Zeitschrift fUr Kristallographie, Bd. 121, S. 321-348 (1965)

The crystal structure of hutchinsonite, (TI,Pb )2As5S9

By Y. TAKEUCHI*, SUBRATAGHOSE** and W.NowAcm

Abteilung fur Kristallographie und Strukturlehre, Mineralogisches Institut,Universitat Bern (Schweiz) 1

With 14 figures

(Received November 14, 1964)

Auszug

Die vollstandige Kristallstruktur von Rutchinsonit wurde bestimmt. Dieneuen chemischen Analysen des Minerals zeigen, daB Ag und Cu keine wesent-lichen Bestandteile sind. Sie ergeben eine Idealformel (TI, Pb )2AsSSO statt wiefriiher angegeben (TI,Pbh(Ag,Cu)AssS1o' Die Raumgruppe ist D~~-Pbca unddie Gitterkonstanten sind a = 10,81 :r 0,01.A., b = 35,36 :r 0,04.A. und c = 8,16

::I::0,01 .A. mit 8 Formeleinheiten pro Zelle. Die direkte Interpretation der drei-dimensionalen Patterson-Funktion lieferte dureh Anwendung geometrischerBeziehungen zwischen "cross vectors" fur die gegebene Raumgruppe die Lageder schweren Atome. Sukzcssive dreidimensionale Fourier-Synthesen ergabendie Orte der anderen Atome. Die Strukturverfeinerung wurde mittels Dif-ferenz-Fourier-Synthesen und schlieJ3lich mittels dreidimensionaler Least-square-Methoden vorgenommen.

Die erhaltene Struktur bestatigt die neue chemische Forme!. Die Strukturbesteht aus zwei Arten von Schichtpaketen parallel (010). In dem einen befindensich parallel c As4Ss-Spiralen, welche - seitlich durch andere AsSa-Pyramidenmiteinander verbunden - eine komplexe Schicht parallel (010) bilden. 1m an-deren treten endliche As2SS-Gruppen auf. Die c-Projektion dieses Paketes ahnelteinem verzerrten PbS-Gittertyp. Die TI- und Pb-Atome sind von sieben Schwe-felatomen koordiniert. Die gefundene Struktur gibt eine Erklarung fUr die guteSpaltbarkeit parallel (010).

Abstract

The crystal structure of hutchinsonite has been determined. The newchemical analyses of the mineral showed that Ag and Cu are not essential com-ponents, and give an ideal formula (TI, Pb hAssSo instead of previously assigned

1 Contribution no. 150. Part 17 of papers on sulfides.

*Present address: Mineralogical Institute, University of Tokyo, Tokyo,

Japan.

** Present address: Institut fUr Kristallographie und Petrographie, E. T.R.,Zurich, Schweiz.

Z. Kristallogr. Bd. 121,5 21

322 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

(TI,Pbh(Ag,Cu)As5SlO" The space group is D~K-Pbca, and the lattice constantsare a = 10.81 ::l:: 0.01 A, b = 35.36 ::l::0.04 A, c = 8.16 ::l::0.01 A. There are8 formula units in the cell. Using geometrical relationships among cross vectorsfor the space group under consideration, a direct interpretation of the three.dimensional Patterson function yielded the locations of the heavy atoms.Locations of other atoms were found by successive three-dimensional Fouriersyntheses. The refinement of the structure was performed by difference-Fouriertrials, and finally by the three-dimensional least-squares method. .

The structure obtained confirms the new chemical formula. The bulk of thestructure consists of two kinds of slabs, both running parallel to (010). In onekind of slab, there are As4SS spiral chains along the c axis. These chains arejoined together laterally by other AsS3 pyramids, forming a complex layer parallelto (010). In the other, As-S groups form a finite group AS2S5. The c axis pro.jection of this slab resembles a distorted PbS-type structure. The Tl and Pbatoms are coordinated by seven sulfur atoms. The proposed structure explainswell the good cleavage parallel to (010).

IntroductionBased upon the ratio As; Pb, the series of sulfosalts whose chemical

formulae are approximately of the type xPb(Tl)S . yAs2S3 may beclassified into three groups. Contained in the first group are jordanite,gratonite (ROSCH, 1963) and lengenbachite. The As; Pb ratios of theseminerals are in the range ~ 0.44 - ~ 0.67, and show a high contentof Pb (cf. NOWACKI, 1964). The structures of these sulfosalts arecharacterized by marked PbS substructures. To the second groupbelong rathite, dufrenoysite (LEBIHAN, 1962; NOWACKIet al., 1963a,b),baumhauerite (LEBIHAN, 1962; NOWACKI et al., 1964) and scleroclase(NOWACKI et al., 1961). For this group the ratio varies from 1.29(rathite I) to 2.00 (scleroclase). The structures of these minerals arebuilt up of layers which have the periodicities 8.4 A (or a multipleof 4.2 A) and 7.9 A in the directions of two-dimensional extension.The ways of stacking these layers, and slight changes in the chemicalcomposition of the layer, differentiate various structures.

The mineral hutchinsonite belongs to the final group, showingthe highest ratio, 2.50. Hutchinsonite is thus the richest in arsenicamong these sulfosalts, and x-ray photographs of this mineral showneither a PbS substructure nor evidence of the layer structure as inthe minerals of the second group. Accordingly a different structuralscheme than that found in other minerals of this series can be expectedfor hutchinsonite. The crystallographic description of the mineral hasbeen presented by NUFFIELD (1947). A brief account of the presentwork has already appeared (TAKEUCHI et al., 1964).

The crystal structure of hutchinsonite 323

ExperimentaJ

Specimens used for the present investigation are those from Lengen-bach in the Binnatal, Valais, Switzerland. Short, prismatic, singlecrystals were separated from dolomite, and good crystals were selectedfor x-ray investigation; the rest was used for the chemical analyses.

The lattice constants previously reported (TAKEUCHI et al., 1964)were re-examined by taking zero-level Weissenberg photographs onwhich calibration powder patterns of KCl were recorded. The unit-celldimensions obtained for the orthorhombic cell are as follows:

a = 10.81 :::I:::0.01 A, b = 35.36:::1::: 0.04 A, c = 8.16:::1:::0.01 A.

For the lattice constant of KCl the value 6.2931 A (SWANSON andTATGE, 1953) was used. These values are in good agreement with

those of NUFFIELD. The space group D~%- Pbca assigned by NUFFIELD(1947) was confirmed. The observed conditions limiting reflectionshkO with h = 2n, hOl with 1 = 2n and Okl with k = 2n only, are uniquefor the space group D~~ - Pbca. There is no possibility of other spacegroups of lower symmetry unless some special arrangements of atomsare assumed.

A spherical specimen with radius 0.118 mm was prepared for theintensity determinations. The three-dimensional intensities were re-corded on multiple films by an integrating Weissenberg camera, usingCUKiX radiation, and they were measured with the help of a J oyce-Loebl microdensitometer. Intensities were corrected for Lorentz,polarization and absorption factors, using IITAKA'S program writtenfor the Bull-Gamma-A.E.T. computer.

Chemical composition

Two chemical analyses have been reported for hutchinsonite fromBinnatal (SMITH and PRIOR, 1907). In his crystallographic investi-gation, NUFFIELD suggested that the above chemical analyses leadto an ideal formula (Pb,Tl)2(Ag,Cu)As5S1o by assuming d = 5.18,in contrast to the observed value d = 4.6 g cm-3 (SMITH and PRIOR,1907). Although the assumption of the specific gravity made byNUFFIELD seems to be reasonable, our new chemical analyses showsomewhat different results. The several analyses are compared inTable 1, from which it can be observed that the contents of Ag and Cuare exceedingly small in the new analyses. To confirm this, a spectro-scopic analysis was performed by S. GRAESER using the fragments of

21*

SMITH and PRIOR New analysis Ideal formula

1I

2 31

4 II

II

Pb 12.5% 16% 18.92% 17.3% 17.06% 19.28%Tl 25 18 21.03 20.0 16.83 19.02Ag 9 2 ca. 0.11 - 8.88Cu - 3 0.96 -Fe - 0.5 - -As 30.5 29.5 31.66 36.8 30.84 34.86Sb - 2 - -S 26 26.5 27.32 26.5 26.39 26.84

1 17.7 8.16 39.6 79.02 16.0 6.4 40.0 80.4

d = 5.18 3 18.9 1.6 41.1 82.84 18.1 - 47.8 80.4

1 15.4 6.4 35.2 70.62 14.6 5.8 36.24 73.2

d = 4.6 3 16.72 1.4 36.4 73.84 15.7 - 42.2 71.0

324 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

Table 1. Ohemical analyses of hutchinsonites

Total 1103.0 97.5 100.0 1100.6 1100.00 1100.00

3. Ordinary microchemical analysis. Original analysis contains 4.63% H20,

< 105°C. The values in the table are normalized to 100% (Fresenius, Wiesbaden)4. Electron-microprobe chemical analysis (NOWACKI and BAHEZRE, 1963).I. (Tl,Pb). AgAssSIO' d = 5.18.II. (Tl,Pb)2 AssSg, d = 4.58.

Table 2. Number of atoms in the cell

calculated from the results of four chemical analyses as given in Table 1

I

Tl + PbI

Ag(+Cu)I

As(+Sb)I

S

the single crystals used for intensity determination. The result showedonly traces of Cu, Ag and Zn in addition to the other main components.

The calculated numbers of atoms in the unit cell are compared inTable 2 for d = 5.18 and d = 4.6 g cm-3. Since it would be reasonableto assume that all the atoms are distributed over the general positionsof the space group D~X- Pbca, the number of atoms is expected tobe a multiple of 8. It is seen in Table 2, that for d = 4.6 the resultsof our new analyses give a unit-cell formula which is close to an idealform, (Tl,Pb)16As4oS72' If we adopt d = 5.18, our results show somedeviation from the formula given by NUFFIELD, especially in the

Thc crystal structure of hutchinsonitc 325

number of Pb + TI atoms. On the other hand, the results by SMITHand PRIOR show better agreement with the formula suggested byNUFFIELD for d = 5.18. Because of this ambiguity, it did not seempossible to draw a definite conclusion from these results. We thereforeproceeded with the structure analysis, bearing both possibilities inmind. In either case, there are two TI(Pb) atoms in the asymmetricunit. Accordingly, if the positions of these atoms could be found, itwas expected it would be possible to determine the structure regardlessof the ambiguity in the chemical formula.

Structure analysisPreliminary

The three-dimensional Patterson map P(uvw) was obtained fromthe F2(hkl)'s. It was observed from the map that most of the heavypeaks are distributed on the sections z = 0, t and }, suggesting thatthe z parameters of the heavy atoms are roughly t or i- Two sections,

w = t and }, are shown in Fig. 1. Since the origin peak of the maphas the weight 1800, the expected single weight in the map is ~ 80for Pb(TI) - Pb(TI), ~ 35 for Pb(TI) - As and - 15 for Pb(TI) - S.The Patterson map is also characterized by heavy peaks arranged

nearly at the intersections of the net ;6 . b X 7 . a, where nand m

are integers. As a matter of fact, F(0,16,0) and F(400) are out-standingly strong reflections. From geometrical relations amonga symmetrical set of atoms for the space group D~~- Pbca [Fig. 2 (b)],the possible candidates for the c-screw satellites of the Pb(TI) - Pb(TI)symmetrical pairs were derived. They are indicated by S, D, E andH in Fig. 1. Since there should be only two c-screw satellites in a quar-ter of the cell, some of them must be spurious. Inversion peaks werederived from each satellite, and then finally eight possible combina-tions of two Pb(TI) atoms were obtained. It should be noted that allthese combinations give positive signs for F(O, 16,0), U = 0.41, andnegative for F(400), U = 0.55, suggesting that most of the heavypeaks are nearly in the shaded areas shown in Fig. 3. The U valuesare the averages of those obtained from the two possible chemicalcompositions.

Among these combinations, only two are consistent with the vectormap P(}vw). They are listed in Table 3. These two possible sets of Pb(TI) atoms may be used to find the correct structure by refining thestructures which would be derived from each set. However, in view of

-II 12 @15 @/6@ @----- ---- -

~I] ~14 17 18I : @ @---I, ,

100 b/2

,_~~~140

, ,, ,'--...

H264

-215

o b/2

8 . 81 ._________L ____?.!? , o§__

02;

01 8:

8x

- - - - -_8__:__8 __ ___?..~__ __: _?..~_

0]8 8

0)

+()sc2y

2x01

o

b)

c)

Fig. 2. (a) Two independent sets of atoms in the space group D~~-Pbca (a glide

and screw axes are not shown) (b) Geometrical relationship between an inversionpeak, I, and its screw (single circle) and glide-reflection satellites (double circle)

in the Patterson diagram having the symmetry D~h-Pmmm. The example

corresponds to the set of white atoms in (a). The z coordinates for each peak are:

1&& & ~ m ~

2z 2z ~-2z t t-2z 0 t(c) An example of peaks due to cross vectors between a set oquivalent to the white

atom x, y, z and a set equivalent to the black atom x', y' ,z'. The z coordinates are:

11 and J6: z' - z, /3 and IS: t - (z +z'),

12 and 15: t + (z' - z), 14and 17: z + z'.

fYT-=Y~ \1+ +11/2-(Y'+Y)

Table 3. Possible combination ot (Tl, Pb) locations

Com- Pb(Tlh1-

Tl(Pb)n Corresponding

c-screwbination

I

satellitex y z x y z

A .1525 .1878 .125

I

.1525 .1878 .625 D

B .37 .25 .125 .336 .123 .125 S,H

The crystal structure of hutchinsonite 327

Fig.3. Shaded arca indicate common area for + F 10,16,0) and -- F (4,0,0). Thefinal atomic positions are indicated. Big solid circle: Pb(Tl); small solid circle:

As; cross: S

the difficulty encounted with the chemical composition, it was stronglydesired to derive the structure by some straightforward means. It wasthen found that a unique solution of the Patterson function could beobtained if we applied the geometrical relationships among crossvectors - the vectors occurring between independent symmetricalsets of atoms.

