1067:
1459:
1246:
1216:
606:
2306:
413:
becomes small. This may be problematic when dealing with a structure with very short interatomic distances, as any nuclei that cross a certain threshold will become strongly (and unphysically) bound to one another at a distance of zero.
190:
1454:{\displaystyle \Phi (r)=\varepsilon \left\{{\frac {6}{\alpha -6}}\exp \left(\alpha \left\right)-{\frac {\alpha }{\alpha -6}}\left({\frac {r_{0}}{r}}\right)^{6}\right\}+{\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r}}}
1756:
1570:
information, the applicability of the BKS potential has been extended to both the silica polymorphs and other tetrahedral network oxides systems that have same cluster structure, such as aluminophosphates,
422:
The modified
Buckingham potential, also called the "exp-six" potential, is used to calculate the interatomic forces for gases based on Chapman and Cowling collision theory. The potential has the form
1084:
427:
1056:
725:
962:
1795:
801:
644:
73:
1529:
913:
874:
664:
936:
1509:
995:
834:
745:
684:
2338:
1966:
1936:
1906:
1876:
391:
2110:
1849:
1822:
1489:
1015:
854:
765:
411:
361:
341:
277:
253:
233:
213:
96:
308:
As explained in
Buckingham's original paper and, e.g., in section 2.2.5 of Jensen's text, the repulsion is due to the interpenetration of the closed
2692:
108:
2105:
An updated version of the BKS potential introduced a new repulsive term to prevent atom overlapping. The modified potential is taken as
1552:
1592:
2672:
2687:
2667:
1234:
1558:
on small silica clusters to describe accurate interaction between nearest-neighbors, which is the function of accurate
1562:. The experimental data is applied to fit larger scale force information beyond nearest neighbors. By combining the
1211:{\displaystyle \Phi _{12}(r)=A\exp \left(-Br\right)-{\frac {C}{r^{6}}}+{\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r}}}
1074:
The
Coulomb–Buckingham potential is an extension of the Buckingham potential for application to ionic systems (e.g.
255:
are constants. The two terms on the right-hand side constitute a repulsion and an attraction, because their first
2682:
2553:"Interatomic force fields for silicas, aluminophosphates, and zeolites: Derivation based onab initiocalculations"
33:
601:{\displaystyle \Phi _{12}(r)={\frac {\epsilon }{1-6/\alpha }}\left-\left({\frac {r_{min}}{r}}\right)^{6}\right]}
2677:
1559:
1540:
283:
1544:
99:
17:
2607:
2564:
2506:
2404:
1020:
689:
313:
25:
2648:
941:
1764:
770:
613:
42:
37:
1514:
879:
312:. "There is therefore some justification for choosing the repulsive part (of the potential) as an
2420:
317:
29:
1551:
atoms. Rather than relying only on experimental data, the BKS potential is derived by combining
2494:
2395:
Buckingham, R. A. (1938). "The
Classical Equation of State of Gaseous Helium, Neon and Argon".
1066:
859:
649:
2627:
2588:
2580:
2530:
2522:
2475:
2301:{\displaystyle \Phi _{12}(r)=\left+{\frac {q_{1}q_{2}}{r_{12}}}+{\frac {D_{12}}{r_{12}^{24}}}}
1567:
1563:
918:
287:
1494:
967:
806:
730:
669:
2619:
2572:
2552:
2514:
2467:
2412:
2313:
1941:
1911:
1881:
1854:
1583:
1582:
The form of this interatomic potential is the usual
Buckingham form, with the addition of a
366:
1827:
1800:
1467:
2608:"Developing empirical potentials from ab initio simulations: The case of amorphous silica"
2652:
2568:
2510:
2408:
1000:
839:
750:
396:
346:
326:
309:
262:
238:
218:
198:
81:
76:
2551:
Kramer, G. J.; Farragher, N. P.; van Beest, B. W. H.; van Santen, R. A. (1991-02-15).
