20:
595:
An alternative method is to grade the lattice constant from one value to another by a controlled altering of the alloy ratio during film growth. The beginning of the grading layer will have a ratio to match the underlying lattice and the alloy at the end of the layer growth will match the desired
431:
117:, that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be distance to the nearest neighbor). Their
216:
Depending on the crystal system, some or all of the lengths may be equal, and some of the angles may have fixed values. In those systems, only some of the six parameters need to be specified. For example, in the
304:
2382:
Roland
Tellgren and Ivar Olovsson (1971): "Hydrogen Bond Studies. XXXXVI. The Crystal Structures of Normal and Deuterated Sodium Hydrogen Oxalate Monohydrate NaHC2O4·H2O and NaDC2O4·D2O".
2404:
495:
2321:
599:
The rate of change in the alloy must be determined by weighing the penalty of layer strain, and hence defect density, against the cost of the time in the epitaxy tool.
290:
The volume of the unit cell can be calculated from the lattice constant lengths and angles. If the unit cell sides are represented as vectors, then the volume is the
592:
Typically, films of different materials grown on the previous film or substrate are chosen to match the lattice constant of the prior layer to minimize film stress.
543:
213:, and the crystal's surface. Parameter values quoted in manuals should specify those environment variables, and are usually averages affected by measurement errors.
185:(lattice types), each with fairly well defined set of lattice parameters that are characteristic of the substance. These parameters typically depend on the
74:
crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths
1718:
282:
of a crystal layer over a substrate of different composition, the lattice parameters must be matched in order to reduce strain and crystal defects.
2349:
2453:
R. V. Lapshin (2019). "Drift-insensitive distributed calibration of probe microscope scanner in nanometer range: Real mode".
561:
change to be formed in a material without introducing a change in crystal structure. This allows construction of advanced
584:
have almost equal lattice constants, making it possible to grow almost arbitrarily thick layers of one on the other one.
426:{\displaystyle V=abc{\sqrt {1+2\cos \alpha \cos \beta \cos \gamma -\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma }}.}
2855:"3.1.7 Data: Crystallographic properties of compounds with perovskite or perovskite-related structure, Table 2 Part 1"
1439:
2891:
731:
868:
2559:
1923:
577:
456:
2788:"Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study"
291:
684:
603:
248:
2721:
Davey, Wheeler (1925). "Precision
Measurements of the Lattice Constants of Twelve Common Metals".
275:
259:
constants are equal, and the angles are 60°, 90°, and 90°, so the geometry is determined by the
2094:
2059:
2037:
554:
2854:
2131:
614:
270:
The lattice parameters of a crystalline substance can be determined using techniques such as
2515:
513:
2802:
2730:
2472:
2419:
755:
562:
218:
8:
740:
2806:
2734:
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2423:
2496:
2462:
2046:
1311:
1296:
1016:
800:
723:
581:
194:
162:
2871:
2362:
Francisco
Colmenero (2019): "Negative area compressibility in oxalic acid dihydrate".