Use of cross vectors to find inversion peaks

In Patterson space, some rules exist regarding the distribution ofpoints due to cross vectors. For axial symmetries the relationshipshave been discussed in some detail by BUERGER (1959, pp. 115). Forglide planes, relationships among cross vectors may offer a possiblecriterion with which to select the correct inversion peaks. An exampleof the distribution of points due to cross vectors is given in Fig.2(c)for the space group D§~ - Pbca. Since the space group has the a glide,in the c-axis projection, the Patterson map has a pseudotranslationa/2, giving rise to a mirror plane at t, y of the actual unit cell. Althoughin three dimensions, the mirror plane is missing, for each point u, v, wdue to a cross vector A - B occurring between independent sets of

WeightEquivalent Equivalent

set I set II

Inversion 1 8 8Screw satellite 2 12 12Glide satellite 4 6 6Cross vector 2 64

328 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

atoms {rA} and {rB}, there is always a "pair point" t - u,v,w' due

to a second vector A-B. This point has the same weight as that ofthe first, and it is related to the first by a mirror operation across theplane t,y,z, plus some component, w' -w, along the c axis. Althougha similar geometrical relation exists between an inversion peak and itsc-screw satellite peak, they have different weight, the weight of thelatter being twice that of the former. So, even if the peaks due tocross vectors occur in the same plane or line where satellite peaks areexpected, they can in principle be distinguished by searching their"pair peaks", i.e. peaks having the same weight at the locationsindicated above. Similar relations can be observed for other sets ofglide planes in D~X - Pbca. However, consideration of the pair peaksdue to one convenient set of glide planes, i.e. the glide planes perpendi-cular to the shortest axis, may generally offer conclusive results.A thorough investigation by listing all possible A - B vectors willnot be necessary to find acceptable inversion peaks.

Table 4. Number of peak8 due to Tl(Pb)-Tl(Pb) vector8

As seen in Table 4, in the unit cell of hutchinsonite there are 116discret peaks due to Pb(Tl) vectors, among which 2 X 26 are thosedue to symmetrical vectors and 64 are the peaks due to cross vectors.These cross vectors have the same weight as those of the screw satel-lites. By using the above rule among cross vectors, they can be easilydistinguished. In Fig. 1, it can be observed that, among possiblecandidates for the c-screw satellites, D and E have well defined pairpeaks D' and E' respectively in the section z = t, suggesting that theyare the cross vectors. Accordingly, they can be immediately rejected.It is now clear that the peak S is one of the c-screw satellites, becauseit has no pair peak with the same weight in any other sections. Theinversion peak I is then found as indicated in Fig. 1. The peak H thenshould be the c-screw satellite of the other (Tl,Pb). However, this peakis multiple with some other peaks, and also in the section w = t thereis an elongated multiple peak at the place where the inversion peak

0 bl2

\)

I

6

""~

~V, c:s GQ

C?ULJ

~I? \l

<Q?OO

The crystal structure of hutchinsonite 329

is expected. Therefore, it was not possible to determine the accurateposition of the inversion peak in the map. The location of this (Tl, Pb)was found by forming a minimum function based upon the inversionpeak I of the first (Tl, Pb) in Fig.4. It was confirmed that the peaksD and E are the cross-vector peaks of the two sets of (Tl, Pb) atoms.Among them, peak D is a cross-vector peak which is called a "con-jugate peak" (BUERGER, 1959, pp.275) (Fig.5). The final structurerevealed that the peak D is actually a multiple of (Pb, Tlh - (Tl,Pbhrand (Pb, Tlh - ASm cross vectors.

Fig. 4. Minimum function, M2(x,y, f), based upon the inversion peak, I, showingthe location of the second Pb(Tl) at H'

b/2

1cr/2

Fig. 5. Inversion peaks of two independent Pb(Tl) atoms and their conjugatepeaks D' (in the section z = !) and C' (in the section z = 0)

Based upon the principle given above, an automatic search of in-version peaks may be possible by computing a difference function

D(u,v,n) = P(t - U,v, t) - P(u,v,n)

for each section n. In a favourable case, where serious overlappingof miscellaneous peaks does not occur, the cross-vector peaks, if any,

0

~CJ

@(@()

al2

330 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

in the section w = t will become zero in D(u,v,n) for some section n,while the c-screw satellite peaks will not become zero, but show a min-imum value corresponding to the weight of the inversion peak for

o ~

H'

%Fig. 6. The difference function D (tt,V, t). Possible positions of inversion peaksobtained from the relationship as shown in Fig.2 (b) are indicated by solid

circles. The correct inversion peaks I and H' are indicated

some section n where the inversion peakoccurs. An example of such a functionis given in Fig. 6.

The above method of correctly iden-tifying satellite peaks can readily beapplied to any other centro symmetricspace groups which have at least a set ofglide planes.

bit,o

Fig. 7

Fig. 7. Composite diagram of the first three-dimensionalContours for Pb(Tl) atoms are omitted

Fig. S. Composite diagram of the second three-dimensional Fourier synthesis,showing the range y = 0/240 to Y = 20/240 along the b axis. The final As-S

bonds are indicated

Fig.S

Fourier synthesis.

The crystal structure of hutchinsonite 331

Three-dimensional Fourier series and difference-Fourier trials

It was not likely that the locations of As and S atoms could beclearly found in the 3D minimum function because the weights ofthe peaks due to TI(Pb) - As and TI(Pb) - S vectors are of the orderof the background heights of the Patterson function. Accordingly,a 3D Fourier series was computed based upon the calculated signsfrom the TI(Pb) atom locations (Fig. 7). Unfortunately, the coordinatesof two TI(Pb) atoms are close to special positions. Therefore, the signsof the F(hkl)'s with h+lj2 eft 2n and l = 2n, could not be determined.Because of this restriction, acceptable signs of only about 1200F(hkl)'s were obtained out of about 2900 reflections. The ill-shapedpeaks G1 and G2 in Fig. 7 are certainly ghost peaks due to the omissionof the above special reflections. In the Fourier map, locations of fiveAs and five S atoms were found with no ambiguity. They were thenused to determine the signs for the second 3D Fourier synthesis, inwhich four further S atoms were found. Part of the composite Fouriermap is shown in Fig. 8. For the second synthesis, 1684 acceptablereflections were used. At this stage R values were found to be 0.199for F(hkO) and 0.313 for F(Okl). The R value for F(Okl) was reducedto 0,225 by a first 2D difference synthesis. Between the two 3D Fouriersyntheses, difference synthesis were computed using F(hkO)'s. Resultsof these steps of analysis are tabulated in Table 5. The 3D Fouriersyntheses were performed at the Computing Center of Oxford Univer-sity using the program written by O. S. MILLS.

Least-squares refinement

The initial stages of the 3D least-squares refinement were performedusing the program written by IITAKA for the Bull-Gamma-A.E.T.computer. This program minimizes the function

and uses the diagonal matrix approximation. The weighting schemechosen was

w(hkl) = 0

if lFa (hkl)] ~ 4 lFa minI

if lFa (hkl)] ~ 4IFa mini

if lFe (hkl) I < F*

w(hkl) = 1jF4 (hkl)

I I 1 , 2 I 3 I 4 I 5 6

x 0.36 0.3648 0.3648 0.3565 0.3580(Pb,Tlh y 0.25 0.2445 0.2445 0.2445 0.2458 0.2458

z 0.125 0.1234 0.118 0.105

x 0.336 0.3360 0.3360 0.3360 0.3360(TI,Pb hI y 0.123 0.1250 0.1243 0.1240 0.1229 0.1229

z 0.625 0.6250 0.630 0.637

x 0.104 0.104 0.104 0.107ASl y 0.192 0.192 0.196 0.1937 0.1934

z 0.70 0.70 0.70

x 0.104 0.104 0.104 0.100ASH y 0.192 0.192 0.192 0.1875 0.1875

z 0.125 0.133 0.133

x 0.4376 0.4376 0.4376 0.4374ASul Y 0.1112 0.1112 0.1112 0.1145 0.1145

z 0.1330 0.133 0.142

x 0.146 0.139 0.139 0.144AsIy Y 0.046 0.0483 0.0483 0.0471 0.0471

z 0.230 0.220 0.220

x 0.375 0.375 0.3742 0.377Asy y 0.0292 0.0292 0.0285 0.0291 0.02\11

z 0.950 0.950 0.950

x 0.375 0.385 0.385 0.385Sl Y 0.188 0.188 0.188 0.189 0.189

z 0.375 0.375 0.374

x 0.383 0.393 0.400 0.400

Sn y 0.188 0.188 0.188 0.1873 0.1872z 0.875 0.875 0.875

x 0.128 0.128 0.120 0.127

SIrl y 0.25 0.250 0.250 0.2521 0.2521

z 0.375 0.368 0.368

x 0.125 0.120 0.120 0.106

SlY Y 0.140 0.144 0.144 0.1415 0.1415z 0.375 0.333 0.333

x 0.130 0.124 0.124 0.108Sy Y 0.145 0.146 0.146 0.1460 0.1460

z 0.875 0.90 0.90

x 0.411 0.411 0.411

SVI y 0.009 0.009 0.009 0.009

I z 0.685 0.685

332 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

Table 5. Atomic coordinates obtained by various methods

I 1 I 2 I 3 I 4 5 I 6

x 0.219 0.219 0.200

SVII y 0.056 0.056 0.0582 0.0582z 0.950 0.950

x 0.482 0.482 0.44

SVIII y 0.0868 0.0868 0.083 0.069z 0.36 0.37

x 0.0093 0.0093 0.020

SIX y 0.0767 0.0767 0.075 0.075z 0.60 0.60

(hkO) 0.47 0.34 0.271 0.206 0.199 0.181R (Okl) 0.62 0.313 0.225

(hkl) 0.295

The crystal structure of hutchinsonite 333

Table 5. (Continued)

1. From Patterson diagram.2. From first 3D Fourier synthesis.3. From first difference Fourier projection I Ie.4. From second difference Fourier projection lie.5. From second 3D Fourier synthesis.6. From first difference Fourier projection Ila.Overall temperature factor B = 2.0 was used for structure-factor calcula-

tions.

where, Fo min' the minimum observable Fo-value, was taken as 50,and a value of F* = 25 was used. Three cycles of refinement reducedthe initial R = 0.295 as follows: 0.295 -+0.257 -+0.224 -+0.193 forall .P(hkl)'s including non-observed ones. This smooth convergenceindicates that the structure with the chemical formula (Tl, Pb )2As5S9is basically correct. Up to this stage, atomic form-factor approxima-tions by VAND et al. (1957) were used, but were later changed to thevalues given by FORSYTH et al. (1959). Atoms were assumed to beunionized throughout the refinement, including the successive stages.

Mainly because of the comparatively slow calculating speed ofthe Bull-Gamma electronic computer, the successive refinement wasperformed on an IBM 7090 computer using a full-matrix, least-squaresprogram, SFLSQ3, written by C. PREWITT. For the final stages ofrefinement, form factors based upon the Thomas-Fermi-Dirac statisti-cal method were employed for Pb and Tl, and those given by FREEMANand WATSON, and DAWSON were used for As and S respectively(International Tables, vol. III, pp. 201 to 212). The weighting scheme

I

x yI

zI

B a(x) X 10-4 i a(y) X 10-4I

a(z) X 10-4 a(B) X 10-2

I

II

I(Pb,Tlh 0.3581

I

0.2469 0.1056 1.92 1.3 0.5 I 2.1 2.7

(Tl,Pb )u 0.3361 0.1223 0.6351 2.85 1.7 0.5 I 2.4 3.0I

ASI 0.1081I

0.1948 0.7040 1.84 3.9 1.1 5.4 7.5

Asu 0.0994 0.1848 0.1261 2.00 4.0 1.2 5.7 7.1

ASuI 0.4362 0.1153 0.1344 1.86 3.9 1.1 5.5 7.2

Aslv 0.1364 0.0480 0.2151 1.94 4.0 1.2 5.5 7.2

Asv 0.3814 0.0288 0.9545

I

1.91 4.0 1.2 5.6 7.3

Sl 0.3934 0.1899 0.3644 1.82 9.4 2.8 13.3 17.8

Su 0.4090 0.1906 0.8628 1.61 8.9 2.6 12.7 20.4

SUI 0.1123 0.2540 0.3704 1.46 8.2 2.5 12.7 13.1

SIV 0.1289 0.1377 0.3247 1.64 9.0 2.7 12.9 18.7

Sv 0.1128 0.1466 0.8953 1.55 8.8 2.6 12.7 17.3

SVI 0.3878 0.0151 0.6838 2.27 10.3 3.0 14.4 17.4

SVII 0.1942 0.0573 0.9521 2.41 10.7 3.1 li>.O 18.9

SVUI 0.4390 0.0672 0.3275 1.99 9.7 2.9 13.8

I

20.8

SIX 0.0086 0.0799 0.5859 1.70 9.1 2.7 13.0 16.2

Table 6. Final atomic parameters of hutchinsonite, and their estimated standard deviations

The crystal structure of hutchinsonite 335

recommended by CRUICKSHANKet al. (1961) was adopted. This hasthe form

w= 1J(a+F+cF2).

For a and c, 90 and 0.002 were used, respectively. Since the Fo's werecollected around the c rotation axis from l = 0 to l = 7 and the Fo'sfor each level have different scale factors, the refinement of scalefactors was carried out as the first step. In the following steps, re-finement of the coordinates and the isotropic temperature factorswas performed seperately. After four such cycles the R value wentdown to 0.145 for all Fo's and to 0.123 for the observed reflectionsalone.

Fig. 9. Final electron-density projection along the c axis. The contours are drawn

at equal, but arbitrary, intervals except for Pb(Tlh where the interval is doubled:the zero contour is dotted

The final atomic parameters are given in Table 6, with estimatedstandard deviations. The comparison of Fo's and Fe's is given inTable 7. The final Fourier projection (! (xy) is shown in Fig. 9.

