The crystal structure of freieslebenite, PbAgSbS 3 *

Zeitschrift für Kristallographie, Bd. 139, S. 85—102 (1974)

The crystal structure of freieslebenite, PbAgSbS3*By TETSTJZO ITO ** and WERNER NOWACKI

Abteihing für Kristallographie und Strukturlehre, Universität Bern

(Received 27 January 1973)

AuszugDie Struktur von Freieslebenit, PbAgSbS3, wurde mittels dreidimensionaler

Zählrohrdaten mit Hilfe der Methode der „Hauptverschiebungen" (key shifts)bestimmt (JR = 3,2°/0). Die erhaltene Struktur ist vom Modell von Hellneb(1957) verschieden; sie ist zu Marrit, PbAgAsSs, dem As-Analogon zu Freies-lebenit, isomorph. Die Daten sind: Raumgruppe P2i/a mit a = 7,518(1),b = 12,809(4), c = 5,940(1) Â, ß = 92,25(1)° und Z = 4.

Die Struktur ist eine Überstruktur einer Substruktur vom PbS-Typ. Wohlwegen des größeren Radius von Sb gegenüber As sind die Verschiebungen derAtome aus der idealen Substruktur bei Freieslebenit kleiner als bei Marrit. Sbhat die normale trigonal-pyramidale Koordination der S-Atome mit denAbständen 2,431, 2,453 und 2,480(4) Â. Die SbS3-Pyramiden sind voneinanderisoliert. Pb weist eine deformiert-oktaedrische Koordination von sechs S-Atomenauf, mit Abständen zwischen 2,806 und 3,167(4) Â. Die AgS3-Gruppe ist beinaheplanar mit den (Ag—S)-Abständen 2,522, 2,575 und 2,687(4) Â. Ungefähr normalzur AgS3-Ebene befindet sich ein viertes S-Atom im Abstand von 2, 928(4) A.Der Temperaturkoeffizient des Ag ist wesentlich größer und anisotroper alsdiejenigen der übrigen Atome, ein gemeinsamer Zug bei Strukturen dieser Art.

AbstractThe crystal structure of freieslebenite, PbAgSbS3, has been determined with

three-dimensional counter data (1Î = 3.2°/o). The structure was solved by themethod of key shifts. The obtained structure is different from the model proposedby Hellneb (1957); instead, it is isomorphous with marrite, PbAgAsS3, an

As analogue of freieslebenite. The crystal is monoclinic, space group P2i/a, witha = 7.518(1), b = 12.809(4), c = 5.940(1) Â, ß = 92.25(1)° and Z = 4.

The structure is a superstructure of a PbS-type substructure. The displace-ments of the atoms from the ideal substructure are less in freieslebenite than inmarrite, probably because of the larger atomic radius of Sb than that of As. Sbhas the usual trigonal-pyramidal coordination of S atoms. The Sb—S distances

* Contribution no. 232; paper no. 68 on sulfides.** On leave from the Institute of Physical and Chemical Research, Rikaga-

kukenkyusho, Wako-shi, Saitama, 351 Japan.

86 Tetsuzo Ito and Weener Nowacki

are 2.431, 2.453 and 2.480(4) Â. The SbS3 pyramids are isolated from each other.Pb is coordinated with six S atoms in a distorted octahedral arrangement. ThePb—S distances range from 2.806 to 3.167(4) A. Ag has three nearest S neigh-bours at the distances 2.522, 2.575 and 2.687(4) A. The AgS3 group is nearlyplanar. A fourth S atom is at a distance of 2.928(4) Â from Ag, the Ag—S beingapproximately perpendicular to the AgS3 plane. The temperature factor of Agis significantly larger and more anisotropic than those of the other atoms ; thisfeature is common among related structures.

IntroductionFreieslebenite, PbAgSbS3, is one of the typical superstructures

based on the PbS-type substructure. Hellster (1957) deduced a

complete structure of freieslebenite by a trial-and-error method usingtwo-dimensional data (R = 31,37 and 41°/0 for the three projections).More recently, Wuensch and Nowacki (1967) determined the struc-ture of marrite, PbAgAsS3, an As analogue of freieslebenite. Theyshowed that marrite is not isomorphous with the Hellner's model offreieslebenite in spite of the same space group P2\/a and of the closesimilarity of the cell dimensions (Table 1). They also observed thatthere were several nearly homometric structures of marrite ; five differ-ent models gave the R values less than 40°/o.

Table 1. Lattice constants of freieslebenite, PbAgSbSs, marrite, PbAgAsSs, andgalena, PbS

Freieslebenite

Presentwork

Palacheet al.

(1938)

Hellner(1957)

Marrite

Wuensch andNowacki

(1967)

Galena*

7.518(1)12.809(4)5.940(1)

92.25(1)°571.57

7.5312.795.88

92°14'5.95(1)

7.2705(6)12.6319(4)5.9853(3)

91°13.7'(2)549.56

8.39 A12.58 Â5.93 Â90°

625.6 Â3a = [llOJpts, & [IlOJpbs and c = [001]Pbs, where a(PbS) = 5.93 A.

In order to check the isomorphism of freieslebenite and marrite andalso to examine more accurately the sulfur coordinations around themetal atoms, a redetermination of the structure of freieslebenite was

undertaken using three-dimensional counter data. As will be describedbelow, freieslebenite was shown to be isomorphous with marrite.

