden":128},[145],[88,1332,1334,1337],{"className":1333},[149],[88,1335],{"className":1336,"style":616},[153],[88,1338,495],{"className":1339,"style":564},[162,166],"两个相。假设",[88,1342,1344,1357],{"className":1343},[91],[88,1345,1347],{"className":1346},[95],[97,1348,1349],{"xmlns":99},[101,1350,1351,1355],{},[104,1352,1353],{},[115,1354,125],{},[138,1356,261],{"encoding":140},[88,1358,1360],{"className":1359,"ariaHidden":128},[145],[88,1361,1363,1366],{"className":1362},[149],[88,1364],{"className":1365,"style":271},[153],[88,1367,125],{"className":1368,"style":218},[162,166],"相的成分为",[88,1371,1373,1399],{"className":1372},[91],[88,1374,1376],{"className":1375},[95],[97,1377,1378],{"xmlns":99},[101,1379,1380,1396],{},[104,1381,1382],{},[112,1383,1384,1386,1388],{},[115,1385,295],{},[115,1387,120],{},[104,1389,1390,1392,1394],{},[115,1391,125],{},[107,1393,129],{"separator":128},[131,1395,133],{},[138,1397,1398],{"encoding":140},"x_i^{\\alpha, 0}",[88,1400,1402],{"className":1401,"ariaHidden":128},[145],[88,1403,1405,1408],{"className":1404},[149],[88,1406],{"className":1407,"style":154},[153],[88,1409,1411,1414],{"className":1410},[162],[88,1412,295],{"className":1413},[162,166],[88,1415,1417],{"className":1416},[170],[88,1418,1420,1460],{"className":1419},[174,175],[88,1421,1423,1457],{"className":1422},[179],[88,1424,1426,1437],{"className":1425,"style":184},[183],[88,1427,1428,1431],{"style":187},[88,1429],{"className":1430,"style":192},[191],[88,1432,1434],{"className":1433},[196,197,198,199],[88,1435,120],{"className":1436},[162,166,199],[88,1438,1439,1442],{"style":205},[88,1440],{"className":1441,"style":192},[191],[88,1443,1445],{"className":1444},[196,197,198,199],[88,1446,1448,1451,1454],{"className":1447},[162,199],[88,1449,125],{"className":1450,"style":218},[162,166,199],[88,1452,129],{"className":1453},[222,199],[88,1455,133],{"className":1456},[162,199],[88,1458,230],{"className":1459},[229],[88,1461,1463],{"className":1462},[179],[88,1464,1466],{"className":1465,"style":237},[183],[88,1467],{},"，而新相的成分为",[88,1470,1472,1498],{"className":1471},[91],[88,1473,1475],{"className":1474},[95],[97,1476,1477],{"xmlns":99},[101,1478,1479,1495],{},[104,1480,1481],{},[112,1482,1483,1485,1487],{},[115,1484,295],{},[115,1486,120],{},[104,1488,1489,1491,1493],{},[115,1490,495],{},[107,1492,129],{"separator":128},[499,1494,501],{},[138,1496,1497],{"encoding":140},"x_i^{\\beta, \\textrm{new}}",[88,1499,1501],{"className":1500,"ariaHidden":128},[145],[88,1502,1504,1507],{"className":1503},[149],[88,1505],{"className":1506,"style":516},[153],[88,1508,1510,1513],{"className":1509},[162],[88,1511,295],{"className":1512},[162,166],[88,1514,1516],{"className":1515},[170],[88,1517,1519,1562],{"className":1518},[174,175],[88,1520,1522,1559],{"className":1521},[179],[88,1523,1525,1536],{"className":1524,"style":538},[183],[88,1526,1527,1530],{"style":187},[88,1528],{"className":1529,"style":192},[191],[88,1531,1533],{"className":1532},[196,197,198,199],[88,1534,120],{"className":1535},[162,166,199],[88,1537,1538,1541],{"style":205},[88,1539],{"className":1540,"style":192},[191],[88,1542,1544],{"className":1543},[196,197,198,199],[88,1545,1547,1550,1553],{"className":1546},[162,199],[88,1548,495],{"className":1549,"style":564},[162,166,199],[88,1551,129],{"className":1552},[222,199],[88,1554,1556],{"className":1555},[162,571,199],[88,1557,501],{"className":1558},[162,575,199],[88,1560,230],{"className":1561},[229],[88,1563,1565],{"className":1564},[179],[88,1566,1568],{"className":1567,"style":237},[183],[88,1569],{},"。