Discussion of the refinement

The effects of dispersion were not taken into account in the abovesteps of refinement. With CUKiX the effect is negligible for As and S,but for Pb (and Tl) it is appreciable, iJf' and iJf" being - 4 and 10 ~ 9

respectively. Since the isotropic temperature factors of the Pb (Tl)atoms are slightly larger than those of the lighter As and S atoms,and it appeared that this might be due to the neglect of dispersion

336 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

Table 7. Comparison of the IFo(hkl) I and the :I: F ,(hkl) values of hutchinsonite

", h k

"

, h k ,

"h k

" "h k

" "0 , 0 19~:"O -170.13 '0 0 168.10 -t72.73 0 , 85.30 -98.79 ,,, 28,15 -2".19 '"62.,6 _,0.26

0, 0 15.35

'"0 O. -13.09

0'O. -22.69 ,,, 93.55 -101r..79 ,,, 50.76 )6.is

0, 0 11.19.00 -1310.7" '15 0 31.00 -H,.12 otO 102.63 113.75 ", 60.92 63.80

'057.%9 _\S."

0 ,0 200.22 202.09 '16 0 710,67 69.:U 010 93.101 102.80

'17 89.55 -98.92'"

89.19 -83."otO 0 152.00 -1%1.53 '17 0 81,.10 -80.770"

210.13 -26.76 '18 22.29 -23.68'1'

O. 1",010 0 120.19 _no.o% '18 0 39.21 26.78 016 138.33 151,82'19 27.87 -25.92 ", 31.99 -33.75

0"0 281.00 272.27 '19 0 15.00 20.09 018 102.5"- 1,,8.15 ,,, 60,8-\ 5%.08 '17 1t8.82 38.68

016 0 -'1610.00 0\95.56

'"0 O. -23.15 0" 1t6.:n 102,95 ,,,

70.71 70.35 '18 98.33 101.38018 0 266.50 _251.010

'"0 "2.87 -33.17 0" 72.87 -7/0..82 ,,, O. 0.91 '19 :n.')1t 27.96

0" 0 %0.30 ItS.59'"

0 6j.'jJ -"7.21 0"70.25 -67.66 ,,, 67.81 -68.85

,,, 63.90 60.660" 0 160.100 -173.30

,,, 0 12/0.95 t11.96 ,,' 63.87 57.103 ,,, 510.38 63.06 ,,,57.510 -50.30

0"0 910.08 98.92

'"0 189.29 2010.91{,

0" 20.00 8.2} ,,, 36.52 _32.3/0

'"107.27 -109.106

0" 0 1{,2.26 37.08,,, 0 61.75 -57.110 0" 129.00 _1210.63 ,,, 100.71 36.7% ,,, 6%.07 63.'10

0" 0 36.20 -6.29'"

0 78.%5 -75.70 0" :53.06 37.20 '22 26.1t7 -23.92'"

210.21 -17.090" 0 221.00 _2110.61

'"0 93.101 96.36 0)6 O. - 1.77 ,,, O. -7.63

'"1{,2.91o_'6.27

0" 0 1108.80 159.87'"

0 39.75 _26./02 0)6 66.66 7"-/07,,, 1110.101 123.02 ,,' o. -7.?Ii0)6 0 50.00 -53.01

'"0 29.1{,0 15.86 0" 35.61 -38.38 ,,, 21.31,; _18./09

"717.109 23.96

0"0 76.03 90.06

'"0 53.56 -/08./00 0" 12.70 _ 1.21 ,,, O. 5.92

'"5/0.06 52.102

0"0 76.98 -810.02

'"0 71.65 73.60 0" 510.51 69.61{, ,,, 7%.62 76.17 ,,' 36.72 -35.h

"00 65.102 65.01

'"0 30.1{,1 27.89 1 1 O. -6.37 ,,, O. _ 1{,.66 ,,0 1010.69-H.31o.., 0 39.10 I{,1. %9

,,, 0 52.35 -'9.93 1, O. 26.69 ,,, 31.95 -30.05

'"25.27 _23.01

0" 0 22.02 11.0%'"

0 10.00 %.35 1 , 53.35 -71.80 ,,, O. _110.00 ,"

3%.89 -32,57, 0 0 22.20 33.86 ,,, 0 23.18 1/0.97 1 . 29.22 -30.96 ,,, 18.65 15.59 ,,, 25.1% _22.210, , 0 178.02 181.67'"

0 23.07 -18.%5, , O. -1.27 ,,, 56.66 62.78

'"1{,0./oJ 37.Jl, , 0 o. 9.85 6" 0 28.06 -27.67 1

, 172.10 _181.50 ,,, 31.U _30.7/0 ,,, 17.18 11.95, , 0 O. 8.7% ,,, 0 26.13 -20.1.r.5 1 7 26./07 33.86 ,,, 27.09 -29.09'"

35.03 u.1t7, . 0 O. -13.1/0 ,,, 0 O. -6.87 1, 55.11 -60.39 ,,, O. 8.20 ,,, 23.%9 -19.95, , 0 13%.01 111.'2

'"0 82.95 81.6/0 1 , %9.02 -51.59 ,,, O. 6.50

'"25.80 -31.",

0 35.00 38.57, 0 0 180.68 161.810 1tO 109.58 %5.97 ,,, 17.89 _16.25 ,,, 29./08 }2.24,

7 0 }63.IoO -376.68, 1 0 20%.28 189.65 1

"

O. -1.76 , 1 123.51 129.92'"

10.0} l/i.99, , 0 138.58 -139.73, , 0 110.00 -71.}2

'"JO.81 22.%0 , , JJ.II.r. _21{,.89 7 1 O. 7.8'\', 9 0 }18.00 318.17 , , 0 70.00 -72.47 1

"O. -12./02 . , 75.109 _83.16 7

,91.91 82.85,to 0 12%.05 117.28 , , 0 197.%1 188.90

'"91.69 -97.98 . . 61.63 52.6\ 7 , 66.81 -52.85

'"0 112.96 116.39 , , 0 O. -20.52

'"78.%% 83.%2 . , 03.1{,1{,-144.83 7 . o. 1.76

'"0 69.2% 55.%1 , , 0 O. %.75 116 60.05 53.61 . , 72.010 69.22 7 , 69.15 _60.59

'"0 187.33 203.78 ,

7 0 170.109 _150.51 117 7%.75 72.77 . 7 51.10 106.15 7 , 28.89 -19.82

'"0 35.00 20.26 , , 0 - o. - 3.8% 118 %3.29 38.610 . , 23.93 17.86 7 7 77.81 6}.19

215 0 135.5/0 -152.51,

9 0 107.40 8\.98 119 37.90 32.79 . 9 81:1.85 92.91 7, 103.08 J7.J?,16 0 54.27 -40.19 ,to 0 116.07 _106.65

'"70.19 67./07 .to 79.85 _83."6 7 , 68.60 57.57

'"0 176.59 186.,:>"

'"0 210.88 -25.%9

'"

31.1,6 19.3"'"

75.\6 -79.23 710 68.37 57.68'18 0 49.6" -36.22

'"0 96.30 86.109

'"90.50 -93.32 ." 87.53 _91.60

7"O. -6.59

'19 0 135.17 132.79'0

0 52.%1 37.77 ,,,58."1 52.53

'"92.91 _105.02

7")7.26 }).9~

'"0 2/0.50 -15.63

'"0 90.22 -77.15 1"

/02.28 29.27 ,

"20.59 20.27 716 O. _6.88

'"0 70.76 61.86

'"0 162.84 _161.U ," 56.63 -51.87 ,

"68.75 70.79 717 101.85 38.n

222 0 O. 2."8 ," 0 O. -0.93 1"

57.68 53.25 ." 87.41 -91.06 718 58.76 105.20,,, 0 293.50 -331.03 '17 0 150.65 135.08 ,

"2/o.4J 5.63 .17 7/0.10 77.87 719 55.52 55.28

'"0 91.21 -8/0.36 '18 0 182.0/0 _201./08

'"55.78 53.95 .18 30.14 _32.0/0

7""6.17 -39.27

'"0 56.53 103.63

'19 0 O. -18.011"

62.39 -57.88'19

O. 12.387"

1{,8.95 -108.)10226 0 87.15 76.70

'"0 110.86 112.87

'"/08.62 -51.91

'"76.97 -70.U 7" 59.56 -55.93227 0 59.67 -51.38

'"0 55.68 /0/0.79

'"21.57 16.91 ." 101.55 -93.89 7"

310.09 ".83'"

0 51./05 37./08 822 0 21.56 12.261"

6/0.27 65.21 '22 29.70 28.10117"

41.20 -J7.67

'"0 O. 8.12 ,,, 0 102.81 -97.12

,

"o. 9.33 ." O. 2.28 725 27.12 19.06

'"0 O. 2.61

'"0 35.22 18.55 1)6 O. _7.83

'"85.89 7/0.69 726 22.49 -15.H

'"0 tJO.71 -151.59

'"0 55.98 50.19

'"46.68 -/02.59

'"87.98 810.2/0

7"27.82 28.11

'"0 /08.71 -41./06 ," 0 62.07 -56.96 ," /01.93 /o4.tJ ," O. _2.710

7",. 5.89,,, 0 75.96 80.09

'"0 o. -15.60 ,,, 56.70 -67.50

'"O. 7.97

7"73.00 -71.52

23'j 0 1{,7.jO 41.96'"

0 59.95 50.105'"

5/0.05 -65.21 ." O. -1.69 7"20.69 _20.10

," 0 29.810 22.88 829 0 39.77 33.26 1

"16.39 22.10

'"52.44 -53.31 7"

o. 12.90,,, 0 73.710 72.7"'"

0 101.80 -35.82 ," 11.67 -5.51,

"72.19 82.68

7" 38.93 -/01.36

'"0 26.32 13.2/0

'"0 86.1') -93.11 ," 16.17 -12.80 ." O. 9.23 7JJ 25.48 -18.79

'"0 57.53 -60.90

'"0 26.00 8.06 1 /02 24.7" -22./09

'"29.67 _32.46

7"38.01 42.68

2/00 0 /05.108 -44.71,,, 0 55.37 55.18

'"23.58 19."6

, JJ o. 10.60 735 20.87 22.1o}

'"0 31.73 30.62

'"0 67.62 -7%.20 1/01, 10.86 18.%3

'"O. _1.08

7"10.79 0.91

'"0 17.28 9.72

'"0 20.55 21.88 , 1 158.60 -15/0.99 ." 32.20 28.69

7" 59.33 -58.0%, 0 0 618.00 -628.35 ,)6 0 62.610 6%.55, , 92.%1 -98.11 ," 73.28 -76.82

, 1 69.67 -57.10, 1 0 1106.25 _1101.26 10 0 0 60./08 -30.85, , 36.92 -38.70 ." 45.02 -51.98 , , O. 2.'0, , 0 217.80 1':10.28 to 1 0 76.810 -62.31, , 20.60 -21.75 ." 24.81 20.07 , , 55.51 105.10, , 0 118.00 111.91 to , 0 o. 10.55, , 40.55 /08.7/0 ." 12.95 -10.65 ,

"O. -J.20, , 0 164.70 _156.26 10 , 0 120.21 _108.65 , , 76.61 102.20

''"n.27 16.',8 , , 71.68 59.09. , 0 87.9/0 7/0.72 10 .

"O. 7.45 , 7 132.00 _136.28 ." 38.92 3"./05

, , O. 0.6,. , 0 O. -7.05 10 , 0 119.%5 99.73, , 23.80 17.75

,

"30.51 -26.98 , 7 36./05 -27.910, 7 0 H2.9/o 142.88 to 6 0 154.16 1102.72 , , O. 5.15 , , 55.95 55.00 , ,

41.46 _28.88, , 0 153.81 _152.86 to 7 0 39.10 37.23 '10 59.36 -62.51, ,

96.95 -93.05,

9 /02.88 -32.37,9 0 121.99 _101.63 10 , 0 190.106 _186.98

'"7".93 90.28 , J 46.52 3".07 ,to 22.82 _12.33

.to 0 1101.1/0 1101.25 10 , 0 O. 2".72'"

27.02 -22.90, , H.9/o 35.68

'"72.37 66.66

'"0 O. -2.31 1010 0 115.11 116.89

'"129.00 12/0.99

, , 38.90 _30.2/0'"

51.61 %8.67,

"0 65.29 55.29 1011

"

61:1.11 -51..61'"

78./03 85.97, ,

163.99 1610.5%

'"78.52 n.J5

'"0 63.95 -%9.93 1012 0 O. 2.87

'"20.80 -18.23

, 7 39.72 31.06'"

37.86 }6.61

." 0 2/03.91 272.27 1013 0 119.60 116.17 ,16 52.92 /08.50, ,

49.5/0 39.75 '15 65.55 -55.J!

'"0 94.87 9/0.83 101" 0 61.72 51.53

'"52.75 -51.86

, 9 57.'J/o 56.75 ,16 61.78 SJ.25,16 0 2%9.70 _267.7% 1015 0 63.02 55.2/0 218 69.18 -72.18 510 70.10 _67.H

'172/0.09 _20.11.

