3300:
393:. The latter requirement is necessary since there are crystals that can be described by more than one combination of a lattice and a basis. For example, a crystal, viewed as a lattice with a single kind of atom located at every lattice point (the simplest basis form), may also be viewed as a lattice with a basis of two atoms. In this case, a primitive unit cell is a unit cell having only one lattice point in the first way of describing the crystal in order to ensure the smallest unit cell volume.
609:
recognize that some lattices have inherent symmetry. One can impose conditions on the length of the primitive translation vectors and on the angle between them to produce various symmetric lattices. These symmetries themselves are categorized into different types, such as point groups (which includes mirror symmetries, inversion symmetries and rotation symmetries) and translational symmetries. Thus, lattices can be categorized based on what point group or translational symmetry applies to them.
1246:
1236:
1226:
1282:
613:
conventionally all lattices that don't fall into any of the other point groups) are called oblique lattices. From there, there are 4 further combinations of point groups with translational elements (or equivalently, 4 types of restriction on the lengths/angles of the primitive translation vectors) that correspond to the 4 remaining lattice categories: square, hexagonal, rectangular, and centered rectangular. Thus altogether there are 5 Bravais lattices in 2 dimensions.
1188:
1086:
each axis while keeping the lattice points fixed. Roughly speaking, this can be thought of as moving the unit cell slightly left, slightly down, and slightly out of the screen. This shows that only one of the eight corner lattice points (specifically the front, left, bottom one) belongs to the given unit cell (the other seven lattice points belong to adjacent unit cells). In addition, only one of the two lattice points shown on the top and bottom face in the
1338:
1390:
1380:
723:
710:
3693:
2756:
2714:
1216:
1041:
1311:
1270:
1178:
33:
194:, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice appears exactly the same from each of the discrete lattice points when looking in that chosen direction.
2709:
2689:
1148:
3705:
2699:
2679:
2669:
1368:
771:
684:
745:
2776:
2766:
2746:
2725:
642:
one of the four lattice points technically belongs to a given unit cell and each of the other three lattice points belongs to one of the adjacent unit cells. This can be seen by imagining moving the unit cell parallelogram slightly left and slightly down while leaving all the black circles of the lattice points fixed.
593:
is the chosen primitive vector. This primitive cell does not always show the clear symmetry of a given crystal. In this case, a conventional unit cell easily displaying the crystal symmetry is often used. The conventional unit cell volume will be an integer-multiple of the primitive unit cell volume.
375:
Despite this rigid minimum-size requirement, there is not one unique choice of primitive unit cell. In fact, all cells whose borders are primitive translation vectors will be primitive unit cells. The fact that there is not a unique choice of primitive translation vectors for a given lattice leads to
371:
There are clearly many choices of cell that can reproduce the whole lattice when stacked (two lattice halves, for instance), and the minimum size requirement distinguishes the primitive cell from all these other valid repeating units. If the lattice or crystal is 2-dimensional, the primitive cell has
359:
There are mainly two types of unit cells: primitive unit cells and conventional unit cells. A primitive cell is the very smallest component of a lattice (or crystal) which, when stacked together with lattice translation operations, reproduces the whole lattice (or crystal). Note that the translations
641:
In the unit cell diagrams in the following table the lattice points are depicted using black circles and the unit cells are depicted using parallelograms (which may be squares or rectangles) outlined in black. Although each of the four corners of each parallelogram connects to a lattice point, only
2237:
Some basic information for the lattice systems and
Bravais lattices in three dimensions is summarized in the diagram at the beginning of this page. The seven sided polygon (heptagon) and the number 7 at the centre indicate the seven lattice systems. The inner heptagons indicate the lattice angles,
384:
Primitive unit cells are defined as unit cells with the smallest volume for a given crystal. (A crystal is a lattice and a basis at every lattice point.) To have the smallest cell volume, a primitive unit cell must contain (1) only one lattice point and (2) the minimum amount of basis constituents
1085:
In the unit cell diagrams in the following table all the lattice points on the cell boundary (corners and faces) are shown; however, not all of these lattice points technically belong to the given unit cell. This can be seen by imagining moving the unit cell slightly in the negative direction of
616:
Likewise, in 3 dimensions, there are 14 Bravais lattices: 1 general "wastebasket" category (triclinic) and 13 more categories. These 14 lattice types are classified by their point groups into 7 lattice systems (triclinic, monoclinic, orthorhombic, tetragonal, cubic, rhombohedral, and hexagonal).
608:
In two dimensions, any lattice can be specified by the length of its two primitive translation vectors and the angle between them. There are an infinite number of possible lattices one can describe in this way. Some way to categorize different types of lattices is desired. One way to do so is to
1074:
Not all combinations of lattice systems and centering types are needed to describe all of the possible lattices, as it can be shown that several of these are in fact equivalent to each other. For example, the monoclinic I lattice can be described by a monoclinic C lattice by different choice of
396:
There can be more than one way to choose a primitive cell for a given crystal and each choice will have a different primitive cell shape, but the primitive cell volume is the same for every choice and each choice will have the property that a one-to-one correspondence can be established between
612:
In two dimensions, the most basic point group corresponds to rotational invariance under 2π and π, or 1- and 2-fold rotational symmetry. This actually applies automatically to all 2D lattices, and is the most general point group. Lattices contained in this group (technically all lattices, but
363:
Another way of defining the size of a primitive cell that avoids invoking lattice translation operations, is to say that the primitive cell is the smallest possible component of a lattice (or crystal) that can be repeated to reproduce the whole lattice (or crystal),
1646:
360:
must be lattice translation operations that cause the lattice to appear unchanged after the translation. If arbitrary translations were allowed, one could make a primitive cell half the size of the true one, and translate twice as often, as an example.
258:
In crystallography, there is the concept of a unit cell which comprises the space between adjacent lattice points as well as any atoms in that space. A unit cell is defined as a space that, when translated through a subset of all vectors described by
376:
the multiplicity of possible primitive unit cells. Conventional unit cells, on the other hand, are not necessarily minimum-size cells. They are chosen purely for convenience and are often used for illustration purposes. They are loosely defined.
165:
523:
354:
1075:
crystal axes. Similarly, all A- or B-centred lattices can be described either by a C- or P-centering. This reduces the number of combinations to 14 conventional
Bravais lattices, shown in the table below. Below each diagram is the
2565:
Bravais, A. (1850). "Mémoire sur les systèmes formés par les points distribués régulièrement sur un plan ou dans l'espace" [Memoir on the systems formed by points regularly distributed on a plane or in space].