根据Gibbs-Duhem关系，",[88,1572,1574,1587],{"className":1573},[91],[88,1575,1577],{"className":1576},[95],[97,1578,1579],{"xmlns":99},[101,1580,1581,1585],{},[104,1582,1583],{},[115,1584,125],{},[138,1586,261],{"encoding":140},[88,1588,1590],{"className":1589,"ariaHidden":128},[145],[88,1591,1593,1596],{"className":1592},[149],[88,1594],{"className":1595,"style":271},[153],[88,1597,125],{"className":1598,"style":218},[162,166],"相相成分的能量切面可以表示为",[88,1601,1604],{"className":1602},[1603],"katex-display",[88,1605,1607,1667],{"className":1606},[91],[88,1608,1610],{"className":1609},[95],[97,1611,1613],{"xmlns":99,"display":1612},"block",[101,1614,1615,1664],{},[104,1616,1617,1625,1627,1644,1650],{},[1618,1619,1620,1623],"msup",{},[115,1621,1622],{},"f",[115,1624,125],{},[107,1626,302],{},[1628,1629,1630,1633,1642],"munderover",{},[107,1631,1632],{},"∑",[104,1634,1635,1637,1639],{},[115,1636,120],{},[107,1638,302],{},[131,1640,1641],{},"1",[115,1643,1267],{},[291,1645,1646,1648],{},[115,1647,295],{},[115,1649,120],{},[112,1651,1652,1654,1656],{},[115,1653,117],{},[115,1655,120],{},[104,1657,1658,1660,1662],{},[115,1659,125],{},[107,1661,129],{"separator":128},[131,1663,133],{},[138,1665,1666],{"encoding":140},"f^\\alpha=\\sum_{i=1}^n x_i \\mu_i^{\\alpha, 0}",[88,1668,1670,1718],{"className":1669,"ariaHidden":128},[145],[88,1671,1673,1677,1709,1712,1715],{"className":1672},[149],[88,1674],{"className":1675,"style":1676},[153],"height:0.9088em;vertical-align:-0.1944em;",[88,1678,1680,1684],{"className":1679},[162],[88,1681,1622],{"className":1682,"style":1683},[162,166],"margin-right:0.1076em;",[88,1685,1687],{"className":1686},[170],[88,1688,1690],{"className":1689},[174],[88,1691,1693],{"className":1692},[179],[88,1694,1697],{"className":1695,"style":1696},[183],"height:0.7144em;",[88,1698,1700,1703],{"style":1699},"top:-3.113em;margin-right:0.05em;",[88,1701],{"className":1702,"style":192},[191],[88,1704,1706],{"className":1705},[196,197,198,199],[88,1707,125],{"className":1708,"style":218},[162,166,199],[88,1710],{"className":1711,"style":387},[386],[88,1713,302],{"className":1714},[391],[88,1716],{"className":1717,"style":387},[386],[88,1719,1721,1725,1799,1803,1843],{"className":1720},[149],[88,1722],{"className":1723,"style":1724},[153],"height:2.9291em;vertical-align:-1.2777em;",[88,1726,1730],{"className":1727},[1728,1729],"mop","op-limits",[88,1731,1733,1790],{"className":1732},[174,175],[88,1734,1736,1787],{"className":1735},[179],[88,1737,1740,1762,1775],{"className":1738,"style":1739},[183],"height:1.6514em;",[88,1741,1743,1747],{"style":1742},"top:-1.8723em;margin-left:0em;",[88,1744],{"className":1745,"style":1746},[191],"height:3.05em;",[88,1748,1750],{"className":1749},[196,197,198,199],[88,1751,1753,1756,1759],{"className":1752},[162,199],[88,1754,120],{"className":1755},[162,166,199],[88,1757,302],{"className":1758},[391,199],[88,1760,1641],{"className":1761},[162,199],[88,1763,1765,1768],{"style":1764},"top:-3.05em;",[88,1766],{"className":1767,"style":1746},[191],[88,1769,1770],{},[88,1771,1632],{"className":1772},[1728,1773,1774],"op-symbol","large-op",[88,1776,1778,1781],{"style":1777},"top:-4.3em;margin-left:0em;",[88,1779],{"className":1780,"style":1746},[191],[88,1782,1784],{"className":1783},[196,197,198,199],[88,1785,1267],{"className":1786},[162,166,199],[88,1788,230],{"className":1789},[229],[88,1791,1793],{"className":1792},[179],[88,1794,1797],{"className":1795,"style":1796},[