Crystal Structure Refinement of Arsenian Ullmannite

American Mineralogist, Volume 62, pages 369-373, 1977

Crystal structurerefinement of arsenianullmannite

Psrsn Bnylrss Departmentof Geology,Uniuersity of Calgary Alberta T2N lN4. Canada

Abstract

A crystalstructure refinement of a pseudo-cubic[a : 5.886(l)A]arsenian ullmannite (Nio.r'cooor)(Sbo.r'Aso osBio olXSo ,rAso.or) showed that the arsenicis concentratedin oneof the four Sb sitesand in oneof the four S sites.This orderingreduces the symmetry P2,3 to pl, and explainswhy the mineralis anisotropic.

Introduction wasanalyzed by electronmicroprobe as describedby The spacegroup of ullmannitehas been deter- Stoutand Bayliss(1975). The analyticalresults and mined as P2,3 by Ramsdell(1925) and confirmedby derived chemical formula based upon a 4 AXY Peacockand Henry(1948), and Bokii andTsenokev modelare presented in Tablel. This4 AXY modelis (1954).The structureof ullmannitehas been refined used,since the synthetic work of Bayliss(1969) shows by Takeuchi(1957) and its absolutestructure deter- that As may substitutesubstantially for Sb and S in mined.The Sb is orderedinto one setof four sites, the NiSbSformula of ullmannite,although Sb does whereasthe S is orderedinto the other set of four not substitutefor S and vice versa. sites.Optical observationsby Klemm (1962) in- A 114.6 mm Debye-Scherrerphotograph was dicatedthat sevenout of eightspecimens contained taken with Cu radiation/Ni filter. All reflectionsare ahisotropicareas in a polishedsection. Since un- indexableon a cubiccell, although the observedre- strainedcubic mineralscannot be anisotropic,an flection 100violates space group P23. A unit cell with : anisotropicspecimen of ullmannitehas been in- c 5.901A was calculatedby the Nelsonand : vestigatedby single-crystalX-ray diffractionto deter- Riley (1945)extrapolation method to 0 90o. A mineits symmetry. crystalwith dimensionsof 68 X 84 X 90 pm was selectedbecause of its well-developedcube form Experimental {100}. This crystalwas aligned on a precessioncamera A sampleof arsenianullmannite (BM88503) from with Cu radiation along an a* axis. Photographs Petersbach,Hamm, Westphalia,Germany was ob- hkl andftOl showed no systematicabsences or devia- tained from Mr. PeterEmbrey of the British Mu- tion from a cubic cell. Thereforethis mineral is seum.This samplewas found to be distinctlyweakly pseudo-cubiclike cobaltite(CoAsS) as shown by anisotropic under reflectedlight. Then the sampl! Gieseand Kerr (1965),and willyamite(CoSbS) as shownby Cabri et al. (1970). Table l. Electron microprobe analysisand atomic proportions Table2.Positional parameters and isotropic Weight 7" Atouric Proportlons temperaturefactors

Ni 27.3 o.e7J Co 0.8 1.00 Atom Site c s (82) 0.03J Occupancy Sb 52.8 1.00 l'1 1.0 Nl Ni o.97 -.0171(1) 0.6s(2) Co 0.03 As SS 0.98 ,3877(2) 0.80(3) 1.00 4D 0.02 s 15.1 Sb As 0.08 .6256(7) 0.62(r) Sb 0.91 Total 100.5 Bi 0.01

