Determination andrefinement ofthecrystalstructure ...rruff.info/uploads/ZK121_87.pdf ·...

Zeitschrift fUr Kristallographie, Bd. 121, S. 87 -113 (1965)

Determination and refinement of the crystal structureof turquois, CuAI6(P04)4 (OH)8 . 4H20

By HILDA ClD-DRESDNER *

Massachusetts Institute of Technology, Cambridge, Massachusetts

With 7 figures

(Received June 9, 1964)

Auszug

Der Turkis hat die Raumgruppe PI, die Gitterkonstanten a = 7,424 A,b = 7,629 A, c = 9,910 A, IX = 68,61 0, f3 = 79,71 0, y

= 65,08° und eine Formel-einheit in der Elementarzelle, so daJ3 Cu an das Inversionszentrurn gebunden ist.Die Reflex-Intensitaten wurden mit einem Proportionalzahler registriert undmit dem Lorentz-Polarisations-Faktor und auf Absorption korrigiert. Aus einerdreidimensionalen Patterson- und einer ebenfalls dreidimensionalen Elektronen.dichte-Funktion, beruhend allein auf den Vorzeichen der Cu-Beitrage, folgteein Strukturvorschlag, der durch Fourier- und Ausgleichs-Methoden bis zuR = 0,07 verfeinert wurde.

Die Struktur kann beschrieben werden als aufgebaut aus Ebenen vonO-Atomen in nahezu dichtester Kugelpackung parallel (001). Zwischen diesenEbenen sind abwechselnd Schichten von Al in oktaedrischer Koordination undvon Cu in (4+2)-Koordination eingelagert. Die oktaedrischen Aniongruppenurn die AI-Atome sind einfach oder doppelt; zwei Tetraeder urn Phosphoratomeverbinden jede Doppelgruppe mit dazu identischen unter Bildung von Tetraeder-Oktaeder-Ketten parallel zur b-Achse. Die P04-Tetraeder ergeben zusammenmit den einfachen Oktaedern urn AI-Atome zickzackformige Ketten in Richtungder c-Achse. Es wurden vier MolekUle H20 pro Zelle festgestellt.

AbstractTurquois is triclinic, space group pI, with cell dimensions a = 7.424 A,

b = 7.629 A, c = 9.910 A, IX = 68.61°, f3= 79.710, y = 65.08°. The cell con-tains one formula of CuAI6(P04)4(OH)s . 4H20, so the Cu atom is fixed in aninversion center. Three-dimensional intensity data were collected on a single-crystal diffractometer using a proportional counter as detector, and werecorrected for Lorentz-polarization factors and absorption. The interpretationof a three-dimensional Patterson function and of a three-dimensional electron-density function based on signs due to the Cu contribution only, gave a trial

* Present address: Cristalografia, Instituto de Fisica y Matematicas, Uni-versidad de Chile, Casilla 2777, Santiago, Chile.

88 HILDA CID-DRESDNER

structure that was refined by Fourier methods and then by least-squares methodsto an R factor of 7%,

The structure can be described in terms of planes of approximately close-packed oxygen atoms oriented parallel to (001). Planes containing the Al inoctahedral coordination and planes containing the Cu in a 4+2 octahedralcoordination alternate between two oxygen layers. The octahedral groups ofanions around the aluminum are single and double; two phosphorus tetrahedralink each double group to its translational equivalent, building a tetrahedra-octahedra chain parallel to the b axis. The P04 tetrahedra together with thesimple aluminum octahedra constitute a zig-zag chain in the direction of thec axis. The water content has been determined to be four molecules per cell.

IntroductionThe turquois group is one of the few examples of a well known

mineral family whose crystal structures have not been worked outup to the present time. Two isomorphous series can be distinguishedin this group. One is the turquois-chalcosiderite series, characterizedby isomorphous substitution of Al203 by Fe203; this includes asmembers turquoisl, henwoodite2, rashleighite3, alumo-chalcosiderite4,and chalcosiderite5. The other series is formed by isomorphous sub-stitution of Cu by Zn and only the two end members, turquois andfaustite6, are known.

Of the whole group, single crystals suitable for x-ray structuredetermination have been reported only for chalco siderite and turquois.A recent x-ray study of chalcosiderite crystals 7, has shown a curiousfeature that can be eXplained as a very thin epitaxial growth of tur-quois on all crystals examined. This fact made chalcosiderite an un-favorable case for structure determination.

For almost eighty centuries turquois had only been known tooccur in the cryptocrystalline state. It was not until 1912 that thefirst single crystals of turquois were described by SCHALLER!. Crystals

1 WALDEl\IAR T. SCHALLER,Crystallized turquois from Virginia. Amer. Jour.

Sci. 33 (1912) 35-40.2 E. FISCHER, Henwoodit, ein Glied der Turkis-Chalkosiderit-Reihe. Chemie

der Erde 21 (1961) 97-100.3 ARTHUR RUSSEL, On rashleighite, a new mineral from Cornwall, inter-

mediate between turquois and chalcosiderite. Min. Mag. 28 (1948) 353-383.4 A. JAHN und E. GRUNER, Alumo-Chalkosiderit, ein neues Mineral vom

Schneckenstein i. V. Mitt. Vogtld. Ges. Naturf. Nr. 8, 1933. (Taken from Ref. 2.)5 N. S. MASKELYNE, On andrewsite and chalcosiderite. Jour. Chern. Soc.

[London] 28 (1875) 586-691.6 RICHARD C. ERD, MARGARET D. FOSTER and PAUL D. PROCTOR, Faustite,

a new mineral, the zinc analogue of turquois. Amer. Min. 38 (1953) 964-971.7 HILDA CID-DRESDNER, X-ray study of chalcosiderite. Amer. Min. (in press).

n1

=!] r'1

-:]

-21 -1 -1-20 0 0

[

1 0

-!] [

1 0

!]

0 0 0 00 1 0 -1

n

]

-1] [--'0

-l]

--20 -1 -1 11 1 0 -1-2 -2

Determination of the crystal structure of turquois 89

from SCHALLER'S original sample were kindly provided by Professor

CLIFFORD FRONDEL, of Harvard University, and by Dr. GEORGESWITZER, ofthe U. S. National Museum, for use in the crystal-structure

determination reported here.