The crystal structure of freieslebenite 87

Crystal dataA specimen of freieslebenite from Vascongadas, Spain (British

museum no. 1948.365) was used for the present investigation. A frag-ment was cut out of the specimen with a razor, and was made into a

sphere with a radius of 0.086 mm by Bond's (1951) method. Thepowder attached to the surface was dissolved away with a hot aqueousHNO3 solution. The unit-cell dimensions were obtained from back-reflection double-radius Wrissenberg photographs of the sphericalcrystal about the a, b and c axes. Diffraction patterns of Si powder(a = 5.43074 A) were used for calibration. The wave length used was

1.54051 A for CuA«i radiation. A least-squares refinement was per-formed with the aid of a program written by N. D. Jones. The resultsagree well with those given by Palache, Richmond and Winchell(1938), and by Hellner (1957) (Table l)1. The unit-cell contentproposed by Hellner (1957), Pb4Ag4Sb4Si2, was assumed for thepresent structure determination, which was subsequently confirmedby the successful analysis of the structure. Microprobe analysesof freieslebenite given by Sveshnikova and Borodayev (1972)confirmed the chemical composition. The calculated density,dx = 6.194 g • cm-3, is in good agreement with the observed value,dm = 6.20 g • cm-3, by Palache et al. (1938). The observed S3^stematicabsences of reflections were : hOl with h odd and OkO with k odd. There-fore, the space group P2\ja reported by Hellner (1957) was con-

firmed.

Intensity measurementsThe intensities were measured with a diffractometer of equi-

inclination type (Buerger-Supper-Pace) using Ni-filtered GuKx radia-tion. The diffracted beams were detected with a proportional counter,and analyzed with a pulse-height analyzer. The spherical ciystal was

rotated in the co-scan mode with the scanning speed from 0.5° (higherangles) to 1.0° per minute (lower angles), about the b (zero to 14thlayer) and the c (zero to 4th layer) axes. The background was measuredbefore and after each Bragg reflection for the time approximatelyequal to the scan time of the reflection. About 1100 independentreflections were measured, of which 972 reflections were consideredto be observed (/ > 2.33 01). These were corrected for Lorentz, polari-

1 Throughout the paper, the estimated standard deviations are given inparentheses in an abbreviated form; for example, 7.518(1) means 7.518 ± 0.001.

88 Tetsuzo Ito and Wehner Nowacki

zation and absorption (sphere with fir = 11.7 for QuKk) effects.Extinction effects were ignored because no systematic discrepanciesbetween F0 and Fc were observed in the course of the refinement.

Solution and refinement of the structureThe asymmetric unit of the structure of freieslebenite consists of

PbAgSbSa. The structure was solved by the method of key shifts (Ito,1973). Since the procedure used for the solution of the structure isdescribed in detail in the above reference, only the results of the analy-sis are given in Table 2. The R value at this stage was 25°/o for all theobserved reflections. The Fourier map calculated with the atomic

Table 2. Approximate coordinates of freieslebenite as deduced by the method ofkey shifts

x/a y/b : c B

0.3650.3520.380

0.0870.4130.766

0.2590.2590.208

1.7 Â21.71.7

Table 3. Atomic coordinates of freieslebenite with standard deviations

x/a y/b z/c

0.36516(12)0.35000(8)0.37786(18)0.1384(5)0.1350(5)0.1475(5)

0.08716(7)0.41512(5)0.75971(11)0.2192(3)0.6215(3)0.9416(3)

0.27172(15)0.25309(10)0.2117(2)0.3457(7)0.1308(6)0.2659(6)

Table 4. Thermal parameters of freieslebenite with standard deviations ( X 104)The thermal parameters refer to the expression:

T = exp {—

2 ji2 (6n/i2a*2 + • • • + 2bi2hka*b* + •••)}i i i i i I

SbPbAgS(l)S(2)S(3)

6u

130(4)194(3)354(7)142(17)170(17)142(17)

622

155(4)237(2)347(7)134(17)198(18)131(16)

&33

162(4)230(3)386(7)249(18)151(17)180(16)

-9(3)5(2)

-141(6)-11(13)

35(14)—

16(13)

613

3(3)12(2)31(6)28(14)24(13)38(13)

623

8(4)13(3)41(6)

—

20(14)-1(14)12(14)


Table 5. Observed and calculated structure factorsh |Fo| Pe h |Fo| Fc b. ]Fo| Fc h |Fo| Fc h (Fj Fe h [Fj F£ h |Fffl| Fc h |Fj

2 40 -39 8 128 -120 1 34 -30 5 108 110 5 64 -65 3 17 16 5 3211 4 71 -72. . .

2 105 109 6 33 -32 6 61 61 H 56 -60 6 552 H5 -135 5 66 66 n 4 58 -58 7 91 -91 7 51 50 5 36 38 7 344 522 -525 6 72 72 -8 83 84 5 49 49 8 24 -26

.

6 47 456 215 208 7 42 -42 -6 47 -49 6 53 -54

.

,

„

* 7 52 -518 196 187

. ..

n -5 67 -67 h -6 143 150 -6 144 145.

9 , -6 11

-

9 -7 11 -10h ' u 1 27 28 -2 99 95 -6 58 58 -7 21 -23 -4 89 88 > -5 27 28 -6 137 1411 64 54 2 41 -43 -1 45 33 -5 69 66 -6 228 -236 -3 66 -63 -8 72 73 -4 96 97 -5 80 852 81 75 3 55 -53 2 84 -84 -4 13-9 -4 1*3 -146 -2 293 -288 -7 12 9 -3 37 38 -4 78 -833 117 -m 4 51 52 4 91 90 -3 52 -50 -3 49 44 -1 16 15 -6 19 -21 -1 94 -95 -3 69 -674 98 -95 5 24 24 5 45 -45 -2 59 -56 -2 502 504 1 62 62 -5 28 29 0 91 -85 -2 151 -1455 57 55 6 17 17 6 31 32 -1 61 -60 0 17 -17 2 288 296 -4 105 -110 1 16 14 -1 76 -756 31 "32 », ,0 n

8 87 -86 0 18 20 1 57 -52 3 27 -27 -3 38 -38 2 16 19 0 122 1237 54 50

.

1 108 110 2 467 -506 4 92 -94 -2 43 48 3 104 106 1 138 1438 88 84 0 216 212 5 2 19 18 4 150 155 5 40 -41 -1 35 34 4 37 34 2 59 609 73 -73 1 40 -42 -7 35 35 4 16 -I9 5 31 31 6 168 -162 0 87 80 5 74 -73 4 88 -92

. _

n 2 34 -35 -6 88 -90 5 91 -89 6 248 247.

lrt „2 41 -49 6 12 -14 5 113 -114

b i 0 3 29 -30 -5 101 -102 6 15 11 7 13 -11 3 60 -65.