2886:
2500:
2488:
2435:
1793:
1703:
1371:
1356:
1326:
1107:
933:
845:
770:
637:
271:
2810:
2738:
2480:
2427:
2387:
2367:
2068:
1955:
1932:
1893:
1873:
1833:
1778:
1748:
1733:
1688:
1431:
1416:
1386:
1341:
1191:
1176:
1001:
918:
815:
785:
611:
573:
2634:
2787:
2484:
2371:
2016:
1970:
1853:
1813:
1763:
1448:
1401:
1251:
1236:
1206:
1130:
1061:
1046:
903:
878:
860:
830:
67:
2513:
62:
is one of the physical dimensions and angles that determine the geometry of the
1463:
1266:
1221:
1153:
210:
202:
198:
182:
150:
24:
2880:
2613:
2492:
2439:
2103:
1281:
1031:
657:
181:
are arranged in space according to one of a small finite number of possible
2742:
2660:
1084:
986:
278:. They can be used as a natural length standard of nanometer range. In the
71:
113:
have the dimension of length. The three numbers represent the size of the
566:
186:
1538:
971:
948:
221:, all of the lengths are equal and all the angles are 90°, so only the
2814:
2431:
2391:
70:, and is proportional to the distance between atoms in the crystal. A
1553:
1478:
708:
239:
134:
130:
114:
63:
2467:
1673:
1643:
1598:
1583:
894:
667:
607:
558:
235:
190:
174:
126:
1658:
693:
648:
279:
226:
206:
166:
118:
2514:
2405:"Automatic lateral calibration of tunneling microscope scanners"
1568:
1523:
1508:
244:
209:
composition. The lattice is usually distorted near impurities,
122:
86:
of the three cell edges meeting at a vertex, and the angles
2684:
1628:
1613:
1493:
170:
19:
137:(pm). Typical values start at a few angstroms. The angles
2687:
Zinc Oxide: Fundamentals, Materials and Device
Technology
178:
2322:"Unit cell definition using parallelepiped with lengths
294:
of the vectors. The volume is represented by the letter
596:
final lattice for the following layer to be deposited.
626:
Lattice constants for various materials at 300 K
2857:. SpringerMaterials - The Landolt-Börnstein Database.
553:
Matching of lattice structures between two different
516:
500:
For orthorhombic, tetragonal and cubic lattices with
459:
307:
537:
489:
425:
2878:
225:length needs to be given. This is the case of
16:Physical dimensions of unit cells in a crystal
2452:
2402:
2564:Argon National Labs (Advanced Photon Source)
2396:
620:
2852:
2689:. Weinheim: WILEY-VCH Verlag GmbH & Co.
2461:. Netherlands: Elsevier B. V.: 1122–1129.
125:, and they are traditionally specified in
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2708:
2706:
2704:
2702:
2700:
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193:(or, more generally, the local state of
18:
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2356:
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2848:
2846:
2844:
2773:Transition Metal Carbides and Nitrides
2554:
2552:
2334:and angles between the sides given by
39:and angles between the sides given by
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2826:
2824:
2720:
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2540:
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2536:
2534:
2532:
2785:
2779:
2770:
2749:
2685:Hadis Morkoç and Ümit Özgur (2009).
2577:
2627:
2516:"4. Direct and reciprocal lattices"
548:
13:
2821:
2529:
610:above 1.9 eV can be grown on
587:
14:
2903:
2865:
490:{\displaystyle V=abc\sin \beta .}
2635:"Fundamental physical constants"
2412:Review of Scientific Instruments
2653:
156:
101:The crystal lattice parameters
2507:
2314:
1:
2853:Goodenough, J. B.; Longo, M.
2307:
436:For monoclinic lattices with
2872:How to Find Lattice Constant
2485:10.1016/j.apsusc.2018.10.149
2372:10.1016/j.matlet.2019.02.077
298:. For the general unit cell
165:in the solid state may form
7:
2775:. New York: Academic Press.
2384:Journal of Chemical Physics
2366:, volume 245, pages 25-28.
129:(Å); an angstrom being 0.1
23:Unit cell definition using
10:
2908:
2795:Journal of Applied Physics
2418:(9). USA: AIP: 3268–3276.
578:aluminium gallium arsenide
621:List of lattice constants
285:
149:are usually specified in
2892:Semiconductor properties
604:indium gallium phosphide
2455:Applied Surface Science
2299:Orthorhombic perovskite
2268:Orthorhombic perovskite
2237:Orthorhombic perovskite
2095:Orthorhombic perovskite
555:semiconductor materials
276:atomic force microscope
2801:(3): 033715–033715–8.
2743:10.1103/PhysRev.25.753
2403:R. V. Lapshin (1998).
2386:, volume 54, issue 1.