2018:
3570:
397:
primitive unit cells and discrete lattice points over the associated lattice. All primitive unit cells with different shapes for a given crystal have the same volume by definition; For a given crystal, if
240:. In this sense, there are 5 possible Bravais lattices in 2-dimensional space and 14 possible Bravais lattices in 3-dimensional space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230
3565:
1064:
Base-centered (S: A, B, or C): lattice points on the cell corners with one additional point at the center of each face of one pair of parallel faces of the cell (sometimes called end-centered)
2107:
3621:
1012:
1528:
428:
formed by a chosen set of primitive translation vectors. (Again, these vectors must make a lattice with the minimum amount of basis constituents.) That is, the set of all points
1733:
877:
591:
562:
385:(e.g., the minimum number of atoms in a basis). For the former requirement, counting the number of lattice points in a unit cell is such that, if a lattice point is shared by
1880:
70:
2178:
951:
431:
262:
1807:
910:
3439:
3626:
3351:
244:. In the context of the space group classification, the Bravais lattices are also called Bravais classes, Bravais arithmetic classes, or Bravais flocks.
3517:
2809:
2622:
2285:
61:
3616:
3608:
3669:
3647:
2538:
2509:
2458:
3662:
3512:
3178:
3043:
2892:
1945:
3652:
3550:
3246:
2449:
2899:
3674:
3532:
3502:
3431:
2246:
In four dimensions, there are 64 Bravais lattices. Of these, 23 are primitive and 41 are centered. Ten
Bravais lattices split into
3384:
1245:
1235:
1225:
3657:
3580:
3454:
3053:
1070:
Face-centered (F): lattice points on the cell corners, with one additional point at the center of each of the faces of the cell
1057:
with one of the centering types. The centering types identify the locations of the lattice points in the unit cell as follows:
3414:
3492:
2409:
1281:
3507:
3497:
2802:
3279:
3631:
2904:
2882:
2647:
603:
3309:
3183:
1187:
368:
that contains exactly one lattice point. In either definition, the primitive cell is characterized by its small size.
2937:
2832:
2684:
1641:{\displaystyle abc{\sqrt {1-\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma +2\cos \alpha \cos \beta \cos \gamma }}}
3299:
2069:
3709:
3540:
2837:
2615:
2317:
977:
3555:
3484:
2942:
2932:
2694:
2674:
3068:
1389:
1379:
3731:
3697:
3421:
3317:
3190:
3153:
2947:
2927:
2795:
2704:
2663:
2608:
1935:
1294:
356:, fills the lattice space without overlapping or voids. (I.e., a lattice space is a multiple of a unit cell.)
3105:
3741:
3545:
3389:
3334:
3083:
3048:
3241:
1053:
In three-dimensional space there are 14 Bravais lattices. These are obtained by combining one of the seven
3058:
2329:
2290:
1067:
Body-centered (I): lattice points on the cell corners, with one additional point at the center of the cell
3163:
1337:
1090:
column belongs to the given unit cell. Finally, only three of the six lattice points on the faces in the
3736:
3598:
3394:
3356:
3115:
2849:
1749:
1215:
1702:
849:
567:
528:
3322:
3195:
3031:
2922:
2719:
2444:
2149:
1827:
1654:
1354:
1109:
654:
2426:
2334:
401:
is the density of lattice points in a lattice ensuring the minimum amount of basis constituents and
3339:
3327:
3202:
3168:
3148:
2751:
2238:
lattice parameters, Bravais lattices and Schöenflies notations for the respective lattice systems.
714:
1269:
1177:
3588:
3399:
3344:
2887:
2280:
2221:
1669:
722:
709:
1310:
635:, shown in the table below. Below each diagram is the Pearson symbol for that Bravais lattice.
160:{\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3},}
3522:
3361:
3289:
3269:
2989:
2859:
2771:
2534:
2505:
2454:
2405:
1831:
1769:
775:
518:{\displaystyle \mathbf {r} =x_{1}\mathbf {a} _{1}+x_{2}\mathbf {a} _{2}+x_{3}\mathbf {a} _{3}}
349:{\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}
424:
Among all possible primitive cells for a given crystal, an obvious primitive cell may be the
3560:
3366:
3284:
3274:
3073:
3006:
2977:
2970:
2497:
2339:
2270:
2142:
1918:
1855:
2593:
2548:
2156:
929:
3449:
3444:
3409:
3229:
3128:
3063:
3026:
3021:
2818:
2741:
2586:
2544:
2526:
2493:
2209:
1925:
688:
626:
53:
45:
1786:
1147:
892:
3259:
3224:
3212:
3207:
3173:
3143:
3133:
3092:
3036:
2960:
2914:
2761:
2631:
2265:
2247:
1838:
1753:
1466:
1076:
1054:
749:
632:
425:
237:
1367:
3725:
3404:
3217:
3016:
2369:
2260:
1046:
3110:
3100:
2994:
2877:
2275:
1779:
1202:
372:
a minimum area; likewise in 3 dimensions the primitive cell has a minimum volume.
17:
787:
The unit cells are specified according to the relative lengths of the cell edges (
2501:
2343:
3593:
3264:
3138:
2965:
2755:
2713:
2213:
1911:
1495:
are the lattice vectors. The properties of the lattice systems are given below:
1061:
Primitive (P): lattice points on the cell corners only (sometimes called simple)
824:
are the lattice vectors. The properties of the lattice systems are given below:
800:
770:
744:
683:
241:
3158:
2844:
2347:
2138:
1848:
1695:
1681:
1256:
1164:
1040:
389:
adjacent unit cells around that lattice point, then the point is counted as 1/
32:
236:
Two
Bravais lattices are often considered equivalent if they have isomorphic
2867:
2295:
1907:
1521:
1402:
1134:
253:
2708:
2688:
3464:
3234:
2982:
2134:
2056:
631:
In two-dimensional space there are 5 Bravais lattices, grouped into four
222:
41:
2489:
36:
The seven lattice systems and their
Bravais lattices in three dimensions
3474:
2698:
2678:
2225:
2048:
226:
202:
2668:
2229:
2217:
2013:{\displaystyle a^{3}{\sqrt {1-3\cos ^{2}\alpha +2\cos ^{3}\alpha }}}
2525:
Brown, Harold; BĂĽlow, Rolf; NeubĂĽser, Joachim; Wondratschek, Hans;
3469:
2787:
2600:
1465:. The volume of the unit cell can be calculated by evaluating the
1038:
230:
31:
2453:(Seventh ed.). New York: John Wiley & Sons. p. 10.