"0 127.15 _134.56 1016 0 65.84 -56.88 '19

23.83 21.27 511 8%.11:1 -85.50 '18 o. 6.07'18

, 227.75 236./02 1017 0 O. 2.80'"

6%.6% -6".%9 512 66.61 -68.89 '19 25.55 -26.97, 19 0 65.%3 "8.103 1018 0 61.09 -5}.55'"

62.39 58.29,,, 75.86 -81.74 820 52.51 46.71

'"0 117.75 _120.10 1019 0 57.02 -45.78

'"/05.55 /07.85

,,,135.00 1}0./o0 821 36.18 25.67

." "52.70 101.77 1020 0 25.56 -12.19 ", 15/0.15 _16%.88 '15 O. -12.00 822 O. 1.82

." 0 86.87 76.57 1021 0 29.66 22.)7 ,,. 2%.87 21.58 ,16 O. 5.2/0 823 30.05 -23.~0

." 0 93.%9 88.67 1022 0 8/0.46 77.3/0 225 47.20 43.99 '17 20./03 12.74 ,,. 59.94 -59.39,,. 0 5%.02 -/02.65 1023 0 O. -3.75 ,,' O. 7.76 ,18 52.16 _49.16 825 51.%7 -51.39

." 0 82.82 -80.710 10210 0 115.22 -129.17"7

O. 3.J}'19 O. 1.49

'"39.2/0 _40.60

." 0 51.01 3".93 1025 0 O. 7.12'"

22.57 _22.61 ,22 70.35 -73.32 '22 20.87 110.79

'"0 26.55 -15.%/0 1026 0 59.71 53.67

'"95.06 97.25 521 65.80 -62.51 828 O. 8.76

'"0 26.10 -19.25 1027 0 76.60 -87.97

'"21.81 30.07 ,22 72.10 70.32 829 /06.26 %8.02

." 0 23.70 -13.94 1028 0 25.17 -30.107'"

O. 0.52,,, 27.87 -25.60

'"O. - 6.H

." 0 117.22 120.8} 1029 0 12.30 -9.19'"

20.68 22.67,,, o. -13.1.6

'"27.01 -24.21,

"0 76.26 73.61 1030 0 31.91 35.75 ,,, O. 4.28 525 35.91 33.0/0 832 11.9% 12.82

." 0 117.21 _122.67

"

0 0 O. -21.25,

"33.96 -30.27 5\!6 25.')7 _22.23

'"9./06 10.99

." 0 65.25 -62.77

"

1 0 127.90 _127.91 ", 28.32 23.710 522 50.62 -/05.51'"

10.98 -17.87, )6 0 70.27 75.87

"

, 0 o. -9.67 ," 36.95 -}6.295"

76./08 -85.1,8 8JJ 20.36 _26.18,

"0 28.48 -18.37

"

, 0 65.96 54.70 ,,, 10%.01 %3.99 529 O. 7.61 9, 6%.89 -49.82

." 0 57.05 -6/0.61

"

, 0 92.21 -91.22 ", 12.12 1%.655" 58."3 60.23 9

,52.21 37.28

." 0 22.79 13."6"

, 0 10/0.30 -30.02'"

68.69 -79.91,,, 1{,8.96 46.72 9 , 42.24 -23.94

'"0 %9.83 60.10

"

, 0 O. 2.37 ,," O. 7.74,,, 15.65 -18.49 , . 26.05-12.101,

"0 ,,6.74 56.22

"

7 0 91.20 99.67'"

2".80 25.53,,, 27.18 28.210 , , 47.28 }1.11

." 0 55.2% -58.85"

, 0 O. 8.31 ,., 19.12 19.22 ,)6 O. 1%.89 , , !.7.20 -?7.0%." 0 47.12 -/09.29

"

, 0 37.09 -25.69'"

55.73 -59.43 5:"5 1,,3.71 4/0.23 9 7 ,. -9.53.., 0 23.07 -27.tIt 1210 0 86.50 72.27 ,.. 21.03 -18.96 ", 46.01 -53.62 , , O. -9.49, 0 0 81.16 64.91 1211 0 73.39 59.81 , 1 118.61 -119.75 '37 O. 9.39 9 , 210.33 -21.111, 1 0 19.40 0.18 1212 0 38.27 -30.3% , , 71.01 -73.27 ", 30.9% 38.71 ,to 310.16 -30.6116 ,

0 }8.90 tit. 8/0 12t} 0 1,,9./06 _108.0/0 , , 103.13 103.11 ,,, 26.62 -7.35 911 n.86 36.23, , 0 112.70 109.05 121/0 0 O. 12.18 , . }6.0/o 27.95 , , 121.51 115.71'"

23.70 21.57, . 0 50.95 -310.51 1215 0 90.n 92.97 , , 139.00 1"0.78, , IJ4.23 116.12

'"37.76 31.35, , 0 169.10 -162.70 1216 0 101.73 37.38 , , O. -13.50

, , 65.85 62.37'"

61.3~ -51.110, , 0 195.21 -180.31 1217 0 11/0.73 -89.15 , 7 39.09 -39.33, ,

"0.23 24.93 915 22.8% -18.08,7 0 97.29 810.52 1218 0 36.58 U.98 , ,

"5.26 -%1.60, , 69.810 -56.67 91' o. 110.89, , 0 221.55 227.79 1219 0 28.52 31.71 , , /01.03 -39.96, , 16/0.50 -IH.94

'"O. 20.22,

9 0 tlt6.50 -139.65 1220 0 75.31 -66.11 ,to 66.64 -68.67,

7 46.11 29.3% 918 O. 11.30'to 0 166.69 -159.97 1221 0 71.H -65.08

'"O. 16.33

, ,42.88 -38./06

'"100.47 36.98

'"0 70.12 55.105 0

,1 106.20 52.66 ,,, 68.60 -69.75 6 ,

36.59 -31.069" 22.50 2}.06

'12 0 O. -tlt.51 0 . 1 53.8/0 -67.05 ,,, 81.}1 8}.91 'to 55.510 109.82'"

61.19 66.810

'"'",,,,,,

'",,,".",".'J!'"'"

.'"

,.. ,'"

,.. ,'"

,

'"7

'".'",

101010111012101310 I~1015101610171018101910201021102210231024102510261027102811.11 ,11,11,11 ,11,11 711.11,111011111112UnHH111511161117111811191120112111221123

".

",

",

",

"5

",

"7

".

",

121012111212121312141215121612171218

1~1~

",. ,. .'10."."'16018

0,"on024.".".,.03'0"0"0)8

."0". 0. .. ,. ,. ,. 5. ,. 7. .. ,'10'"'"..,."..,.16"7

'022.0027.5631.8}36.7728.4125.HIroJ.8lt

o.32.91050.4917.6630.91030.9072.4844.5222.8066.80

o.o.

43.28o.

28.9426.87

o.o.

210.66o.o.

30.57n.DS

o.o.

57.7322.0930,81102.0535.3411.7523.5932.45104.9029.673o.8J

o.o.

23.761ro5.7621.5431.0920.8)13.8715.6515.2617.38

o.46.0620.5539.17

o.12,2134.472J.H

o.45.61

o.19.50

o.38.25

o.o.

18.7834.74H.BS15.0719.7';35.6726.1918.2625.7118.2216.96..b9.6062.3066.',)69.28

103.""40.7389.7961.25?o.n75.31

o.58.2590.7027.3066.5161.3139.67)6,03

o.22.87

291.00128.00n9.10

18.67o.o.

1~6.10350.002~2.0Cl329.50

o.38.nl27.9235.78

152.07107.67257.00

~0.100

.-12.95-23.56

30.73-31.57-23.56

21.71104.7J

6.5C1-3C1.M-1t8.63

110.06-20.09

19.77-65.710

28.7910.77

60.78I. ~9

-0.70

310.870.77

20.910-25.62

- 9.7711.1121.1'9

6.6112.7"

-20. ~2-100.~2

- 9.1810.29

59.67-16.25-31.77

102.702~. 710

-10.23-110.81

20.17-310.3"-20.96-18.75

7. ~53.95

17.38-~0.28

19.0~-33.29-20.91

10.7"-110.87

110.55-110.97

0.7133.11

-13.07-29.27

1.7108.02

28.78-20.15

3.2/,H.08

-7.6815. 6~

9.78-33.11-11.17

- 5.n-21,.29

27.69-16.32-16.06-t5.6~-n.92

25.30-16.05-31.1,6

20.2619.06

<).Jl>78.39

-67.6690.03

-78.23116.51-39.99-90.69-52.92-56.39-71.81

9.22-55.60

83.55

6~:~~63. 2~33.70n.0212.77

-~2.5'j-292.22

122.80137.20-11.19

28.09-tJ.50136.76

-418.88-251.99

376.10513.4~

-39.0531.8929.25

193.109-118.77-255.09

35.21

z. Kristallogr. Ed. 121, 5

The crystal structure of hutchinsonite

'18, 19.","'"."."'25.26.27."."1JO

'J!')0,".","

, J6, J7, )8, J9."'", 0, ., ,, ,, ,, 5, ,, 7, ., ,210'"212'I)

'"215,"'17'18'19'",,,222

'"221,225,"'27

'"'"'JO'J!232

'"'"'","'J7')8239,,,

'"3 0, ., ,, ,, ,3 5, ,, 7, ., 9'10311312'I)

'"'15,,,'17'18'19,,,

3"322

3"3 2~

'25,,,'27328

'",JO3J!

'3',,,'"'35,"'J7')8'J9'"'", 0, ., ,, ,, ,, ,, ,, 7, ., ,'"'"

F,

o.5~.87

o.131t.51103.111109.3)18~.00128.79

o.101.6246.3578./i)

123.8162.8970.8627.3635.1929.6738.3066.0560.8275.285~.5616.5733.6695.0023.00)6.6625.10685.90

o.108.71

25.5682.73

o.27.910

o.28.~3

o.67.00~5.1828.75

o.1105.7036.69

o.36.7439.3236.3~

o.o.o.o.

30.1729.109

O.o.o.o.

61.5~o.

19.~118.02

O.o.

21,.81128.702610.00

60.73o.

30.6960.5861,.82

359.0065.29

259.0061.56

108.88o.

n.5712',.441')5.00119.010200.50

51.50o.

28.8381.0~')').92

182.5065.06

137.22o.

33.62o.

62.0896.06

103.39o.

63.0522.1618.17

o.40.8~20.8575.61

o./07.6888.09

o.o.o.

63.7937.101310.77~0.29

110.8~32.0057.1850.~5

'.8.61

/i6.6)13.88

130.81101.08

_169.6"-171,.99

110/0.09

1.5"_36.2529.5076.61

132.02-6).88_76. tit.-15.17

31.0225.7/025./0570.0662.110

_8~.83-57.00

21.51-26./05101.98

110.56-37.73_22.80117.25

7.2~93.9723.3567.66

5.7825.}I,

-3.86

26.791.02

-72.77-36.75

12.92-7.20

_1108.81-210.96-1.73

21.56-26.32

26.71~.81

12.92

-9.581.08

-9.60-9.12_10.010.-110.65

3.372.52

-70.103-7.10.0

18.1,7110..85

_10.878.9~

22.32-121.70-259.02

66.275.17

-17.45-5~ ./05

59.01310.3.32-56.86

_262.55-45.49116.95-12.09-30.30n5.33146.5')

_126.41_204.0t}

-39.26_5.20-25.18_610..89

37.42178.62-53.90

_149.68

-5.106

29.775.15

-57.2199.79

105.752.03

_61.6813.60_

8.03

-~.77

_~O. 5217.4886.7')

0.09-52.~1o.

75.370.75

13.632.89

-510..54-27.15

25.5722.90

-lM.87-20.15

It6.0740.1,4

Table 7. (Continued)

'12'I)

'"'15

'"'17'"'19'"'",,,

'"'"'25'""7'"'"'JO'J!'3',,,

'"'35

'"'J7')8'J9'"5 05 .5 ,5 ,, ,5 55 ,5 75 .5 ,5"5115.1251)

5"515

5"'175"519,

"5",,,5"521,5255265275

"'"'JO5J!5)053353',535

5"5"5"5J9

'", 0, ., ,, ,, ,, 5, ,6 7, ., 9,,,611,,,'I)611,61')

'"'17'18'19'20,,,,,,

'"'"'25",'27,,,",'JO'J!'3''"'"'35",'J7')8707 .7 ,7 ,7 ,7 ,7 ,777 .7 ,710

'074.5535.2667.69

o.77.50o.

53.910o.

60.810o.

83.96o.o.o.

50.79o.

81.22106.7532.89

o.71.28

o.51.89

o.o.o.o.o.0.01

201.0078.87

122.5739.2090.1078.70

l~Io. 99179.63156.67139.11127.781It1.~9

46.8753.1195.49

116.5517~ .00

106.047~.683~. 90~7 .1182.3986.0674.39

127. ~O8~. 3471.10.967.7323.1'975.3767.86M.69

101.2549.~~67.0820.992~.1929.1770.07101.5164.315~. 98

116.1564.~260.75105.65

119.1539.5082.38~3.1458.~9~5. 58

o.63.8832.16

o.81.7463.6733.2852.8278.1832.00

o.~6.5030.0025.00

o.o.o.o.o.o.o.o.o.

20.8338.5818.2617.6312.64

103.79186.54

o.157. ~O121.86

63.31Its.75

1J~.29167.28127.37

1j2.75

'0-72.41_20.68109.19

-3.6967.51

2.5837.673.56

56.13-

7.3875.28

3.770.05

-12.72J8.2212.60

-79.,6-39.27_21.~8-11.09_66.108-6.13-50,69

6.77-9.93

10.02

-8.~8

10.~0_8.210214.61

66.96_120.71

29.10079.61

-68.19-147.30

182.71152.51

-139.33-123.11

H7.5938.69

-~8.09-106.23-117.00

209.2838.1,4

-66.3226.0941.05

-76.95_80.87

57.32H6.51o-83.35-66.54

66.48-H.76-78.29-67.56-49.71103.54

107.15-65.04

20.14_23.46-30.27-59.72

27.2275.M37.49

-94.48-46.53-37.73

27.19_106.06

_21.01_66.06-25.85-1,1.16

27.73

-3.~7

106.5816.35

~.9172.04~3.11

-18.85-37.79

67.2223.~8

-12.27-31.33

20.11-1~.58

2.103.43

11.161.66

16.710.90

16.457.911.95

-20.3841.6820. 9~

-20.87_16.78

-102.H167.17

-7.47

_1/00.07110.17

43.2230.44

-126.33-160.83

123.2629.70

71171271)

7"715

7"717718

7"720721720

7"7"7'5726

7'77"7297JO

7"73273)

7"735736. 0. ., ,. ,. ,. 5. ,. 7, .. ,'10'"."'1)."."'16'17'18"9'20."'20'".""5'26"7.""9'"."'3', 09 ., ,, 3, ,, 5, ,, 79 ,, ,,10

'"'129"'"'"'16"7918

9"920'21'209"'""5'269'7

'"9'9"0'"10 0

10 ,10 ,10 ,10 ,10 ,10 ,10 710.10 ,101010111012101]lOtI,10151016101710181019102010211022to 231024

"0II .II ,

II ,

.119.4)77.H81.0722.27

123.92100.45

151.0621.5780.3570.8966.2962.~569.9661.6876.5232.4870.3218.3639.8016.6076.263~.4777.7438.9522.9420.32

o.o.o.o.o.