369 370 BAYLISS: STRUCTURE REFINEMENT OF ALLMANNITE

Table3. Observedand calculated structure factors

'L .LFoFc LFo Fo fc LFoFc LFaFc LFoFc LFoFc LFaFc LFaFC LFAFC 0403943L321605E h=0 k-o L 28 21 2 100 100 -2 12 I\ -3 80 78 -2 63 64 7 51 53 h- 4 k=-7 14848 -l 29898 ! 24 23 h-5 k=6 2 22 21 141 2 70 6a 3I37130 -l 49 49 -2 23 11 -L 26 24 h=3 k'o 29 30 -1 34848 25657 -2 9 9 35249 2 142 97 3 19 18 4 54 5r O 7l 78 -1 95100 0 32 30 20 21 0 1 1 36570-r4342416I0 341 410r0 59796 15150 09493 12724 '66365 r2929 4222r 4 Lg L5 o 44 L3 h'6 k=5 49892 h=o k=8 6 53 52 2 L2 12 I 94 97 2 62 63 -5 40 40 h=4 k--6 5t815 -4 -4 lE 65861 55658I4443-21514 5152 -2 lg 20 I 11 n 3 42 40 2 2l 14 3 20 18 28 2a 19 -I -3 h=5 k'-Z 2 9 8 45 46 63433 -1 27 27 8 21 21 4 59 60 3 83 81 4 24 24 -3 61 61 21 2l -2 -2 -6 14 13 h= 6 k'-5 0 45 45 742 0 98 96 h=I k-o 5 47 48 L 45 44 5 14 13 56 55 23 23 -1 -I -6 25 25 -54A49 -2L312 14645 8 104 101 L 2a 27 -8 28 30 h=I k=J 5 65 64 h=2 k'J l0 23 53 53 -5 43 -46563 -14948 214!3 l=0 k=1 2 18 18 -1 32 30 -4 4 2 6 16 13 -3 45 45 0 9 3 0 21 2A 41 -4 -3 57 56 o 41 L5 h= 1 k=-L .-8 5 5 h=7 k=-A -6 18 18 -l 51 51 7 48 50 -2 12 8 t 3t 20 I 54 55 39 38 -3 62 -2191314948-r33 -1 47 4A -1 21 20 _5 39 38 -2 LB 48 h-2 k=O -1 40 40 2 5a 56 2 25 25 6A -2 16 46 -160622L4r10109 -5 82 8l o 7 4 -L 23 22 -1 17 17 -8 23 2r O 46 46 3 64 62 3 20 20 0 88 87 h-6 k=-4 | 2 2 -5 70 68 r 22 22 -3 65 62 o 46 45 -7 68 11 L 40 39 4 21 26 4 18 18 04950 1 63 64 -4 16 L6 h= 1 k=-3 -4 I 3 h-I k--1 -2 9t 94 1 16 1s -6 34 33 2 Lr 7 5 42 4A h-4 k=-5 -3 -53436 r4214 2L7 12 -35!52 11 1l -3 23 22 -4 4 L -153 41 247 46 -5889A 34444 66565 -24445 '1 2 4l 49' 357 56 -22324 -2 r35 115 -3 53 51 A 2 I 3 50 50 -4 53 57 h=2 k-8 1 2A 19 A 9 -3 16261 -16160 -15050 -L 50 49 -2 4l 44 L 54 50 4 4 2 -31lll1o 0 22 19 h=3 k=t L3 14 35960 -2 s4850 a2128 01818 031 -1 18 17 2 ga s4 h'1 k-8 -2 82 18 h=3 k'-1 -7 51 51 65 64 43931 -L 6!2131626115151 14750 a 46 45 3 66 6r -I 2A 20 -1 r38 134 -3 L2 \O -6 44 14 25 24 54T47 h-5 2 135 135 r 18 L8 4 22 2A O 1 5 0 90 9r -2 45 44 -5 25 24 0 18 18 62424 k=3 .-6414a3535331212 32124 2 49 48 5 42 39 1 20 19 rr41L34 -r 51 5t -4 38 16 1 26 25 h=4 -3 -6 54 54 -5 26 26 4 17 17 h' 7 k'-2 3 54 53 6 18 17 h=2 k.-8 2 82 76 O 2 2 27 27 2 67 65 -3 -2 -5 46 47 -4 26 26 h= 6 k=-3 43 43 5696E 4 3 r 7 32 29 0 22 19 3r14ll0 t 51 52 85 A1 3 L5 L7 -2 -Ir2l13O -4 14 14 .