Q

,

6 14 150 79 55 4 157 -154 -4 31 34 19 8 140 -141 -6 87 -92 5 57 56 v ' 7 66 671 84 77 5 39 38 -3 44 42 n

. .

-5 38 41 6 22 23 -6 96 -99 h ,

.

2 67 -59 lit n -2 90 84 -5 31 -32 -4 60 62 7 29 26 -4 168 169 '

3 30 -21 5 -1 121 1 18 -4 85 86 -7 35 36 -3 12 11 8 29 -27 -3 47 -45 -7 12 114 35 -34 1 16 17 0 48 -50 -3 14 -12 -6 156 162 -2 80 79

.

,

-

-2 62 62 -6 129 1255 65 -68 2 76 78 1 141 -142 -2 258 -258 -5 66 -69 -l 37 -41 > -I 18 16 -4 92 976 92 92 3 36 -39 3 15 -12 -I 53 33 -4 42 -46 0 82 -87 -8 81 81 0 253 -255 -3 15 -147 74 75 4 51 -51 4 35 40 1 13 13 -3 37 34 1 36 39 -7 27 -28 1 35 34 -2 283 -27299 5 5 22 23 5 110 HI 2 256 263 -2 202 -185 2 13 -10 -6 127 134 2 30 30 0 17 1?

.

6 45 -44 3 28 -28 -1 62 62 4 61 63 -4 257 -261 4 194 199 1 11 11")0 758 -56 4 72 -73 0 92 93 5 40 -40 -3 37 37 5 19 -20 2 268 2821 53 41 0 49 47 8 16 -17 5 13 -13 1 123 -122 6 36 -35 -2 81 -81 6 73 -72 3 13

-

92 675 669 1 39 39 h 6 1 h 11 1 2 84 82 -1 15 -15 h .„ ,

4 102 -I053 45 -41 2 24 -23

h " ' h 13 1 , ?1 35 h 11 2 0 ftl0 %0? h 10 3 fi ,55.,^4 184 -180 4 32 -33 -8 107 110 -5 9

-

6 4 74 -80 -6 34 37 1 32 -31 -6 52 -60 7 7 75 '9 -'5 h n -6 183 -18'' 7k 75 5 95 95 -5 23 -23 2 52 -55 -5 34 -33 h

.

k6 306 -304 n " u -5 44 43 -3 29 29 7 84 -84 -4 46 45 3 13 15 -4 109 -1127 25 24 1 26 26 -4 117 -115 -2 67 67 8 37 37 -3 48 47 4 287 -303 -3 34 36 -7 22 -228 174 170 uni

~2 1,05 '9° 0 108 -,°9 0 -2 58 -60 5 16 16 -2 112 115 -6 131 -132-1 50 -48 1 11

-

4 > -1 30 -26 6 108 107 0 55 56 -5 43 46* -8 104 -107 1 22 19 2 10 9 -8 90 94 1 27 -25 7 10

-

9 1 19 -20 -4 48 500 121 -107 -6 186 194 2 392 -399 3 29 -30 -7 36 36 2 45 48 8 131 132 2 108 -115 -3 31 -311 130 116 -4 109 116 3 32 31 4 82 83 -6 35 -35 3 49 51 h

.

, 3 31 34 -2 153 1452 65 59 -2 458 -451 4 105 106 , -4 118 -120 4 48 -49 B * 3 4 20 22 -1 34 -354 71 72 2 472 462 5 14 -13 " * 1 -3 74 -75 5 22 -21 -8 85 -89 5 16 -18 0 84 -885 96 -97 4 128 -125 6 207 204 -4 39 40 -2 79 78 -6 60 65

.

,, ,1 88 89

6 99 -96 6 223 -215 7 17 -15 -3 49 46 -1 86 85 -5 53 54 3 2 75 -737 68 67 8 110 109 8 104 -102 -1 61 -60 0 62 60 -5 40 42 -4 109 111 -5 38 -38 3 31 -32

" ' 1 15 -13 2 69 -76 -3 22 -20 -2 122 -II9 -2 79 79 5 73 -725 -8 23 -23 -8 27 26 2 11 9 3 109 -117 -2 42 41 0 52 -51 -1 20 18 7 72 701 23 -26 -7 64 -65 -7 62 62 3 78 77 4 32 33 -1 47 -46 1 22 23 0 16 -18

.

2 34 35 -6 91 -94 -6 99 101

. .

5 59 59 0 214 -213 2 105 "0 1 109 -Hi 5

3 72 72 -5 47 55 -4 83 -82 5 6 31 33 I 31 31 3 32 -38 2 48 -48 -7 52 -534 78 -77 -4 59 62 -3 64 -56 -2 38 37 7 58 55 2 33 33 4 40 -39 3 41 43 -6 58 605 53 -52 -3 34 30 -2 67 -66 -1 24 -22 8 52 -52 3 34 34 5 25 2? 4 17 19 -5 21 207 27 -25 -2 63 61 -1 23 -14 0 206 -203 c 4 166 166 6 50 -50 5 77 81 -4 131 1298 74 70 -1 83 -73 0 110 1 14 1 22 20 5 30 -30 7 20 20 -3 85 82

. ,

n 0 101 -83 1 29 22 2 32 32 -8 106 108 ...

