1853:
36:
2458:
690:
2282:
544:
406:
known as the susceptibility tensor. Many linear dielectrics are isotropic, but it is possible nevertheless for a material to display behavior that is both linear and anisotropic, or for a material to be non-linear but isotropic. Anisotropic but linear susceptibility is common in many crystals.
1990:
187:. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material (and store energy). It is in this way that the electric susceptibility influences the electric
1684:
2453:{\displaystyle \mathbf {P} (\mathbf {r} )=\varepsilon _{0}{\frac {N\alpha (\mathbf {r} )}{1-{\frac {1}{3}}N(\mathbf {r} )\alpha (\mathbf {r} )}}\mathbf {E} (\mathbf {r} )=\varepsilon _{0}\chi _{\text{e}}(\mathbf {r} )\mathbf {E} (\mathbf {r} )}
2271:
958:
1136:
1196:
1019:
889:
2180:
281:
742:
1537:
685:{\displaystyle \mathbf {D} \ =\ \varepsilon _{0}\mathbf {E} +\mathbf {P} \ =\ \varepsilon _{0}(1+\chi _{\text{e}})\mathbf {E} \ =\ \varepsilon _{\text{r}}\varepsilon _{0}\mathbf {E} \ =\ \varepsilon \mathbf {E} }
1867:
1452:
1347:
795:
490:
2512:
2196:
2080:
2035:
1060:
441:
896:
526:
2585:
2462:
This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the
1282:
368:
335:
165:
2541:
2109:
1071:
392:
306:
1831:
1787:
1754:
1721:
1478:
1409:
1302:
1255:
1148:
971:
2834:
1856:
Plot of the dielectric constant as a function of frequency showing several resonances and plateaus, which indicate the processes that respond on the time scale of a
844:
1501:
968:
is the number of molecules per unit volume contributing to the polarization. Thus, if the local electric field is parallel to the ambient electric field, we have:
231:
1389:
1369:
1235:
1215:
2863:
1414:
1309:
1864:
In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is
2718:
2118:
446:
2883:
2822:
1756:, corresponds to the linear susceptibility described above. While this first term is dimensionless, the subsequent nonlinear susceptibilities
698:
2755:
207:
If a dielectric material is a linear dielectric, then electric susceptibility is defined as the constant of proportionality (which may be a
100:
748:
72:
53:
17:
2596:
1026:
1679:{\displaystyle P=P_{0}+\varepsilon _{0}\chi ^{(1)}E+\varepsilon _{0}\chi ^{(2)}E^{2}+\varepsilon _{0}\chi ^{(3)}E^{3}+\cdots .}
1511:
In many materials the polarizability starts to saturate at high values of electric field. This saturation can be modelled by a
893:
This introduces a complication however, as locally the field can differ significantly from the overall applied field. We have:
79:
2842:
2736:
2681:
2659:
1985:{\displaystyle \mathbf {P} (t)=\varepsilon _{0}\int _{-\infty }^{t}\chi _{\text{e}}(t-t')\mathbf {E} (t')\,\mathrm {d} t'.}
495:
86:
2805:
119:
68:
1351:
In this second definition, the polarizability would have the SI unit of C.m/V. Yet another definition exists where
2472:
2040:
1800:
materials in which the susceptibility is not uniform in every direction. In these materials, each susceptibility
2001:
417:
2611:
2276:
1065:
57:
222:
176:
2888:
2186:
2835:
10.1093/oso/9780198726500.001.0001/oso-9780198726500-chapter-1#oso-9780198726500-chapter-1-displaymaths-20
1064:
Otherwise, one should find a relation between the local and the macroscopic field. In some materials, the
2554:
2548:
2469:
Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e.
1852:
1520:
2643:
1260:
346:
313:
143:
2266:{\displaystyle \mathbf {P} (\omega )=\varepsilon _{0}\chi _{\text{e}}(\omega )\mathbf {E} (\omega ).}
93:
2717:
Freeman, Richard; King, James; Lafyatis, Gregory (2019). "Essentials of
Electricity and Magnetism".
1860:. This demonstrates that thinking of the susceptibility in terms of its Fourier transform is useful.