-32322 -42121 9 1 68180 h=I k=-6 a 29 29 h=2 k--7 4 55 53 2 46 46 4 9 10 -t -3 2A -2 53 52 -l 48 49 45 4b -5 48 48 l=I l-I i 45 44 5 90 90 3 13 L2 o 6L 50 5 33 36 20 -2 89 91 -19092-2181806867 854 -4 61 60 -8 20 21 -2 M 6 35 34 h' J k=-6 | I25 r29 h= 4 k=-4 _6 -r 35 35 04141-1414014546 h-O k-2 -3 43 Ll -7 18 t9 -1 41 40 7 71 7! -4 53 53 2 84 a6 18 17 _5 26 79192 06364 2 1 5 -8 L9 20 -2 15 tL -6 5t 50 O 46 46 I 22 2A -3 50 49 3 26 27 9 E 021 -4 25552!424r34545 -7 48 50 -r 51 50 -5 gg 97 L 42 42 h=2 k-1 -2 8 7 4 3A 37 65 65 -3 281 90 3 2L 23 2 18 19 h=1 k=-r -6 32 32 o ll l1 -4 52 49 2 11 6 -1 48 50 -1 50 49 5 22 22 13 13 -42929 '2 42525 34850 -5 37 35 1 52 50 -3135132 I 45 45 -6 17 13 A 16 76 6 4L 42 37 36 31920 'L 41313 524254192r-35150 -4 53 s3 2 14 13 -2 96 97 h=2 k=-6 -5 65 64 7 49 49 t 50 52 23 22 -2 54645 6 41 49 h= 6 k=-2 39 3a -3 56 56 3 44 43 -I 41 47 -5 15 13 -4 46 45 2 I t h=3 k= 2 0150153 -l -7 65453 h-5 k-o -5 9 9 Ll 11 -2 81 80 4 63 63 0 48 48 -4 22 23 i 8A 79 3 53 52 44 46 1 24 22 -6 .-61648 -42321 03027 -r 95 94 5 50 50 r 4a 47 -l 21 1E -2 24 \4 4 54 55 2A 2A 2 41 3l -6 L8 17 -51910-37611919 09691 h= 7 k=-5 2 94 9l -2 64 64 -t 95 96 h= 3 k=-5 -5 59 57 3 13 13 -4 -5 t0 10 -41818-2626524034 1E993 -6 44 42 3133133 -l 26 25 0 91 94 -5 55 56 91 93 4 65 67 -4 65 65 -32017-113r135150 2 72 15 :5 25 25 4 50 41 o 35 33 I 93 98 -4 44 45'3 64 65 5 1t l0 -3 14 13 -234360343243030 35657 -4 r4 14 5 96 95 r 21 26 2 20 13 -3 66 68 -2 L6 16 6 19 18 -I --1 59 65 I 14 13 h=l k=0 45452 -3 23 21 6 50 51 2 65 65 3 7a 18 -2 51 57 16 1a h=4 k-'3 -4 -6 -L 21 19 0 3 | 26365 A 6 53136 -2 66 64 7 19 18 3 23 2L 4 43 44 -l 24 23 0106r08 54 53 -3 -5 0 144 r49 \7167 3 E 8 3 l 63532 -1 94 93 I 2r 21 4 21 25 5 65 65 0 19 15 7 12 7a 47 41 -247 -4 23616 42324 4b 7 5041 A 6A 6J h=! k=2 5 t5 15 6 16 15 I 26 25 2 15 L6 14 Ll r212A -l 23535 3201551010-r4746 81919 7 96 94 -1 42 42 h=2 k=-5 1 46 48 2 58 57 I 65 66 20 20 '2 1l 12 4 19 18 h-6 k=-L 0 3 ? h=0 k=3 2 68 64 -6 26 26 -6 11 8 h=2 k=2 3 6a 69 4 81 90 86 90 3 3 25 24 -5 56 54 -5 41 48 -7 10 I 4 47 48 5 58 56 -1 35 36 4636) 52010-5454514a46 64646-4515324145 -6 80 80 4 14 14 -410110r -4 39 4L -6 65 61 5 57 60 6 20 18 A 26 24 588 h=5 k=I -3 50 49 3 4 2 -5 r1 11 5 25 24 _3 85 87 -3 55 56 -5 13 11 h 1 k=-4 7 46 45 I 1A 31 51817 k=5 -64848-22626415 -4 5 4 6 47 48 -2 16 15 -2 t] 13 -4 41 47 -6 19 20 h-3 k=3 2 89 9l h=4 -5 36 -5 26 26 -1 50 50 h-l k=I -3 63 67 h- I k=-4 -l 96 98 -l 54 53 -l 17 16 -5 16 16 -1 11 13 3 21 22 34 -4 10 Ll --42524 o t7 17 -4 29 2A -2 113 110 -7 29 29 O !)2 r34 0 35 36 -2 110 114 '4 12 12 -6 51 52 4 15 15 _5 .