„ . ,

,5 -2 116 -113h 6 0 1 45 43 2 42 -43

. „ -

-7 18 19 h 13 2 h 5 3 _u 6fj _6g _, ,o6 _)0,0 530 -539 2 6l 55 3 44 42 n -6 130 135 -4 50 -55 -7 17 -18 -3 8

-

7 0 83 -811 66 62 4 45 48 4 72 -74 -8 135 -136 -5 52 -52 -3 26 28 -6 86 90 -2 167 167 1 31 -322 93 86 5 48 -50 6 90 89 -6 164 -177 -4 308 -302 -2 76 75 -5 31 33 -I 23 -22 2 103 HI3 38 38 6 94 -90 7 54 -53 -4 379 398 -2 65 -65 0 12 12 -3 34 -35 0 13 11 3 120 1274 375 364 7 50 49 8 20 19 -2 92 91 -1 77 74 1 13 -12 -2 110 -109 2 174 -179 5 43 -435 51 -49 9 7 4 k « 1

0 605 ~625 0 1,35 ^ 2 68 ~69 -1 23 "22 3 14 14 6 59 -596 153 -151 h „

2 1 16 1 16 2 85 -87 3 17 20 0 24 25 4 45 48

.

,

"

.

7 14 -12 -7 65 63 4 400 405 3 60 -59 4 33 35 1 91 93.

,

8 145 -136 -9 52 54 -4 87 -84 6 173 -172 4 304 -312.

„ 2 60 57 5 5 -6 108 -111

. _

0 -8 76 -78 -3 108 -103 8 152 -149 5 22 20 D * * 3 44 -46 -3 10 -10 -5 24 24-7 53 -55 -2 26 30 h 1 2 6 U1 137 "2 15 15 * 21 "23 "2 83 "85 ~h 192 186

1 62 -59 -6 28 32 -1 106 104 7 34 33 -1 29 27 5 67 -67 -1 23 24 -3 16 -122 101 -100 -5 31 -33 0 50 50 -8 127 131 n -7 o 0 40 -41 7 79 77 0 99 104 -2 57 573 108 106 -4 97 97 1 49 49 -7 46 -48 ' * 1 29 -29

,

, ,1 20 -22 -1 27 -24

4 83 80 -3 117 118 2 32 -36 -6 14 -16 -7 36 38 2 22 22 3 2 21 20 0 277 -2765 31 -32 -2 61 -61 3 135 -135 -4 189 -196 -6 26 28

.

-6 130 135 h

,

1 17 196 50 50 -1 73 -67 5 40 41 -3 77 84 -5 24 25 3 -5 50 -50 " ** 5 2 53 537 64 -62 0 28 -28 6 23 24 -2 72 73 -4 144 143 0 13 13 -4 109 111 -1 74 80 3 17 148 81 -76 1 86 -77 7 75 70 -1 133 -120 -3 64 -66

.

-3 18 15 0 41 42 4 208 209-17

3 112 114 y 2 91 -95 -1 48 47 -8 1 19 123 -1 50 50 6 98 -95h 9

58 -59 -7 36 -36 3 142 147 0 99 -98 -6 l64 -171 0 18 -16 -6 1101 57 -56 5 30 -30 -6 113 116 4 24 -22 1 20 22 -4 118 -129 1 27 -22 -4 202 -2082 40 40 6 25 -27 -4 254 -252 5 82 -81 2 84 89 -2 367 384 2 312 31? -2 45 -484 22 26 7 56 -55 -3 48 45 6 55 56 3 79 -83 2 391 -409 3 32 -32 0 310 3135 49 47 8 67 65 -2 68 -67 7 69 -68 5 47 49 4 107 104 4 83 -79 2 76 -796 71 -70 9 54 53 0 345 360 8 31 -28 6 52 -52 6 230 223 5 18 16 4 222 -2247 53 "51 h 1 1

1 39 -40

. _-

7 43 43 8 102 -102 6 187 -181 6 1 17 115h q 0 2 ^9 -50 h fi 2 h 1 1 7 '5 16 h , «.1 9 0 -8 101 -100 4 265 -266 -7 27 30 h R 2 h13 h141 50 -49 -7 24 23 5 25 25 -6 143 -150 -7 36 -37 -8 25 27 7 3 -7 51 512 326 -317 -6 120 -126 6 102 102 -5 64 -70 -6 76 78 -7 55 56 -7 50 -51 -6 34 353 59 55 -4 317 314 h m 1 ~* 47 50 "5 *9 50 -6 97 100 -6 107 -113 -5 12 .134 95 94 -3 34 -33 -3 54 54 -4 59 -60 -5 23 -27 -5 27 29 -4 156 1625 26 25 -2 75 71 -7 23 -24 -2 177 165 -3 15 -12 -4 63 -70 -4 97 101 -3 74 -796 169 164 -1 28 20 -6 50 51 -1 62 62 -2 55 -53 -3 30 -27 -3 28 27 -2 91 -937 41 -39 0 512 -495 -5 53 53 0 98 -93 -1 55 -55 -2 95 -98 -2 93 93 -1 106 100h 10 n 1 33 29 -4 99 98 1 153 -153 0 69 74 -1 31 37 -1 41 -41 0 130 -124

2 79 79 -2 108 -108 2 56 -54 1 73 77 0 96 93 0 133 -134 I 20 230 98 99 4 325 331 -1 36 -32 3 44 42 2 23 -23 1 32 -33 1 22 24 2 94 1031 67 -67 6 122 -125 0 26 -25 4 62 69 4 39 -42 2 15 13 4 88 92 3 121 -126

90 Tetsuzo Ito and Werner Nowacki

Table 5. (Continued)ti |Fn| Fc h |Fo| Fc 1, |FJ Fß h |Fq| h (Fj Fc h | Fj Ffi h | ?g | Fc li [ Fo | Fe h |Fj

-2 85 79 h .. . -2 126 126 2 197 -201 -2 50 -50 fc

-

. 3 18 16 -1 15-1 16 41 " * 0 76 -79 "15 , ,2 _,2 0 ,5B l53 1 66 -65 0 67

0 98 -99 -1 55 -57 1 52 56 -6 10 -10 1 16 13 1 13 11 -5 52-52 , 1 7963 3 33 -33 -1 136 -129

.