183],"height:1.2777em;",[88,1798],{},[88,1800],{"className":1801,"style":1802},[386],"margin-right:0.1667em;",[88,1804,1806,1809],{"className":1805},[162],[88,1807,295],{"className":1808},[162,166],[88,1810,1812],{"className":1811},[170],[88,1813,1815,1835],{"className":1814},[174,175],[88,1816,1818,1832],{"className":1817},[179],[88,1819,1821],{"className":1820,"style":355},[183],[88,1822,1823,1826],{"style":358},[88,1824],{"className":1825,"style":192},[191],[88,1827,1829],{"className":1828},[196,197,198,199],[88,1830,120],{"className":1831},[162,166,199],[88,1833,230],{"className":1834},[229],[88,1836,1838],{"className":1837},[179],[88,1839,1841],{"className":1840,"style":377},[183],[88,1842],{},[88,1844,1846,1849],{"className":1845},[162],[88,1847,117],{"className":1848},[162,166],[88,1850,1852],{"className":1851},[170],[88,1853,1855,1895],{"className":1854},[174,175],[88,1856,1858,1892],{"className":1857},[179],[88,1859,1861,1872],{"className":1860,"style":184},[183],[88,1862,1863,1866],{"style":187},[88,1864],{"className":1865,"style":192},[191],[88,1867,1869],{"className":1868},[196,197,198,199],[88,1870,120],{"className":1871},[162,166,199],[88,1873,1874,1877],{"style":205},[88,1875],{"className":1876,"style":192},[191],[88,1878,1880],{"className":1879},[196,197,198,199],[88,1881,1883,1886,1889],{"className":1882},[162,199],[88,1884,125],{"className":1885,"style":218},[162,166,199],[88,1887,129],{"className":1888},[222,199],[88,1890,133],{"className":1891},[162,199],[88,1893,230],{"className":1894},[229],[88,1896,1898],{"className":1897},[179],[88,1899,1901],{"className":1900,"style":237},[183],[88,1902],{},[56,1904,1905,1906,1599],{},"同理，",[88,1907,1909,1922],{"className":1908},[91],[88,1910,1912],{"className":1911},[95],[97,1913,1914],{"xmlns":99},[101,1915,1916,1920],{},[104,1917,1918],{},[115,1919,495],{},[138,1921,606],{"encoding":140},[88,1923,1925],{"className":1924,"ariaHidden":128},[145],[88,1926,1928,1931],{"className":1927},[149],[88,1929],{"className":1930,"style":616},[153],[88,1932,495],{"className":1933,"style":564},[162,166],[88,1935,1937],{"className":1936},[1603],[88,1938,1940,1994],{"className":1939},[91],[88,1941,1943],{"className":1942},[95],[97,1944,1945],{"xmlns":99,"display":1612},[101,1946,1947,1991],{},[104,1948,1949,1955,1957,1971,1977],{},[1618,1950,1951,1953],{},[115,1952,1622],{},[115,1954,495],{},[107,1956,302],{},[1628,1958,1959,1961,1969],{},[107,1960,1632],{},[104,1962,1963,1965,1967],{},[115,1964,120],{},[107,1966,302],{},[131,1968,1641],{},[115,1970,1267],{},[291,1972,1973,1975],{},[115,1974,295],{},[115,1976,120],{},[112,1978,1979,1981,1983],{},[115,1980,117],{},[115,1982,120],{},[104,1984,1985,1987,1989],{},[115,1986,495],{},[107,1988,129],{"separator":128},[499,1990,501],{},[138,1992,1993],{"encoding":140},"f^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\\left.-\\Delta G_m^{\\alpha \\rightarrow \\beta}\\right|_{\\mathbf{x}=\\mathbf{x}^{\\beta, \\text { new }}}=G_m^{\\alpha, 0}+\\sum_{i=1}^{n-1}\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\tilde{\\mu}_i^{\\alpha, 0}-G_m^{\\beta, 0}-\\sum_{i=1}^{n-1}\\left(x_i^{\\beta, \\text { new }}-x_i^{\\beta, \\text { new }}\\right) \\tilde{\\mu}_i^{\\beta, 0} \\\\\n& =G_m^{\\alpha, 0}-G_m^{\\beta, 0}+\\sum_{i=1}^{n-1}\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\tilde{\\mu}_i^{\\alpha, 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\\left.