799:). The area of the unit cell can be calculated by evaluating the
60:), is an infinite array of discrete points generated by a set of
2775:
2765:
2745:
2724:
218:
2791:
2604:
2576:(English: Memoir 1, Crystallographic Society of America, 1949).
2316:
Aroyo, Mois I.; MĂĽller, Ulrich; Wondratschek, Hans (2006).
3571:
197:
The
Bravais lattice concept is used to formally define a
3566:
2487:
233:, and the lattice provides the locations of the basis.
3459:
2427:"Materials & Solid State Chemistry (course notes)"
2159:
2072:
1948:
1858:
1789:
1705:
1531:
980:
932:
895:
852:
570:
531:
434:
265:
73:
3640:
3607:
3579:
3531:
3483:
3430:
3377:
3308:
3091:
3082:
3005:
2913:
2858:
2825:
2734:
2656:
417:, so every primitive cell has the same volume of 1/
64:operations described in three dimensional space by
2172:
2101:
2012:
1874:
1801:
1727:
1640:
1405:which are the relative lengths of the cell edges (
1006:
945:
904:
871:
585:
556:
517:
348:
159:
2531:Crystallographic groups of four-dimensional space
2492:. Vol. A (5th ed.). Berlin, New York:
2404:. Saunders College Publishing. pp. 71–72.
405:is the volume of a chosen primitive cell, then
2102:{\displaystyle {\frac {\sqrt {3}}{2}}\,a^{2}c}
1401:The unit cells are specified according to six
2803:
2616:
1007:{\displaystyle {\frac {\sqrt {3}}{2}}\,a^{2}}
8:
205:is made up of one or more atoms, called the
3637:
3088:
2910:
2855:
2810:
2796:
2788:
2623:
2609:
2601:
2587:Catalogue of Lattices (by Nebe and Sloane)
2400:Ashcroft, Neil; Mermin, Nathaniel (1976).
2333:
2164:
2158:
2090:
2085:
2073:
2071:
1996:
1974:
1959:
1953:
1947:
1863:
1857:
1788:
1715:
1704:
1591:
1572:
1553:
1541:
1530:
998:
993:
981:
979:
937:
931:
894:
859:
851:
577:
572:
569:
542:
530:
509:
504:
497:
484:
479:
472:
459:
454:
447:
435:
433:
340:
335:
328:
315:
310:
303:
290:
285:
278:
266:
264:
148:
143:
136:
123:
118:
111:
98:
93:
86:
74:
72:
2322:International Tables for Crystallography
2286:Translation operator (quantum mechanics)
1497:
1096:
826:
644:
27:Geometry and crystallography point array
2308:
57:
2481:
2479:
2477:
1094:column belong to the given unit cell.
7:
3704:
3044:Phase transformation crystallography
2395:
2393:
2391:
2374:Online Dictionary of Crystallography
3551:Journal of Chemical Crystallography
2450:Introduction to Solid State Physics
25:
2533:, New York: Wiley-Interscience ,
3703:
3692:
3691:
3298:
2774:
2764:
2754:
2744:
2723:
2712:
2707:
2697:
2687:
2677:
2667:
1728:{\displaystyle abc\,\sin \beta }
1388:
1378:
1366:
1336:
1309:
1280:
1268:
1244:
1234:
1224:
1214:
1186:
1176:
1146:
1045:2×2×2 unit cells of a
872:{\displaystyle ab\,\sin \theta }
769:
743:
721:
708:
682:
586:{\displaystyle \mathbf {a} _{i}}
573:
557:{\displaystyle 0\leq x_{i}<1}
505:
480:
455:
436:
336:
311:
286:
267:
144:
119:
94:
75:
1510:Axial distances (edge lengths)
1417:) and the angles between them (
836:Axial distances (edge lengths)
3493:Bilbao Crystallographic Server
795:) and the angle between them (
201:and its (finite) frontiers. A
1:
213:, at each lattice point. The
188:primitive translation vectors
2648:Crystallographic point group
2502:10.1107/97809553602060000100
2344:10.1107/97809553602060000537
1352:
1325:
1292:
1254:
1200:
1162:
1132:
758:
732:
697:
671:
604:Crystallographic point group
3541:Crystal Growth & Design
2833:Timeline of crystallography
2594:"The Bravais Lattices Song"
3758:
3352:Nuclear magnetic resonance
2592:Smith, Walter Fox (2002).
1079:for that Bravais lattice.
624:
601:
251:
3687:
3556:Journal of Crystal Growth
3296:
2638:
2443:Kittel, Charles (1996) .
2318:"Historical Introduction"
2148:
1934:
1847:
1778:
1694:
1520:
1353:
1293:
1255:
1201:
1163:
1133:
1114:
1105:
1102:
1099:
659:
650:
647:
3422:Single particle analysis
3280:Hermann–Mauguin notation
2705:trigonal & hexagonal
2486:Hahn, Theo, ed. (2002).
2432:. UC Berkeley. Chem 253.
3546:Crystallography Reviews
3390:Isomorphous replacement
3184:Lomer–Cottrell junction
1516:Corresponding examples
199:crystalline arrangement
3059:Spinodal decomposition
2291:Translational symmetry
2174:
2103:
2014:
1876:
1875:{\displaystyle a^{2}c}
1803:
1729:
1642:
1050:
1008:
947:
906:
873:
587:
558:
519:
350:
177:are any integers, and
161:
37:
3599:Gregori Aminoff Prize
3395:Molecular replacement
2425:Peidong Yang (2016).