, „ 3 1016 1 62 65 -3 38 36

,„27 5 18 -18 -2 91 91 -5 12 -11-55 6 13 13 -1 29 -29 -1 78 -80 -3 51-59 h o ç

0 102 99 -2 108 -105 -2 91

13 -2 83

91-58 -1 107 107

29 -2 13 -100 1791 29 -30 0 95 -97

.

1 86 -81 " " 0-5 23 23

122 115 -1 79 -7917 16 -2 151 119

175 -171525 27 -6 107 102 1 11 10 -2 89 86 -1 66 -61 2 39 35 0 11 10 1 10 -3963 61 -1 126 129 5 65 -66 -1 18 -H -3 11- 8 1 112 135 2 161 -162 2 17 -1313 12 -2 210 -233 6 31 -32 0 25 -30 -2 19 19 , 3 20 21 3 11 11,„4

0 18 -46 1 69 -70 -1 66 63 » 1 6 1 58 54 , ,

2 244 263 " > 5 2 58 -56 0 57 54 -4 91 -87.

, ,

h 7 6

41 -43 1 50 -16 -6 126 -124 3 57 56 1 26 -26 -3 54 53 14 0 _^ ^ _2514 -11 6 170 -164 -1 162 158 1 27 26 2 22 -21 -2 92 9! -1 61 -65 -2 63 -6188 -86

.

-2 67 90 5 51 50 3 72 -70 -1 59 -59 -3 21 23 -1 35 3565 68 0 218 -25t h ft « 1 21 -21 0 56 51 -2 71 -73 0 57 -5619 -20 -6 112 -109 4 211 206 -*

fco« 1 17 -17 -1 31 30 2 68 6939 38 -5 13 9 6 66 -62 -1 97 -97 n V 5 2 Q1 _gl Q 86 8828 30 -1 43 15 -2 185 178 -1 101 -96 3 81 78 1 63 -63 6 8 6

52 -53 -3 11 -13 0 30 30 -3 8

-

7 2 30 27 -2 73 -71

parameters of Table 2 revealed reasonable peaks for the three sulfuratoms.

The whole structure was then refined by a block-diagonal least-squares method. Unit weights were given to all reflections. After threecj'cles of isotropic refinement R was 9°/o- Additional several cyclesof anisotropic refinement reduced R to the final value of 3.2%. Theatomic scattering factors for the neutral atoms were used2. The finalatomic coordinates and the thermal parameters are given in Tables 3and 4, respectively. The observed and calculated structure factors are

compared in Table 5.

Discussion of the structureI s o m o r p h i s m

The present analysis has shown that freieslebenite, PbAgSbSs, isisomorphous with marrite, PbAgAsSs (Wuensch and Nowacki, 1967),and that Hellner's model of freieslebenite (1957) is one of the nearlyhomometric models (Ito, 1973). Therefore, the discussions on the struc-ture of marrite given by Wuensch and Nowacki are generally validalso for freieslebenite.

Several isomorphous pairs of As and Sb sulfosalts have beenreported (Table 6). Two isomorphous pairs of Sb and Bi sulfosalts or

sulfides are also known: wolfsbergite, CuSbS2 and emplectite, CuBiS2(Hofmann, 1933a); stibnite, Sb-zSs and bismuthinite, Bi2S3 (Hof-

2 International tables for x-ray crystallography (1962), Vol. Ill, pp. 202 (S andAg) and 210 (Sb and Pb). Birmingham: Kynoch Press.

The crystal structure of freieslebenite ill

Table 6. Isomorphous pairs of As and Sb sulfosaltsStructure

type * As sulfosalt Sb sulfosalt Formula**

I.II.II.II.

VI.VI.

Claiaiai

binnite1marrite 3

proustite5seligmaimite6arsenopyritc7gersdorffite9

tetrahedrite2freieslebenite4pyrargyrite 5

bournonite 0

gudmundite8ullmannite10

CU12X4S13PbAgXSaAg3XS3PbCuXS3FeXSNiXS

1 Wuensch et al. (1900).2 Wuensch (1904).3 Wuensch and Nowacki (19074 Present work.5 Engel and Nowacki (1906).* Classification of sulfosalts by Nowacki (1909)* X = As or Sb.

6 Hellnek and Leineweber (1950).7 Buergeb (1930).8 Buebgeb (1939).9 Bayliss and Stephenson (1967).

10 Takéuchi (1957).

mann, 1933b). However, no As—Sb—Bi isomorphous series have thusfar been reported. Buergbr (1939) attributed the non-existence of theisomorphous series to the differences of the atomic radii of X (X = As,Sb and Bi) in the case of the arsenopyrite-type compounds, FeXS.

It seems that another important factor of the non-existence is thedifferent bonding nature of X. In As sulfosalts, coordinations of Sabout As are usuallj' ASS3 pyramids. In Bi sulfosalts, however, fivefoldcoordinations (or 3 -4- 2 coordinations) of S about Bi are almost as

common as BiS3 pyramids : for example, cosalite, Pb2Bi2S5 (Srikrish-xax and Nowacki, 1974) and aikinite, CuPbBiSs (Ohmasa andNowacki, 1970). In other words, the bonding nature of As is charac-terized by p3 (or sp3 with one lone-pair of electrons) orbitals of As,whereas that of Bi is more complicated because it is more easilyinfluenced by the contribution of d orbitals of Bi. Coordinations of Sabout Sb are generally more similar to those of As than of Bi. Instibnite (Suavnicar, 1960; Bayliss and Nowacki, 1972), however,one Sb is coordinated with three S (an ordinary SbS3 pyramid) but theother is coordinated with five S (a distorted square pyramid).

Ciystal structure

The atomic arrangements in freieslebenite are shown in Fig. 1.SbS3 trigonal pyramids are isolated from each other. Therefore, freies-lebenite belongs to the structure type II.ai of Nowacki's classificationof sulfosalts (1969).