Unit cell and space group

Turquois is triclinic and the space group is P I, as reported bySCHALLER1and GRAHAM8. The determination of the unit cell wasbased on data from two precession photographs, GRAHAM'Sa and baxes being the precession axes. As is customarily done for tricliniccrystals, a reduced cell was chosen according to BUERGER'S andBALASHOV'Sconvention 9,10. This convention uses the three shortestnon-coplanar translations of the lattice as crystallographic axes andrequires the interaxial angles to be all-acute or all-obtuse. The orienta-tion of the set is completely defined by the condition a < b < c.

The relations of the chosen reduced cell to the previous work ofSCHALLER and GRAHAM are given below. It should be noted thatGRAHAM'SceJl is a reduced cell that satisfied PEACOCK'S conventionsfor the setting of a triclinic crystal 11.His set includes the three shortestnon-coplanar translations of the lattice and satisfies the relationsa < c < b; ex,fJ > 90 0, y < 90 o.

Direct transformation Inverse transformation

SCHALLER to GRAHAM

GRAHAM to Cm-DRESDNER

SCHALLER to Cm-DRESDNER

8 A. R. GRAHAM, X-ray study of chalcosiderite and turquois. Univ. Toronto,Stud. Geol. Soc. 52 (1948) 39-53.

9 M. J. BUERGER, Reduced cells. Z. Kristallogr. 109 (1957) 42-60.- M. J.

BUERGER, Note on reduced cells. Z. Kristallogr. 113 (1960) 52-56.10V. BALASHOV, The choice of the unit cell in the triclinic system. Acta

Crystallogr. 9 (1956) 319-320.11 M. A. PEACOCK, On the crystallography of axinite and the normal setting

of triclinic crystals. Amer. Min. 22 (1937) 588-620, 987-989.

GRAHAM'S values forthe all-acute cell 7.46A 7.65A 9.91A 68.35° 69.43 ° 64.62°This work 7.424 7.629 9.910 68.61 69.71 65.08

::t:.004 A ::J::.003A ::J::.004A ::J::.03° ::J::.04° ::!:.03°


Final cell constants were obtained by refinement of data fromthree axial photographs taken with a precision back-reflection Weis-senberg camera12. Five cycles of least-squares refinement using BURN-HAM'S LCLSQ 3 program 13 for the IBM 7094 computer yielded thelattice constants listed in Table 1, where they are compared withGRAHAM'Svalues. The centro-symmetric space group was confirmedby a piezoelectric test.

Table 1. Twrquois cell constants

a b c IX fJ y

The refined cell parameters of Table 1 and SCHALLER'S analysisof crystalline turquois from Virginia 1were used to determine the unit-cell contents. The original formula of turquois 1 was given asCuA16(P04)404' 9H20, since the chemical analysis reported 20 non-water oxygens. The values listed below have been normalized to 20oxygens since the available values of the specific gravity10 were notconsidered satisfactory.

0.944.025.990.02

20.009.33

This formula corresponds to the ideal composition CuA16(P04)4(OH)s' (4H20 + H20). Whether or not this extra water moleculebelonged in the atomic arrangement of turquois was to be elucidatedfrom the structure determination.

Intensity dataA small turquois crystal of average dimension 0.18 mm was

selected for intensity measurements. The shape of the crystal was anirregular tetrahedron with truncated corners. Although this irregular

12 M. J. BUERGER, The precision determination of the linear and angularlattice constants of single crystals. Z. Kristallogr. (A) 97 (1937) 433-468.

13 CHARLES W. BURNHAM, Lattice constants refinement. Carnegie lust.of Washington Ann. Rept. 61 (1962) 132-135.


shape precluded an accurate absorption correction, the choice of thisparticular crystal was made on account of its transparency, perfectextinction under the polarizing microscope, and the good shape of thex-ray diffraction spots that were obtained with it.

Of the 2600 reflections in the positive hemisphere of the Ewaldsphere for CuK radiation, 1650 which were within the instrumentlimit, were measured on a single-crystal counter diffractometer. Theinstrument was based on equi-inclination, Weissenberg geometry 14,andthe parameters rand f{!as well as the Lorentz-polarization factor foreach reflection were obtained using a program written by PREWITTl5 forthe IBM 7094 pomputer. A proportional counter was used as a detector.

Counter-intensity data for each reflection consisted of the scancount [i.e., the total number of counts while the crystal was rotatedthrough the maxima, from a position f{!lto f{!2,where f{!l< f{!(hkl) < f{!2]and fixed-time background counts for the positions f{!land f{!2'Theaverage background count from these last two measurements wassubtracted from the total scan count.

The calibration of the absorbing foil was made in the followingway. The integrated intensities of ten medium-sized reflections weremeasured twice; first with the Al foil and then without it. The ratiobetween the two measurements gave a good approximation of thefactor by which the strongest reflection had been reduced. In addition,a separate scale factor for these reflections was allowed in the lastcycles of refinement.

The calculation of the observed structure factors was madethrough two data-reduction programs16 written for the IBM 7094computer. The first computed the integrated intensities, allowingappropriate scaling adjustments for the reflections measured withAl foils; the second one applied Lorentz-polarization and absorptioncorrections to the integrated intensities. In this case an approximationto the absorption correction. was made by applying a spherical-absorption correction since the lack of well-developed crystal facesmade it impossible to use a prismatic correction 16. Since the product

14 M. J. BUERGER, New single-crystal counter-tube technique. Acta Crystal-logr. 9 (1956) 834.

15 C. T. PREWITT, The parameters Y and cp for equi-inclination with applica-tion to the single crystal-counter diffractometer. Z. Kristallogr. 114 (1960)355-360.

16 CHARLES W. BURNHAM, The structures and crystal chemistry of thealuminum-silicate minerals. Ph. D. thesis (1961) Mass. lnst. of Technology,Cambridge, Mass.


of the linear-absorption coefficient and the average radius of the"sphere" was 0.835, the error introduced by this approximation wasnot expected to affect the results greatly, even if it showed up asa temperature effect.