58.9639.81028.0973.0058.70

O.68.2)63.58

o.3~ .~331. 3~~3. 7725.99"2.109

o.62.7734.0561.192'.~~

o.~5. 73

o.24.6850.3231.~516.18

o.31.28

119.71137.55

89.1182.84

122.9276.101

126.17~5. 2269.8136.(}3

117.14135.35

91.5~o.

7~ .58139.83

95.1167.6057.4150.4093.455~ .8566.8270.7681. 2~32.8949.3276.1318.24

O.57.8083.89

'.59.52M.7334.9940.8749.01,25.84~0.982<).)2~3.5050.1224.~9H.05

o.24.50~8.63o.o.

53.20o.o.o.o.o.o.

122.75112.1,1~7.6897.86

'.-99.03

82.7770.10615.310

-113.99-23.70169.76

11,.20-73.65

56.0956.~3109.41,

-62.27-64.77

78.38-33.85-70.55

13.3131.0119.49

-70.101-H.82102.25-37.33-13.78-8.lt8-6.96

-1.fl91.39

-1.609.23

39.26-23.96-12.28

57. ~3~1. 56

-4.73-50.55

1,1.955.65

-23.17-18.31-32.36-17.49-36.77-7.01-59.87

21.27-57.93

19.4610.1640.81

2.80-13.73

108.563~ .05

9.95-5.J5

39.63-93.29

-126.3669.16

-57.28-104.37

57.53117.33

27.08-58.84

21.15102.10

-137.68-77.62-1.03

62.62HO.16-85.31-59.99

56.1'9-43.H-flJ.13

48.Gl59.8368.17

-7&.3132.2350.81

-83.4~-19.03

5.3947.8173.94

9.1'91t'.1370.542~ .18

-27 .~739.92

-12.6529.81

-15.9234.00

-37.9616.28

-31.12-10.99

16.06-39.60_2~. 93

7.51~1. 55

-26.64-24.84-0.25

19.09-12.92

2.50114.68

-102.31-25.31

96.~6

11 ,II 5II ,II 7II .II ,111011111112

11tJ111411151116

111711181119112011211122112311 2~

0'0'0'O.0100120"0"018020022I} 2~

0"028OJO')2o H

0"0)8

0"012. ,. ,1 ,. ,. 5. ,. 7. .. 9.10'". "'1)."115.16'17.18'19.20

."

2 58.552 32.522 53.272 ~8.792 115.1~, o.2 62.072 57.292 57.812 85.072 70.792 68.042 63.342 86.73, O.2 77.212 15.702 55.752 610.132 19.332 68.883 100.003 194.003 ~7. 923 150.003 83.813 100.8~3 55.1103 29.913 64.373 ~8.183 166.003 57.223 12.003 27.603 58.303 2J.023 52.063 48.353 75.183 ~~.~23 50.173 77.203 115.503 55.203 21.25,

'.3 61.53J 26.210)

20.223 42.923 101.253 27.983 51.723 25.0')3 79.10, o.3 79.383 28.323 81.053 57.963 58.633 61.173 84.823 52.093 ~O. 583 48.223 35.38, o., o.3 47.773 96.503 18.603 38.503 60.~5J o.3 5~. 903 57.853 40.343 27.973 61.573 26.223 55.803 61,.683 26.183 ~8.873 ~O. 793 35.053 o.3 41.633 52.123 80.973 ~1.033 166.003 83.043 70.133 54.683 51.H3 38.903 92.923 54./,83 123.15, o.3 24.003 25.003 28.353 18.003 58.1,83 32.523 65.~03 45.893 158.90, o., o., o.3 48.893 28.273 I,0.~5, o.3 54.9"

12312/,125126."128

129'JO'J!'3''))

."'35."'37')8'J9, ., ,, ,, ,, 5, ,, 7, ., ,210'"'"'I)'",.,,"'17'18'19,,,,,,

'""3'",,,,"'"'"'"'JO'J!'3''))

'"235,"'J7')8'J9

337

. '0-~7.67-33.31-1,3.08

40.13139.31

-7.66

-~9. 5652.24

_48.~2-83.57_60.64

62.5257.510

-93.91-4.63

76.49-7.55-33.02-55.81

16.765~.35

121.10236.01-51.85130.36106.17

-103.35_52.05

25.23-61.94

~7. 76-H5.ltO

51.1,811. 9~23.22

-63.72_12.18_46.07

1,9.76-82.35

~6. 5130.17

-113.76-138.26

-65. 2~-27.26_18.06

89."7-29.5~-19.31

51.00-131.09

32.13_46.86

21.0497.25

7.59_88.66-29.~2_86.16

55.76_~8.08

51.6483.69

-~5. ~930.313}.47

_22.18

-1.~1

16.7333.16

102.80-12.97-32.~8-')3.76-2.40

51.65-59.05

40.3823.28

-50. 2~-26.100-73.33

86.4213.88

-55.01~3.63

_~~ .810.-11.40_~8. 72_60.80

-114.68_~I,. 17170.103111.53-72. 8~

55.5848.~9

-32.9~105.23_108.66

12/'.312.42

-23.86-6.94

19.73-8.53-60.78_28.68

70.11,~~. 99

-158.5210.55

-10.61_8.46

-43.1,2-29.22

42.6712.98

-510.910

22

338

b'

'"'", ., ,, ,, ,, ,, ,, 7, ., ,,,,, U'12,,,,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,",,,,,,,,,,,,,,,,",,,,",,,,'J',,,"~a,,,, ., ,, ,, ,, ,, ,, 7, ., ,'", U'12'", ","

,.,,", 18

'"'"'"'"'"'"'",,',"'28,"

,"'"",

'"'"'",,6,"'J', ., ,, ,, ,, ,, ,, 7, ., ,

'", u'"'"'"'",.,'"'"'"'"'", ", "'"'",,''",,,'"'"'"'"'"'"">",'", ., ,, ,, ,

'0..36.109

161.00..

38.}2

29.0367.2358.1589.0239.2185.86..62.310..

161.50%2.76

'.135.2981.9128.5037.50..

109."7..62.97..7~.07....61r..72105.74-107.062/0.3580,085J.Ol27.75..

27.26-'105.310

'.32.6/036.75100.8365.'1

126.3100.78

66.3792.62

113.20l1J.JJ121.22

42.76105.5337.26510.1734.3039.25102.2181.39..

50.9298.2683.7036.82105.9157.8736.30n.oo

'.41.2/0103.76......31.8428.9050.49510.8575.8645.69

H2.981I7.n

108.8987.M

166.8/0100.16..97.63

162.0631.50

115.5158.6698.1665.3315.0028.1089.27

'.52.0530.0289.66

..106.1578.83....

58.93..

76.}031.6323.2536.63..

27.8954.91{,17.35",,}.J}

151.1132.5/0..

Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

"8.103

:".52155.10626.03

_1,0.65-22.36-t!Io.92_60.}7110.611-J7.~2

98.90-16.59_67.60-8.07

-162.58-3~. 78

0.27_1100.56

86.1111.103

-29.16-0.710

_108.8113.78

".9012.0868.~~17.67n.6065.56

-109.88~1. 76_8.H

_83.81053.2126.00

_3.63-2).13-5~ .68

9.10235.1930.59

-36.36-51.56

-119.57-136.106

57.91107.30

-128.70119.90

-132.87-37.59

J~.90-36.55

~2. 9220.9927.6531.1o~79.b6

9.51_510.82

_112.1282.5131.Y7

-37.8651.2523.6720.56

-9.70-39.~5

100.10-6.30

5.3610.8129.7127.107

-55.68-55.92

63.3232.56

151.16109.66-310.27

82.76-16).77

_27.08

-9.96

_100.58155.16

21.109116.98

~7 .62_105.66

_66.981).92

-19.9085.13

-110.13~0.5121.05

-90.59_10.11-1010.106-85.00

12.5816.8250.7715.910

-77.51_27.82_16.510

27.61-6.78_25.610

56.7819.16JJ.95

lu.60-17.29

10.32

, ,, ,, 7, ,, ,,,.,"'",,,

6",,,,.,'",,,'"'",,,,,,'25",,,',,''"'28'25".".'",))'",,,7 .7 ,7 ,7 ,7 ,7 ,7 77.7 ,7"7

"7"7117"7"7"7"7187197"72'7"7"72'725

7"7277"7257,0

7"7"7))

~)~. ,. 3. ,, ,, ,, 7. ,. ,.,.. u'"'"'"'","'".18..,'"."."."'"'"."'27'"'""."., ., ,, 3, ,, ,, ,, 7, ., ,'109

"'"'"'"'",.6'"'"'"'"'"'"'"'"

.O.

53.31o.

39.2931o.1,r,6

32.67BIo.0378.8395.31

1100.00100.~830.1,r,638.5768.3736.10937.6081.9761.0631.3921.7325.0533.0953.18

101.6/a102.2056.8383.97

'.o.O.

82.6/a1010.7671.53..o.68.9589.6260.9235.9668.30

O.60.8863.38

1103.0875.610O.

79.3259.10568.861,r,2.5826.1570.61101.32210.~O23.7255.7031.2617.8935.8183.3118.00

o.1010.89..58.50o.

35.35O.

85.6190.91..91.9159.0972.101106.52510.12..o.38.93100.99....62.7237.07o.

85.0952.10036.96..O.37.88..32./a325.7218.61019.28..105.5071.8868.1278.8970.99

o.o.

27.6630.61010).9368.2522.BIo25.92

103.80310.2132.3132.5920.01

O.33.2837.51029.31..

"16.53-102.00-2.58-2-11.51

17.9-1112.10875.5667.52

-9-11.52_128.08

25.31_11.75-29.99

58.107-31.23

28.07_89.23_57.82

-9.576.60

-23.1,r,928.0850.2192.1,r,3

_38.28-55.57

82.07_1.H-0.83-17.36

66.82-91.20-58.02

8.86_7.08

51.8677.50

-101.1021.38

_52.1610.55

H.69,1.80

121.0063.97

1.1.2069.13

_1.19.108

-62.67-31.66_11.22

57.2538.29

-19.59_18.06-50.57_29.06-9.25-27.57

85.508.797.11

10.6.36_12.82_65.210

10..5525.51

8.10578.2990.81

-1,r,.37_80.H

108.59-52.25

29.1610.2.06

-/a.05_10.10.8

26.50-31.53

1.75-11.73-58.510_35.66

7.8681.22

-10.9.30_32.60

2.193.93

-:53.9100.33

30.8525.9017.69

_20.031,r,.12

-32.610-57.77

102.72-61.29

107.27-1.92_2.60

23.21-19.73-JJ.73-56.27_16.70

11.10586.109

_29.16210..76

_25.92_2.11

8.31-25.31

29.7927.80

5.59

Table 7. (Continued)

'"9"'"'",. .,. ,,. ,,. ,,. ,,. ,,. 7,. .

",

10101011101210 1310110101510161017101810191020102110221023102101025

".

u ,u ,

",

u ,"

,"

7"

."

,1110111111 12

11131111011 151116

111711181119

".

",

",

",

-125

",

12 7

".

",

1210121112121213121101215

0'0'0'o..,.0120"0"0"0"0"."."0"0"."."0"."0". .. ,. ,. ,, ,. ,. ,. 7, .. ,,,..".12."'",".".","'".20

'"'"'".".".".","'".".".".))

.".","

'0~3.86100.2031o.1,r,9

22.5239.75"2.02.\3.8255.7J37.0719.96

o.o...

27.02107.5860.61028.0291.1726.710

O.107.02

'.16.510o.

3~. 9117.5317.%258.0230.91..o.

56.90o.

26.1562.91103.66..10%.01O...

%2.30O.

19.98..25.5830.3835.26

0.3026.5326.~318.5718.10.037.81100.2320.86~2.59

o.o...o.

57.6720.662~.50

270.00109.501106.00288.00

36.8751.83

177.~0375.00133.57

31.07128.7110~.61

H.0269.30

162.17139.99

28.10921.05

111o.1,r,1,r,

18.21135.00

105.13123.50

96.00210.38"9.1,r,560.3626.3862.1656.22~8.09

1010.97127.210

31.02..119.92

105.1523.33"8.6597.5335.910.

102.3122.70101.60%5.10725.0863.10623.9088.81027.90..27.9031.7160.5350.9338.8118.60

'0"2.35U.23

-30.50-19.09

21.81-21.53-29.72

37.89-25.59_12.96

2.50_12.86_

0.2215.510

-32.85-53.56

20.8877.9518.100

-3.3736.59

-1.96-10.10-3.27

310.7213.1717.72

-100.0128.63

10.138.88

,,6.32.\.65

18.18-57.99_)8.20_12.10_100.210

-3.23_0.31

-1010.32_3.60-19.103

0.26_18.~1o-210.03

28.393%.68

-18.90110.2813.78

-16.71-33.75-38.00

20.02-102.69-7.109

2.600.957.97

1,r,1o.77

-15.1,r,221.71

299.09119. 5~1106.01

-Hl.3929.50

-58.32217.80

-382.38126.BIo

29.1071106.90

_1110.38_21.110_69.30196.28

-159.6026.01

_7.1088.20

_16.105107.96

80.2.\11010.65

-109.25-25.07

67.2690.7326.210

-810.79-71.63

50.91-107.23-155.88

-310.105_8.13

_120.66-32.29

210.28108.19

-93.39_32.61

98.85110.5637.63

-3~. 7817 .~655.2813.61

_910.2813.70

0.60_5.82

-15.3352.11102.53

-31..\7_7.68

,"

,".".", 0, ., ,, ,, ,, ,, ,, 7, ,, ,

'10,"'"

'"'"'"'"'"'"'"'"'"'"72,

'"'","'27'"'"230

'"'"'))'"'"'"'"'"'"'", 0, ., ,, ,, ,3 ,3 ,, 7J ,3 ,'103",,,,,,,,,315,,,,,,J",,,'20J21,,,,,,,,,,,,3'6'27J"J'9,,,

J"3"3"33103353",,,J",,,, 0, ,, ,, ,, ,, ,, ,, 7, ., ,'"'"'"'",

"'"'"'", 18'"'"'"'"'"'"'"'", 27'"'"'"'"'"'"'"

.28.0023.0061.5530.0025.00

2106.9026.7622.95110.0062.35210.87

222.0088.12

123.11~5. 7049.1925.0029.29

o.287.00

27.87U~.107

21.9028.3818.60

105.0925.~7

180.8381.78

113.781,r,0.09

106.6732.23H.3325.9397.38I,r,O.2961,~3

o.1,r,3.5625.1156.1620.87

106.2151.7867.0175.0~65.6265.5235.58

110.9688. 3~22.7039.11050.3569.25

113.71088.0621.7050.9992.7976.6722.3031.1799.7622.3076.27..o.