02 ïetsuzo Ito and Werner Nowacki

(c)

Fig. 1. Atomic arrangements in freieslebenite, viewed along the c axis : (a) theatomic layer at z «a 1/4 and (b) at z 3/4, and (c) = (a) + (6), i.e. the wholestructure. The thick broken lines indicate the longest Ag—S bonds, the blackarrowheads indicate the bonds between the adjacent layers, and the signed

numbers in (a) are the deviations (in Ä) of the atoms from z = 1/4


Table 7. Displacements, A, oj the atoms oj jreieslebenite from the ideal PhS-typestructure

[dealcoordinates

FreieslebeniteAv

MarritcAm If In

Sb or x

As yz

Ar

I'll

Ag

S(l)

8(2)

S(3)

x

yz

Ar

x

yz

Ar

x

yz

Ar

x

yz

\r

z

\r

3/81/12I 1

3/85/12

3 S

9/121/4

1/83/121/4

1/87/121/4

1/811/12

1/4

-

0.074 Â+ 0.050+ 0.129

0.159

-

0.188

-

0.020+ 0.018

0.191

+ 0.0224- 0.124

-

0.2280.261

+ 0.101

-

0.395+ 0.568

0.696

-

0.075+ 0.489

-

0.7080.866

-

0.169

-

0.319

-

0.0940.372

-

0.140 Â+ 0.092+ 0.171

0.242

-

0.207

-

0.071+ 0.013

0.276

+ 0.096

-

0.168

-

0.3880.430

+ 0.1530.448

+ 0.7880.917

+ 0.202+ 0.501

-

0.9421.089

+ 0.297+ 0.397+ 0.221

0.541

+ 0.53+ 0.54+ 0.75

0.66

+ 0.70+ 0.28+ 1.38

0.09

+ 0.23+ 0.74+ 0.59

0.60

+ 0.66+ 0.88+ 0.72

0.76

+ 0.37+ 0.98+ 0.75

0.80

+ 0.57+ 0.80+ 0.43

0.69

Freieslebenite is a superstructure of a PbS-type substructure. Thedisplacements of the atoms from the ideal PbS-type structure are givenin Table 7. The magnitudes of the displacements, especially those ofthe S atoms, are so large (up to 0.9 A) that the S coordinations aroundthe metal atoms are essentially different from those in PbS ; althoughPb is coordinated with six S in a similar way as in PbS, Sb and Ag are

coordinated with three and four (or 3 -4- 1) S, respectively. It can beseen from Table 7 that the directions of the displacements in freies-lebenite and marrite are almost the same, but the magnitudes infreieslebenite are systematically less than those in marrite, probably

94 ïetsuzo Ito and Werner Nowacki

because of the larger covalent radius of Sb (1.41 A) than that ofAs (1.21 A) 3.

It should be noted that even the ideal PbS-type structure of freies-lebenite (or marrite) is different from the true PbS structure, becausethe unit cell of freieslebenite (marrite) is significantly deformed com-

pared with the corresponding cell of the true PbS ; the a axis of freies-lebenite (marrite) is shorter as much as 10% (13°/o) than that of PbS,whereas the b and c axes and the ß angle remain approximately thesame (Table 1). The above deformation of the unit cell results in thefollowing differences in coordinations: the metal—S distance parallelto (001) in the ideal freieslebenite (marrite) structure is 2.84 (2.78) A,whereas the Pb—S distance in PbS is 2.96 A; the S—metal—S anglesin the former deviate from that in the latter (90°) up to 7.3 (8.4°).

The structure of freieslebenite consists of two kinds of atomiclayers parallel to (001) alternately piled up along the c direction. Onelayer at z <=» 1/4 and the other atz * 3/4 (Figs, la and b, respectively)are related by the inversion center and also by the 2i screw along theb axis. The deviations of the atoms from the plane at 2 = 1/4 are givenin Fig. la; the S atoms deviate more (up to 0.71 A) than the metalatoms (up to 0.23 A). Each layer is an infinite two-dimensional net-work of metal—S bonds (Fig. 1). It is combined to the neighbouringtwo layers also by metal—S bonds, as indicated by the black arrow-

heads in Fig. 1 ; it should be noted that the Sb—S and Ag—S bondsalternately combine the successive layers. Thus, the structure of freies-lebenite can be looked upon as an infinite three-dimensional networkof metal—S bonds (Fig. 2).

The metal-S arrays along the c direction can be seen from Figs, lcand 2. Pb, Ag and Sb make up their own metal—S arrays ; no two metalsare mixed within each array because one pair of metal—S constitutesthe unit of repetition. The Pb-S array is an infinite chain, whereas Ag-Sand Sb-S arrays are terminated at every metal-S pair. Two adjacentPb-S chains are directly connected to form an infinite double chain alongthee axis: _Pb_S_Pb_S_

—S—Pb-S—Pb- .

The Pb-S double chains seem to serve as backbones of the structure;the surrounding Ag-S and Sb-S arrays connect adjacent Pb-S

3 Unless otherwise stated, the atomic radii used in the discussion are alltaken from Pauling (1960).

The crystal structure of freieslebenite !)."»

Sb S Ag Pb

Fig. 3. Structure of the metal-sulfur array along [320] within each layer infreieslebenite

double chains and fill in the space between them as shown in Figs, lcand 2.

Figure 3 shows the structure of the metal-S array along [320]within each layer parallel to (001). The array is of a mixed-metal typecontrary to those along the c direction; the six pairs of metal—S,2(Pb—S, Ag—S and Sb—S), constitute the unit of repetition. There are

no infinite metal-S chains like the Pb-S chains along the c direction,because the two Sb and one of the two Ag terminate the chain.

Bond distances and anglesThe bond distances and angles in freieslebenite and marrite

(Wuensch and Nowacki, 1967) are compared in Tables 8 and 9,respectively ; they are in fairly good agreement with each other exceptthose associated with Sb or As. The coordination around the individualatoms are shown in Fig. 4.