-3242314949-35149 -I 62 61 -.6 54 55 1 91 99 1 55 53 -1 18 15 -3 20 22 66 68 5 41 48 -2 63 62 --25551225r\-24140 442 -5 24 25 2 15 15 2 16 11 O 7A 19 -2 60 62 -4 20 21 6 54 54 -r11 -r 24 24 --I 93 94 I 52 50 r7 15961 -4 ?6 22 3 81 84 3 58 58 1 17 11 -I 48 48 -3 88 9L h=1 k=-2 '6 01818 O Jb 17 * 5l 54 0 r0 2E 2 105 109 -3 )6 37 4101100 1 41 43 2106l14 o 12 1 -2 62 6f 23 24 -5 r 90 91 5 4) L\ r 16 16 -2 43 43 5 56 51 5 48 50 3 L5 14 1 50 48 -\ 26 27 42 42 12625 35961 -4 2 54 5I h=6 k=o 2 41 40 -r 47 46 6 26 25 6 11 g 4 41 41 2 67 6l O 58 59 40 f6 26361 31414 12423 -54545 35249 5 15 15 410r0 42425 -q2a28 42828 68117 51334 5 24 25 -3 16 l5 h=1 k=2 722 64149-21131-34443 -1 -2 l .4 IJ 16 h=5 k=2 19 76 9 -7 8 8 -141 46 -3 20 20 -6 15 t4 O l1 ll -6 29 29 bb -2 24 24 -5 4949 1 81 76 0 67 -5 19 19 -L 51 52 ..4646323632r4345 -4 r53 156 6 5 02128 -3 58 57 371 75 2 -3 27 26 14343 15151 --277 L7 42A27 -2 53 52 k'1 2232J -l 61 62 5 48 45 h=7 -r 23 22 -3 14 13 )2120 O 81 86 h=6 k=l 0 91 91 -2 -6 62 477\6 16051-54443-243q2 12120 4 11 41 ) 25 ?1 5 66 67 I 80 8l 0 62 6r 6a 6r 61 -I49 4A 2 L5 1O -45555 25152 -l 27 28 35755-1504801920 32124 -2 49 081 1t65 $ 26 25 1 49 4 143 15r r2427 54A49-149412424L 518r8 61414017183I01r 62421 -2aE h=5 k=3 I 49 48 h=1 k=4 777 -1 45 44 --5565622626-112 h=O k-5 .-12!163494701211 -6 41 4a 14445 -.364654545411? -5 ll 12 k=-2 298 -2 55 55 5 43 43 h= a -I 24 23 h=6 k=2 O 2l 11 -t 41 39 -5 k=-I -4 f4 35 0 38 39 10 t h=8 -2 90 89 12222-42525-12020 -r 37 37 -2 4a 47 25455-1119o2826 o12 2 -26264 -r 26 25 36465 12220 t4019 -1 k=0 01912 q 2l 11 13 l0 l=8 28687 -22218 r2524 5 55 55 0 31 29 t1838 -1 6 ! 25049 h=5 k=4 I 12 12 499 09492 35651 --53435 26264 5IIL2 41637 -41010198175 64645 219 r8 h- 5 k--4 --34641 42524 h=o k=6 k=r -5 32 3) -2 42 43 5 9 8 h=8 -5 48 48 -1 21 20 -4 10 10 _t \2 12 h-6 k=3 -4 29 29 -3 44 47 089-4r9r902726 -3 66 65 -349 22 -2 42 44 lr2L2 49 123 -2 3t 3r -2 k=2 -L 13 13 2 39 4I L9 19 h'A -1 17 Ll -L -5 9 11 099 34546-r444202219 03232 7 48 4r -r 94 95 1 r8 13 50 5L 23 23 1 48 4E 5 -4 28 11414 49806062 l17rl h=1 k=-r o 65 64 2111116 0 J3 34 16 36 2 I 6 6 28 -3 242q) 5333414140 2f232 -a 22 23 r 94 93 I 17 15 r 52 5r 29 29 3 48 48 I 12 ra -2 h=5 k=5 2 19 19 -7 16 !6 2 62 62 4 51 51 2 16 13 81 8l 4 51 51 h'1 k=r 34541 36462 -1124128 -7 -.4343434949 -6 52 51 3 24 23 5 14 12 3 54 55 h=3 k=7 4 2 499 42128 -6 -3555641818 -5 96 95 4 13 13 6 61 61 4 41 42 o 64 6r _3 14 13 60 60 53436 -2 -5 h= 5 k=-3 -2 41 46 h=6 k=q k=7 -4 52 49 5 25 25 1 9 1 5 15 46 1130133 41 43 ]9 14 h=O -4 -r 24 24 -4 r7 16 -4 t2 11 l13tt3o 6 43 44 h=2 k=-1 6 10 9 2 83 83 1 49 50 21 2l -l -4 22 16 01811-35251 -3 20 20 -2 95 99 h-r k-6 -7 41 48 h=2 k=6 3 ?1 2a 0 4 2 49 50 -2 t2524-22423 -2 70 lo ..t 46 48 -5 49 50 -6 18 14 -5 15 14 4 35 35 l. 50 50 99 99 -r -2 55 24646-15957 -1 52 51 -4 6L 6l -5 66 65 -L 25 26 5 25 26 ? 42 42 49 a9 54 28 28 0 1545502727 042 1 4L 45 -1 45 43 -4 46 45 -3 2L 19 6 42 42 3 12 l0 0 22 ?3 BAYLISS: STRUCTURE REFINEMENT OF ULLMANNITE 371