2175:
2173:{\displaystyle a^{3}}
2104:
2015:
1877:
1804:
1730:
1643:
1457:is the angle between
1445:is the angle between
1433:is the angle between
1044:
1009:
948:
946:{\displaystyle a^{2}}
907:
874:
727:Centered rectangular
625:Further information:
588:
559:
520:
351:
162:
35:
2905:Structure prediction
2157:
2070:
1946:
1856:
1787:
1703:
1529:
1115:14 Bravais lattices
978:
930:
893:
850:
568:
529:
432:
263:
71:
62:discrete translation
3169:Cottrell atmosphere
3149:Partial dislocation
2893:Restriction theorem
2402:Solid State Physics
1802:{\displaystyle abc}
1110:Schönflies notation
660:5 Bravais lattices
655:Schönflies notation
380:Primitive unit cell
54:Auguste Bravais
18:Crystalline lattice
3589:Carl Hermann Medal
3400:Molecular dynamics
3247:Defects in diamond
3242:Stone–Wales defect
2888:Reciprocal lattice
2850:Biocrystallography
2568:J. École Polytech.
2281:Reciprocal lattice
2170:
2099:
2010:
1872:
1799:
1750:Monoclinic sulphur
1725:
1638:
1403:lattice parameters
1129:Face-centered (F)
1126:Body-centered (I)
1123:Base-centered (S)
1051:
1004:
943:
905:{\displaystyle ab}
902:
869:
583:
554:
515:
346:
157:
38:
3719:
3718:
3683:
3682:
3290:Thermal ellipsoid
3255:
3254:
3164:Frank–Read source
3124:
3123:
2990:Aperiodic crystal
2956:
2955:
2838:Crystallographers
2785:
2784:
2540:978-0-471-03095-9
2511:978-0-7923-6590-7
2460:978-0-471-11181-8
2235:
2234:
2083:
2079:
2008:
1636:
1399:
1398:
1032:
1031:
991:
987:
785:
784:
699:Orthorhombic (o)
598:Origin of concept
409:= 1 resulting in
192:primitive vectors
16:(Redirected from
3749:
3707:
3706:
3695:
3694:
3638:
3561:Kristallografija
3415:Gerchberg–Saxton
3310:Characterisation
3302:
3285:Structure factor
3089:
3074:Ostwald ripening
2911:
2856:
2812:
2805:
2798:
2789:
2778:
2768:
2758:
2748:
2727:
2716:
2711:
2701:
2691:
2681:
2671:
2657:Seven 3D systems
2625:
2618:
2611:
2602:
2597:
2575:
2552:
2551:
2527:Zassenhaus, Hans
2522:
2516:
2515:
2483:
2472:
2471:
2469:
2467:
2440:
2434:
2433:
2431:
2422:
2416:
2415:
2397:
2386:
2385:
2383:
2381:
2366:
2360:
2359:
2357:
2355:
2346:. Archived from
2337:
2313:
2271:einstein problem
2179:
2177:
2176:
2171:
2169:
2168:
2108:
2106:
2105:
2100:
2095:
2094:
2084:
2075:
2074:
2019:
2017:
2016:
2011:
2009:
2001:
2000:
1979:
1978:
1960:
1958:
1957:
1881:
1879:
1878:
1873:
1868:
1867:
1808:
1806:
1805:
1800:
1734:
1732:
1731:
1726:
1647:
1645:
1644:
1639:
1637:
1596:
1595:
1577:
1576:
1558:
1557:
1542:
1498:
1482:
1392:
1382:
1370:
1340:
1313:
1284:
1272:
1248:
1238:
1228:
1218:
1190:
1180:
1150:
1097:
1043:
1013:
1011:
1010:
1005:
1003:
1002:
992:
983:
982:
952:
950:
949:
944:
942:
941:
911:
909:
908:
903:
878:
876:
875:
870:
827:
815:
813:
773:
747:
725:
712:
686:
645:
592:
590:
589:
584:
582:
581:
576:
563:
561:
560:
555:
547:
546:
524:
522:
521:
516:
514:
513:
508:
502:
501:
489:
488:
483:
477:
476:
464:
463:
458:
452:
451:
439:
355:
353:
352:
347:
345:
344:
339:
333:
332:
320:
319:
314:
308:
307:
295:
294:
289:
283:
282:
270:
166:
164:
163:
158:
153:
152:
147:
141:
140:
128:
127:
122:
116:
115:
103:
102:
97:
91:
90:
78:
21:
3757:
3756:
3752:
3751:
3750:
3748:
3747:
3746:
3732:Crystallography
3722:
3721:
3720:
3715:
3679:
3636:
3603:
3575:
3527:
3479:
3450:CrystalExplorer
3426:
3410:Phase retrieval
3373:
3304:
3303:
3294:
3251:
3230:Schottky defect
3129:Perfect crystal
3120:
3116:Abnormal growth
3078:
3064:Supersaturation
3027:Miscibility gap
3008:
3001:
2952:
2909:
2873:Bravais lattice
2854:
2821:
2819:Crystallography
2816:
2786:
2781:
2735:Four 2D systems
2730:
2652:
2643:Bravais lattice
2634:
2632:Crystal systems
2629:
2591:
2583:
2564:
2561:
2559:Further reading
2556:
2555:
2541:
2524:
2523:
2519:
2512:
2494:Springer-Verlag
2485:
2484:
2475:
2465:
2463:
2461:
2442:
2441:
2437:
2429:
2424:
2423:
2419:
2412:
2399:
2398:
2389:
2379:
2377:
2370:"Bravais class"
2368:
2367:
2363:
2353:
2351:
2335:10.1.1.471.4170
2315:
2314:
2310:
2305:
2300:
2256:
2244:
2242:In 4 dimensions
2160:
2155:
2154:
2086:
2068:
2067:
2054:
1992:
1970:
1949:
1944:
1943:
1929:
1922:
1915:
1859:
1854:
1853:
1842:
1835:
1828:Rhombic sulphur
1785:
1784:
1773:
1765:
1761:
1757:
1701:
1700:
1689:
1685:
1677:
1673:
1666:
1662:
1658:
1587:
1568:
1549:
1527:
1526:
1504:Lattice system
1501:Crystal family
1469:
1363:
1333:
1306:
1265:
1211:
1173:
1143:
1107:
1103:Lattice system
1100:Crystal family
1055:lattice systems