2621:
2616:
2517:
2085:
375:
289:
2764:
2601:
1803:
1759:
1726:
1257:
has the dimension of a volume (m). Another definition would be to keep SI units and to integrate
812:
191:
of the material and thus influences many other phenomena in that medium, from the capacitance of
46:
2606:
1145:
The definition of the molecular polarizability depends on the author. In the above definition,
953:{\displaystyle \mathbf {P} =N\mathbf {p} =N\varepsilon _{0}\alpha \mathbf {E} _{\text{local}},}
1693:
1463:
1394:
1287:
1240:
531:
411:
2112:
1483:
8:
2728:
2463:
2190:
338:
2037:. The upper limit of this integral can be extended to infinity as well if one defines
1374:
1354:
1220:
1200:
175:"receptive") is a dimensionless proportionality constant that indicates the degree of
2857:
2838:
2801:
2732:
2677:
1131:{\displaystyle {\frac {\chi _{\text{e}}}{3+\chi _{\text{e}}}}={\frac {N\alpha }{3}}.}
1998:
of the electric field at previous times with time-dependent susceptibility given by
2830:
2793:
2724:
2669:
1857:
1531:
1516:
133:
2665:
1480:
the dimension of a volume, as in the first definition, but with a value that is
1191:{\displaystyle \mathbf {p} =\varepsilon _{0}\alpha \mathbf {E_{\text{local}}} ,}
1014:{\displaystyle \chi _{\text{e}}\mathbf {E} =N\alpha \mathbf {E} _{\text{local}}}
884:{\displaystyle \mathbf {p} =\varepsilon _{0}\alpha \mathbf {E_{\text{local}}} }
806:
212:
196:
184:
2673:
2877:
2797:
1687:
1524:
2175:{\displaystyle \chi _{\text{e}}(\Delta t)=\chi _{\text{e}}\delta (\Delta t)}
276:{\displaystyle \mathbf {P} =\varepsilon _{0}\chi _{\text{e}}{\mathbf {E} },}
1530:
The standard definition of nonlinear susceptibilities in SI units is via a
188:
1995:
1797:
399:
737:{\displaystyle \varepsilon \ =\ \varepsilon _{\text{r}}\varepsilon _{0}}
402:(different depending on direction), susceptibility is represented as a
219:
192:
180:
2544:
1523:(such as used to convert infrared light into visible light, in green
1457:
2189:
and write this relationship as a function of frequency. Due to the
1023:
Thus only if the local field equals the ambient field can we write:
35:
819:
811:
A similar parameter exists to relate the magnitude of the induced
834:), and the dipole moment resulting from the local electric field
1447:{\displaystyle \mathbf {p} =\alpha \mathbf {E_{\text{local}}} .}
1342:{\displaystyle \mathbf {p} =\alpha \mathbf {E_{\text{local}}} .}
1841:
403:
208:
790:{\displaystyle \varepsilon _{\text{r}}\ =\ 1+\chi _{\text{e}}}
168:
485:{\displaystyle \chi _{\text{e}}\ =\varepsilon _{\text{r}}-1}
2706:(4 ed.). Cambridge University Press. pp. 181–190.
2821:
Freeman, Richard; King, James; Lafyatis, Gregory (2019),
2557:
2520:
2475:
2285:
2199:
2185:
It is more convenient in a linear system to take the
2121:
2088:
2043:
2004:
1870:
1806:
1796:
The nonlinear susceptibilities can be generalized to
1762:
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234:
146:
202:
2820:
2763:(84 ed.). CRC. pp. 10–163. Archived from
2716:
60:. Unsourced material may be challenged and removed.
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2265:
2174:
2103:
2074:
2029:
1984:
1825:
1781:
1748:
1715:
1678:
1534:of the polarization's reaction to electric field:
1495:
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1403:
1383:
1363:
1341:
1296:
1276:
1249:
1229:
1209:
1190:
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1054:
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883:
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520:
484:
435:
386:
362:
329:
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275:
159:
2862:: CS1 maint: DOI inactive as of September 2024 (
1237:are in SI units and the molecular polarizability
2875:
2661:Materials Handbook: A Concise Desktop Reference
2657:
826:that induced the dipole. This parameter is the
1690:materials, the built-in polarization is zero,
1140:
2787:
2507:{\displaystyle \chi _{\text{e}}(\Delta t)=0}
2075:{\displaystyle \chi _{\text{e}}(\Delta t)=0}
2697:
2695:
2693:
2111:. An instantaneous response corresponds to
1847:
1506:
800:
2030:{\displaystyle \chi _{\text{e}}(\Delta t)}
1515:. These susceptibilities are important in
1055:{\displaystyle \chi _{\text{e}}=N\alpha .}
436:{\displaystyle \varepsilon _{\textrm {r}}}
2823:"Essentials of Electricity and Magnetism"
2701:
2651:
1965:
964:is the polarization per unit volume, and
120:Learn how and when to remove this message
2788:Butcher, Paul N.; Cotter, David (1990).