Table4.Positionalparameters,anisotropictemperaturefactors(xlCf)andextinctionparameter

Atom Site R R -33R '72RAA '13 '23 rT -22 0ccupancy

Ni1 Ni 0,97 - .or74 (4) -.0162(4)-.0179(4) 60(s) 39(s) s0(5) 4(4) 7(4) 7(4) LO U.UJ N1, Ni 0.97 (4) -2(4) - .516s .01-84(4).4841(4) s0(5) 38(s) ss(s) 2(4) s(4) Co 0.03 Nir Ni 0.97 . (4) -2(4) - 481r. .5170(4) .0164(4) sl(s) 4s(s) 47(s) 2(4) 9(4) Co 0,03 Nla Nt 0.97 (4) (4) (s) (s) (s) -2(4) ' .0163 .4833 .sr7r(4) s4 36 47 4(4) 2(4) Co 0.03 s] s 0.99(1) . (8 -13(8) - 3818 ) .3829(8) .381s(8) 73(1r.)47(10) s2(r0) 3(8) 8(8) As 0.01 S, S (8) -11(8) -4(8) - 1.00(1) . r-200 .6200(8) .8815(8) 6e(11)40(r.0) s0(10) 0(8) As 0. s1 s 0.95(1) - .8816(8) .1193(8) .6186(8) 76(10)63(10) 6s(r0) 11(8) 4(8) 12(8) As 0.05 s/ s 1,00 (8) - .618e .883s(8) .118s(8) 73(11)41(10) 49(10) 9(8) 6(8) 1(8) As o. Sb' es 0.04(1) (3) - .6249 .6266(J) .62s9(3) 48(3) 39(3) 49(3) 0(2) 6(2) 6(2) sb 0.96 Bi 0.00(1) Sbr As 0.06(1) - .8736(3) .3744(3) .12s5(3) 50(3) 40(3) 48(3) r(2) 3(2) 4(2) sb 0.91 Bi 0.03(1) Sb. As 0.03(1) -1(2) - ,1256(3) .8748(3) .3743(3) 52(3) 38(3) 48(3) 3(2) 6(2) sb 0.96 Bi 0.01(1) Sb, As 0.20 -1(2) - .3744(3) .L262(3) .874s(3) 46(3) 32(3) 42(3) 5(2) 3(2) sb o.8o Bi 0.00