1039:
1037:
1035:In 3 dimensions
994:
976:
975:
933:
928:
927:
891:
890:
848:
847:
830:Lattice system
805:
803:
778:
774:
766:
752:
748:
740:
734:Tetragonal (t)
728:
726:
717:
713:
705:
691:
687:
679:
673:Monoclinic (m)
652:
648:Lattice system
633:lattice systems
629:
627:Lattice (group)
623:
621:In 2 dimensions
606:
600:
571:
566:
565:
538:
527:
526:
503:
493:
478:
468:
453:
443:
430:
429:
382:
334:
324:
309:
299:
284:
274:
261:
260:
256:
250:
238:symmetry groups
217:may consist of
185:
175:
142:
132:
117:
107:
92:
82:
69:
68:
50:Bravais lattice
46:crystallography
28:
23:
22:
15:
12:
11:
5:
3755:
3753:
3745:
3744:
3742:Lattice points
3739:
3734:
3724:
3723:
3717:
3716:
3714:
3713:
3701:
3688:
3685:
3684:
3681:
3680:
3678:
3677:
3672:
3667:
3666:
3665:
3660:
3655:
3644:
3642:
3635:
3634:
3629:
3624:
3619:
3613:
3611:
3605:
3604:
3602:
3601:
3596:
3591:
3585:
3583:
3577:
3576:
3574:
3573:
3568:
3563:
3558:
3553:
3548:
3543:
3537:
3535:
3529:
3528:
3526:
3525:
3520:
3515:
3510:
3505:
3500:
3495:
3489:
3487:
3481:
3480:
3478:
3477:
3472:
3467:
3462:
3457:
3452:
3447:
3442:
3436:
3434:
3428:
3427:
3425:
3424:
3419:
3418:
3417:
3407:
3402:
3397:
3392:
3387:
3385:Direct methods
3381:
3379:
3375:
3374:
3372:
3371:
3370:
3369:
3364:
3354:
3349:
3348:
3347:
3342:
3332:
3331:
3330:
3325:
3314:
3312:
3306:
3305:
3297:
3295:
3293:
3292:
3287:
3282:
3277:
3272:
3270:Ewald's sphere
3267:
3262:
3256:
3253:
3252:
3250:
3249:
3244:
3239:
3238:
3237:
3232:
3222:
3221:
3220:
3215:
3213:Frenkel defect
3210:
3208:Bjerrum defect
3200:
3199:
3198:
3188:
3187:
3186:
3181:
3176:
3174:Peierls stress
3171:
3166:
3161:
3156:
3151:
3146:
3144:Burgers vector
3136:
3134:Stacking fault
3131:
3125:
3122:
3121:
3119:
3118:
3113:
3108:
3103:
3097:
3095:
3093:Grain boundary
3086:
3080:
3079:
3077:
3076:
3071:
3066:
3061:
3056:
3051:
3046:
3041:
3040:
3039:
3037:Liquid crystal
3034:
3029:
3024:
3013:
3011:
3003:
3002:
3000:
2999:
2998:
2997:
2987:
2986:
2985:
2975:
2974:
2973:
2968:
2957:
2954:
2953:
2951:
2950:
2945:
2940:
2935:
2930:
2925:
2919:
2917:
2908:
2907:
2902:
2900:Periodic table
2897:
2896:
2895:
2890:
2885:
2880:
2875:
2864:
2862:
2853:
2852:
2847:
2842:
2841:
2840:
2829:
2827:
2823:
2822:
2817:
2815:
2814:
2807:
2800:
2792:
2783:
2782:
2780:
2779:
2769:
2759:
2749:
2738:
2736:
2732:
2731:
2729:
2728:
2717:
2702:
2692:
2682:
2672:
2660:
2658:
2654:
2653:
2651:
2650:
2645:
2639:
2636:
2635:
2630:
2628:
2627:
2620:
2613:
2605:
2599:
2598:
2589:
2582:
2581:External links
2579:
2578:
2577:
2560:
2557:
2554:
2553:
2539:
2517:
2510:
2473:
2459:
2435:
2417:
2410:
2387:
2361:
2350:on 4 July 2013
2307:
2306:
2304:
2301:
2299:
2298:
2293:
2288:
2283:
2278:
2273:
2268:
2266:Crystal system
2263:
2257:
2255:
2252:
2248:enantiomorphic
2243:
2240:
2233:
2232:
2207:
2193:
2180:
2167:
2163:
2152:
2146:
2145:
2132:
2118:
2109:
2098:
2093:
2089:
2082:
2078:
2065:
2061:
2060:
2052:
2046:
2033:
2020:
2007:
2004:
1999:
1995:
1991:
1988:
1985:
1982:
1977:
1973:
1969:
1966:
1963:
1956:
1952:
1941:
1938:
1932:
1931:
1927:
1920:
1913:
1905:
1891:
1882:
1871:
1866:
1862:
1851:
1845:
1844:
1840:
1833:
1825:
1811:
1809:
1798:
1795:
1792:
1782:
1776:
1775:
1771:
1763:
1759:
1755:
1747:
1737:
1735:
1724:
1721:
1718:
1714:
1711:
1708:
1698:
1692:
1691:
1687:
1683:
1675:
1671:
1664:
1660:
1656:
1652:
1650:
1648:
1635:
1632:
1629:
1626:
1623:
1620:
1617:
1614:
1611:
1608:
1605:
1602:
1599:
1594:
1590:
1586:
1583:
1580:
1575:
1571:
1567:
1564:
1561:
1556:
1552:
1548:
1545:
1540:
1537:
1534:
1524:
1518:
1517:
1514:
1511:
1508:
1505:
1502:
1467:triple product
1397:
1396:
1386:
1376:
1374:
1364:
1361:
1358:
1351:
1350:
1348:
1346:
1344:
1334:
1331:
1328:
1324:
1323:
1321:
1319:
1317:
1307:
1304:
1301:
1298:
1291:
1290:
1288:
1278:
1276:
1266:
1263:
1260:
1253:
1252:
1242:
1232:
1222:
1212:
1209:
1206:
1199:
1198:
1196:
1194:
1184:
1174:
1171:
1168:
1161:
1160:
1158:
1156:
1154:
1144:
1141:
1138:
1131:
1130:
1127:
1124:
1121:
1120:Primitive (P)
1117:
1116:
1113:
1104:
1101:
1077:Pearson symbol
1072:
1071:
1068:
1065:
1062:
1036:
1033:
1030:
1029:
1023:
1014:
1001:
997:
990:
986:
973:
969:
968:
962:
953:
940:
936:
925:
921:
920:
914:
912:
901:
898:
888:
884:
883:
881:
879:
868:
865:
862:
858:
855:
845:
841:
840:
837:
834:
831:
783:
782:
780:
767:
764:
761:
760:Hexagonal (h)
757:
756:
754:
741:
738:
735:
731:
730:
719:
706:
703:
700:
696:
695:
693:
680:
677:
674:
670:
669:
666:
665:Primitive (p)
662:
661:
658:
649:
622:
619:
599:
596:
580:
575:
553:
550:
545:
541:
537:
534:
512:
507:
500:
496:
492:
487:
482:
475:
471:
467:
462:
457:
450:
446:
442:
438:
426:parallelepiped
381:
378:
343:
338:
331:
327:
323:
318:
313:
306:
302:
298:
293:
288:
281:
277:
273:
269:
252:Main article:
249:
246:
181:
173:
168:
167:
156:
151:
146:
139:
135:
131:
126:
121:
114:
110:
106:
101:
96:
89:
85:
81:
77:
52:, named after
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3754:
3743:
3740:
3738:
3735:
3733:
3730:
3729:
3727:
3712:
3711:
3702:
3700:
3699:
3690:
3689:
3686:
3676:
3673:
3671:
3668:
3664:
3661:
3659:
3656:
3654:
3651:
3650:
3649:
3646:
3645:
3643:
3639:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3614:
3612:
3610:
3606:
3600:
3597:
3595:
3592:
3590:
3587:
3586:
3584:
3582:
3578:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3538:
3536:
3534:
3530:
3524:
3521:
3519:
3516:
3514:
3511:
3509:
3506:
3504:
3501:
3499:
3496:
3494:
3491:
3490:
3488:
3486:
3482:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3437:
3435:
3433:
3429:
3423:
3420:
3416:
3413:
3412:
3411:
3408:
3406:
3405:Patterson map
3403:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3383:
3382:
3380:
3376:
3368:
3365:
3363:
3360:
3359:
3358:
3355:
3353:
3350:
3346:
3343:
3341:
3338:
3337:
3336:
3333:
3329:
3326:
3324:
3321:
3320:
3319:
3316:
3315:
3313:
3311:
3307:
3301:
3291:
3288:
3286:
3283:
3281:
3278:
3276:
3275:Friedel's law
3273:
3271:
3268:
3266:
3263:
3261:
3258:
3257:
3248:
3245:
3243:
3240:
3236:
3233:
3231:
3228:
3227:
3226:
3223:
3219:
3218:Wigner effect
3216:
3214:
3211:
3209:
3206:
3205:
3204:
3203:Interstitials
3201:
3197:
3194:
3193:
3192:
3189:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3141:
3140:
3137:
3135:
3132:
3130:
3127:
3126:
3117:
3114:
3112:
3109:
3107:
3104:
3102:
3099:
3098:
3096:
3094:
3090:
3087:
3085:
3081:
3075:
3072:
3070:
3067:
3065:
3062:
3060:
3057:
3055:
3052:
3050:
3049:Precipitation
3047:
3045:
3042:
3038:
3035:
3033:
3030:
3028:
3025:
3023:
3020:
3019:
3018:
3017:Phase diagram
3015:
3014:
3012:
3010:
3004:
2996:
2993:
2992:
2991:
2988:
2984:
2981:
2980:
2979:
2976:
2972:
2969:
2967:
2964:
2963:
2962:
2959:
2958:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2921:
2920:
2918:
2916:
2912:
2906:
2903:
2901:
2898:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2870:
2869:
2866:
2865:
2863:
2861:
2857:
2851:
2848:
2846:
2843:
2839:
2836:
2835:
2834:
2831:
2830:
2828:
2824:
2820:
2813:
2808:
2806:
2801:
2799:
2794:
2793:
2790:
2777:
2773:
2770:
2767:
2763:
2760:
2757:
2753:
2750:
2747:
2743:
2740:
2739:
2737:
2733:
2726:
2721:
2718:
2715:
2710:
2706:
2703:
2700:
2696:
2693:
2690:
2686:
2683:
2680:
2676:
2673:
2670:
2665:
2662:
2661:
2659:
2655:
2649:
2646:
2644:
2641:
2640:
2637:
2633:
2626:
2621:
2619:
2614:
2612:
2607:
2606:
2603:
2595:
2590:
2588:
2585:
2584:
2580:
2573:
2570:(in French).
2569:
2563:
2562:
2558:
2550:
2546:
2542:
2536:
2532:
2528:
2521:
2518:
2513:
2507:
2503:
2499:
2495:
2491:
2490:
2482:
2480:
2478:
2474:
2462:
2456:
2452:
2451:
2446:
2439:
2436:
2428:
2421:
2418:
2413:
2407:
2403:
2396:
2394:
2392:
2388:
2375:
2371:
2365:
2362:
2349:
2345:
2341:
2336:
2331:
2327:
2323:
2319:
2312:
2309:
2302:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2261:Crystal habit
2259:
2258:
2253:
2251:
2249:
2241:
2239:
2231:
2227:
2223:
2219:
2215:
2211:
2208:
2205:
2201:
2197:
2194:
2192:
2188:
2184:
2181:
2165:
2161:
2153:
2151:
2147:
2144:
2140:
2136:
2133:
2130:
2126:
2122:
2119:
2117:
2113:
2110:
2096:
2091:
2087:
2080:
2076:
2066:
2063:
2062:
2058:
2050:
2047:
2045:
2041:
2037:
2034:
2032:
2028:
2024:
2021:
2005:
2002:
1997:
1993:
1989:
1986:
1983:
1980:
1975:
1971:
1967:
1964:
1961:
1954:
1950:
1942:
1940:Rhombohedral
1939:
1937:
1933:
1930:
1923:
1916:
1909:
1906:
1903:
1899:
1895:
1892:
1890:
1886:
1883:
1869:
1864:
1860:
1852:
1850:
1846:
1843:
1836:
1829:
1826:
1823:
1819:
1815:
1812:
1810:
1796:
1793:
1790:
1783:
1781:
1777:
1774:
1767:
1751:
1748:
1745:
1741:
1738:
1736:
1722:
1719:
1716:
1712:
1709:
1706:
1699:
1697:
1693:
1690:
1679:
1667:
1653:
1651:
1649:
1633:
1630:
1627:
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1603:
1600:
1597:
1592:
1588:
1584:
1581:
1578:
1573:
1569:
1565:
1562:
1559:
1554:
1550:
1546:
1543:
1538:
1535:
1532:
1525:
1523:
1519:
1515:
1513:Axial angles
1512:
1509:
1506:
1503:
1500:
1499:
1496:
1494:
1490:
1486:
1480:
1476:
1472:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1420:
1416:
1412:
1408:
1404:
1395:
1391:
1387:
1385:
1381:
1377:
1375:
1373:
1369:
1365:
1359:
1356:
1349:
1347:
1345:
1343:
1339:
1335:
1329:
1326:
1322:
1320:
1318:
1316:
1312:
1308:
1302:
1300:Rhombohedral
1299:
1296:
1289:
1287:
1283:
1279:
1277:
1275:
1271:
1267:
1261:
1258:
1251:
1247:
1243:
1241:
1237:
1233:
1231:
1227:
1223:
1221:
1217:
1213:
1207:
1204:
1197:
1195:
1193:
1189:
1185:
1183:
1179:
1175:
1169:
1166:
1159:
1157:
1155:
1153:
1149:
1145:
1139:
1136:
1128:
1125:
1122:
1119:
1118:
1111:
1098:
1095:
1093:
1092:Face-centered
1089:
1088:Base-centered
1084:
1080:
1078:
1069:
1066:
1063:
1060:
1059:
1058:
1056:
1048:
1047:diamond cubic
1042:
1034:
1027:
1024:
1022:
1018:
1015:
999:
995:
988:
984:
974:
971:
970:
966:
963:
961:
957:
954:
938:
934:
926:
923:
922:
918:
915:
913:
899:
896:
889:
887:Orthorhombic
886:
885:
882:
880:
866:
863:
860:
856:
853:
846:
843:
842:
838:
835:
832:
829:
828:
825:
823:
819:
812:
808:
802:
798:
794:
790:
781:
777:
772:
768:
762:
759:
755:
751:
746:
742:
736:
733:
724:
720:
716:
711:
707:
701:
698:
694:
690:
685:
681:
675:
672:
668:Centered (c)
667:
664:
663:
656:
646:
643:
640:
636:
634:
628:
620:
618:
614:
610:
605:
597:
595:
578:
551:
548:
543:
539:
535:
532:
510:
498:
494:
490:
485:
473:
469:
465:
460:
448:
444:
440:
427:
422:
420:
416:
412:
408:
404:
400:
394:
392:
388:
379:
377:
373:
369:
367:
361:
357:
341:
329:
325:
321:
316:
304:
300:
296:
291:
279:
275:
271:
255:
247:
245:
243:
239:
234:
232:
228:
224:
220:
216:
212:
208:
204:
200:
195:
193:
189:
184:
180:
176:
154:
149:
137:
133:
129:
124:
112:
108:
104:
99:
87:
83:
79:
67:
66:
65:
63:
59:
55:
51:
47:
43:
34:
30:
19:
3737:Tessellation
3708:
3696:
3641:Associations
3609:Organisation
3101:Disclination
3032:Polymorphism
2995:Quasicrystal
2938:Orthorhombic
2878:Miller index
2872:
2826:Key concepts
2722:(isometric)
2685:orthorhombic
2642:
2571:
2567:
2530:
2520:
2488:
2464:. Retrieved
2448:
2438:
2420:
2401:
2378:. Retrieved
2373:
2364:
2352:. Retrieved
2348:the original
2328:(1.1): 2–5.
2325:
2321:
2311:
2276:Miller index
2245:
2236:
2218:copper metal
2203:
2199:
2195:
2190:
2186:
2182:
2128:
2124:
2120:
2115:
2111:
2043:
2039:
2035:
2030:
2026:
2022:
1901:
1897:
1893:
1888:
1884:
1821:
1817:
1813:
1780:Orthorhombic
1743:
1739:
1492:
1488:
1484:
1478:
1474:
1470:
1462:
1458:
1454:
1450:
1446:
1442:
1438:
1434:
1430:
1426:
1422:
1418:
1414:
1410:
1406:
1400:
1393:
1383:
1371:
1341:
1314:
1285:
1273:
1249:
1239:
1229:
1219:
1203:Orthorhombic
1191:
1181:
1151:
1106:Point group
1091:
1087:
1082:
1081:
1073:
1052:
1025:
1020:
1016:
964:
959:
955:
916:
839:Axial angle
821:
817:
810:
806:
796:
792:
788:
786:
651:Point group
638:
637:
630:
615:
611:
607:
423:
418:
414:
410:
406:
402:
398:
395:
390:
386:
383:
374:
370:
365:
362:
358:
257:
242:space groups
235:
231:solid matter
214:
210:
206:
198:
196:
191:
187:
182:
178:
171:
169:
49:
39:
29:
3594:Ewald Prize
3362:Diffraction
3340:Diffraction
3323:Diffraction
3265:Bragg plane
3260:Bragg's law
3139:Dislocation
3054:Segregation
2966:Crystallite
2883:Point group
2752:rectangular
2666:(anorthic)
2445:"Chapter 1"
2214:zinc blende
924:Tetragonal
844:Monoclinic
715:Rectangular
229:strings of
3726:Categories
3378:Algorithms
3367:Scattering
3345:Scattering
3328:Scattering
3196:Slip bands
3159:Cross slip
3009:transition
2943:Tetragonal
2933:Monoclinic
2845:Metallurgy
2695:tetragonal
2675:monoclinic
2411:0030839939
2303:References
2064:Hexagonal
1849:Tetragonal
1696:Monoclinic
1327:Hexagonal
1257:Tetragonal
1165:Monoclinic
972:Hexagonal
602:See also:
170:where the
3485:Databases
2948:Triclinic
2928:Hexagonal
2868:Unit cell
2860:Structure
2772:hexagonal
2664:triclinic
2330:CiteSeerX
2296:Zone axis
2006:α
2003:
1984:α
1981:
1965:−
1936:Hexagonal
1908:White tin
1723:β
1720:
1634:γ
1631:
1625:β
1622:
1616:α
1613:
1601:γ
1598:
1585:−
1582:β
1579:
1566:−
1563:α
1560:
1547:−
1522:Triclinic
1429:), where
1295:Hexagonal
1135:Triclinic
867:θ
864:
776:Hexagonal
536:≤
254:Unit cell
248:Unit cell
223:molecules
3698:Category
3533:Journals
3465:OctaDist
3460:JANA2020
3432:Software
3318:Electron
3235:F-center
3022:Eutectic
2983:Fiveling
2978:Twinning
2971:Equiaxed
2574:: 1–128.