2690:
1851:
2597:Application of tensor theory in physics
537:is related to the polarization density
14:
2884:Electric and magnetic fields in matter
2876:
2750:
2748:
2757:CRC Handbook of Chemistry and Physics
521:{\displaystyle \chi _{\text{e}}\ =0.}
410:The susceptibility is related to its
398:In materials where susceptibility is
1391:are expressed in the cgs system and
58:adding citations to reliable sources
29:
2829:, Oxford: Oxford University Press,
2745:
2634:
2580:{\displaystyle \chi _{\text{e}}(0)}
1435:
1330:
1179:
875:
339:electric permittivity of free space
183:material in response to an applied
24:
2729:10.1093/oso/9780198726500.003.0001
2658:Cardarelli, François (2000–2008).
2521:
2489:
2193:, the integral becomes a product,
2163:
2135:
2089:
2057:
2018:
1967:
1906:
1723:.) The first susceptibility term,
25:
2900:
2668:. pp. 524 (Section 8.1.16).
203:Definition for linear dielectrics
2790:The Elements of Nonlinear Optics
2443:
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2427:
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2201:
1947:
1872:
1431:
1419:
1326:
1314:
1277:{\displaystyle \varepsilon _{0}}
1175:
1153:
1001:
986:
937:
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871:
849:
678:
661:
627:
581:
573:
549:
380:
363:{\displaystyle \chi _{\text{e}}}
330:{\displaystyle \varepsilon _{0}}
294:
265:
236:
160:{\displaystyle \chi _{\text{e}}}
34:
2704:Introduction to Electrodynamics
2275:This has a similar form to the
1994:That is, the polarization is a
370:is the electric susceptibility;
45:needs additional citations for
2814:
2792:. Cambridge University Press.
2781:
2710:
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2015:
1962:
1951:
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1741:
1735:
1652:
1646:
1613:
1607:
1581:
1575:
623:
604:
13:
1:
2627:
2536:{\displaystyle \Delta t<0}
2104:{\displaystyle \Delta t<0}
2466:properties of the material.
1519:and lead to effects such as
822:to the local electric field
492:so in the case of a vacuum,
387:{\displaystyle \mathbf {E} }
308:is the polarization density;
301:{\displaystyle \mathbf {P} }
7:
2723:. Oxford University Press.
2702:Griffiths, David J (2017).
2641:"Electric susceptibility".
2590:
1826:{\displaystyle \chi ^{(n)}}
1782:{\displaystyle \chi ^{(n)}}
1749:{\displaystyle \chi ^{(1)}}
1141:Ambiguity in the definition
541:by the following relation:
10:
2905:
2612:Clausius–Mossotti relation
2549:Kramers–Kronig constraints
2277:Clausius–Mossotti relation
1521:second-harmonic generation
1066:Clausius–Mossotti relation
804:
2827:Electromagnetic Radiation
2720:Electromagnetic Radiation
2674:10.1007/978-1-84628-669-8
69:"Electric susceptibility"
2798:10.1017/CBO9781139167994
2664:(2nd ed.). London:
2617:Linear response function
1848:Dispersion and causality
1513:nonlinear susceptibility
1507:Nonlinear susceptibility
828:molecular polarizability
801:Molecular polarizability
18:Nonlinear susceptibility
2837:(inactive 2024-09-12),
2644:Encyclopædia Britannica
2602:Magnetic susceptibility
1716:{\displaystyle P_{0}=0}
1473:{\displaystyle \alpha }
1404:{\displaystyle \alpha }
1297:{\displaystyle \alpha }
1250:{\displaystyle \alpha }
138:electric susceptibility
2581:
2551:on the susceptibility
2537:
2508:
2454:
2267:
2176:
2105:
2076:
2031:
1986:
1861:
1827:
1783:
1750:
1717:
1680:
1497:
1474:
1448:
1405:
1385:
1365:
1343:
1298:
1278:
1251:
1231:
1211:
1192:
1132:
1056:
1015:
954:
885:
791:
738:
686:
530:At the same time, the
522:
486:
437:
414:(dielectric constant)
394:is the electric field.