Structure determination

a) Two- dimensional work

An attempt was made to solve the structure in projections. Thethree Patterson projections P(xy), P(xz) and P(yz) were calculated withthe FORTRAN program ERFR2 on the IBM 7094 computer!7. The

Fig. 1. Minimum function JYI4(yz)

projection P(yz) was studied first since it should show less superposi-tion. The two strongest peaks were assumed to define the interatomicvectors from the copper atom to two other cations. Two minimumfunction M2(yz), based on the corresponding inversion peaks, werecalculated and combined to produce the function M4(yz) which isillustrated in Fig. 1. The maxima from M4(YZ) provided the coordinatesy and z for a model structure, the x coordinates being obtained by

correlation of M4(YZ) with the other two Patterson projections. Thismodel structure was refined independently in the three projectionsby successive Fourier syntheses followed by structure-factor calcula-tions to discrepancy factors R = 49.3% for p (xy), R = 53.0% forp (xz), and R = 36.5% for p (yz). At this stage the three projections

17 W. G. SLY, D. P. SHOEl\IAKER and J. H. VAN DER HENDE, ERFR2, a twoand three-dimensional crystallographic Fourier summation program for theIBM 7090 computer. Esso Research and Engineering Co., Lenden, N. J. Pub.lication No. CBRL-22m-62.


could not be correlated any longer, and neither the Fourier refinementnor least-squares refinement succeeded in attaining further con-vergence. It was decided then that full three-dimensional data werenecessary to solve the structure. Accordingly the model structure wasdiscarded and a new start in three dimensions was made.

b) Three-dimensional work

A three-dimensional Patterson function, based on the 1600 inten-sities collected, was calculated. In the interpretation of the Pattersonfunction the following features were taken into consideration:

1. Turquois can be treated as a structure composed of a heavyatom at the origin and a residual structure of atoms randomly dis-tributed through the unit cell. The ratio of the contribution fromthe heavy atom and the maximum contribution of the residue isonly 12%, Nevertheless the heavy atom is always making a maximumpositive contribution. On the other hand, the contribution of residualatoms will never attain more than a fraction of their maximum valuedue to the fact that they are randomly distributed. Hence, in spiteof the small ratio, the probabilities are that most of the structure-factor signs will be positive. If so, an electron-density function cal-culated with [Fo,hkl\as coefficients will approximate the real structure.

2. In the absence of a substructure the strongest peaks in thePatterson map should correspond to vectors from the Cu atom tothe Al and P atoms. The next highest peaks should be the Cu-Ointeractions of approximately the same height as an AI-P peak, butboth about half of the Cu-AI peak. (Actually it was not expected thatthis would hold rigorously since structures based on oxygen are likelyto show some kind of a substructure.)

3. The Cu is expected to be in a distorted octahedral coordination 18

with four oxygens at an approximate distance of 2 A and the othertwo at a distance of 2.5 A. The Al is expected to be in octahedralcoordination with approximate AI-O distances of 1.9 A, and the P willbe surrounded by an oxygen tetrahedron with approximate P-Odistances of 1.5 A.

4. At least the peaks chosen as the cations in the structure shouldproject as a peak in the old M4(YZ) function.

18 F. ALBERT COTTON and G. WILKINSON, Advanced inorganic chemistry.Interscience Publishers (1962) 560-610.


An electron-density function, with all signs positive, was calculated,and from it a model structure which fulfilled all the preceding condi-tions was chosen. This model was refined by four successive electron-density functions followed by structure-factor calculations from theoriginal discrepancy factor R = 62 % to R = 27 %. In the courseof the Fourier refinement five of the oxygens and one of the phosphorusatoms from the original model were found to be incorrect. The peakerroneously assumed to be a phosphorus was a substructure peak dueto the superposition of the almost identical Al(1)-P(1) and Al(2)-P(2)vectors.

At this point the Fourier refinement had converged. The electron-density function whose atomic coordinates gave an R of 27% showedround peaks of correct relative heights in the atomic locations andno spurious peaks. Consequently the structure was considered solvedand the model was submitted to least-squares refinement. Only fourwater molecules were included in the structure, since no extra peakthat could be attributed to the other oxygen had been found. On theother hand, the 28 oxygens per cell fulfilled the coordination require-ments of all the cations, and if a fifth water molecule were to beplaced in the unit cell it could not be attached to the cations in anyof the usual ways.

Refinement of the structureLeast-squares refinement of the turquois structure was done on

an IBM 7094 computer using the full-matrix program written byPREWITT 19. Atomic scattering factors for CuH, 0, AI+!, P, togetherwith individual isotropic-temperature factors, were used in the firstfour cycles of least-squares refinement. The initial temperature coef-ficients were taken from the pseudomalachite structure 20, for Cu, 0and P, and from the andalusite21 structure for AI. These values were0.5 for Cu, 0.15 for P, 0.6 for 0 and 0.25 for AI.

Only one scale factor for all reflections was used in the initial stagesof the refinement. No rejection test was included, but, at this point,a special weighting scheme was used. The product of the discrepancyfactor of a group of reflections and the weight of these reflections

19 C. T. PREWITT, Structures and crystal chemistry of wollastonite andpectolite. Ph. D. thesis (1962) Mass. Inst. of Technology, Cambridge, Mass.

20 SUBRATA GHOSE, The crystal structure of pseudomalachite, CuS(P04)2

(OH)4' Acta Crystallogr. 16 (1963) 124-128.21 CHARLES W. BURNHAM and M. J. BUERGER, Refinement of the crystal

structure of andalusite. Z. Kristallogr. 115 (1961) 269-290.


was maintained constant by this weighting scheme 22. It was designedto give a larger weight to those structure factors that showed a betteragreement, because this is desirable in the initial stages of the refine-ment.

One cycle of least-squares refinement, varying the atomic coordi-nates and the scale factor but not the temperature factors, improvedthe R factor from 27% to 14.2%' Three more cycles in the same con-ditions gave an R of 13.5% and no movement in the atomic positionslarger than the standard deviation was observed.

At this point the weighting scheme was changed. All reflectionswere given the same weight in order to allow more reflections toinfluence the refinement. Three more cycles of refinement only im-proved the R factor to 13.2%.

Two scale factors, one for the reflections measured with an Alabsorber and one for aU the rest, were used from this point on. Onecycle, varying isotropic temperature factors together with both scalefactors, was run in order to study the interaction among these para-meters. This was done through the Geller matrix coefficients 23obtainedfrom the least-squares refinement program. Rather large correlationcoefficients were obtained for interactions between scale factor (1)and scale factor (2), and for interactions between scale factors andtemperature factors. Accordingly, the scale factors and temperaturefactors were varied in consecutive independent cycles.