2529:(1978),
2466:21 April
2380:8 August
2354:21 April
2254:See also
2135:Graphite
2057:cinnabar
1483:, where
816:, where
814:‖
804:‖
42:geometry
3710:Commons
3658:Germany
3335:Neutron
3225:Vacancy
3084:Defects
3069:GP-zone
2915:Systems
2742:oblique
2549:0484179
2250:pairs.
2226:Diamond
2131:= 120°
2127:= 90°,
2049:Calcite
1507:Volume
1049:lattice
1028:= 120°
689:Oblique
227:polymer
203:crystal
56: (
3653:France
3648:Europe
3581:Awards
3111:Growth
2961:Growth
2762:square
2547:
2537:
2508:
2457:
2408:
2376:. IUCr
2332:
2230:Silver
2206:= 90°
2059:(HgS)
1904:= 90°
1824:= 90°
1746:= 90°
1491:, and
1453:, and
967:= 90°
919:= 90°
750:Square
525:where
3675:Japan
3622:IOBCr
3475:SHELX
3470:Olex2
3357:X-ray
3007:Phase
2923:Cubic
2720:cubic
2430:(PDF)
2150:Cubic
2051:(CaCO
1770:PbCrO
1355:Cubic
1083:Note:
833:Area
779:(hp)
753:(tp)
729:(oc)
718:(op)
692:(mp)
639:Note:
225:, or
219:atoms
215:basis
211:motif
207:basis
190:, or
3617:IUCr
3518:ICDD
3513:ICSD
3498:CCDC
3445:Coot
3440:CCP4
3191:Slip
3154:Kink
2535:ISBN
2506:ISBN
2468:2008
2455:ISBN
2406:ISBN
2382:2019
2356:2008
2210:NaCl
1926:CaSO
1839:BaSO
1762:·10H
1670:CuSO
1461:and
1449:and
1437:and
1357:(c)
1297:(h)
1259:(t)
1205:(o)
1167:(m)
1137:(a)
820:and
801:norm
791:and
564:and
549:<
413:= 1/
186:are
58:1850
48:, a
44:and
3632:DMG
3627:RAS
3523:PDB
3508:COD
3503:CIF
3455:DSR
3179:GND
3106:CSL
2498:doi
2340:doi
2222:KCl
2143:CdS
2139:ZnO
2055:),
1994:cos
1972:cos
1919:TiO
1912:SnO
1832:KNO
1717:sin
1674:·5H
1628:cos
1619:cos
1610:cos
1589:cos
1570:cos
1551:cos
1473:· (
1394:cF
1384:cI
1372:cP
1342:hP
1315:hR
1286:tI
1274:tP
1250:oF
1240:oI
1230:oS
1220:oP
1192:mS
1182:mP
1152:aP
861:sin
366:and
209:or
40:In
3728::
3670:US
3663:UK
2572:19
2545:MR
2543:,
2504:.
2496:.
2476:^
2447:.
2390:^
2372:.
2338:.
2326:A1
2324:.
2320:.
2228:,
2224:,
2220:,
2216:,
2212:,
2202:=
2198:=
2189:=
2185:=
2141:,
2137:,
2123:=
2114:=
2042:=
2038:=
2029:=
2025:=
1924:,
1917:,
1910:,
1900:=
1896:=
1887:=
1837:,
1830:,
1820:=
1816:=
1768:,
1758:SO
1754:Na
1752:,
1742:=
1686:BO
1680:,
1668:,
1659:Cr
1487:,
1477:Ă—
1441:,
1425:,
1421:,
1413:,
1409:,
1332:6h
1305:3d
1264:4h
1210:2h
1172:2h
1112:)
1019:=
958:=
809:Ă—
657:)
421:.
407:nv
221:,
2811:e
2804:t
2797:v
2624:e
2617:t
2610:v
2596:.
2514:.
2500::
2470:.
2414:.
2384:.
2358:.
2342::
2204:Îł
2200:β
2196:α
2191:c
2187:b
2183:a
2166:3
2162:a
2129:Îł
2125:β
2121:α
2116:b
2112:a
2097:c
2092:2
2088:a
2081:2
2077:3
2053:3
2044:Îł
2040:β
2036:α
2031:c
2027:b
2023:a
1998:3
1990:2
1987:+
1976:2
1968:3
1962:1
1955:3
1951:a
1928:4
1921:2
1914:2
1902:Îł
1898:β
1894:α
1889:b
1885:a
1870:c
1865:2
1861:a
1841:4
1834:3
1822:Îł
1818:β
1814:α
1797:c
1794:b
1791:a
1772:3
1766:O
1764:2
1760:4
1756:2
1744:Îł
1740:α
1713:c
1710:b
1707:a
1688:3
1684:3
1682:H
1678:O
1676:2
1672:4
1665:7
1663:O
1661:2
1657:2
1655:K
1607:2
1604:+
1593:2
1574:2
1555:2
1544:1
1539:c
1536:b
1533:a
1493:c
1489:b
1485:a
1481:)
1479:c
1475:b
1471:a
1463:b
1459:a
1455:Îł
1451:c
1447:a
1443:β
1439:c
1435:b
1431:α
1427:Îł
1423:β
1419:α
1415:c
1411:b
1407:a
1362:h
1360:O
1330:D
1303:D
1262:D
1208:D
1170:C
1142:i
1140:C
1108:(
1026:θ
1021:b
1017:a
1000:2
996:a
989:2
985:3
965:θ
960:b
956:a
939:2
935:a
917:θ
900:b
897:a
857:b
854:a
822:b
818:a
811:b
807:a
797:θ
793:b
789:a
765:6
763:D
739:4
737:D
704:2
702:D
678:2
676:C
653:(
579:i
574:a
552:1
544:i
540:x
533:0
511:3
506:a
499:3
495:x
491:+
486:2
481:a
474:2
470:x
466:+
461:1
456:a
449:1
445:x
441:=
437:r
419:n
415:n
411:v
403:v
399:n
391:m
387:m
342:3
337:a
330:3
326:n
322:+
317:2
312:a
305:2
301:n
297:+
292:1
287:a
280:1
276:n
272:=
268:R
183:i
179:a
174:i
172:n
155:,
150:3
145:a
138:3
134:n
130:+
125:2
120:a
113:2
109:n
105:+
100:1
95:a
88:1
84:n
80:=
76:R
20:)
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