2455:
2661:
2623:
1548:
75:
for the interaction of two atoms that are not directly bonded as a function of the
2456:"Transport Properties of Gases Obeying a Modified Buckingham (Exp-Six) Potential"
2518:
2495:"Force fields for silicas and aluminophosphates based onab initiocalculations"
256:
2631:
2584:
2576:
2526:
2479:
2534:
2416:
2606:
Carré, Antoine; Ispas, Simona; Horbach, Jürgen; Kob, Walter (2016-11-01).
2592:
686:
is the measurement of the repulsive energy steepness which is the ratio
316:". The Buckingham potential has been used extensively in simulations of
1576:
1075:
185:{\displaystyle \Phi _{12}(r)=A\exp \left(-Br\right)-{\frac {C}{r^{6}}}}
2471:
2424:
1572:
294:
2493:
van Beest, B. W. H.; Kramer, G. J.; van Santen, R. A. (1990-04-16).
1065:
302:
1751:{\displaystyle \Phi _{12}(r)=\left+{\frac {q_{1}q_{2}}{r_{12}}}}
298:
1971:
The BKS potential parameters for common atoms are shown below:
393:
term diverges, the
Buckingham potential becomes attractive as
291:
2340:
were chosen to have the following values for Silica glass:
1240:
The above equation may be written in its alternate form as
1797:
is the interatomic potential between atom i and atom j,
1586:
term. The formula for the BKS potential is expressed as
646:
is the interatomic potential between atom i and atom j,
323:
Because the exponential term converges to a constant as
1233:
are suitable constants and the additional term is the
2316:
2113:
1944:
1914:
1884:
1857:
1830:
1803:
1767:
1595:
1517:
1497:
1470:
1249:
1087:
1023:
1003:
970:
944:
921:
882:
862:
842:
809:
773:
753:
733:
692:
672:
652:
616:
430:
399:
369:
349:
329:
265:
241:
221:
201:
111:
84:
45:
1968:
are constant parameters based on the type of atoms.
856:
which can achieve the minimum interatomic potential
282:
Buckingham proposed this as a simplification of the
2332:
2300:
1960:
1930:
1900:
1870:
1843:
1816:
1789:
1750:
1523:
1503:
1483:
1453:
1210:
1050:
1009:
989:
956:
930:
907:
868:
848:
828:
795:
759:
739:
719:
678:
658:
638:
600:
405:
385:
355:
335:
271:
247:
227:
207:
184:
90:
67:
1078:materials). The formula for the interaction is
876:. This potential function is only valid when
8:
1070:Example Coulomb–Buckingham potential curve.
1017:at which the potential is maximized; when
2321:
2315:
2290:
2285:
2275:
2269:
2258:
2247:
2237:
2230:
2214:
2209:
2199:
2193:
2179:
2169:
2145:
2118:
2112:
1949:
1943:
1919:
1913:
1889:
1883:
1862:
1856:
1835:
1829:
1808:
1802:
1772:
1766:
1740:
1729:
1719:
1712:
1696:
1691:
1681:
1675:
1661:
1651:
1627:
1600:
1594:
1516:
1496:
1475:
1469:
1439:
1421:
1411:
1404:
1390:
1375:
1369:
1346:
1325:
1316:
1273:
1248:
1196:
1178:
1168:
1161:
1150:
1141:
1092:
1086:
1035:
1030:
1022:
1002:
975:
969:
943:
920:
893:
881:
861:
841:
814:
808:
778:
772:
752:
732:
705:
696:
691:
671:
651:
621:
615:
587:
566:
560:
528:
519:
484:
468:
453:
435:
429:
398:
374:
368:
348:
328:
279:are negative and positive, respectively.
264:
240:
220:
200:
174:
165:
116:
110:
83:
50:
44:
2436:
2434:
2342:
1973:
2442:Introduction to Computational Chemistry
2387:
1535:Beest Kramer van Santen (BKS) potential
418:Modified Buckingham (Exp-Six) potential
1511:is a free dimensionless parameter and
915:, as the potential will decay towards
7:
2546:
2544:
1531:is the depth of the minimum energy.
1058:, the potential is set to infinity.