31.7066.3~61.2~37.2458.8565.99

o.20 .5~22.93O.

21.2890.602~. 18

O.O.O.

2~0.00121.002~5.00..20.~237.5070.5079.61

19~. 50123.98

86.90~1.00

100.102o.

132.7788.78

222.1087.31

128.~5o.

1,r,7.2626.7182.9058.6353.88

101.n50.6829.7073.18

o.111.65

71.56121.110

51.2756.92

F

16.061~.50

-%7.1817.89

-11.38-250.310

-29.03-21.510

6. 9~-82.38_18.~62~7.32112.20

-H).77-~3. 710_102.68-21.45

18.42-5.62292.10

23.59-120.39

-19.65-13.72-12.09

_112.67-22.52171.37

70.~2-112.37

_~0.41o-102.)7

-25.35-29.15

16.0196.2937.95

_60.8~

- ~.1741.31

-21.61-57.78-22.11

98.20101.0168.83

-82.1067.6107L3226.00

_122.60106.1,8

17.17-31.35

38.9172.71

128.26-97.27_20.68-102.510

97.77_62.1'7-10.35-20.105101.!!)_6.28_80. 9~-2.98

- 10.93-27.29-55. 7~

56.51-25.58-56.45_610.06-1.04

22.27-2~ .~O-5.38

19.0804.81

9.89-15.00

1.9721.72

2~6.26112.109

-2109.52-7.69

17.0020.00

-77.07-78.30201.58129.51,r,-78.11-40.83101.32

9.101-1100.25

-95.48235.79

79.78-118.96

-7.910~7 .68

-28.29-77.34-56.10

56.10799.23

-51.410_10.41

70.0114.13

-113.77_81.18127.1,,1j,1,r,0.65

'--102.29

,,,'"'"'"'", 0, ., ,, 3, ,, ,, ,, 7, ,, ,'",,,512'"'"'",.6'",..'"'"'"'"'"'"'",,''"'"'"'"'"'"'"'",,,'", 0, ., ,, 36 ,6 ,, 6, 76 ., ,'10,,,,,,'136"615

'"'17,..6",,,

'",,,623,,,,,''266",,,

'"'"'"'",))'"'"'"7 07 .7 ,7 37 ,7 ,7 ,7 77 .7 97"7"7127"7"7157"7177187"7207"7"7"7"7"7"7"7"72'7"7", 0. .. ,. ,, ,. ,, ,, 7. ,

. '.25.U...

-26.11

-59."-41."-52."-78.01

-1J9.31~7.6132.51127.2'~,6.0I18.7\

10M?

1°'.11-31.1.2..1t

10\.0

30.'1-30.1i

5MO~.~

-43.66_\8."64.01..~

-16.n-27.1'9.1631."7."-52..50

-7'-'264.11-2'.?}-19..3

-~.79

13.16~26.7'-2~.~

27.1\

3%.9'-61..1

55.\02).91

-102.9'-13.78

111.\6104.62-47.73

-192.7630.306'.20

-7~.0010.\338.06

7.91-78.69~58.5J

55.\736.\5

-89.3139.7156.6986.H

-37.16-1109.88

93.1744.\5tJ.~o30.1216.H2.09

-15.\\46.62

56.03-1.84-63.33

6.87-66.92

28.53-32.85-85.09~67.66

56.18-~7.00-44.96

50.Mi49.88

_28.63-109.09

3.8945.3911,66

-88.~2100.H

-22.4163.95

-63.59-7.18

60.6925.68

-13.59n.3160.36

-24.78

'-828.1355.77

-15.57-21.59-2.30

-142.19118.58

7.17-108.89

-30.13%7.48

119.20-21.\9

31.41O.

36.1858.284~.8861.01,r,83.95

153.2551.51~3. 3134.076~.5828.02

116.05103.105

35.7635.8198.2538.2531.2856.~6100.29~7.8761.2966.6~57.3321.3027.06

o.30.89

o.60.5~78.5367.6~31.2017.78

o.19.57H.98~0.1827.37103.9673.9966.28~,29.70

115.8023. 7~

119.5011~.10

58.310186.60

~6.9278.3174.3515.6561.5021.8987.2459.7560.8234.7886.01H.8860.0182.8632.78

150.8097.2046.)625.0436.3616.67

o.22.2655.9877.52o.

90.50o.

67.8928.10836.0195.5380.006~.8756.891,r,6.7456.5057.7732.0455.27

o.~7.0618.5086.87109.6330.1766.6672.79O.

58.7829.1020.591,0.466().10921.101....75.6228.3329.7730.35

16~. 73129.91,

2~. 71133.1}

43.1,r,662.109

146.63310.25

. .

. .'10.U."'".n'\5.1<"7...."82.....22."82'82,."827."82'."'J!, .. ,. 2, ,, ., 5, ,, ,, .. .".'U'",n'"~.15.1<

'",..'"92',..'22."'".2592'92'10.10.

"2

",10.10,10,

",

".

".

101010111012101310 H101510161017101111019102010211022102310 2~

".

".

"2

",U.

",

",

"7

".U .

111011t11112l1lJ11 1~111511161117

".

",

12 2

",12.12,12,

12 712.12 .121012111212121}. 2. .. ,...".12.11.".18.20.22

."

P163.66

90..\633.57

152.6150,0317.90

153.8729.2881.23

115.02..93.63....92.82..90.%279.692%.61

105.2571".3838.9286.17

"".2539.1182.8939.7926.1:1382.6)5%.97..60.0259.5638.55"7..\858.10%6,80..61.8257.90..50,6023."33.7227.811t1o.9726.2"21.551'5.88'<5.5%72.7966.97.\'.2632.810

103.15..86.61

120.75107.80

135.9831.6052.8)78.25..105.78"0.31..60.31....105.26".1t5.7"

131.29100.8985.8162.3126.210..19.3071.0070,3318.50"-5.50/'\6.9637.9621.806u.71o17.1,,632.2%18.(,0

"0.26....7J,oO113.110

%6.2332.9877.0269.3030.9787.5023.6081.9952.97510.6990.6069.0013.91..

108.5030.111,81.01103.2656.0823.8116.57109.8052.8339.7\

The crystal structure of hutchinsonite

P

-1109.9386.1-'033.22

-157.~0_1,,1.v2

7.63137.21-30.63-73.56109.20

0.05_810.5\-12.95

3.15810.20

-9.21-76.75

75.6825.100

_68.78-58.50

27.1388.-'15_31.6829.10672.39

-29.35-13.13-710.58

109.29-10.33-57.66-51.32

26.27

35."6-59.75_1010.86

5.60-60.93-51.76-7.79

\2.99-17.55-28.16

16.101,33.8516.30

-19.38_8.56

36.2262.01060.11028.86

_26.2692.J5

5.57-79.28-96.31-H. 210

152."322.82

-107.8579.10

-5.510_101.02_103.08-3.10

57."87.390.98

70.150.52

_n.21-105.28

-310.5085.1855.70

_21.369.359.76

62.H-60.33

16.10738."8

-27.98_27.86_10.12

51.686.89

-23.67-13.09

JJ.5°-1.39_10.11-53.109

93.107-JJ.13-17.75

53.10553.75

-19.91-78.22

10.1385.79

-39.38-109.011

70.0955.21011.78

8.69131.70

25.79_82.87

107.3859.8523.21

-12.31_37.28

106.07-37.22

026502850305032 ,

03" 5036,OJ85, 1 ,12,

",. . ,

",. , ,. 7,,. ,. 9,1105

111 51125113 51110 51155116511751185119512051215122512J 51210 512551265127512851295130 ')131 ')132 ')133')

13" ')13551365137 '}13851395

2',

22')2, ,2. ,2, ,2' 5

7528')2952105211 52125213521/0 52155216521752185; ~~ ~2215222522352210 5

22552265

22752285

22952305231 52325

233')2310 5

2355236523752385, , ,, 2 5, , ,, , 5, , 5365, 7 5, , ,, 9 53105J11 5312531J 531/0 531553165317531853195J2053215J225J2J 53210 5325')3265327532853295330533153325J JJ 5

J3" 533'j 53365

Table 7. (Continued)

P,

1210.15"1.10925.6818.7927.1313./r,585.8217.0712.2196.5093.5057.61\1.3/r,105.8126.6,..H.Ol36.82..70.7153.2960.01100.108/r,5.0038.1935.8755.8533.50

109.98..106.2733.6117.1139.9035.22210.106108.98'58.9217.88..21.2725.11023.90

12.8"62.5017.8/0

17.75100.00131.50

18.92

"2.10181.2155.10329.27/,7.910

52.80

30.3832.88

51.0753.26

107.J/,

22.29

70.51610.9933.10326.10820.107

55.6862.05103.85....18.60'8.5573.92

O.21.2019.'1

O.17.5128.691/0.6357.10712.5053.16

100.78118.06100.21

56.9322.3755.3926.22103.0515.6035.351,6.7559.5227.6576.31"3.5527.2872.22107.0238.5663.3072.7619.810109.89..17.5351.29..

108.35..109.5719.60..28.1333.3"9.50

_1100.79-38.73

19.75-11.23-JJ.56_10.18

76.2521.38

7.30123.310

_103.30_62.67

1010.32_108.50_27.09-0.51-JJ.99_38.69

11.5172.10658.12

-62.53"5.3710".2039.6236.28

_61.37_25.15105.77

5.110_52.17

35.27_21.59-J5.09-101.38

27.105108.81

_710.01

-1".09-

5.1523.66

_26.52_27.110

21.0165.106

_11.118.80

99.59-139.92

12.72_100.25

-73."95/'.58_26.103106.92510.32210.10100.57

-38.97-5\.09117.106_20.21

75.0558.82

-35.7522.82_

5.100-56.93

58.95-103.77_2.106

12.55_16.96

102.59_710.98_10.70

25.65-19.67

5.791/0.26

_30.6717.53

_10".108_110.07

/09.1293.8/0

_110.26-99.23_51o.JJ

15.75105.07

_23.17/01.89

_10.6239.61105.09

-51.26_23.81

87.8336.73

_2/'.0370.11

_105.19_36.80_72.76

83.7610.63

-56.5102.11

-13.10259.15

2.96_107.61

11.6757.56

_13.90

-3.52

2/r,.50Io9./r,6

- 5.09

h k

33753385. 1,. 2,. , ,. . ,. , ,. , ,. 7,. , ,. 9,10105"11 5"125"135

'I"5

10155

"165/0175101851019510205

'215102251023510210 5/0255/026510275102851029510305

"31510325

'JJ 5/03" 5"355/036510375

51', 2 55'

,5'

5555

5'5, 7 ,

5'5

5955105511 55125513')51/0 551555165

517'5185519552055215922552355210 5525')5265527552855295530 ,5315532553355310 55355, . ,, , 5, , 5, , 5, 5 ,, , 5675, , ,, 9 5610 ')611 5612561356110 5615561656175618561956205621562256235

62" 56255626562756285629563056315632563j 56310 5

7' 5725735

7'5

7'5

7'5

77'7'

57957105711 57125

29.8936.53

116.0033.17/09.5757.67

136.9283.6856.8850.91083.8932.5876.10/065.1J71.76510.671010.1029.8079.5520."5..65.76

10".32210.50O.O.

56."782.9/'1".0641.8835.62..O...

39.21..27.710..26.5020.6563.15

107.1371.0166.7735.62/01.61020.}}45.6130.10768.6139.0523.6999.2010/0.71"5.0155.70..53.015/..1056.5865.2133.51027.9618.25

O.47.81055.07..106.1322.3611.0/0

8.6}20.4018.692".59

133.7891.05..50.5593.2836.82..55.2792,12107.7962.13..

105.91059.3950.92/00.7566.76

O.30.8019.9755.01..36.109..12.3327."6100.0518.10637.56..26.9122.0533.02O.

8/0.1158.8586.0753.910..66.89..39.JJ....100.69

P,

-36.33H.81

-107.1823.610

"1.59"10.30

1}2.H-78.51-53.18-103.93-86.58

22.7682.21

-55.6567.83

_48.20-38.95-30.48-91.28

17.%1-5.108

62.59107.62-17.23

9.5116.12

-'is.''''910.0212.31410.01031.77

4.13_10.12-7.30-109.25

5.3/0-JO.Io6

8."735.6108.710

58.75-86.38

69.3363.22

-23.56-35.108

17.99_"0.8'

21.7262."827.81

-11.70-100.55

101.59-103.13-58.61-8.'1-109.55

67.91058.610

-69.H_28.101

2/0.92-12.67_2.18

"5.01067.81

-3."6-53.75

22.10111.88

-10.')3-21.22

19.6/017.':16

-121.0878.32

0.17r.t.2078.n

-28.01;5.02

-10".89-82.72-39.78-57.67

2.86101.19-53.30

"5.62_100./06-75.12-5.21_28.66

18.5763.76

-7.1/03".21

10.108-15.22-27.25-"10.56

15.70101.66

6.9527.3821.68

-32.25-0.67_81.62

"".6772.691,2.89

0.90_60.5/0

1.58-38.78

-8.18

-7.010-38.11

713711715716717718719720721722725

7"725726727726729730

7", .,2, ,, .