After three cycles of refinement of the isotropic temperaturecoefficients the discrepancy index R had attained 10%. A three-dimensional difference-Fourier synthesis was calculated in order tosee the hydrogen atoms. There are eight hydrogens in the asymmetricunit of turquois, four are attached to two water molecules and theother four belong to OH radicals. If those hydrogens were found, itwould be the best way to differentiate an OH radical from an H20molecule.

The difference-synthesis maps showed two types of anomalies;these were, peaks in six out of the eight expected locations of thehydrogens, and also the characteristic combination of positive andnegative peaks attributed to anisotropic motion of the atoms. Again,

22 BERNHARDT J. WUENSCH, The nature of the crystal structures of somesulfide minerals with substructures. Ph. D. thesis (1963) Mass. Inst. of Techno-logy, Cambridge, Mass.

23 S. GELLER, Parameter interaction in least-squares structure refinement.Acta Crystallogr. 14 (1961) 1026-1035.


no peak that could be interpreted as the fifth water molecule wasfound. When the six hydrogens were included, but not varied in a finalcycle of isotropic refinement, the resulting R factor became 9.5%.

Four cycles of anisotropic refinement with the six hydrogens,included but not varied, converged to an R factor of 7.20/0' Duringthis refinement five oxygens did not maintain a definite positivecharacter, even though their equivalent isotropic temperature factors

Fig. 2. The eight hydrogens of the turquois structure

were always positive. This was attributed to errors in the absorp-tion correction due to the deviation of the shape of the crystal froma sphere.

A final three-dimensional difference-Fourier synthesis, using theresults from the final cycle of anisotropic refinement, with the sixhydrogens excluded, was calculated. The positions from the six hydro"gens plus two others were recovered from it. The eight hydrogenpeaks are shown in Fig. 2. When the hydrogen coordinates obtainedfrom the last three-dimensional difference-Fourier synthesis wereincluded in the refinement, a final discrepancy index of 70/0 wasattained.


Table 2. Observed and calculated structure factors of turquois

F0

F F0

F h k I F0 F k I F0 F0

0 0 19.71 20.21 16.93 15.26 _63

_1 17.59 17.28 -1 0 -2 23.39 2/..890 0 -87.1) _8Z.Hi 5.'.3 1..31 -6 -} -1 13.37 12.87 1 0 _2 ZIt.(1) 27.280 0 35.'.8 jll,')', 22,88 20.86 6 -3 -1 - 9.16 -12,71 -2 0 -2 8.8} 15.7',a 0 7'.,85 69.45 13.25 13.15 7 3 -I - 1.38 - l.}O 0 -2 55.27 51.31a 0 19.00 16.96 _20,2} -:w.oo -7 -3 -I -111.36 _14.61 -3 a

-"}2.15 }0.2"

a a 111.35 13.97 15.70 11..52 _8-3

_1 3.56 2. }6 3 0 _0- 8.61 - 5.85

B a a 12.73 12.13 a '._1 15.74 15.55 -'. n _2-',1..33 _1.1.77

1 1 0 23.26 25.62-

0 -1 15.71, 16.94 a -'._1 1'.,1.3 11..(,(, a -2 -50.79 _43.11

1 -1 a 20.68 20,Id a -1 45.78 1,1,.50 1 ,-1 77.27 78. }6 5 0

-"},).97 }4.50

1 a 93./.8 100.02 -} a -1 10.80 1"-0} -1 '._1 2.37 1,/.7 -5 0

-"12.2') 12.86

. -1 0 -15.77 - 5.93}

a -1 1116.02 1',0.24 -1 -, -1 50.00 h7.'.6_6 a -2 66.27 67.90

3 1 0 13.1,1, 15.70 -', 0 -1 33.93 33.27 1 -, -1 65.15 61.9'. 6 0 -2 50,07 ,,6.593 -1 0 111.23 1,1.33 , 0 -1 - 6.85 - 'L51 '. 1 18.38 19./,1 -7 0 -2 9.29 9.82, 1 U -',0.00 -31.87 -5 0 _1 -12.45 _10.82

-"4 -1 27.27 28.24 7 0

-" - 7.71 8.78-, 1 a 78.H:; 81,.46

-~ "-1 24.90 2!,.1) -. -'. -1 17.00 1H.86 -8 0 -2 -2'1.97 -27.69

; 1 a 'J.8<; 10.65 0 -1 5.)1\ 0.33 -'. -1 9.29 9.5') a 1 _2-58.3(' -')3.16

~-1"

- 3.88 - 2.26

"-1 21.118 19.1"1" 3 '. -1 - 2.64 - 0.',6 0 _1

-. 10.)11 12.911 a 12.\}\} 12.2D -7 0 _1

- .:;.93 - 5.28 -J, -1 }0.83 30.5',

_1 1 _2 22.13 24.056 -1 a -27.98 -27.<)6 0 -1

}.5(, ').09 -} -'._1

- 6.G5 -1.8(, 1 1

-"3}.60 }4.00

1 0 6.5} :;.50 -8 u -1 17.39 19.82 3 -'._1 -}7.')') -}/,.37 _1

-1-"

26.55 26.7}-1 0 2}.01 24.01 0 1 -1 20.22 22.24 '. '. -I '1.28 4.}} 1 -1 -2 16.01 18.68

8 1

"111.54 13.82

"-1 -] 21.87 2}.60 -, ,

-1 /,.22 ".51 1 -2 20.'19 24.04a 2

"7.17 8.82 1 1 -1 -11.

}}- B.8H -'. -'.

_1 19.04 20.'J} . -1-"

62.58 ')5.151 2

"23.78 24.72 -1 -1 -1 5}.36 51.27 , -, -1 11.40 12.12 -. -1

_2 52.95 56.151 -2 0 2/,.10 2',.15 1 _1

-I 119.',1 1,6.2} J '. -1 -21.')1, -20.51-"

1 -. -G\).77 _56.68

". 0 -43.17 -3).17 1 -1 19.50 20.')8 -} ,

-1 -22.7} -2'1.20 -3 1 -- - 5.53 - 3.43. -2 a 59.19 58.00 -2 1 -1 24.70 2}.03 -5 -, -1 37.29 }7.18 -3 -1 -2 29.97 27.843 2.