1878:is the distance between atoms, and
964:. This is corrected by identifying
2397:Proceedings of the Royal Society A
2115:
1769:
1597:
1250:
1089:
925:
775:
618:
432:
113:
47:
14:
2344:Parameter value for Silica glass
1543:that may be used to simulate the
666:is the minimum potential energy,
1491:is the minimum energy distance,
286:, in a theoretical study of the
2624:10.1016/j.commatsci.2016.07.041
2612:Computational Materials Science
2460:The Journal of Chemical Physics
2454:Mason, Edward A. (2004-12-29).
1051:{\displaystyle r\leq {r_{max}}}
720:{\displaystyle \sigma /r_{min}}
2310:where the constant parameters
2130:
2124:
1784:
1778:
1612:
1606:
1259:
1253:
1235:electrostatic potential energy
1104:
1098:
957:{\displaystyle r\rightarrow 0}
948:
790:
784:
633:
627:
447:
441:
128:
122:
62:
56:
1:
2693:Quantum mechanical potentials
1790:{\displaystyle \Phi _{12}(r)}
796:{\displaystyle \Phi _{12}(r)}
639:{\displaystyle \Phi _{12}(r)}
68:{\displaystyle \Phi _{12}(r)}
1851:are the charges magnitudes,
1524:{\displaystyle \varepsilon }
1062:Coulomb–Buckingham potential
908:{\displaystyle r>r_{max}}
2519:10.1103/physrevlett.64.1955
2709:
1556:quantum chemistry methods
869:{\displaystyle \epsilon }
659:{\displaystyle \epsilon }
34:Pauli exclusion principle
2577:10.1103/physrevb.43.5068
997:, which is the value of
931:{\displaystyle -\infty }
2673:Computational chemistry
2499:Physical Review Letters
2444:, 2nd ed., Wiley, 2007,
1539:The BKS potential is a
1504:{\displaystyle \alpha }
990:{\displaystyle r_{max}}
829:{\displaystyle r_{min}}
740:{\displaystyle \sigma }
679:{\displaystyle \alpha }
284:Lennard-Jones potential
2417:10.1098/rspa.1938.0173
2334:
2333:{\displaystyle D_{ij}}
2302:
1962:
1961:{\displaystyle C_{ij}}
1932:
1931:{\displaystyle B_{ij}}
1902:
1901:{\displaystyle A_{ij}}
1872:
1871:{\displaystyle r_{12}}
1845:
1818:
1791:
1752:
1525:
1505:
1485:
1455:
1212:
1071:
1052:
1011:
991:
958:
932:
909:
870:
850:
830:
797:
761:
741:
721:
680:
660:
640:
602:
407:
387:
386:{\displaystyle r^{-6}}
357:
337:
273:
249:
229:
209:
186:
100:interatomic potentials
92:
69:
2688:Intermolecular forces
2668:Theoretical chemistry
2335:
2303:
1963:
1933:
1903:
1873:
1846:
1844:{\displaystyle q_{2}}
1819:
1817:{\displaystyle q_{1}}
1792:
1753:
1545:interatomic potential
1526:
1506:
1486:
1484:{\displaystyle r_{0}}
1456:
1213:
1069:
1053:
1012:
992:
959:
933:
910:
871:
851:
831:
798:
762:
742:
722:
681:
661:
641:
603:
408:
388:
358:
338:
274:
250:
230:
210:
187:
98:. It is a variety of
93:
70:
18:theoretical chemistry
2649:Buckingham potential
2314:
2111:
1942:
1912:
1882:
1855:
1828:
1801:
1765:
1593:
1515:
1495:
1468:
1247:
1085:
1021:
1001:
968:
942:
919:
880:
860:
840:
807:
771:
751:
731:
690:
670:
650:
614:
428:
397:
367:
347:
327:
314:exponential function
263:
239:
219:
199:
109:
82:
77:interatomic distance
43:
38:van der Waals energy
32:which describes the
22:Buckingham potential
2569:1991PhRvB..43.5068K
2511:1990PhRvL..64.1955V
2409:1938RSPSA.168..264B
2345:
2295:
2219:
1976:
1701:
2343:
2330:
2298:
2281:
2205:
1974:
1958:
1928:
1898:
1868:
1841:
1814:
1787:
1748:
1687:
1521:
1501:
1481:
1451:
1208:
1072:
1048:
1007:
987:
954:
928:
905:
866:
846:
826:
793:
757:
737:
717:
676:
656:
636:
598:
403:
383:
353:
333:
318:molecular dynamics
269:
245:
225:
205:
182:
88:
65:
30:Richard Buckingham
2557:Physical Review B
2505:(16): 1955–1958.