\\Delta G_m^{\\alpha \\rightarrow \\beta}\\right|_{\\mathbf{x}=\\mathbf{x}^{\\beta, \\text { new }}}=\\sum_{i=1}^n x_i^{\\beta, \\text { new }} \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }} \\\\\n& =\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^n x_i^{\\alpha, 0} \\mu_i^{\\alpha, 0} \\\\\n& =\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+G_m^{\\alpha, 0} \\\\\n& =G_m^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right)\\left(\\mu_i^{\\alpha, 0}-\\mu_n^{\\alpha, 0}\\right)+\\mu_n^{\\alpha, 0} \\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\\\\n& =G_m^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^{n-1}\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\tilde{\\mu}_i^{\\alpha, 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88,10472,230],{"className":10473},[229],[88,10475,10477],{"className":10476},[179],[88,10478,10480],{"className":10479,"style":4496},[183],[88,10481],{},[88,10483,10485],{"className":10484},[170],[88,10486,10488,10528],{"className":10487},[174,175],[88,10489,10491,10525],{"className":10490},[179],[88,10492,10494,10505],{"className":10493,"style":184},[183],[88,10495,10496,10499],{"style":187},[88,10497],{"className":10498,"style":192},[191],[88,10500,10502],{"className":10501},[196,197,198,199],[88,10503,120],{"className":10504},[162,166,199],[88,10506,10507,10510],{"style":205},[88,10508],{"className":10509,"style":192},[191],[88,10511,10513],{"className":10512},[196,197,198,199],[88,10514,10516,10519,10522],{"className":10515},[162,199],[88,10517,125],{"className":10518,"style":218},[162,166,199],[88,10520,129],{"className":10521},[222,199],[88,10523,133],{"className":10524},[162,199],[88,10526,230],{"className":10527},[229],[88,10529,10531],{"className":10530},[179],[88,10532,10534],{"className":10533,"style":237},[183],[88,10535],{},[88,10537,230],{"className":10538},[229],[88,10540,10542],{"className":10541},[179],[88,10543,10545],{"className":10544,"style":7749},[183],[88,10546],{},[56,10548,10549],{},"以下为一个演算示例",[10551,10552,10557],"pre",{"className":10553,"code":10554,"language":10555,"meta":10556,"style":10556},"language-python shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","# 能量数据为Pandat软件计算结果，Ni-Al体系的fcc与L12_fcc的计算结果，数据库为Pandat的镍基高温合金数据库。\nx_matrix_al = 0.2\nx_matrix_ni = 0.8\nmu_matrix_al = -157793.0\nmu_matrix_ni = -51148.8\ngm_matrix = -72477.6\n\nprint(\"gm: \", gm_matrix, x_matrix_al * mu_matrix_al + x_matrix_ni * mu_matrix_ni)\n\nx_l12_al = 0.24\nx_l12_ni = 0.76\ngm_l12 = -79069.11\nmu_l12_al = -182955.13\nmu_l12_ni = -46263.00\nprint(\"gm: \", gm_l12, x_l12_al * mu_l12_al + x_l12_ni * mu_l12_ni)\nprint(\"dp l12: \", mu_l12_al - mu_l12_ni)\n\ndriving_force_v1 = x_l12_al * (mu_matrix_al - mu_l12_al) + x_l12_ni * (mu_matrix_ni - mu_l12_ni)\nprint(\"driving_force_v1: \", driving_force_v1)\n\ndriving_force_v2 = gm_matrix - gm_l12 + (x_l12_al - x_matrix_al) * (mu_matrix_al - mu_matrix_ni)\nprint(\"driving_force_v2: \", driving_force_v2)\n","python","",[10558,10559,10560,10567,10573,10579,10585,10591,10597,10604,10610,10615,10621,10627,10633,10639,10645,10651,10657,10662,10668,10674,10679,10685],"code",{"__ignoreMap":10556},[88,10561,10564],{"class":10562,"line":10563},"line",1,[88,10565,10566],{},"# 能量数据为Pandat软件计算结果，Ni-Al体系的fcc与L12_fcc的计算结果，数据库为Pandat的镍基高温合金数据库。