539:
538:{\displaystyle V=abc.}
491:
427:
51:
2124:Tetragonal perovskite
2038:Tetragonal perovskite
563:light-emitting diodes
540:
492:
450:, this simplifies to
428:
292:scalar triple product
197:within the crystal),
98:between those edges.
22:
634:Lattice constant (Å)
617:with index grading.
514:
457:
305:
2807:2010JAP...107c3715S
2771:Toth, L.E. (1967).
2735:1925PhRv...25..753D
2614:"Semiconductor NSM"
2560:"Lattice Constants"
2477:2019ApSS..470.1122L
2424:1998RScI...69.3268L
627:
557:allows a region of
2352:on 4 October 2008.
625:
582:aluminium arsenide
535:
487:
423:
163:chemical substance
52:
2815:10.1063/1.3291117
2786:Saha, B. (2010).
2432:10.1063/1.1149091
2392:10.1063/1.1674582
2364:Materials Letters
2305:
2304:
1054:Zinc blende (FCC)
1039:Zinc blende (FCC)
994:Zinc blende (FCC)
941:Zinc blende (FCC)
926:Zinc blende (FCC)
911:Zinc blende (FCC)
853:Zinc blende (FCC)
838:Zinc blende (FCC)
823:Zinc blende (FCC)
808:Zinc blende (FCC)
793:Zinc blende (FCC)
778:Zinc blende (FCC)
763:Zinc blende (FCC)
748:Zinc blende (FCC)
732:Zinc blende (FCC)
638:Crystal structure
418:
272:X-ray diffraction
267:constants alone.
195:mechanical stress
60:lattice parameter
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2639:physics.nist.gov
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2353:
2348:. Archived from
2318:
2280:
2249:
2218:
2192:
2180:Cubic perovskite
2174:
2162:Cubic perovskite
2156:
2144:Cubic perovskite
2137:
2109:
2074:
2060:Cubic perovskite
2052:
2022:
2009:Cubic perovskite
2003:
1976:
1903:
1879:
1859:
1839:
1819:
1799:
1471:Caesium chloride
1456:Caesium chloride
1440:Caesium chloride
628:
624:
612:gallium arsenide
574:gallium arsenide
549:Lattice matching
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280:epitaxial growth
249:hexagonal system
247:. Similarly, in
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56:lattice constant
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2723:Physical Review
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203:magnetic fields
183:crystal systems
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68:crystal lattice
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2866:External links
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2208:
2205:
2202:
2197:
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2167:
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2158:
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2138:
2130:
2129:
2126:
2123:
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2110:
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2101:
2098:
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2077:
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2055:
2053:
2045:
2044:
2041:
2039:
2036:
2033:
2028:
2025:
2023:
2015:
2014:
2011:
2008:
2005:
1997:
1996:
1993:
1990:
1987:
1982:
1979:
1977:
1969:
1968:
1965:
1962:
1959:
1957:
1954:
1953:
1950:
1947:
1944:
1939:
1936:
1934:
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1234:
1231:
1228:
1225:
1223:
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1189:
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1168:
1165:
1160:
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1134:
1132:
1129:
1128:
1125:
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1068:
1065:
1063:
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1038:
1035:
1033:
1030:
1029:
1026:
1023:
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1018:
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1008:
1005:
1003:
1000:
999:
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990:
988:
985:
984:
981:
978:
975:
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969:
966:
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960:
955:
952:
950:
947:
946:
943:
940:
937:
935:
932:
931:
928:
925:
922:
920:
917:
916:
913:
910:
907:
905:
902:
901:
898:
896:
893:
890:
885:
882:
880:
877:
876:
873:
870:
867:
864:
862:
859:
858:
855:
852:
849:
847:
844:
843:
840:
837:
834:
832:
829:
828:
825:
822:
819:
817:
814:
813:
810:
807:
804:
802:
799:
798:
795:
792:
789:
787:
784:
783:
780:
777:
774:
772:
769:
768:
765:
762:
759:
757:
754:
753:
750:
747:
744:
742:
739:
738:
735:
733:
730:
727:
725:
722:
721:
718:
716:Diamond (FCC)
715:
712:
710:
707:
706:
703:
701:Diamond (FCC)
700:
697:
695:
692:
691:
688:
686:
683:
680:
675:
672:
669:
665:
664:
661:
659:
658:Diamond (FCC)
656:
653:
650:
646:
645:
641:
639:
636:
633:
630:
629:
618:
616:
613:
609:
605:
602:For example,
600:
597:
593:
585:
583:
579:
575:
572:For example,
570:
568:
564:
560:
556:
532:
529:
526:
523:
520:
517:
510:
509:
508:
504:
484:
481:
478:
475:
472:
469:
466:
463:
460:
453:
452:
451:
447:
440:
420:
415:
412:
407:
403:
399:
396:
393:
388:
384:
380:
377:
374:
369:
365:
361:
358:
355:
352:
349:
346:
343:
340:
337:
334:
331:
328:
325:
320:
317:
314:
311:
308:
301:
300:
299:
297:
293:
283:
281:
277:
273:
268:
266:
262:
258:
254:
250:
246:
241:
237:
233:
228:
224:
220:
214:
212:
208:
204:
200:
196:
192:
188:
184:
180:
176:
172:
169:in which the
168:
164:
154:
152:
148:
144:
140:
136:
133:(nm), or 100
132:
128:
124:
120:
116:
112:
108:
104:
99:
97:
93:
89:
85:
81:
77:
73:
69:
65:
61:
57:
50:
46:
42:
38:
34:
30:
27:with lengths
26:
21:
2798:
2794:
2781:
2772:
2726:
2722:
2686:
2680:
2668:. Retrieved
2665:Spi Supplies
2664:
2661:"Substrates"
2655:
2643:. Retrieved
2638:
2629:
2617:. Retrieved
2567:. Retrieved
2563:
2519:. Retrieved
2509:
2458:
2454:
2448:
2415:
2411:
2398:
2383:
2378:
2363:
2358:
2350:the original
2343:
2339:
2335:
2331:
2327:
2323:
2316:
2293:
2288:
2283:
2262:
2257:
2252:
2231:
2226:
2221:
2200:
2195:
2118:
2113:
2088:
2083:
2078:
2031:
2026:
1985:
1980:
1942:
1937:
1924:Orthorhombic
1917:
1912:
1907:
1163:
1158:
1140:
1135:
1117:
1112:
1094:
1089:
1071:
1066:
1024:Halite (FCC)
1009:Halite (FCC)