"

4.11, 8.17 -1 -1 23.1.6 26.07}

-'._1 33.',0 3}.'}8 3 -1

_2 16.93 16.'183 -2 a ').0') 11.03 . -1 -1 28.1,(0 2H.I,0 6 '. -1 27.1>7 2'}.13 3 1 _2 5.34 6.44, . a 47.75 1,1,.9(0 }

1 -I V'. 17 31'.71 -(.-'. -1 I'}. 7(, 20.49 -'. 1 -2 55.67 55.16

'. -2 a -27.53 _2:;.',0 -} 1 -1 -';0.97 -H').52 7 '. -I 2',.18 25.08 4 1 -2 1,6.90 42.015 2

"

32.25 }2.0} -} -1 -1 2.21, 2.17 -7 -'. -1 21,./,', 21'.59 -'. -1-"

15.'.8 13.96}-2

"!L08 6.1,6 J -1 -I 67.00 6}.27 _H -, _1 10.28 9.5')

,-1

_0 }').3} 37.306 2 U - 6.111 - 4.06 '. 1 -1 28.33 28.67 0 0 -1 It.07 9.45 -5 1 -2 14.16 1}.836

-"a - 6.01 - 4.')6 -'. 1 -1 22.iJO 22.87 a -':; -1 12.38 11.')9 5 1

-"11.86 12.20

7 2 0 - 9.37 - 8.B3 -'. -1 -1 5.99 7.35 1} _1

-')1.2') -116.7} 5 _1 _2 23.72 22.618 0 - 8.27 - 8.99 '.-1 -1 - 2.50 -

2.1,3 -1 5 -1 20.36 21.74 -5 -1_2 23.72 24.}3

a 3

"48.92 ',7.46 5 1 -1 3.8') 0.08 -1 -5 -1 56./.6 56.33 -6 1 -2 -22.40 -22.91

-1 -3"

18.16 19.2'1 -'3 -1 -1 65.7/, 65.16 1 -5 -I -71.21 -67.61 6 1 -2 - 6.65 - 4.011 -3 0 23.20 21..OJ t -1 -1 -58.37 -53.71 , -1 22.07 21.95 -6 -1 -. -32.35 -32.932 3 0 75.0') 7&. }O 1 -I 1.91 1.60 -2

j-1 ].80 G.24 6 -1 -2 10.28 13.53

-3 a 61.71 bO.01 _G 1 -1 1,.68 3.64 -. -5 -1 20.95 22.73 -7 -1 -2 8.04 6.')33 3 a 14.99 15.32 -6 -1 -1 25.}6 25.50 . -5

_1 19.76 18.9'1 -7 1 -2 - 7.91 - 8.693 -3 a - 1.68 - 0.92 6 -I -1 41.70 1,2.37 3 5

_1 ',}.28 '11.27 7 1 -. 17.33 16.73, }a -68.56 -65.93 7 1 -1 19.83 22.14 -} 5

_11"-76 13.')1 7 _1 _0

-10.08 -10.96,-3 0 8.66 7.86 -7 1 -1 - 2.61,

- 2.68 -3 -5 -1 -1(0.07 -16.61 -8 -1 -2 53.75 57.52, 3 a 21.58 21.73 -7 -1 -1 8. }7 7.72}

-5 -1 58.',} 00.06 a 2 -2 1,6.71 1,6.87,-3

"27.')2 27.14 7 -1 -1 51.25 55.81 '. 5 -1 - 5.27 - 11.65 0 _2 _2

-28.85 _16.82(,3

"17.96 16.83

"8 -1 -1 - 3.23 - 3.')0 -'.}

-1 5.73 3.73 1 2 _2 20.88 20.69b -} 0 HI.72 48.52 0 -I 21.7', 23.06 -, -} _1 12.32 I}.',} -1 2 -2 7.77 9.')27

}a 15.12 11'.55 0 -.

_1 25.11.. 26.55 '. -} -1},(,') 1,.26 -1 -2

"

25.36 26.78B 3

"

4.7H 3.101 1 _1')11.81 9').39 5 5

_1-21.08 -19.99 1 _2 _2

12.85 15.180

,

"-31.60 -25.43 1 -2 -1 26.6H 28.01 -5 -] -1 27.60 27.76 2 2 -2 41.04 39.20

1 ,

"11,.',7 15.00 -1 -. -1 12.7H 15.')0 6 5 -1 IIt.69 16.21, -2 . -. 75.18 75.71

1 -4 0 18.03 ly.I'7 -1 2 -1 -27.40 -}2.39 -6 -5 -1 0.')9 1.63 -2_2

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-"-2 6.59 7.21

2 -, a 56.93 50.15 -2 -1 12./1') 1}.82 -7 -5_1 -13.37 -13.31 3 2 -2 32.1:11 }1. 70

3,

"20.87 22.97 -2 -2 -1 21..02 28.21 -8 -5

_1 1').68 16.59 -3 2 -2 23.25 24.573

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-1 3."3 1.')0

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6 _1 8.04 8.72"3 -2

-"8.70 9.51, ,

"66.0'1 64.27 3 -I -36.89 -2';1.88

"

_6-1 10.28 9.26 3 -2 -2 25.56 25.82

'.-'. 0 19.45 19.57 -3 2 -1 1.5.13 1.6.51 1(, _1 25.96 28.05 '. . -2 1'5.4':; /12.82

5 , 0 - 1.1'9 - 0.1,1 -3 -2 -1 -20.]5 - ').61, -1 6 -1 115.32 ',',.OB -, 2-"

-1,3.1,8 _112.86} -, 0 26.75 26.87 3 -2 -I -15.'12 -13.11 -1 -6 -I -60.28 -59.',7,

- -2 6.26 6.076 ,

"-21t.49 -21.25 , 2 -1 2:;.36 25.56 1 _6 _1 2(J.22 2',.22 -, _2

-. 71.71 73.09, a 16.41 1').')8 -, . -1 H.W 13.76 -2 -6 -1 12.06 13.05 5"

-. - 2.70 - 1. 798 '. 0 36.25 33.81 -'.