. 5

. ,

: z

: 1~

'"'12813

'"'158"'17'18'19820821.22

."82/,

'25826827'268299 ., 2.

,

9 ,9 59 ,9 79

,

9 .'10911912.13

."915

."917918919

".,21922923

'"925.2610'10 2

'"

,10 ,10 510

,

10 710 .10 .101010111012101310t/olOtS101610171018101910201021102211 .11 211,11,11,11,11 711 .

11 9

1110111111121113

111"1115111612.12 212 ,12 ,12 512 ,. 2. .

P310.12"1."250.55107.59..106.37..100.2271.2533.80..18.1325.70..29.3719.5314.107110.5753.50102."2".27.J5

103.508t."7

O.60.5132.006".5328.23510.83"2.10332.9620.15

O.1010.13110.36..13.5160.2"71.17}1.93

1".8813.10536.31,110.5710.71,

110.5"9.73O.

38.0853.0128.10'55.51039.2230.0121.7228.2228.8725.1736.10123.61107.':;811.7111.7111.7118.1912.6715.06610.2720.9259.7123.7710.6712.7934.11/02.0"

O.O.

13.7711.7911.6"21.1,7

o.O.

26.8221.8937.1735.8016.0010.}213.8020.3529.6716.13..21."725.2130.00110.8534.7122.8810.1olo21.10313.71..13.77110.0515."529.3225.13

6.7523.10628.95100.97..O...17.9531.81

128.20

P

35.6237.74

-"9.18-IoJ.57

9.71-102.89-11.38

36.1>270.102

-}Io.G60.58

17.7329.52

-12.30-36.59-2".3718.0815.66

-56."632.2/,8.80

-18.90-310.59-71.71

6.7555.2126.3665.10625.26

-51.393B.JG

-23.8115.9911.105"2.1,015.00

9.8"-17.23-62.15_67.102-}6.8/o

16.17-12.68

1olo.109-16.100-15.80-19.48-10.63-5.93-32.97

53.78-21.89-51.26-28.85

210.10-110.73

25.3225.710

-16.99-33.18

19.6651.88

-13.2106.03

12.1320.0211.12

-15.95-55.110

21.0155.08

-23.JIo10.6911.72

-36.3738.8"