979:Halite (FCC)
958:
953:
888:
883:
678:
673:
601:
598:
594:
591:
571:
567:diode lasers
552:
502:
499:
445:
438:
435:
295:
289:
269:
264:
260:
256:
252:
243:at 300
231:
229:, which has
222:
219:cubic system
215:
160:
157:Introduction
146:
142:
138:
110:
106:
102:
100:
95:
91:
87:
83:
79:
75:
72:simple cubic
59:
55:
53:
48:
44:
40:
36:
32:
28:
698:5.431020511
274:or with an
187:temperature
2881:Categories
2645:17 January
2619:19 October
2569:19 October
2468:1501.06679
2308:References
205:, and its
135:picometres
64:unit cells
2501:119191299
2493:0169-4332
2440:0034-6748
2206:Hexagonal
1991:Hexagonal
1988:= 13.8631
1948:Hexagonal
685:Hexagonal
482:β
479:
416:γ
413:
400:−
397:β
394:
381:−
378:α
375:
362:−
359:γ
356:
350:β
347:
341:α
338:
175:molecules
131:nanometer
127:angstroms
115:unit cell
2887:Crystals
1983:= 5.1483
1169:Wurtzite
1146:Wurtzite
1123:Wurtzite
1100:Wurtzite
1077:Wurtzite
895:Wurtzite
891:= 10.053
668:graphite
631:Material
608:band gap
559:band gap
207:isotopic
199:electric
191:pressure
167:crystals
2803:Bibcode
2731:Bibcode
2473:Bibcode
2420:Bibcode
2291:= 5.329
2286:= 5.179
2234:= 7.464
2229:= 5.275
2198:= 5.673
2121:= 4.152
2116:= 3.904
2091:= 7.645
2086:= 5.443
2081:= 5.381
2056:3.98805
2034:= 4.034
2029:= 3.994
1945:= 2.837
1940:= 2.906
1920:= 2.830
1915:= 5.545
1910:= 11.47
1678:3.3058
1663:3.3008
1648:3.0399
1166:= 5.693
1161:= 3.533
1143:= 5.185
1138:= 3.189
1120:= 4.982
1115:= 3.112
1074:= 6.756
1069:= 4.160
886:= 3.086
681:= 6.708
676:= 2.461
649:diamond
234:= 3.57
227:diamond
151:degrees
121:is the
119:SI unit
2670:17 May
2641:. NIST
2521:9 June
2499:
2491:
2438:
2296:= 7.37
2265:= 7.85
2260:= 5.57
2255:= 5.53
2224:= 5.27
2203:= 4.71
2006:3.9885
1963:Halite
1886:Halite
1866:Halite
1846:Halite
1826:Halite
1806:Halite
1786:Halite
1771:Halite
1756:Halite
1741:Halite
1726:Halite
1711:Halite
1696:Halite
1424:Halite
1409:Halite
1394:Halite
1379:Halite
1364:Halite
1349:Halite
1334:Halite
1319:Halite
1304:Halite
1289:Halite
1274:Halite
1259:Halite
1244:Halite
1229:Halite
1214:Halite
1199:Halite
1184:Halite
1097:= 6.26
1092:= 3.82
1051:4.5380
1036:3.6150
1021:6.4620
1006:5.9362
956:= 3.25
908:5.8320
869:Halite
835:6.0583
805:6.0959
775:5.4505
760:6.1355
745:5.4510
728:5.6605
615:wafers
580:, and
286:Volume
251:, the
238:= 357
145:, and
109:, and
94:, and
82:, and
2791:(PDF)
2497:S2CID
2463:arXiv
2408:(PDF)
2245:SrRuO
2214:CaMnO
2188:BaMnO
2177:3.767
2159:3.838
2141:7.810
2133:EuTiO
2105:PbTiO
2070:CaTiO
2048:SrTiO
2018:BaTiO
1972:LiNbO
1883:4.456
1863:4.470
1843:4.166
1823:4.640
1803:4.698
1783:4.328
1768:4.392
1753:4.149
1738:4.136
1723:4.392
1708:4.577
1693:4.249
1633:4.920
1618:4.065
1603:3.912
1588:3.155
1573:4.079
1558:3.859
1543:3.142
1528:3.597
1513:3.499
1498:2.856
1483:4.046
1468:4.567
1453:4.291
1436:4.123
991:5.420
976:4.580
961:= 5.2
938:6.482
923:6.050
871:(FCC)
865:4.212
850:6.479
820:5.869
790:5.653
713:5.658
654:3.567
642:Ref.