_2-1 10./11 11.7/1 -2 6 _1

- 2.1"1 - 2.85 -j 2 _?Y.88 9.20

a 5 a 56.28 53.&9 '.-. -1 31.29 30.63 6 _1 9.09 8.25 5 - -- - 8.1,}- 4.20

1 5 0 14.09 12.19 5 - -1 17.06 17.')8"

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-"6.8') 5.20

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-"21.}I. 17.29, 0 -38.71 -36.2} -j -1 -)0.07 _1'7.'j') -}

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-2 I').}O 18.87-j 0 - 4.')1 - 2.49 i -1 ')1,.22 ')2.7', -3 -b

_1HI.I'5 1').71 _6

-2_0

37.29 39.563

}a 18.03 19.80 -1 1,.',1 3.76 3 -6 -1 - /1.28

-}.96 6 -2 -2 7.',', 6.90

3 -5 0 19.58 19.90 -6"

-I 0.86 1.95, 6 -1 12.25 13.}2 -7 -2 -2 16.3/1 16.55, j

"5.04 6.59 _G

-"-1 9.55 9.6'. -, -h

_1 17.52 17.1,1 7 2 -2 30.01, 29.98,-5 0 -2/1.56 _24.88 G

-"-1 2.24 3.69 5 6 _1 33.66 33.81, _8

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-~ -6 -1 28.26 26.81

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3_0 1111.6/, 117.17

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8 5

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_6 _1 1').22 16.14"1 3 -2 23.98 2"-220

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"8.47 7.71) 1 3 -1 ')1.9/, 90.21

"-7

_1 12.12 12.')9 1 -3_2 13.37 13.70

1 -6"

6.72 5.23 -1} _1

- 3.82 - 0.82 1 7 _1 23.8] 2}.78

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3 -. -50.26 -113.002 6 0 17.')0 16.35 -I -3 -1 -57.71 -')2.15 -1 7 -1 17.33 17. }5 _2

3 -2 -78.79 -76.892 -6 a -21.71 -19.91

}-1 10.67 10.12 -1 -7

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"13.12 12.08 -2 3 -I 2').58 2').91 1 -7

_1 ::;.93 8.}!' 3 3 _2 28.66 29.04J _6 a 6.91 7.03 _2

-3 -1 18.64 20.17"

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"-3 -1 ',.81 ].29 -2 -7

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6 6 a -23.59 -22.83 -3 3 -1 6:1.58 61.66 -3 -7_1

- 5.01 - 3.24 -, J -2 00.1,7 61.917 f, a 14.'11 12.91 -3 -3 -1 _1].71,

- 7.80 '. 7 -I 9.29 10.99 '. J -2 85.6'1 83.730 7 0 -33.28 -311.36 J -3 -1 4').1,1 /,8.72 -', -7

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_2 6.72 6.102 -7 a 48.85 :;1.57 '. -3 -I 17.65 17.73 0 -8

_1 16.}/, 16.73 5 -3 -2 2.17 0.483 7 a 12.34 11.91 5 3 -1 65.28 62.':;1 -I' -8

_1 -31.03 -33.117 -5 -3 -. 8.}0 8.01

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"7.82 6.90 3 -1 - }.')6 - 1.11 -5

_8 _1 -18.0') -20.02 6 -3 -2 1.45 1.26

Z. Kristallogr. Bd. 121.2/4 7


Table 2. (Continued)

h k 1 F0

F h k 1 F0

F

"

h k 1 F0 F

"

h k 1 F0 F

-, -, -- Hi. 67 17.7J -'._8

-":!3.~1 21,.64 -, -J -J 17.07 16.21.1 -'. -9 -, - 2.16 - 1.37, , ]').'2.4 17.')8 -, -B

-"2.97 2.90 5 -, -J 8.77 7.IJO-, -,

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7.02 7.0} -6 J -J - 1.75 - 2.01 -1 0 -, 15.24 16.09

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}1.2g 1 0 -, 22,66 21.3t".,'. -" 1').7<1 20.24 -'I -'.i -2 32.01, 32.9"

, J -, 11.7', 11.79 -, 0 -, - 9.1)8 - 9.8)-1 '. -"

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'._0 17.33 17.1)1 -1 0 -, 21.99 23.62 0 -, -J 20.2/, 21.')5 , 0 -, 15.72 16.13

'.-, 11.00 11.85 1 0 -, -7').52 -59.98 0 '.-, 11./,0 11.113 -'. 0 -, 62.19 65.17'. -2 - 8.70 - 8.83 _0 0 -J 27.39 25.18 1 ,

-J - 9.85 - 8.27 , 0 -, -28.13 -23.41-'. -'2 JIB.Ht 1,8.1:\1 0 -, 26,78 26./17 -, '. -J 9.11 7.82 -5

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"-J 27.1:! 2}.I,9 1 -, -J 8.50 8.86 -b 0 -'. 23.14 23.22,

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1 -'.8.2} 6.83,

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, -, -22.53 -21.0') -1 1 -'. 20.84 21.49,'. -2 15.1,2 16.90 , 0 -, -tit. 91 -13.19 -3 -'. -3 -31.77 -27.M , , -, 15.01, 16.24

-5 -'. 1".30 13.29 -, 0 -J -',.25 2.38 ,-'. -, - 7.112 _11,.09 -, -1 -, 37.77 36.59

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- }5.77 32.02 0 -1 -, 113.98 'd.37_!,

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-3 -1,5.60 _lll.I,) -1 -, _Hi.12 -11.72,-2 - 3.10 -

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-'J 11.5<) 'J.79 -"-, -, 25.65 2),.}6 -6 -'. -, 21.32 2C.I'7 -, , -, 28.1,7 26.1,6

I , -2 I}.2I, 12.86 -1 -, 10.66 12.35 -, -, -J 21.}8 21.5'1, 1 -'. 52.95 1,8.91

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-1 -, -15.18 -13.815 -- 15.1,2 10.07 -, -1 -, 37.71, 35.87

"-5 -, 17.5" 17.99 -, 1 -, 2.56 0.59

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-1 -'I 7.1:; 6.511 5 -, - 0.99 - 1.61, -, -, -, 15.38 1}.76 ,

-5 -J 1,3.37 1,0.8'. -6,

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-, -'j -"12.2') 13.36 5 1 -3 12.1,1 12.56

-"-, -, 9.78 11.',6 6 -, -'. 33.66 32.52

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, -, 20./,1, 19.56 1 -'. ]2.28 1:;.80-,. -,

-" 85.';10 HR.37 -, 1 -, 111.68 I,G.III -'., -J 5.33 3.51 -1

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- 6.39 _8-1 -J 20.10 21.31 , , -, 6S.7/' (,1'.30 -'.