Sb has the usual trigonal-pyramidal coordination of S atoms.The three Sb—S distances are 2.431, 2.453 and 2.480(4) A. The mean

value, 2.46 A, is in good agreement with the covalent Sb—S distance(2.45 A) and also with those found in some sulfosalts of the II.ai type:2.46, 2.46 and 2.463 A in bournonite, PbCuSbSs (Edenharter,


Table 8. Bond distances in freieslebenite and marriteX = Sb or As for freieslebenite or marrite, respectively. Notation of the sym-metry operations : single primed ... a glide ; double or triple primed . . . 2i screw

Freies-lebenite Marrite Freies-

lebenitc Marrite

X-S(2")-S(l)-S(3)

Mean

Pb-S(l')-8(8"')-S(S')-8(1)

Mean(4)Pb-S(3")

-8(2)Mean(2)Mean (6)

Ag-S(2')-8(2)

Mean(2)Ag-S(l"')Mean(3)Ag-S(3)Mean(4)

2.431 A2.4532.480

(2.455)

2.80G2.8772.8923.033

(2.902)3.1023.167

(3.135)(2.980)

2.5222.575

(2.549)2.687

(2.595)2.928

(2.678)

* 0.004

2.259 A2.2792.269

(2.269)

2.8372.7992.9762.962

(2.894)3.2603.136

(3.198)(2.995)

2.4732.518

(2.496)2.682

(2.558)2.912

(2.646)

> 0.014

S(l)-X-Ag"-Pb'

I'b

S(2)-X"-Ag'-Ag-Pb

S(3)-X—Pb"—Pb'-Ag-Pb"

2.453 A2.6872.8063.033

2.4312.5222.5753.167

2.4802.8772.8922.9283.102

0.004

2.279 A2.6822.8372.962

2.2592.4732.5183.136

2.2692.7992.9762.9123.260

0.014

Nowacki and Takéuchi, 1970), pyrostilpnite, Ag3SbS3 (Kutogllt,1968) and pyrargyrite, Ag3.Sb.S3 (Engel and Nowacki, 1966), respec-tively. The other three S atoms around Sb are far apart; the Sb—Sdistances are 3.239, 3.477 and 3.576(4) A.

Pb"'

S(2")Fig. 4. Coordinations around the individual atoms in freieslebenite


Table 9. Bond angles in freieslebenite and marrite(X = Sb or As respectively)

Freieslebenite Marrite

S(2") —X

8(1) -X-Mean

S(l') -Pb-

S(3"')—Pb-

8(3') -Pb-

8(1) -Pb-

S(3") -Pb-

S(2') -Ag-

8(2) -Ag-Sum

8(8) -Ag-

8(1)-8(3)-S(3)

-S(3"')-S(3')-S(l)-S(3")-S(2)-8(3')-8(1)-8(3")-8(2)-S(l)-S(3")-8(2)-S(3")-8(2)-8(2)

-8(2)-8(1"')-S(l"')

-S(2')-8(2)-8(1"')

94.5°98.593.3

(95.4)

84.478.182.2

103.1160.185.784.3

166.996.5

158.685.582.2

107.1117.772.8

157.3111.6

89.5(358.4)

90.198.689.8

0.1

97.9°99.397.3

(98.2)

81.371.980.4

110.0

81.882.4

98.3

88.581.4

112.6126.465.3

152.7116.088.5

(357.2)91.1

103.485.3

» 0.3

The mean S—Sb—S bond angle and S • • • S contact distance in theSbSß pyramid are 95° and 3.63 Â, respectively; the correspondingvalues in the AsSs pyramid of marrite are 98° and 3.43 A. If we con-

sider an ideal model of XS3 pyramids (X = As, Sb and Bi) in whichS—X—S = 90° (p3) and S...S = 3.70 A (van der Waals distance),both the angle and the distance in the SbS3 pyramid of freieslebeniteare nearer to the ideal values than those in the ASS3 pyramid of marrite.

Pb is coordinated with six S atoms in a distorted octahedralarrangement. The six Pb—S distances range from 2.806 to 3.167(4) A;these values (the mean 2.98 A) are quite normal for Pb with the coordi-

Z. Kristallogr. Bd. 139, 1/2 7

98 Tetsuzo Ito and Weener Nowacki

nation number of six (Nowacki, 1969). If we look at them more closety,however, the six Pb—S distances can be grouped into the four shorter(the mean 2.90 Â) and the two longer (the mean 3.14 Â). The lattertwo, 3.102 and 3.167(4) Â, are longer than the sum (3.04 Â) of the ionicradii of Pb2+ and S2~. Therefore, these two Pb—S bonds are very weakbonds. It is interesting to note that this 4 + 2 coordination of S aroundPb (in a more exaggerated form) is quite common among Pb salts ofdithioacids, a quite different class of compounds from sulfosalts(Iwasaki and Hagihara, 1972; Ito, 1972). The two smallest S—Pb—Sangles, 72.8 and 78.1° (65.3 and 71.9° in marrite), belong to the two

four-membered chelate rings around Pb, X<^/Pb (X = Sb or As).The smallest angle is also associated with the two longer Pb—S distan-ces mentioned above.

Ag has three nearest S neighbours at the distances, 2.522, 2.575 and2.687(4) A. The AgS3 group is almost planar; the sum of the threeangles is 358.4°. A fourth S atom is at a distance of 2.928(4) A; thecorresponding Ag—S bond (shown in the figures with broken lines) isapproximately perpendicular to the AgSß plane (Table 9). If we applythe Pauling's (1960) relation for fractional bonds, D(n) = D(l) + 0.60log n, to the four observed Ag—S distances, the corresponding bondnumbers are: n = 0.70, 0.55, 0.37 and 0.15, respectively4. Therefore,the fourth bond (2.928 A) is a weak bond, although it is shorter thanthe sum (3.10 A) of the ionic radii of Ag+ and S2~.

Very similar 3+1 coordinations are also found in smithite,AgAsS2, where Ag(l)—S = 2.51, 2.56, 2.68 and 2.84 A, Ag(2)—S = 2.52,2.55, 2.65 and 2.90 A (Hellner and Burzlaff, 1964) and in hatchite,PbTlAgAszS5, where Ag—S = 2.48, 2.52, 2.54 and 2.93 A (Martjmoand Nowacki, 1967). The other two S atoms around Ag in freieslebniteare far apart; the Ag—S distances are 3.288 and 3.349 A.