2472:10.1063/1.1740026
2379:
2378:
2296:
2264:
2220:
2103:
2102:
1746:
1702:
1449:
1384:
1362:
1331:
1289:
1206:
1156:
1010:{\displaystyle r}
849:{\displaystyle r}
760:{\displaystyle r}
581:
540:
492:
477:
406:{\displaystyle r}
356:{\displaystyle 0}
336:{\displaystyle r}
288:equation of state
272:{\displaystyle r}
248:{\displaystyle C}
228:{\displaystyle B}
208:{\displaystyle A}
180:
91:{\displaystyle r}
2700:
2683:Chemical bonding
2636:
2635:
2603:
2597:
2596:
2563:(6): 5068–5080.
2548:
2539:
2538:
2490:
2484:
2483:
2451:
2445:
2438:
2429:
2428:
2403:(933): 264–283.
2392:
2346:
2339:
2337:
2336:
2331:
2329:
2328:
2307:
2305:
2304:
2299:
2297:
2294:
2289:
2280:
2279:
2270:
2265:
2263:
2262:
2253:
2252:
2251:
2242:
2241:
2231:
2226:
2222:
2221:
2218:
2213:
2204:
2203:
2194:
2189:
2185:
2184:
2183:
2174:
2173:
2150:
2149:
2123:
2122:
1977:
1967:
1965:
1964:
1959:
1957:
1956:
1937:
1935:
1934:
1929:
1927:
1926:
1907:
1905:
1904:
1899:
1897:
1896:
1877:
1875:
1874:
1869:
1867:
1866:
1850:
1848:
1847:
1842:
1840:
1839:
1823:
1821:
1820:
1815:
1813:
1812:
1796:
1794:
1793:
1788:
1777:
1776:
1757:
1755:
1754:
1749:
1747:
1745:
1744:
1735:
1734:
1733:
1724:
1723:
1713:
1708:
1704:
1703:
1700:
1695:
1686:
1685:
1676:
1671:
1667:
1666:
1665:
1656:
1655:
1632:
1631:
1605:
1604:
1530:
1528:
1527:
1522:
1510:
1508:
1507:
1502:
1490:
1488:
1487:
1482:
1480:
1479:
1460:
1458:
1457:
1452:
1450:
1448:
1444:
1443:
1427:
1426:
1425:
1416:
1415:
1405:
1400:
1396:
1395:
1394:
1389:
1385:
1380:
1379:
1370:
1363:
1361:
1347:
1342:
1338:
1337:
1333:
1332:
1330:
1329:
1317:
1290:
1288:
1274:
1217:
1215:
1214:
1209:
1207:
1205:
1201:
1200:
1184:
1183:
1182:
1173:
1172:
1162:
1157:
1155:
1154:
1142:
1137:
1133:
1097:
1096:
1057:
1055:
1054:
1049:
1047:
1046:
1045:
1016:
1014:
1013:
1008:
996:
994:
993:
988:
986:
985:
963:
961:
960:
955:
937:
935:
934:
929:
914:
912:
911:
906:
904:
903:
875:
873:
872:
867:
855:
853:
852:
847:
836:is the value of
835:
833:
832:
827:
825:
824:
802:
800:
799:
794:
783:
782:
766:
764:
763:
758:
747:is the value of
746:
744:
743:
738:
726:
724:
723:
718:
716:
715:
700:
685:
683:
682:
677:
665:
663:
662:
657:
645:
643:
642:
637:
626:
625:
607:
605:
604:
599:
597:
593:
592:
591:
586:
582:
577:
576:
561:
551:
547:
546:
542:
541:
539:
538:
520:
493:
485:
478:
476:
472:
454:
440:
439:
412:
410:
409:
404:
392:
390:
389:
384:
382:
381:
362:
360:
359:
354:
342:
340:
339:
334:
278:
276:
275:
270:
259:with respect to
254:
252:
251:
246:
234:
232:
231:
226:
214:
212:
211:
206:
191:
189:
188:
183:
181:
179:
178:
166:
161:
157:
121:
120:
97:
95:
94:
89:
74:
72:
71:
66:
55:
54:
2708:
2707:
2703:
2702:
2701:
2699:
2698:
2697:
2658:
2657:
2645:
2640:
2639:
2605:
2604:
2600:
2550:
2549:
2542:
2492:
2491:
2487:
2453:
2452:
2448:
2439:
2432:
2394:
2393:
2389:
2384:
2365:
2317:
2312:
2311:
2271:
2254:
2243:
2233:
2232:
2195:
2175:
2165:
2161:
2157:
2141:
2140:
2136:
2114:
2109:
2108:
2000:
1993:
1986:
1975:BKS parameters
1945:
1940:
1939:
1915:
1910:
1909:
1885:
1880:
1879:
1858:
1853:
1852:
1831:
1826:
1825:
1804:
1799:
1798:
1768:
1763:
1762:
1736:
1725:
1715:
1714:
1677:
1657:
1647:
1643:
1639:
1623:
1622:
1618:
1596:
1591:
1590:
1537:
1513:
1512:
1493:
1492:
1471:
1466:
1465:
1435:
1428:
1417:
1407:
1406:
1371:
1365:
1364:
1351:
1321:
1309:
1305:
1301:
1297:
1278:
1272:
1268:
1245:
1244:
1192:
1185:
1174:
1164:
1163:
1146:
1123:
1119:
1088:
1083:
1082:
1064:
1031:
1019:
1018:
999:
998:
971:
966:
965:
940:
939:
917:
916:
889:
878:
877:
858:
857:
838:
837:
810:
805:
804:
774:
769:
768:
749:
748:
729:
728:
701:
688:
687:
668:
667:
648:
647:
617:
612:
611:
562:
556:
555:
524:
512:
508:
504:
500:
483:
479:
458:
431:
426:
425:
420:
395:
394:
370:
365:
364:
345:
344:
325:
324:
310:electron shells
261:
260:
237:
236:
217:
216:
197:
196:
170:
147:
143:
112:
107:
106:
80:
79:
46:
41:
40:
12:
11:
5:
2706:
2704:
2696:
2695:
2690:
2685:
2680:
2678:Thermodynamics
2675:
2670:
2660:
2659:
2656:
2655:
2644:
2643:External links
2641:
2638:
2637:
2598:
2540:
2485:
2466:(2): 169–186.
2446:
2430:
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2385:
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2380:
2377:
2376:
2373:
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2367:
2363:
2359:
2358:
2355:
2352:
2349:
2327:
2324:
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2288:
2284:
2278:
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2268:
2261:
2257:
2250:
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2240:
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2202:
2198:
2192:
2188:
2182:
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2148:
2144:
2139:
2135:
2132:
2129:
2126:
2121:
2117:
2101:
2100:
2097:
2094:
2091:
2087:
2086:
2083:
2080:
2077:
2073:
2072:
2069:
2066:
2063:
2059:
2058:
2055:
2052:
2049:
2045:
2044:
2041:
2038:
2035:
2031:
2030:
2027:
2024:
2021:
2017:
2016:
2013:
2010:
2007:
2003:
2002:
1998:
1995:
1991:
1988:
1984:
1981:
1955:
1952:
1948:
1925:
1922:
1918:
1895:
1892:
1888:
1865:
1861:
1838:
1834:
1811:
1807:
1786:
1783:
1780:
1775:
1771:
1759:
1758:
1743:
1739:
1732:
1728:
1722:
1718:
1711:
1707:
1699:
1694:
1690:
1684:
1680:
1674:
1670:
1664:
1660:
1654:
1650:
1646:
1642:
1638:
1635:
1630:
1626:
1621:
1617:
1614:
1611:
1608:
1603:
1599:
1536:
1533:
1520:
1500:
1478:
1474:
1462:
1461:
1447:
1442:
1438:
1434:
1431:
1424:
1420:
1414:
1410:
1403:
1399:
1393:
1388:
1383:
1378:
1374:
1368:
1360:
1357:
1354:
1350:
1345:
1341:
1336:
1328:
1324:
1320:
1315:
1312:
1308:
1304:
1300:
1296:
1293:
1287:
1284:
1281:
1277:
1271:
1267:
1264:
1261:
1258:
1255:
1252:
1219:
1218:
1204:
1199:
1195:
1191:
1188:
1181:
1177:
1171:
1167:
1160:
1153:
1149:
1145:
1140:
1136:
1132:
1129:
1126:
1122:
1118:
1115:
1112:
1109:
1106:
1103:
1100:
1095:
1091:
1063:
1060:
1044:
1041:
1038:
1034:
1029:
1026:
1006:
984:
981:
978:
974:
953:
950:
947:
927:
924:
902:
899:
896:
892:
888:
885:
865:
845:
823:
820:
817:
813:
792:
789:
786:
781:
777:
756:
736:
714:
711:
708:
704:
699:
695:
675:
655:
635:
632:
629:
624:
620:
596:
590:
585:
580:
575:
572:
569:
565:
559:
554:
550:
545:
537:
534:
531:
527:
523:
518:
515:
511:
507:
503:
499:
496:
491:
488:
482:
475:
471:
467:
464:
461:
457:
452:
449:
446:
443:
438:
434:
419:
416:
402:
380:
377:
373:
352:
332:
268:
244:
224:
204:
193:
192:
177:
173:
169:
164:
160:
156:
153:
150:
146:
142:
139:
136:
133:
130:
127:
124:
119:
115:
87:
64:
61:
58:
53:
49:
13:
10:
9:
6:
4:
3:
2:
2705:
2694:
2691:
2689:
2686:
2684:
2681:
2679:
2676:
2674:
2671:
2669:
2666:
2665:
2663:
2654:
2650:
2647:
2646:
2642:
2633:
2629:
2625:
2621:
2617:
2613:
2609:
2602:
2599:
2594:
2590:
2586:
2582:
2578:
2574:
2570:
2566:
2562:
2558:
2554:
2547:
2545:
2541:
2536:
2532:
2528:
2524:
2520:
2516:
2512:
2508:
2504:
2500:
2496:
2489:
2486:
2481:
2477:
2473:
2469:
2465:
2461:
2457:
2450:
2447:
2443:
2437:
2435:
2431:
2426:
2422:
2418:
2414:
2410:
2406:
2402:
2398:
2391:
2388:
2381:
2374:
2371:
2368:
2361:
2360:
2356:
2353:
2350:
2348:
2347:
2341:
2325:
2322:
2318:
2308:
2291:
2286:
2282:
2276:
2272:
2266:
2259:
2255:
2248:
2244:
2238:
2234:
2227:
2223:
2215:
2210:
2206:
2200:
2196:
2190:
2186:
2180:
2176:
2170:
2166:
2162:
2158:
2154:
2151:
2146:
2142:
2137:
2133:
2127:
2119:
2106:
2098:
2095:
2092:
2089:
2088:
2084:
2081:
2078:
2075:
2074:
2070:
2067:
2064:
2061:
2060:
2056:
2053:
2050:
2047:
2046:
2042:
2039:
2036:
2033:
2032:
2028:
2025:
2022:
2019:
2018:
2014:
2011:
2008:
2005:
2004:
1996:
1989:
1982:
1979:
1978:
1972:
1969:
1953:
1950:
1946:
1923:
1920:
1916:
1893:
1890:
1886:
1863:
1859:
1836:
1832:
1809:
1805:
1781:
1773:
1741:
1737:
1730:
1726:
1720:
1716:
1709:
1705:
1697:
1692:
1688:
1682:
1678:
1672:
1668:
1662:
1658:
1652:
1648:
1644:
1640:
1636:
1633:
1628:
1624:
1619:
1615:
1609:
1601:
1589:
1588:
1587:
1585:
1584:Coulomb force
1580:
1578:
1574:
1569:
1565:
1561:
1557:
1555:
1550:
1546:
1542:
1534:
1532:
1518:
1498:
1476:
1472:
1445:
1440:
1436:
1432:
1429:
1422:
1418:
1412:
1408:
1401:
1397:
1391:
1386:
1381:
1376:
1372:
1366:
1358:
1355:
1352:
1348:
1343:
1339:
1334:
1326:
1322:
1318:
1313:
1310:
1306:
1302:
1298:
1294:
1291:
1285:
1282:
1279:
1275:
1269:
1265:
1262:
1256:
1243:
1242:
1241:
1238:
1236:
1232:
1228:
1224:
1202:
1197:
1193:
1189:
1186:
1179:
1175:
1169:
1165:
1158:
1151:
1147:
1143:
1138:
1134:
1130:
1127:
1124:
1120:
1116:
1113:
1110:
1107:
1101:
1093:
1081:
1080:
1079:
1077:
1068:
1061:
1059:
1042:
1039:
1036:
1032:
1027:
1024:
1004:
982:
979:
976:
972:
951:
945:
922:
900:
897:
894:
890:
886:
883:
863:
843:
821:
818:
815:
811:
803:is zero, and
787:
779:
754:
734:
712:
709:
706:
702:
697:
693:
673:
653:
630:
622:
608:
594:
588:
583:
578:
573:
570:
567:
563:
557:
552:
548:
543:
535:
532:
529:
525:
521:
516:
513:
509:
505:
501:
497:
494:
489:
486:
480:
473:
469:
465:
462:
459:
455:
450:
444:
436:
423:
417:
415:
400:
378:
375:
371:
350:
330:
321:
319:
315:
311:
306:
304:
300:
296:
293:
289:
285:
280:
266:
258:
242:
222:
202:
175:
171:
167:
162:
158:
154:
151:
148:
144:
140:
137:
134:
131:
125:
117:
105:
104:
103:
101:
85:
78:
59:
51:
39:
35:
31:
27:
23:
19:
2615:
2611:
2601:
2560:
2556:
2502:
2498:
2488:
2463:
2459:
2449:
2441:
2400:
2396:
2390:
2309:
2107:
2104:
2051:16,008.5345
1970:
1760:
1581:
1553:
1549:Silica glass
1538:
1463:
1239:
1230:
1226:
1222:
1220:
1073:
609:
424:
421:
363:, while the
322:
307:
281:
194:
28:proposed by
21:
15:
2618:: 323–334.
2440:F. Jensen,
2079:9,034.2080
2023:18,003.757
1568:macroscopic
1564:microscopic
1560:force field
1541:force field
257:derivatives
2662:Categories
2382:References
2009:1388.7730
2653:SklogWiki
2632:0927-0256
2585:0163-1829
2527:0031-9007
2480:0021-9606
2191:−
2163:−
2155:
2116:Φ
2057:130.5659
2029:133.5381
2015:175.0000
1770:Φ
1673:−
1645:−
1637:
1598:Φ
1554:ab initio
1519:ε
1499:α
1437:ε
1433:π
1356:−
1353:α
1349:α
1344:−
1314:−
1303:α
1295:
1283:−
1280:α
1266:ε
1251:Φ
1194:ε
1190:π
1139:−
1125:−
1117:
1090:Φ
1028:≤
949:→
926:∞
923:−
864:ϵ
776:Φ
735:σ
694:σ
674:α
654:ϵ
619:Φ
553:−
517:−
506:α
498:
490:α
474:α
463:−
456:ϵ
433:Φ
376:−
163:−
149:−
141:
114:Φ
48:Φ
2535:10041537
2369:3423200
2351:Si - Si
2085:19.8793
2082:5.19098
2062:Al - Al
2054:4.79667
2034:Si - Si
2026:4.87318
2012:2.76000
1547:between
2593:9997885
2565:Bibcode
2507:Bibcode
2405:Bibcode
2366:(eV•Å)
2354:Si - O
2048:Al - O
2020:O - Si
2001:(eV•Å)
1577:silicon
1076:ceramic
292:gaseous
26:formula
2630:
2591:
2583:
2533:
2525:
2478:
2423:
2357:O - O
2090:P - P
2076:P - O
2006:O - O
1761:where
1573:carbon
1464:where
1229:, and
1221:where
767:where
610:where
295:helium
195:Here,
20:, the
2425:97239
2421:JSTOR
1987:(eV)
303:argon
24:is a
2628:ISSN
2589:PMID
2581:ISSN
2531:PMID
2523:ISSN
2476:ISSN
2375:113
1994:(Ă…)
1980:i-j
1938:and
1824:and
1575:and
1566:and
887:>
301:and
299:neon
290:for
235:and
36:and
2651:on
2620:doi
2616:124
2573:doi
2515:doi
2468:doi
2413:doi
2401:168
2372:29
2152:exp
1634:exp
1292:exp
1114:exp
938:as
495:exp
138:exp
16:In
2664::
2626:.