1,.25 5.0S_8 -, _2-2".51 -25.62 0 -J 22.10 "l3.';I0 -'j -') -J -H8.03 -89.9G -, -- -, 77.8') 71.1,1,

",._2 -11.1/1 -33.67 II _2 -, 12.5" 11.')2 0 5 -, -10.93 -11.73 -2 -, 1,1,.92 1,3.06

0 -b -, -20.!!:.! _20.68 1 ,-3 -!'~L23 -/,0.56 -6 -, -J IIi.70 1}.11I -J

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-2 11,.10 13.55 1 -- -, -to.3::! - G.60 -B -5 -, J'.79 ',.1,9 -3 -, -, 20.98 22.261 _6 -, 18.25 17.78 -3 2].16 2'1.3', 0 0 -, 15.58 15.20 J -'. 15.18 fI'.39_1 _6 _0

11.')2 ]2.22 -3 20.~i1 21.37 0 -b -3 31.91 31.91 -'. - -, 13.69 13.876 -- 66.14 (j1,.'.O

-- -- -3 }I,.87 32,{.1, 1 6 -, 70.1:; {,(,.06'. -, -/,0.00 -33.87_6

-2 1,.22 2.89 - -- -3 23.11. 23.08 -1 6 -3 7.76 ('.32 -, -, -, -12.41 - 7.')1_2 6 -- 39.92 }S.92 3 -3 1]1,.18 112.1,2 -1_6

-3 -'.7.35 -1,3.8] '. -2 -, 59.56 51,.58-- -6 -, ')1.()! ')1.51 -, -J 5.19 :;.1,8 , -6 -, 53.15 "9.1,5 -, 2 -, 21,.55 27.11,, 6

-"1.7H 0.53 -, -, -, 111.81, 10.76 6 ., 1.89 1.21 , 2 -'. 26.1,/, 21,.56

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-2 7.GI, 7.1,0 '. -3 - 4.32 - ::i.I,')-"

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.'. -6 --_1,(j.I,I,

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_6-3 2.16 1.]2 _8 -, -, -31.97 -31,.1,6

6 f, -:1 1.52 :1.18 ,-- -J 3.2'1 IJ,7 , 6 -J 37.J7 37.67

"J -, -80.79 -82.1,6

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"-, -, -Hi.')9 -12.51,_H-6 -, 11.00 JO.5(; _6

-J IIi.17 1'5.21 _6 _6 -, 9.71 9.69 1 , -, 27.86 27.92

"-, -, 3.81, 0.36 _6 -, -, ':i.06 J,.H} -, -6 -J -19.1,9 -19.29 -1

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-- 6.6ii 1,.61, -, -, -, }.11 }.61, 0 -, -, 6.27 6.78 3 -, 51.67 1,9.50_1 7 -- 16.12 lh.')I, _H-"

-, 21.99 23.'1') 1 , -, 21.72 21.16 -2 J -, 23.51, 21,.871 -, -. J1.53 II).lo9 0 J -3 20.78 ~1.22 .1 -, -, 38.}1 37.1,1 -, -, -, 99.89 102.59

-, -, -'!9.07 -26.83"

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-"().75 (,.')9 -1 -, -, -"9.98 _I,:!.1,7 -, -) 3.78 3.22 -3 -, -, 12.95 13.78

J -- H'.')3 1(,.1,6 1 -J -3 IS.::!11 ]2.08 3 , -, 22.h6 ]').68 J -3 -'. 1.01 0.54-'. -, -- :;8.62 56.70 J -J 27.12 26.11 -, -, -, -19.56 _18.}6 '. , -, -26.85 -24.09'. 7 -- 42.')0 1,0.H8 -:1 , -, 11.1,0 12.77 -'. -, -, 7.55 6.85 -, J -, - 3.78 - 1.51,

-, -,-"

7.28 5.}5 -, -, -J JIJ.91 11,.16 -5 -, -, 9.31 10.77 -'. -3 -, -24.82 -20.45:J ,

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_8-J 32.38 33.58 -, -, -, 6.95 8.56_1 -8 -- 12.JIi 12.72 '.

, -J 6.1,8 3.76 -, _B-, 9.71 9.60 5 -, -, 31.57 30.301 -8 -, 0.u7 ',.03 -'.

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-J -, _0 5.26 5.06 , J -, 38.72 31,.46 -6 -8 -J 3.37 2.08 _B -3,-1, - 2.09 - 0.22, . -" 8.23 7.79 -} , -, -1IJ.7° -]0.0') -J -9 -J - 8.:;7 -12.96 0 , -, J5.55 3',.77



h k 1 F0 F0

h k 1 F0 F0 h k 1 F0 F0 h k 1 F, F0o _1.1_It 1.16.75 1.16.12 o -1 -5 15.11 15.92 _8 -1.1-5 18.35 19.18 -7 1 _6

- 0.90_ 0.64

1 . -. 7.15 }.93 -1 1 -5 }2.75 52.33 -9 -It -5 - 5.80 - 7.04 -7 -1_6 11.21.1 11.32

-I . -. 12.88 12.78 1 1 -5 ItJ.21a "1.20 0 5 -5 J.8" It.59 -8 -I _6 28.56 35.01-1 -, -, 17.7" 18.1:15 -1 -1 -5 -18.89 -17.05 o -5 -5 -15.38 -15.26 0 2 _6 41.1.39 "2.98

1 -1.1_I, 15.72 16.17 1 -1 -5 1.lt8 1.64 1 5 -5 -46.21 -1t3.90 o -2 -6 - 9.18 - 5.212 , -, _28.80 _26.41 -2 1 -5 22.73 2'1.J..1 -1 5 -5 1.9.31 47.73 -1 2 -6 22.62 22.32