Extinctlon parameter -0.000002

This crystalwas aligned along an a* axison a four- The extinction factor described by Zachariasen circle diffractometerwith reflections800, 800 and (1967) and extendedby Coppensand Hamilton 080.A least-squaresanalysis of20 high 2d reflections (1970)was calculated.From four quadrants,1186 gavea cubiccell of 5.886(l)4.Integrated intensities symmetry-independentreflections were measured of all reflectionsfrom four quadrantswere collected and I 185were observed above the lo level.All reflec- with MoKa radiation and a graphite002 mono- tions,except if lF'"-f"l is greaterthan 8, wereincluded chromator.A scanningspeed of l/2. 20per minute in the refinementof the crystalstructure by the least- wasused in the o-20 scanmode within a 60 to 6oo?i squaresprogram (RnnINn 2) of Finger(Carnegie In- range.Twenty-second background counts were made stitution,unpublished report, 1972).All observations beforeand aftereach reflection. A standardreflection wereweighted according to w : I f op2,whercop is the was measuredafter every50 reflections. standarddeviation based on countingstatistics. Ini- Sincethe spacegroup P2,3 requires the systematlc tial positionalparameters were taken from Takeuchi absencesof /,00 with ft odd, 0k0 with k odd, and 00/ (1957).The neutral atomic scatteringfactors and with / odd, the possibilitythat thesereflections were anomalousdispersion corrections were taken from observedbecause of the Renningereffect was in- the International Tablesfor X-ray Crystallography vestigated.The intensityand backgroundof four re- (1974).The datawas first refinedin spacegroup P2,3 flections(0k0 with k odd from k : I to /c = 7) were to an R factorof 0.041.The atomiccoordinates and measuredas the crystalwas rotated about the scatter- temperaturefactors are listedin Table 2. ing vector.This test confirmpdthat thesereflections This R factorindicates that the structureis basi- are not causedby the Renningereffect. callycorrect, but spacegroup P2r3requires system- Background,Lorentz polarization, and absorption atic absences.From this group all l2 reflectionswere correctionswere made following the method of recordedabove the 2o level.The only spacegroup Wuenschand Prewitt(1965). The linearabsorption which allows all reflectionsto be observedwith this coefficientof arsenianullmannite is 239 cm-r and crystal structureis Pl. This is similar to the crystal resultsin transmissionfactors between 0.14 and0.2'7. structureof gerdorffite,NiAsS (Baylissand Ste- 5tz BAYLISS: STRUCTUREREFINEMENT OF ULLMANNITE

Table5. Interatomicdistances and angles Table 6. R, for different crystal structure models

Atom nistance (8) angle (o) P 2r1 - (lsotropic (aolsotropLc Ni-S 2.3s 2.39 S- Ni- s 100 teqerature tempelature Nl-Sb 2.s3- 2.54 D- Ni- Sb 83 and 85 factors) factola) s -sb 2.49- 2.sL JO- Ni- sb 91 Ni- J- Nl 7t7 Nunber of 65 Ni- sb- Ni LI7 varlables 5- sb 101 NuDber of 1767 1171 LL7 6 Ni- sb- s 101 Reflectiona R, 4.3 4,r 3.8