2614:.
2610:.
2587:.
2579:.
2571:.
2561:43
2559:.
2555:.
2543:^
2529:.
2521:.
2513:.
2503:64
2501:.
2497:.
2474:.
2464:22
2462:.
2458:.
2433:^
2419:.
2411:.
2399:.
2364:ij
2292:24
2287:12
2277:12
2260:12
2211:12
2201:12
2181:12
2171:12
2147:12
2120:12
2099:0
2096:0
2093:0
2071:0
2068:0
2065:0
2043:0
2040:0
2037:0
1999:ij
1992:ij
1985:ij
1864:12
1774:12
1742:12
1693:12
1683:12
1663:12
1653:12
1629:12
1602:12
1579:.
1237:.
1225:,
1094:12
780:12
727:,
623:12
437:12
320:.
305:.
297:,
215:,
118:12
102:.
52:12
2634:.
2622::
2595:.
2575::
2567::
2537:.
2517::
2509::
2482:.
2470::
2427:.
2415::
2407::
2362:D
2326:j
2323:i
2319:D
2283:r
2273:D
2267:+
2256:r
2249:2
2245:q
2239:1
2235:q
2228:+
2224:]
2216:6
2207:r
2197:C
2187:)
2177:r
2167:B
2159:(
2143:A
2138:[
2134:=
2131:)
2128:r
2125:(
1997:C
1990:B
1983:A
1954:j
1951:i
1947:C
1924:j
1921:i
1917:B
1908:,
1894:j
1891:i
1887:A
1860:r
1837:2
1833:q
1810:1
1806:q
1785:)
1782:r
1779:(
1738:r
1731:2
1727:q
1721:1
1717:q
1710:+
1706:]
1698:6
1689:r
1679:C
1669:)
1659:r
1649:B
1641:(
1625:A
1620:[
1616:=
1613:)
1610:r
1607:(
1477:0
1473:r
1446:r
1441:0
1430:4
1423:2
1419:q
1413:1
1409:q
1402:+
1398:}
1392:6
1387:)
1382:r
1377:0
1373:r
1367:(
1359:6
1340:)
1335:]
1327:0
1323:r
1319:r
1311:1
1307:[
1299:(
1286:6
1276:6
1270:{
1263:=
1260:)
1257:r
1254:(
1231:C
1227:B
1223:A
1203:r
1198:0
1187:4
1180:2
1176:q
1170:1
1166:q
1159:+
1152:6
1148:r
1144:C
1135:)
1131:r
1128:B
1121:(
1111:A
1108:=
1105:)
1102:r
1099:(
1043:x
1040:a
1037:m
1033:r
1025:r
1005:r
983:x
980:a
977:m
973:r
952:0
946:r
901:x
898:a
895:m
891:r
884:r
844:r
822:n
819:i
816:m
812:r
791:)
788:r
785:(
755:r
713:n
710:i
707:m
703:r
698:/
634:)
631:r
628:(
595:]
589:6
584:)
579:r
574:n
571:i
568:m
564:r
558:(
549:]
544:)
536:n
533:i
530:m
526:r
522:r
514:1
510:(
502:[
487:6
481:[
470:/
466:6
460:1
451:=
448:)
445:r
442:(
401:r
379:6
372:r
351:0
343:→
331:r
267:r
243:C
223:B
203:A
176:6
172:r
168:C
159:)
155:r
152:B
145:(
135:A
132:=
129:)
126:r
123:(
86:r
63:)
60:r
57:(
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