388:
364:
331:
302:
277:
161:
27:Degree of polarization
2582:
2538:
2509:
2455:
2268:
2177:
2106:
2077:
2032:
1987:
1855:
1828:
1784:
1751:
1718:
1681:
1498:
1496:{\displaystyle 4\pi }
1475:
1449:
1406:
1386:
1366:
1344:
1299:
1279:
1252:
1232:
1212:
1193:
1133:
1057:
1016:
955:
886:
792:
739:
687:
532:electric displacement
523:
487:
438:
412:relative permittivity
389:
365:
332:
303:
278:
162:
2622:Green–Kubo relations
2555:
2543:), a consequence of
2518:
2473:
2283:
2197:
2119:
2113:Dirac delta function
2086:
2041:
2002:
1868:
1804:
1760:
1727:
1694:
1538:
1484:
1464:
1415:
1411:is still defined as
1395:
1375:
1355:
1310:
1288:
1261:
1241:
1221:
1201:
1149:
1072:
1027:
972:
897:
845:
749:
699:
545:
496:
447:
418:
376:
347:
341:(electric constant);
314:
290:
232:
223:polarization density
144:
54:improve this article
2889:Physical quantities
2607:Maxwell's equations
2191:convolution theorem
1915:
2577:
2533:
2504:
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2263:
2172:
2101:
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2027:
1982:
1898:
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1713:
1676:
1493:
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1444:
1401:
1381:
1361:
1339:
1294:
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1227:
1207:
1188:
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950:
881:
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433:
384:
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327:
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273:
157:
2844:978-0-19-872650-0
2738:978-0-19-872650-0
2683:978-1-84628-668-1
2565:
2483:
2420:
2382:
2351:
2234:
2187:Fourier transform
2154:
2129:
2051:
2012:
1923:
1437:
1384:{\displaystyle E}
1364:{\displaystyle p}
1332:
1230:{\displaystyle E}
1210:{\displaystyle p}
1181:
1123:
1105:
1101:
1084:
1037:
1008:
982:
944:
877:
818:of an individual
784:
770:
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713:
707:
673:
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633:
620:
593:
587:
561:
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357:
260:
154:
132:In electricity (
130:
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104:
16:(Redirected from
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1555:
1532:Taylor expansion
1517:nonlinear optics
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1068:holds and reads
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134:electromagnetism
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2200:
2198:
2195:
2194:
2151:
2147:
2126:
2122:
2120:
2117:
2116:
2115:susceptibility
2087:
2084:
2083:
2048:
2044:
2042:
2039:
2038:
2009:
2005:
2003:
2000:
1999:
1971:
1966:
1954:
1946:
1935:
1920:
1916:
1910:
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1892:
1888:
1871:
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1313:
1311:
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1307:
1289:
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1268:
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1262:
1259:
1258:
1242:
1239:
1238:
1222:
1219:
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1202:
1199:
1198:
1178:
1174:
1173:
1164:
1160:
1152:
1150:
1147:
1146:
1143:
1112:
1110:
1098:
1094:
1087:
1081:
1077:
1075:
1073:
1070:
1069:
1034:
1030:
1028:
1025:
1024:
1005:
1000:
999:
985:
979:
975:
973:
970:
969:
941:
936:
935:
926:
922:
911:
900:
898:
895:
894:
874:
870:
869:
860:
856:
848:
846:
843:
842:
840:
809:
803:
781:
777:
756:
752:
750:
747:
746:
728:
724:
718:
714:
700:
697:
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677:
660:
654:
650:
644:
640:
626:
617:
613:
598:
594:
580:
572:
566:
562:
548:
546:
543:
542:
503:
499:
497:
494:
493:
470:
466:
454:
450:
448:
445:
444:
426:
425:
421:
419:
416:
415:
379:
377:
374:
373:
354:
350:
348:
345:
344:
321:
317:
315:
312:
311:
293:
291:
288:
287:
264:
263:
257:
253:
247:
243:
235:
233:
230:
229:
218:to the induced
205:
151:
147:
145:
142:
141:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
2902:
2892:
2891:
2886:
2870:
2869:
2843:
2813:
2806:
2780:
2744:
2737:
2709:
2689:
2682:
2650:
2632:
2631:
2629:
2626:
2625:
2624:
2619:
2614:
2609:
2604:
2599:
2592:
2589:
2576:
2573:
2570:
2561:
2532:
2529:
2526:
2523:
2503:
2500:
2497:
2494:
2491:
2488:
2479:
2449:
2445:
2441:
2437:
2433:
2429:
2425:
2416:
2410:
2406:
2402:
2399:
2395:
2391:
2387:
2380:
2376:
2372:
2369:
2366:
2362:
2358:
2355:
2350:
2347:
2342:
2339:
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2330:
2326:
2323:
2320:
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2308:
2304:
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2262:
2259:
2256:
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2245:
2242:
2239:
2230:
2224:
2220:
2216:
2213:
2210:
2207:
2203:
2171:
2168:
2165:
2162:
2159:
2150:
2146:
2143:
2140:
2137:
2134:
2125:
2100:
2097:
2094:
2091:
2071:
2068:
2065:
2062:
2059:
2056:
2047:
2026:
2023:
2020:
2017:
2008:
1981:
1977:
1974:
1969:
1964:
1960:
1957:
1953:
1949:
1945:
1941:
1938:
1934:
1931:
1928:
1919:
1913:
1908:
1905:
1901:
1895:
1891:
1887:
1884:
1881:
1878:
1874:
1849:
1846:
1820:
1817:
1814:
1810:
1789:have units of
1776:
1773:
1770:
1766:
1743:
1740:
1737:
1733:
1712:
1709:
1704:
1700:
1675:
1672:
1669:
1664:
1660:
1654:
1651:
1648:
1644:
1638:
1634:
1630:
1625:
1621:
1615:
1612:
1609:
1605:
1599:
1595:
1591:
1588:
1583:
1580:
1577:
1573:
1567:
1563:
1559:
1554:
1550:
1546:
1543:
1525:laser pointers
1508:
1505:
1492:
1489:
1469:
1443:
1433:
1428:
1425:
1421:
1400:
1380:
1360:
1338:
1328:
1323:
1320:
1316:
1293:
1271:
1267:
1246:
1226:
1206:
1187:
1177:
1172:
1167:
1163:
1159:
1155:
1142:
1139:
1127:
1122:
1118:
1115:
1109:
1097:
1093:
1090:
1080:
1051:
1048:
1045:
1042:
1033:
1003:
998:
995:
992:
988:
978:
949:
939:
934:
929:
925:
921:
918:
914:
910:
907:
903:
873:
868:
863:
859:
855:
851:
838:
807:Polarizability
805:Main article:
802:
799:
798:
797:
780:
776:
773:
767:
755:
744:
731:
727:
717:
710:
704:
680:
676:
670:
663:
657:
653:
643:
636:
629:
625:
616:
612:
609:
606:
601:
597:
590:
583:
579:
575:
569:
565:
558:
551:
517:
514:
502:
481:
478:
469:
465:
453:
424:
396:
395:
382:
371:
353:
342:
324:
320:
309:
296:
272:
267:
256:
250:
246:
242:
238:
213:electric field
211:) relating an
204:
201:
197:speed of light
185:electric field
150:
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
2901:
2890:
2887:
2885:
2882:
2881:
2879:
2865:
2859:
2846:
2840:
2836:
2832:
2828:
2824:
2817:
2809:
2807:9781139167994
2803:
2799:
2795:
2791:
2784:
2770:on 2016-10-06
2766:
2759:
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2749:
2740:
2734:
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2713:
2705:
2698:
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2694:
2685:
2679:
2675:
2671:
2667:
2663:
2662:
2654:
2646:
2645:
2637:
2633:
2623:
2620:
2618:
2615:
2613:
2610:
2608:
2605:
2603:
2600:
2598:
2595:
2594:
2588:
2571:
2559:
2550:
2546:
2530:
2527:
2524:
2501:
2498:
2492:
2477:
2467:
2465:
2460:
2414:
2408:
2404:
2400:
2367:
2353:
2348:
2345:
2340:
2337:
2321:
2318:
2310:
2306:
2302:
2278:
2273:
2260:
2254:
2240:
2228:
2222:
2218:
2214:
2208:
2192:
2188:
2183:
2166:
2157:
2148:
2144:
2138:
2123:
2114:
2098:
2095:
2092:
2069:
2066:
2060:
2045:
2021:
2006:
1997:
1992:
1979:
1975:
1972:
1958:
1955:
1939:
1936:
1932:
1929:
1917:
1911:
1903:
1899:
1893:
1889:
1885:
1879:
1859:
1854:
1845:
1843:
1837:
1815:
1808:
1799:
1794:
1771:
1764:
1738:
1731:
1710:
1707:
1702:
1698:
1689:
1688:ferroelectric
1673:
1670:
1667:
1662:
1658:
1649:
1642:
1636:
1632:
1628:
1623:
1619:
1610:
1603:
1597:
1593:
1589:
1586:
1578:
1571:
1565:
1561:
1557:
1552:
1548:
1544:
1541:
1533:
1528:
1526:
1522:
1518:
1514:
1504:
1490:
1487:
1467:
1459:
1454:
1441:
1426:
1423:
1398:
1378:
1358:
1349:
1336:
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1291:
1269:
1265:
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1224:
1204:
1185:
1170:
1165:
1161:
1157:
1138:
1125:
1120:
1116:
1113:
1107:
1095:
1091:
1088:
1078:
1067:
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1049:
1046:
1043:
1040:
1031:
1021:
996:
993:
990:
976:
967:
963:
947:
932:
927:
923:
919:
916:
908:
905:
891:
866:
861:
857:
853:
841:is given by:
837:
833:
829:
825:
821:
817:
814:
813:dipole moment
808:
778:
774:
771:
765:
753:
745:
729:
725:
715:
708:
702:
695:
694:
693:
674:
668:
655:
651:
641:
634:
614:
610:
607:
599:
595:
588:
577:
567:
563:
556:
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536:
533:
528:
515:
512:
500:
479:
476:
467:
463:
451:
422:
413:
408:
405:
401:
372:
351:
343:
340:
322:
318:
310:
286:
285:
284:
270:
254:
248:
244:
240:
227:
224:
221:
217:
214:
210:
200:
198:
194:
190:
186:
182:
178:
174:
173:susceptibilis
170:
148:
139:
135:
124:
121:
113:
110:November 2010
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
2848:, retrieved
2826:
2816:
2789:
2783:
2772:. Retrieved
2765:the original
2756:
2719:
2712:
2703:
2660:
2653:
2642:
2636:
2468:
2461:
2274:
2184:
1993:
1863:
1835:
1833:becomes an (
1795:
1529:
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835:
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810:
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534:
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215:
206:
189:permittivity
177:polarization
172:
137:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
1996:convolution
1798:anisotropic
1686:(Except in
400:anisotropic
2878:Categories
2850:2022-02-18
2774:2016-08-19
2628:References
2547:, imposes
2464:dispersion
1456:Using the
228:such that
220:dielectric
193:capacitors
181:dielectric
80:newspapers
2560:χ
2545:causality
2522:Δ
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2241:ω
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2158:δ
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2136:Δ
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2019:Δ
2007:χ
1933:−
1918:χ
1907:∞
1904:−
1900:∫
1890:ε
1840:)-degree
1809:χ
1765:χ
1732:χ
1671:⋯
1643:χ
1633:ε
1604:χ
1594:ε
1572:χ
1562:ε
1491:π
1468:α
1458:cgs units
1427:α
1399:α
1322:α
1292:α
1266:ε
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1171:α
1162:ε
1117:α
1096:χ
1079:χ
1047:α
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997:α
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726:ε
716:ε
703:ε
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2858:citation
2591:See also
1976:′
1959:′
1940:′
820:molecule
1503:lower.
692:where
337:is the
195:to the
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94:scholar
2841:
2804:
2735:
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1858:period
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1460:gives
960:where
769:
763:
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672:
666:
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632:
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560:
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283:where
209:tensor
96:
89:
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75:
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2768:(PDF)
2761:(PDF)
1791:(m/V)
1436:local
1331:local
1284:into
1180:local
1007:local
943:local
876:local
839:local
179:of a
169:Latin
101:JSTOR
87:books
2864:link
2839:ISBN
2802:ISBN
2733:ISBN
2678:ISBN
2528:<
2514:for
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1371:and
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2800:.
2747:^
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991:=
987:E
981:e
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909:N
906:=
902:P
872:E
862:0
854:=
850:p
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830:(
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108:(
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