-3.18-0.65-15.28

1".103-8.30

17.18

-1.582.08

27."720.15103.48

-38.3511.10

-6.210_6.16

15.2228.99

-17.0106.010

-21.75-23.21

30.7610.56

-39.61-21.08-10.67

21.31016.57

5.5013.8518.3217.3/025.77

-27./r,913.2125.101023.28

-101."3-8.8"-2.01-6./07

20.9J59.17

-12/0.25

. ,. ,'10'12."."'18.'".22.".26.26'300320"0)6. 0. I. 2. ,. ,. ,"171819110

'"112'13."'15."'17.18

~~~121122123

12"'25. 26127.26'29'30."')2."."1 352 02 .2 22 ,,2 '),

72829210211212

'132"215,,,2172182192202212222"2"2252262272282292"2"2)2

2"234235, 0, ., 2, ,, ,, 5, ,, 7, 8, 9'10

'"'12'13

'"315,,,'17'18'19'20321

'22'25

'"325,26

'27'26'29

".'"

339

F89.0022.33

123.00123.50

106.8221.9969.1580.2919.09610.7552.10155.8945.2512.2626.05102."7

121.301010.50

20.1931.583:2.4161.8957.73

11S.90163.00160.00

1olo.10523.0921.38

".89."688.0786.11210.9023.2030.0679.9063.8975.39

1102.1367.3732.803~:,)9

3".5817.3l133.5639.89

115.3621.6"57.15..12.9()30.7617.102

138.9029.M71.50o.

59.0"o.58.9316.5683.76..72.1'928.1830.5827.27

5".39O.93.2932.74.33.6725.871,2.6121.7759.1118.0186.73

'19.6917.310

o...15.9533.7719.5655.2730.8"

139.100..o.18.606,.8636.0988.6}86.77

159.0017.36

O.19.9/027.0375.28

117.06O.

69.71..510.6088.7522.53107.06

121.182".9065.6618.21

O.70,2815.01022.8285.66

95.09-21.86113.01

-118.7953.1"23."565.95

-92.0725.05

-59.75108.72

_62.124.7.26

-8.7516.76

-"0.108139.01

-12:';.110-25.15-101.07-"0.28-77.85-72.38120.81170.29

-163.10-IoJ.I,O-27.20-10.109-5.29-89.92100.61

95.54.-20.99_13.06

29.103-91.32-65.49-88.23110".69

71.58-35.8"-36.26_6.02

30.97-16.25-39.05

4.2.6189.9812.4.7105.6510.11014.1'5

-36.72-16.97129.80

3'.2/0-76.71_

8.62610.73

-2.52-63.25-17."2

90.278."2

-81.37-23.60

31."625.51

-107.~n6./'3

103.4.230.8J

-33.52-22.70

39.80-2l1.38-52.58-16.9"

85.6216.07

_22.64.3.617.29

13.89-29.72-9.95

5l1.8828.01

1"5.10610.03

-2.101-16.91

72."5-J2.52-95.109

96.85160.107-13.76

2.7620.3523.31

-77.53-123.78

-1.97

73.978.16

-510.28-85.810

21.101-/07.62

-1210.3123.31073.57

-17.9612.0072,1318,75

-22,65-69.35

22*

340

'"'"'", 0, ,, ,. ,, ,, 5. ,. 7. ,, 9.

".

", 12

'"."."."

,"'"."."."~ 22

'25

'"''5."'27.". '9'30'". 30."'", 0, ,5 ,5 ,5 ., 55 ,5 7, ,5 95"5"512,,,5"5155","5"')19

520521522'25'"5'55"'27

'"529530

5"'30, 0, ,, 2, ,, ,, 5, ,, 7, ,, 9,,,,,,'12'",,,61':;'"

10.5.9339.5555.24

n."-?35.1660.7527.11.77.5942.0060.3120.6942.6]

O.91.3646.2057.86}6.4268.93

O.O.

)8.4026.1517.7170.1:!037.0042.73

O.J1.10

O.10.8.39)1:1./,848.5523.672"-.91

o.

37.""20.350.66

85.0721.1571.0719.1829.36

100.1.852.07H.41

1}6.9071.3210.9.3837.79}0.91

O.53.1216.7969.'1028.4082.6065.67)8.9"68.4763.3458.177"-.26

O.10.7.1238.3318.2720.2812.10.011.198S.0j64.3760.5727.37}6.5059.1554.3952.'>967.1:1021,27n.,s28.445'5.506~. 7833.412"-.56',':J.7f1}8.60

Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

"310..2933.9110.5.73

7.5032.59

-55.89-23.20

87.1010.2.33

-61.05-15.5"

10.6.093.02

-95.}0-45.84

57.50}4.66

-66.61-10..61

11.0532. 7~

-18.92-21.77

76.3537.25

-~~.21)-9.1)1)

3D.75-11).79-~3.11)-31).61

51.8628.73

-25.981).67

31.91,12.79

- 5.91)-79.41

16.6671.76

1.33_26.~211)8.21

51). 9~-6.51

-137.8571).1)151.1)1

-37.12-32.81)

~. 7753.8011). 9~

-73.1)~-25.56

83.19-66.79

3~. 5767.7665.31

-52.43-71).69

6.1~5°.31

-35.22-16.78-11.51

7.969.05

-88.75-58.13

63.M26.~3

-3'>.~5

-63.1253.0652.H

-67.6717.75~0.1119.96

-5~ .1~-&~. y8

31.2127.21,

_~6. 96-33.50

'",,,'"'20,,,622'25'"''5'"'27,,,''9'>07 07 ,7 27 ,7 ,7 ,7 ,7 77 ,7 97"7U7"7"7"7"7"7"7"7"720

'"722725

7"7'5726727728

~2b, ,, ,, ,, ,, 5, ,, 7, ,, 9'", u'"'"81/,815

'"'"'"81')'20'"822'25

'""59 09 ,9 ,9 ,9 ,9 59 ,9 79 ,9 99"9U9"'"91',9"9""7

"50.55~O. 5337.0839.5827.8629.135t.2110.3825.3013. 7~57.7826.~723.8426.13

107.92115.98

~1. 97~0.8555.8588.9722.3116.29~0.11,80.0621.71~9.M62.~039.2812.7299.8585.3961.19

O.65.8237.3626.8830.9537.292~. 9569.0~55. ~615.0670.2318.1'966.383).8221.7358.8916.3040.8366.8722. 5~22.3137.3938.83~7. ~931.5148.5729.6711.9531.4331.7"10.S0~0.6912.72~~. 71,53.2713.6633.9619.1735.20~5.2876.2651.335~. 7459.3341.2665.568If.~615.6023.5J~3. 3&54.131~.16~O.I)I,79.3632.1,538.79

55.%1041.60

-32.51-36.31

26.0029.23

_50.70_6.65

21.H10.35

_50.21_27.~2

16.0822.87

102.08_t05.72

-34.3937.82

-56.03-91.03_21.22

9.793~.~0

_85.9818.96106.87

_56.102-33.84

8.88101).88

93.07_60.94

8.6066.763~. 79

_22.78_30.11

n.~927.08

-59.7135.15H.76

_62. 3~_19.28_6~ .26-30.57

13.9858.86

-11.27-35.90

63.1115.72

-23.05-32.58

37.01~3. 78

_28.75_~I,.1,6

28.51,13.910

_30.16_}1.~~

H.Ol~~.I,6

_8.80_41.06

"3.36_1.(,1_33.60_12.99

29.01~3. ~2

-71.054~ .6150.90

_61.~9-33.27_63.13

7~ .08-1.90_20.90

~o.n51,.20

_H.86-31.93_72.71

27.3926.29

Table 7. (Continued)

h k

9"9"'"9"922

"0

",

"2

",

",

",

",

"7

",

"9

10101011101210131014101510161017

U 0U ,U ,U ,

" .U ,U ,U 702

0'0'0'0"0"0"0"0"020022o 2~0260"0>00)2, ,, 2, ,, ,, 5, ,, 7, ,, 9,

",

"112'"111,,

"11(,

'","

,"'"'"122

'OJ

'"125

'26127

'"'29'50

'"'30'n2 ,222 ,, '.2,, ,, 7, ,

,99.2395.9516.3526.49105.1929.2549.5266.61

O.81.6921.3723.106~6.5526.3339.8432.2~

O.~2.109

O.5~.61~0.3~26.1221.9592.2770.1157.363~ .0037.1064.~427. 9~12.91

6.059.08

88.6013. 9~19.2385.4033.66~6.5835.2':;29.4065.7758.35

o.37.4912.2846.5913.9637.801,2.2659.3629.1539.9818.8332.96111.2071.3846.4739.1521.0748.5737.3540.3512.17111.3878.1122.7011.7754.3613.3018.8921.0142.5611.3312.7811.3430.81,42.2328.0029.H25.72

O.52.2~27.5917.8428.6056.38

O.

"-82.7J79.2~16.01

-19.48_5~.40

15.95-39.09-49.38

8.0069,,~0

_5.24

_14.8637.2320.76

-30.27_22. 5~

3.5535.50

-2.29_49.4~

39.2927.45

_29.80_78.82

57.6450.16

-26.973~. 9763.0726.5310.40

_8.27_16.31119.65

14.2320.0388.1830.12

-1,9.3330.27

_32.3153.78

_1,2.0910.57

_29.41_3.16-40.03

18.9~56.89

-56.9776.6935.55

..J,4.13

-12.5"-34.)110.7478.9341.83

-39.32-15.87_5°.68

36.37-36.43-10.49

16.32-87.37

22.64

-5.83

-56.80-12.35

14.9220.2746.06

-3.393.36

_6.01-23.79

38.88-22.91

27.86_26.83

7.60-~5. 33-29.05_16.21-26.56-5~. 37

6.53

h k, 92", U2"'"'"'"2"2"'"2"2"2"'22225

'"''5,262272"2'9'>0

'", ,, 2, ,, ,, 5, ,, 7, ,, 9'", U'"'"'"'",,,

'"'"'"'20'",22,OJ

'"325

'26327

'"329

'"'", ,. ,. ,, ,. 5. ,. 7, ,. 9'". U,"'"."."."

'"."'"."."'22'25'"'25,26

'27

'"."5 ,5 ,5 ,5 ,5 5

,

36.3034.4459.8942.1856.1522.9666.38

o.43.70

O.34.%1

o.18.6920.2750.26

O.13.72o.

44.0630.6759.3621.5457.2427.9148.27

105.9679.72)0.31o.

68.09~3. 5792.18H.08

o.M.~981.4937.8229.79

o.~8.65~5. 8750.24

O.56.1338.5724.1533.544~. 53

o.o.

~O. 7839.94H.8642.~025.67O.

11.78O.

~O. 5~98.50~6.42

o.31.0516.3332.7763.3122.4048.10O.

13.02o.

~2.4922.0235.89~9. 2728.4825.1658.49O.

14.72n.7327.66J~. 7223.72

100.1721.78~5. 5487.16

"-35.4632.8563.7845.75

-58.57-20.54

73.17-<;.92

~6. 542.80

39.203.22

-21.77_15.22

~5.1,~1.67

-10.57-0.29

31.8719.69

_67.20-14.85

58.62-33.33-49.17

Y4.9669.7026.80

5.09_64.y6

45.98-99.35

17.<;0~ .23

-64.988~.6339.20

_28.80

-0.6/.

-51 .~2_42.10

57.51~. 66

60.07-32.71

23.1336.79

-47.1,14.142.13

-31.3927.13

9.58-33.81_26. ~1

-3.81

-5.79

-~.25

39.01-100.79

-38.911.97

_27.620.61

27.96-64.n

24.59_40.44-1.08

11.77-3.62-3<;.67-23.31

35.9535.1,8

-18.67-16.96

~9.29_6.14_11.68

1.8420.6331.3119.26

-107. 7~16.34

-41.14-90.26

5,

575

,595"5"5"5"5"5"5"5"5"5"5205"5225'55"525, 265275", ,, 26,6 ,, 5, ,, 7, ,, 9'", U'",,,

'"'"'"'",,,

'"62062.16226236 2~'2,7 ,727 ,7 ,7 ,7 ,777 ,797"7 U7"7"71/,7157"7"7"7"72072172272.3

7"7'5, ,, 2, ,, ,, 5, ,, 7, ,, 9'"'"'"102.

"56.~337.97

O.39.3672.8242.9"-20.7122.~868.1~

O.55.3119.2738.8827.11,23.7647.3748.8450.3522.5937.4151.96

O.50.8853.69~2. 563~.9218.5813.1019. 9~18.37

O.O.

21.3566.1768.18

54.1"-44.5921.~322.9021.8124.1551.07

o.n.49~8.0J37.20

o.13.1931.9555.0149.4051.6750.78o.30.3323.3565.~215.7115.~~29.6130.995~. 7719.~3

O.33.7855.334L~011.3359.63

9.8218.5216.70

O.19.09O.

24.48o.

30.2761.3753.76

O.22.8318.7131.6337.1225.75

'.5J.l~36.79

-6.5235.69

-83.16

-46."-19.60

1404082.0J

-1.2254.8'2t.1i7

-36.9226.70

-19.n-\7.46

42.0142.1117.9728.72

-4J.66-].99-~5.70

49.5'-39.J8

32.9812.'011.1815.'821.H

-1.5t-3.51-13.23-58.70-60.91

~2.4232.33

-21.2J-12.66-H.62-17.66-34.63-3.26

12.8036.59

-39.61-5.0J-10.00

29.6153.56

-~5.63-48.9<\-46.29-11.20

27.70_20.64

67.787.606.02

29.06_28.H-59.20

H.OO2.73

25.%151.91

-31.31-9.69-5~.67

8.5~-20.4J-14.87

38.361}.13

_4.6618.57

3.92-26.35

53.2838.52

6.0413.83lL75

-20.57-41.19

18.46

effects, test least-squares computations were performed usmg atomicform factors of (Tl,Pb) corrected for dispersion. The result turned outto give B=1.35 for (Pb,Tlh and B=2.32 for (Tl,Pbhr as shown IIITable 8. However, no appreciable improvement of R value was ob-tained, R being 0.121 for observed F(hkl)'s. And atomic coordinatesagree well with those of Table 6 within the estimated errors. Theatomic coordinates listed III Table 6 were, therefore, accepted asfinal ones and they were used to calculate bond lengths and bondangles.

I

xI

y zI

B

(Pb,TIJrI

0.3581 0.2469 0.1056 1.35(Tl,Pb) 11 0.3361 0.1223 0.6350 2.32ASI 0.1082 0.1948 0.7040 1.87Asu 0.0994 0.1848 0.1261 1.96

ASui 0.4361 0.1153 0.1343 1.85

Aslv 0.1365 0.0480 0.2151 1.92Asv 0.3814 0.0288 0.9545 1.89

SI 0.3933 0.1898 0.3640 1. 73

Sn 0.4092 0.1906 0.8628 1.57

SIn 0.1123 0.2541 0.3704 1.42

SIV 0.1289 0.1377 0.3244 1.67Sv : 0.1129 0.1466 0.8956 1.58

Svr 0.3877 0.0150 0.6839 2.31

SVII 0.1942 0.0573 0.9521 2.36

SVIII 0.4390 0.0671 0.3276 2.03

SIX 0.0087 0.0800 0.5856 1.70

The crystal structure of hutchinsonite 341

Table 8Results of least-squares refinements using dispersion corrections for Pb and TlAppreciable differences from the values in Table 6 are observed only for B's of

(TI,Pb)

Description of the structure

The interatomic distances and bond angles are tabulated in Table 9and Table 10. A diagrammatic representation of the structure isgiven in Fig. 10, from which it can be observed that the structureconsists of two kinds of slabs, A and B, parallel to (010). The A slabs

A B B A

Fig. 10. The c-axis projection of the structure of hutchinsonitc. Large open

circle: Pb (TI), solid circle: As, and small open circle: S. The slabs A' and B' arerelated respectively to A and B by the b-glide or b-screw operations

~>I'-t-:>

Table 9. (Tl, Pb )-8 and As-8 distances in hutchinsonite

Sr SH SIll SLY Sy Svr SVII SVIIJ SIXI

0'(l)~mean

f-,3iJ>

2.94AI

I

~2.86AI

2.77Al'j,

Pb(Tlh qa

3.00 3.10 3.43 3.05A ~:<

3.28 :f: 0.010enqbO

3.43 A 3.33A (3.79)A 3.37 A 3.30 A::0

Tl(Pb)n 3.31 3.15 iJ>>-J

3.12 3.29*iJ>

0

~ASr 2.30 2.26 2.31 2.29 000l'j

I"ASH 2.24 2.35 2.32 2.30 Jjp..

ASrIl 2.25 2.32 2.33 2.30 :f: 0.01r ~Z

AsIV 2.26 2.26 2.27 2.260

~a

As~. 2.26 2.27 2.29 2.27 ~>-<

* Excluding Pb(Tl)Il-SVIl distance.

The crystal structure of hutchinsonito 343

Table 10Bond angles and S-S edge lengths oj As-S pyramids in hutchinsonite

ASI pyramid

SUI-SV 3.52 A SUI-As-Sv 105.90

SnI-Sn 3.66 SlII~As-Sn 106.3

Sv-Sn 3.59 Sv-As-Sn 102.1

mean 3.59 104.8

Asu pyramid

SIV-SV 3.52 S IV-As-Sv 97.9

SIV-SI 3.50 SIy-As-SI 99.7

Sy-SI 3.44 SV-AS-SI 97.9

mean 3.49 98.5

ASm pyramid

SVIlI-SIX 3.49 SVIII-As-SIX 97.2

SnII-Slv 3.46 SVIII-As-SIV 98.2

SIX-SIV 3.23 SJX-As-SIV 89.6

mean 3.39 95.0

AsIV pyramid

SYIl-SVI 3.30 Svn-As-SvI 93.9

Svn-SvIIl 3.31 Svu-As-SvnI 94.1

SVI-SVIII 3.46 SVI-As-SV1Il 99.7

moan 3.36 95.9

Asv pyramid

SVI-SVU 3.38 SVI-AS~Svn 96.6

Svr-S IX 3.24 Svr-AS-SIX 90.6

Svn-Slx 3.50 Svn-AS-SIX 100.6

mean 3.37 95.9

a(l) = ::i:: 0.014 A a(8) = ::I: 0.50

are composed of infinite spiral chains of As-S pyramids around thetwo-fold screw axes. These chains are extended along the c axis, a con-figuration which is somewhat similar to that found in lorandite TIAsS2(ZEMANNand ZEMANN,1959). The chains in hutchinsonite are, however,laterally bonded together by additional AsS3 pyramids to forma complex layer parallel to (010), Fig.1t. The bond lengths and anglesof these spiral chains are shown in Fig. 12.

The B slabs are composed of Pb(TI), As and S, and the structureof these slabs is somewhat similar to a distorted PbS-type structure.Accordingly, the As atoms in the B slabs (As!> Asu) have six neigh-bouring sulfur atoms at distances AsI: 2.30, 2.26, 2.31, 3.43, 3.50,3.83 A; Asu: 2.24, 2.32, 2.35, 3.16, 3.22, 3.72 A. If account is takenof the nearest neighbours only, each As atom has a pyramidal coordi-nation of three sulfurs, just as in an A slab. These As-S groups form

344 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

c

ra

Fig.ll. The b-axis projection of the slab A. Large circle: As, small circle: S. Theshaded large circle indicates ASm. The c-screw axis and center of symmetry

are shown

c

Fig. 12 Fig. 13

Fig. 12. As-S spiral chain, as viewed along the b axis

Fig. 13. As2S6 groups in the slab B, as viewed along the a axis

The crystal structure of hutchinsonite 345

a finite group As2SS which is shown in Fig. 13. The A and B slabs arejoined together by (TI,Pb hI and ASIII atoms, and thus they buildup the bulk of the structure. This nature of the structure explainswell the good cleavage parallel to (010). The configuration of theASIII-S group is given in Fig. 14.

The unit cell contains 72 S, 40 As and 16 (TI,Pb) atoms, givingthe chemical formula (TI, Pb )2AsSS9' In Table 2, it is observed that,for d = 4.6, the total number of Ag + As is close to 40 for the analyses

SIX

Fig. 14. AsurS pyramids, as viewed along the a axis.

1,2 and 3. This fact suggests that Ag may replace some sites of As.Though such an example has not been reported, it is conceivablebecause examples have been reported where Ag has trigonal pyramidalcoordination.

In miargyrite, AgSbS2 (KNOWLES, 1964) and smithite, AgAsS2(HELLNER and BURZLAFF, 1964), Ag has six neighbours of S atoms,of which the three nearest form a pyramidal coordination as for As inAsS3. An attempt was made to prove the above hypothesis by examin-ing Wiesloch hutchinsonite which is reported to be rich in Ag, thougha complete chemical analysis is not given (SEELIGER, 1954). The in-tensity distribution of the (hkO) reflections does not show any differencesfrom that of the Binnatal specimens which we used. A calculationshowed that even if there are 8 Ag atoms in the unit cell and they aredistributed over the 40 As sites, the electron number for each sitewill be increased to 34.4, which is higher only by 1.4 than that ofAs. If this is the case, it is hardly possible to detect the difference.

It should be noted that the As-S bond lengths in the As4SS spiralchains are nearly equal, and they give a mean value 2.27 ::I::0.01 A,which shows good agreement with the value 2.28 ::I::0.007 A for theASIII-S single-bond length (CAMERMANand TROTTER, '1964). On the

other hand, each of the ASIlC, ASIC and AsI-S pyramids is characteri-

346 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

zed by having one short As-S bond length of about 2.25 A and twolonger ones of around 2.32 j... The contents of Cu as shown in thechemical analyses 2 and 3 in Table 1, are not essential to the structure.A discussion of the possible locations of this atom is beyond the scopeof the present investigation.

The chemical analyses show that there are about the same numbersof Pb and Tl atoms in the unit cell. Calculation of interatomic dis-tances shows that the mean (TI, Pb )n-S distance is bigger than the(Pb, Tlh-S distance, and also the temperature factor of the formeris somewhat higher than that of the latter. The configuration of sevensulfur atoms coordinated to a (Pb,Tlh atom is similar to the con-figuration of Pb in other sulfosalts, while the irregular configurationfor (Tl,Pb)n (coordination number = 7 + 1) is uncommon for Pb.An irregular configuration of sulfur atoms around Tl has been reportedin lorandite (ZEMANNand ZEMANN, 1959). This fact may suggest thatthe (Pb, Tlh site is mainly occupied by Pb and the (TI, Pb hI site byTI. Since, for the structure-factor calculation, the mean of the formfactors of these atoms was used, a possible ordering of these atomswas tested using F(hkO) data. If we assume complete ordering byplacing Pb at the (Pb, TI)I site and Tl at the (TI, Pb hI site, the R valuefor the F(hkO) data improves by 0.4%. If we use !Pb for both sites,the temperature factor of (Pb, Tlh decreases by only 0.01, while thatof (Tl,PbhI increases by 0.2. Although the changes are very smalland may not be significant, they are consistent with the assumptionthat (Pb, Tlh sites are mainly occupied by Pb and (TI, Pb hI by T1.

In the B slabs, each Pb(TI) atom and its neighbouring S atom buildup a chain along the c axis. These chains are joined laterally bysharing a S atom to form the framework of B slabs. This kind oflinkage of Pb-S is common to most of the sulfosalts which have sofar been investigated (IITAKA and NOWACKI,1962; LEINEWEBER, 1956;NnzEKI and BUERGER, 1957; NOWACKIet al., 1961, 1963a; WEITZ andHELLNER, 1960).

The Pb-S chains have a periodicity of around 4 A. The S-S dis-

tances in the SbS3 pyramids are close to 4 A. Therefore, in the sulfosaltscontaining Pb and Sb, SbS3 pyramids may form a chain or a groupwhich fits to the 4 A period of the Pb-S chain. On the other hand,the S-S distances of the AsS3 pyramids are around 3.5 A. Accordingly,the AsS3 pyramids do not fit to the Pb-S chain, and they tend toform a complex group, causing the complexity of the structure. It wasreported by LEBIHAN (1962) that the xPbS . yAS2S3 sulfosalts of the

The crystal structure of hutchinsonite 347

second group mentioned in the introduction have infinite AsS2 chainsalong the Pb-S chains. However, refined structures (NOWACKIet al.,1963a) have proved that every four AsS3 pyramids form a complexfinite group in these structures. This fact explains why the shortaxis (4 A) does not occur in the sulfosalts containing As, as comparedto those containing Sb. It is interesting to note that the above situationobserved in sulfosalts is somewhat similar to the structures of silicateswhere a misfit between octahedral and tetrahedral configurationscauses complexity of the structure (TAKEUCHI, 1964).

Acknowledgements. - We thank Dr. H. BURKI and cando phil.V. KUNZ for various help and Dr. N. D. JONES for having improvedthe English of this paper; Dr. J. S. ROLLETT (Oxford UniversityComputing Laboratory), Prof. W. NEF and Dr. R. HUSSER (Rechen-zentrum der Universitat und der Finanzdirektion des Kantons Bern),Dr. C. A. HERITIER (I.B.M. Geneva) for many invaluable calculations.The IBM Corporation kindly put at our disposal its 7090 machineat CERN, Geneva. Hutchinsonite crystals were kindly provided byDr. H. ADRIAN (Naturhistorisches Museum Bern), Prof. E. SEELIGER(Berlin) and the Mineralogisches Institut in Heidelberg. Dr. ST. GRAE-SER kindly made a spectrochemical analysis. The investigation wasgenerously supported by Schweizerischer Nationalfonds and Kom-mission zur Forderung der wissenschaftlichen Forschung and by theStiftung Entwicklungsfonds Seltene Metalle.

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348 Y. TAKEUCHI, SUBRATA GHOSE and W. NOWACKI

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