505:= 90°
448:= 90°
441:= 90°
177:, or
171:atoms
123:meter
66:in a
2672:2017
2647:2020
2621:2014
2571:2014
2523:2015
2489:ISSN
2436:ISSN
2276:YAlO
2170:CaVO
2152:SrVO
1999:KTaO
1960:4.52
1877:0.99
1857:0.99
1837:0.97
1817:0.99
1797:0.97
1681:BCC
1666:BCC
1651:BCC
1449:CsBr
1432:CsCl
1421:6.02
1406:7.35
1391:6.89
1387:RbBr
1376:6.59
1372:RbCl
1361:5.65
1346:7.07
1331:6.60
1316:6.29
1301:5.34
1286:6.47
1271:5.97
1267:NaBr
1256:5.64
1252:NaCl
1241:4.63
1226:6.01
1211:5.50
1207:LiBr
1196:5.14
1192:LiCl
1181:4.03
1017:PbTe
934:CdTe
919:CdSe
846:InSb
831:InAs
801:GaSb
786:GaAs
756:AlSb
724:AlAs
565:and
263:and
255:and
201:and
179:ions
2811:doi
2799:107
2739:doi
2481:doi
2459:470
2428:doi
2388:doi
2368:doi
1956:ScN
1875:TaC
1855:NbC
1815:HfC
1795:ZrC
1779:TiC
1764:NbN
1749:CrN
1719:HfN
1704:ZrN
1689:TiN
1636:FCC
1621:FCC
1606:FCC
1591:BCC
1576:FCC
1561:FCC
1546:BCC
1531:FCC
1516:FCC
1501:BCC
1486:FCC
1464:CsI
1417:CsF
1402:RbI
1357:RbF
1327:KBr
1312:KCl
1282:NaI
1237:NaF
1222:LiI
1177:LiF
1154:InN
1131:GaN
1108:AlN
1085:ZnS
1062:CdS
1002:PbS
987:ZnS
972:ZnO
949:ZnO
904:CdS
879:SiC
861:MgO
816:InP
771:GaP
741:AlP
666:C (
647:C (
476:sin
404:cos
385:cos
366:cos
353:cos
344:cos
335:cos
58:or
2883::
2823:^
2809:.
2797:.
2793:.
2751:^
2737:.
2727:25
2725:.
2695:^
2663:.
2637:.
2579:^
2562:.
2531:^
2495:.
2487:.
2479:.
2471:.
2457:.
2434:.
2426:.
2416:69
2414:.
2410:.
2342:,
2338:,
2330:,
2326:,
1933:WC
1895:Cr
1835:VC
1734:VN
1674:Ta
1659:Nb
1629:Pb
1614:Au
1599:Pt
1569:Ag
1554:Pd
1539:Mo
1524:Cu
1509:Ni
1494:Fe
1479:Al
1342:KI
1297:KF
1047:BP
1032:BN
709:Ge
694:Si
576:,
569:.
443:,
240:pm
189:,
173:,
161:A
153:.
141:,
105:,
90:,
78:,
54:A
47:,
43:,
35:,
31:,
2817:.
2813::
2805::
2745:.
2741::
2733::
2674:.
2649:.
2623:.
2573:.
2525:.
2503:.
2483::
2475::
2465::
2442:.
2430::
2422::
2390::
2370::
2346:"
2344:γ
2340:β
2336:α
2332:c
2328:b
2324:a
2294:c
2289:b
2284:a
2278:3
2263:c
2258:b
2253:a
2247:3
2232:c
2227:b
2222:a
2216:3
2201:c
2196:a
2190:3
2172:3
2154:3
2135:3
2119:c
2114:a
2107:3
2089:c
2084:b
2079:a
2072:3
2050:3
2032:c
2027:a
2020:3
2001:3
1986:c
1981:a
1974:3
1943:c
1938:a
1918:c
1913:b
1908:a
1901:2
1899:C
1897:3
1644:V
1584:W
1164:c
1159:a
1141:c
1136:a
1118:c
1113:a
1095:c
1090:a
1072:c
1067:a
959:c
954:a
889:c
884:a
679:c
674:a
670:)
651:)
533:.
530:c
527:b
524:a
521:=
518:V
503:β
485:.
473:c
470:b
467:a
464:=
461:V
446:γ
439:α
421:.
408:2
389:2
370:2
332:2
329:+
326:1
321:c
318:b
315:a
312:=
309:V
296:V
265:c
261:a
257:b
253:a
245:K
236:Å
232:a
223:a
147:γ
143:β
139:α
111:c
107:b
103:a
96:γ
92:β
88:α
84:c
80:b
76:a
49:γ
45:β
41:α
37:c
33:b
29:a
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