Thermal vibrationsThe root-mean-square amplitudes of the atoms along the principal

axes of the vibration ellipsoids are given in Table 10. The most inter-esting feature of the thermal vibrations in freieslebenite is the largeamplitudes of Ag compared to those of the other atoms. In fact, thisfeature is common among sulfosalts containing Ag (Table 11). In thesestructures the B values of Ag are more than twice as large as those of

4 The single bond distance, -D(l), of Ag—S was taken as the sum (2.43 A)of the covalent radius of S (1.04 A) and that of Ag in linear bonds (1.39 A).


Table 10. Root-mean-square amplitudes of the atoms of freieslebenite along theprincipal axes of the vibration ellipsoids and the direction cosines ( x 103) of the

axes with respect to a, b and c*

Be B I

8b

IM)

Ag

8(1)

8(2;

8(3)

1.2 A2

1.7

2.9

1.4

I A

1.2

1.33 A21.191.01

1.951.741.52

3.913.091.57

2.021.110.99

1.761.291.04

1.561.160.84

0.130 A0.1230.113

0.1570.1480.139

0.2230.1980.141

0.1600.1190.112

0.1490.1280.115

0.1400.1210.103

-

211

-

220952

100

-

6995

690264674

170822543

574479664

467

-

571675

581755304

789609

-

83

70635

708

172518838

808401367

44777628

786

-

01732

000793

-

56

-

103964

-

211

970

-

23653

130747

-

052

883263

-

389

the other atoms; only in miargyrite the differences between them arenot significant. This means that the Ag atoms are less tightly boundthan the other atoms in these structures.

The observed anisotropy of vibration of Ag in freieslebenite givesus hints for the explanation of the larger amplitudes of the atom. Theprincipal axis with the largest amplitude (B = 3.91 A2) is almost per-pendicular (90° ± ca 8°) to the AgSs plane and parallel (7.9°) to theweakest bond with Ag—S = 2.928 A. The other two axes lie in theAgS3 plane; the axis with the smallest amplitude (B = 1.57 A2) isparallel (8.5°) to the strongest bond with Ag—S = 2.522 A, whereasthe third axis with the intermediate amplitude (B = 3.09 A2) isdirected between the two remaining bonds but roughly along (24.0°)the weaker bond with Ag—S = 2.687 A. In other words, Ag vibratesmost out of the AgSs plane along the weakest Ag—S bond, next alongthe weaker bond within the plane, and least along the strongest bond.


Table 11. Temperature factors of the atoms in sulfosalts containing AgCrystal

Proustite1Ag3AsS3

Pyrargyrite1Ag3SbS3

Xanthoconito-Ag3AsS3

Pyrostilpnite 3

Ag3SbS3

Marrite4PbAgAsSs

Atom

AgAsS

AgSI.S

Ag(l)Ag(2)Ag(3)As

<3S>*

Ag(l)Ag(2)Ag(3)Sb

<3S>

AsPb

<3S>

B

6.1 A22.02.3

4.71.11.2

4.34.24.02.12.1

4.65.64.32.93.8

2.40.9l.l1.2

Crystal

Freieslebenite5PbAgSbSs

Hatchite6PbTlAgAs2S5

Smithite7AgAsS2

Trechmannite8AgAsS2

Miargyrite8AgSbSa

Atom

Agsi,Pb

<3S>

Ag<2As><5S>(Pb,Tl)(Tl,Pb)

Ag(l)Ag(2)Ag(3)Ag(4)

<3As><6S>

AgAs

<2S>

Ag(l)Ag(2)

<2Sb><4S>

5

2.91.21.71.3

4.02.42.82.64.2

3.13.93.43.11.01.4

2.41.71.4

1.21.20.91.1

1 Engel and Xowacki (1966).2 Engel and Xowacki (1968).3 Kutoglu (1908).4 Wuensch and Nowacki (1907).5 Present work.* < > denotes the mean value; for example, <3S> is the mean of the

three S atoms.

6 Marumo and Nowacki (1967).7 Hellner and Burzlaff (1904).8 Matsumoto and Nowacki (1909).s> Knowles (1964).

It should be noted that the least amplitude (B = 1.57 Â2) is of thesame order of magnitude as those of the other atoms (the mean

B = 1.4 A2). It may be concluded from these observations that Agvibrates more than the other atoms because it is tightly bound onlywithin a plane (or almost linearly) in the structure. The above con-

clusion seems to be valid also for the other sulfosalts listed in Table 11.In contrast to the vibration of Ag, that of Sb is quite normal with

less anisotropy and less amplitudes. This is probably because that the


SbS3 pyramid vibrates as an almost rigid unit of a large volume and,therefore, it has less freedom to move in the structure. The observedanisotropies of the three S atoms can, at least qualitatively, beexplained by a larger libration of the SbS3 pyramid around the approxi-mate threefold symmetry axis passing through Sb.

CalculationsThe main part of the numerical calculations was performed on the

Bull-Gamma 30 S computer and the IBM 370/155 computer at Rechen-zentrum der Universität Bern with the program system, "Kristallo-graphische Programme, 1970 and 1972" written by P. Engel (Bern).

AcknowledgementsWe would like to thank Dr. G. F. Claringbtjll of the British

Museum for the specimen of freieslebenite, and Dr. P. Engel and Mr.A. Edenharter (Bern) for their kind help in experiments and calcu-lations. One of us (T.I.) is indebted to the Institute of Physical andChemical Research (Saitama, Japan) for a travel grant for coming toSwitzerland. The investigation was supported by SchweizerischerNationalfonds zur Förderung der wissenschaftlichen Forschung(project no. 2.188.69) and Stiftung Entwicklungsfonds Seltene Metalle.

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Documents

The crystal structure of freieslebenite, PbAgSbS 3 *