\n",[88,10568,10570],{"class":10562,"line":10569},2,[88,10571,10572],{},"x_matrix_al = 0.2\n",[88,10574,10576],{"class":10562,"line":10575},3,[88,10577,10578],{},"x_matrix_ni = 0.8\n",[88,10580,10582],{"class":10562,"line":10581},4,[88,10583,10584],{},"mu_matrix_al = -157793.0\n",[88,10586,10588],{"class":10562,"line":10587},5,[88,10589,10590],{},"mu_matrix_ni = -51148.8\n",[88,10592,10594],{"class":10562,"line":10593},6,[88,10595,10596],{},"gm_matrix = -72477.6\n",[88,10598,10600],{"class":10562,"line":10599},7,[88,10601,10603],{"emptyLinePlaceholder":10602},true,"\n",[88,10605,10607],{"class":10562,"line":10606},8,[88,10608,10609],{},"print(\"gm: \", gm_matrix, x_matrix_al * mu_matrix_al + x_matrix_ni * mu_matrix_ni)\n",[88,10611,10613],{"class":10562,"line":10612},9,[88,10614,10603],{"emptyLinePlaceholder":10602},[88,10616,10618],{"class":10562,"line":10617},10,[88,10619,10620],{},"x_l12_al = 0.24\n",[88,10622,10624],{"class":10562,"line":10623},11,[88,10625,10626],{},"x_l12_ni = 0.76\n",[88,10628,10630],{"class":10562,"line":10629},12,[88,10631,10632],{},"gm_l12 = -79069.11\n",[88,10634,10636],{"class":10562,"line":10635},13,[88,10637,10638],{},"mu_l12_al = -182955.13\n",[88,10640,10642],{"class":10562,"line":10641},14,[88,10643,10644],{},"mu_l12_ni = -46263.00\n",[88,10646,10648],{"class":10562,"line":10647},15,[88,10649,10650],{},"print(\"gm: \", gm_l12, x_l12_al * mu_l12_al + x_l12_ni * mu_l12_ni)\n",[88,10652,10654],{"class":10562,"line":10653},16,[88,10655,10656],{},"print(\"dp l12: \", mu_l12_al - mu_l12_ni)\n",[88,10658,10660],{"class":10562,"line":10659},17,[88,10661,10603],{"emptyLinePlaceholder":10602},[88,10663,10665],{"class":10562,"line":10664},18,[88,10666,10667],{},"driving_force_v1 = x_l12_al * (mu_matrix_al - mu_l12_al) + x_l12_ni * (mu_matrix_ni - mu_l12_ni)\n",[88,10669,10671],{"class":10562,"line":10670},19,[88,10672,10673],{},"print(\"driving_force_v1: \", driving_force_v1)\n",[88,10675,10677],{"class":10562,"line":10676},20,[88,10678,10603],{"emptyLinePlaceholder":10602},[88,10680,10682],{"class":10562,"line":10681},21,[88,10683,10684],{},"driving_force_v2 = gm_matrix - gm_l12 + (x_l12_al - x_matrix_al) * (mu_matrix_al - mu_matrix_ni)\n",[88,10686,10688],{"class":10562,"line":10687},22,[88,10689,10690],{},"print(\"driving_force_v2: \", driving_force_v2)\n",[56,10692,10693],{},"验算结果为",[10551,10695,10699],{"className":10696,"code":10698,"language":571},[10697],"language-text","gm:  -72477.6 -72477.64000000001\ngm:  -79069.11 -79069.1112\ndp l12:  -136692.13\ndriving_force_v1:  2325.703199999998\ndriving_force_v2:  2325.7419999999975\n",[10558,10700,10698],{"__ignoreMap":10556},[1247,10702,10703],{"id":10703},"参考说明",[56,10705,10706],{},[80,10707],{"alt":10708,"src":10709},"Hillert, M.","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fwebsites\u002Fmynote\u002Fmaterials\u002Fthermodynamics\u002Fdriving-force-original-note.png",[10711,10712,10713],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: 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var(--shiki-dark-text-decoration);}",{"title":10556,"searchDepth":10569,"depth":10569,"links":10715},[10716],{"id":18,"depth":10569,"text":18,"children":10717},[10718,10719,10720,10721],{"id":1249,"depth":10575,"text":1249},{"id":3748,"depth":10575,"text":3748},{"id":6949,"depth":10575,"text":6949},{"id":10703,"depth":10575,"text":10703},"2026-09-06","基于 Gibbs-Duhem 关系与扩散势，推导多元两相体系中相变驱动力的两种表达形式及其等价关系，并附 Pandat 计算数据的验算示例。","md",{},{"title":18,"description":10723},"eGgw8vJWCf9PSuev2ZmuWuxpzo6sT35NU6mUkgNFnT4",[10729,10731],{"title":14,"path":15,"stem":16,"description":10730,"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.",{"title":22,"path":23,"stem":24,"description":10732,"children":-1},"从零开始掌握 Python 环境管理，包括 Conda 环境创建、配置文件使用、镜像源配置等实用技巧。",1792686186190]