phenson,1968). The data werethen refinedin this spacegroup initially with isotropictemperature factors.The Co wasdistributed uniformly over the four odd, and00/ with / odd),(3) a greaterthan 3o move- Ni sites,because of their similarsize and scattering ment of some atomic coordinatesfrom the cubic characteristics.The occupanciesof the four S sites crystalstructure to the triclinic crystalstructure, and were varied within the restraintsimposed by the (4) a significantreduction of R, at the 0.005level. chemicalcomposition. The S content of three sites The decreasein symmetryis attributeddirectly to was variedwith the S contentof the fourth site reset the preferentialoccupancy of As in sitesSr and Sbn so that the total S contentremained constant. In (Table4). Thereare no significantvariations of inter- additionthe As contentof thesefour S siteswas reset atomicangles between the cubiccrystal structure and so that each site had an occupancyof exactlyone, the triclinic crystal structure,and only small varia- (Table whichalso meant that the total As contentremained tionsof interatomicdistances 5). constant.Similarly the occupanciesof the four Sb siteswere varied within the restraintscomposed by Acknowledgment the chemicalcomposition. Financial assistance was provided bv the National Research Finally anisotropictemperature factors were used Council of Canada. with a seriesof site occupancyleast-squares cycles. The data was finally refinedto an R factor of 0.034. References Table 3 containsthe observedand calculatedstruc- ture factors;Table 4 containsthe atomiccoordinates Bayliss,P. (1969) Isomorphous substitution in syntheticcobaltite and temperaturefactors; and Table 5 containsthe and ulfmanniteAm. Mineral 54,426-430. - and N. C. Stephenson(1968) The crystalstructure of gers- interatomicdistances and ansles. dorffhte(III), a distortedand disorderedpyrite structure.Mur- eral. Mag. 36,940-94'1. Bokii, G. B. and L. I. Tsenokev(1954) X-ray examinationof Discussion cobaltite,gersdorffite and ullmannite.Trudy Inst. Kristallogr. Of the twelve reflectionslisted in Table 3 which Akad. Nauk. SSSR9, 239.[Abstr. C.A. 48, 13553H,. violatethe systematicabsences of spacegroup P2,3, Cabri, L. J., D. C. Harris,J. M. Stewartand J. F. Rowland(1970) Willyamiteredefined. Aust. Inst. Min. Metall.Proc.233,95-100. ten have Fo) F. whereasonly two haveFo < ,F".If Coppens,P. and W. C. Hamilton (1970)Anistropic extinction this systematictrend is real, there appearsto be no correctionsin the Zachariasenapproximation. Acta Cryslallogr. logicalexplanation. A26,7l-83. Table 6 givesa list of R. (weightedR factor), Giese,R. F. Jr. and P. F. Kerr (1965)The crystalstructures of number of observedreflections, and number of pa- orderedand disorderedcobaltite. Am Mineral.J0, 1002-1014. Hamilton,W. C. ( 1965)Significance tests in thecrystallographic R rametersin orderto usethe significancetest described factor.A cta Crystallogr.18, 502-510. by Hamilton (1965).The reductionof R, is signifi- Interuat.ionalTables for X-ray Crystallography(1974) Vol. IV. Ky- cant at the 0.005level between the cubiccrystal struc- nochPress, Birmingham. ture and the triclinic crystalstructure. Klemm, D. D. (1962)Anistropieeffekte bei kubischenErzminera- Evidencewhich supportsthe conclusionthat this lien, NeuesJahrb. Mineral. Abh. 97, 33'l-356. Nelson,J. B. and D. P. Riley(1945) An experimentalinvestigation arsenianullmannite is triclinic (pseudo-cubic)in- of extrapolationmethods in the derivationof accurateunit-cell cludes(1) opticalanisotropy, (2) presenceof forbid- dimensionsof crystals.Proc. Phys Soc.57, 160-177. den reflectionsfor P2,3 (ft00with ft odd, 0k0 with k Peacock,M. A. and W. G. Henry (1948)The crystalstructure of BAYLISS: STRUCTURE REFINEMENT OF ULLMANNITE 373

cobaltite (CoAsS), gersdorffite (NiAsS), and ullmannite Wuensch,B. J. and C. T. Prewitt (1965)Corrections for X-ray (NiSbS).Uniu. Toronto Studies Geal. Ser.52,7l-80. absorption by a crystal of arbitrary shape.Z. Kiistallogr. 122' Ramsdell,L. S. (1925)The crystal structureof some metallic 24-59. sulphides.Am. Mineral. 10, 281-3M. Zachariasen,W. H. (1967)A generaltheory of X-ray diffractionin Stout, M. Z. and P. Bayliss(1975) Crystal structure of a natural crystals.A cta Crystallogr.2 3, 558-564. titanomagnetite.Can. Mineral /J' 86-88. Takeuchi, Y. (1957)The absolutestructure of ullmanite (src), Manuscript receiued,Nouember 24, 1975; accepted NiSbS.Mineral. J. 2.90-102. for publication,September t,3, 1976