-2, -, 15.72 15.92 2 1 -5 18.62 17.58 -1 -5 -5 67.99 69.87 1 2 -6

- 6.53 - 5.61-2

_It -, ".92 5.40 _2 _1-5 12.68 11t.}1t 1 -5 -5 -35.21 -}}.81 -1_2 _6

10."7 IIt.072 -It

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-} , -, 2.63 2.44 , 1 -5 7.35 6.91 -2 -5 -5 20.30 21.40 2 2 _6-

7.0q- 7.36

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-4 -. -7 - 8.',3 -12.21 -, -8 -, }I.. 33 )1..02 0 -(, _8 20.91 31.23 -, 0 _'0 _10.27 _12.11, -, -, - 7.1'9 - 8.84 _6-8 -7 11.2(; 10.2') -I -6

_8 1').83 '.W.72 ,

"_10 12.99 16.27

-, 2 -7 -24.76 -27.99 -7 -8 -7 - 7.82 - 7.25 -. -6 -8 -22.53 -21..73 -J 0 _'0 13.2] 13.05-5 -, -, ')2.01 56.05 -, _6

-8 - (J.Rl - OJ,3-'.

0 _10 1,.85 1.18_6-- -, 9.65 ').28 0 0 _8 34.'!.7 33.(,0

-'. -6_8

- 2.!13 - 0./,11 0 I _10 2').1,7 32.00-, -. -7 1').38 111./,6 -,

"-8 27.93 31.93 -, _6

-8 - 6.',1 - 8.113 0 -, _'0 22.62 21.49-8

_2-7 - 1.1,8 - 1.55 , 0 -8 6.81 5.83 _6 _6

-8 :.!~.88 28.0G 0-"

_10 21.')2 17.1/00 ,

-7 - 2.70 - 2.'14 -. 0 -8 -)}.93 -1/7.51 0 -, -8 -12.G8 -21.98 0 -3_10 IH.118 17.02

0 -, -7 - 0.94 -{J.71 0 _8 -I1.HO -10.74 -, -, _8

- ('.3" - 6.91 0 -', _10- 3.30 - 3.21

-, , -, 36.56 3G.VI -, 0 -8 1.'18 1.71, - -. _B GO.}7 G1.8') 0 -5 _10- 2.26 - 9.j6

Results from the refinement

Table 3 lists the discrepancy indices R as obtained at the variousstages of the refinement. These values were obtained from the relation

R L'llFol - IFel1- L'IFoJ

Atom I x a(x)I

y a(y) z a(z)

Cu I 0 0 0

PI 0.3504 0.0006 0.3867 0.0006 0.9429 0.0004

P2 0.8423 0.0006 0.3866 0.0005 0.4570 0.0004

All 0.2843 0.0006 0.1766 0.0006 0.7521 0.0005

Al2 0.7520 0.0006 0.1862 0.0006 0.2736 0.0005

Al3 0.2448 0.0007 0.5023 0.0007 0.2438 0.0005

01 0.0675 0.0014 0.3633 0.0014 0.3841 0.0011

O2 0.8058 0.0014 0.3435 0.0014 0.6262 0.0011

03 0.2757 0.0014 0.3554 0.0014 0.1129 0.0011

04 0.0663 0.0015 0.0639 0.0015 0.1973 0.0011

05 0.2375 0.0015 0.0739 0.0015 0.6287 0.0012

06 0.7334 0.0014 0.0857 0.0014 0.1243 0.0011

07 0.2978 0.0015 0.4016 0.0014 0.6060 0.0011

08 0.3249 0.0014 0.2227 0.0014 0.9049 0.0011

09 0.9857 0.0014 0.2807 0.0014 0.8471 0.0011

010 0.5756 0.0016 0.0467 0.0015 0.6855 0.0012

On 0.7866 0.0014 0.4067 0.0015 0.1319 0.0011

012 0.4630 0.0014 0.2950 0.0014 0.3277 0.0011

013 0.7864 0.0014 0.2281 0.0014 0.4323 0.0011

014 0.5779 0.0014 0.3660 0.0014 0.8987 0.0011


Table 3. Discrepancy index R for the different stages of determination and refine-ment of the structure of turquois

R

Originial coordinatesResults of Fourier refinementLeast-squares isotropic refinementLeast-squares anisotropic refinement

62%27%

9.5%7%

Table 4. Coordinates for the non-hydrogen atoms of turquois

In Table 4 are listed the final refined coordinates for the non-hydrogen atoms in turquois together with the standard deviationsas given by the least-squares program. Table 5 lists the refinedanisotropic coefficients fJii for the non-hydrogen atoms together withthe equivalent isotropic temperature factor as calculated from HA-MILTON'Sformula24

4B =

_3

}; }; R.. (a. . a. )'1

, 1 .i i

Values marked with a star correspond to those coefficients responsiblefor the non-definitive positive character of the temperature vibration.

24 W. C. HAMILTON, On the isotropic temperature factor equivalent toa given anisotropic temperature factor. Acta Crystallogr. 12 (1959) 609-610.

Atom fli; B Atom i I fliiI

BI !

Ou 01i

0.00091flu 0.0076 1.6 flu 0.74fl22 0.0079 fl22 0.0042 ifl33 0.0047 fl33 0.0014 !

ifl12 - 0.0027 flu - 0.0012

I

fl13 0.0012 fl13 0.0025

fl23 - 0.0012 fl33 0.0001

PI O2flu I 0.0015 0.26 flu 0.0038 0.56ifl22 0.0015 fl22 0.0036

fl33 0.0008 fl33 0.0007*,

flI2 - 0.0005 flI2 - 0.0032*fl13 - 0.0003 fl13 0.0016

fl23 - 0.0003 fl23 0.0001

P2 03

flu 0.0012 0.21 flu 0.0032 0.62fl22 0.0012 fl22 0.0040

fl33 0.0006 fl33 0.0011

flu - 0.0004 fl12 - 0.0027fl13 - 0.0002 fl13 0.0019

fl23 - 0.0002 fl23 - 0.0003

All 04flu 0.0028 0.40 flu 0.0058 0.82fl22 0.0008 fl22 0.0029

fl33 0.0012 fl33 0.0024fl12 - 0.0012 fl12 - 0.0016fl13 0.0010 fl13 - 0.0008

fl23 - 0.0002 fl23 0.0002

Al2 05flu 0.0016 0.39 flu 0.0048 0.68fl22 0.0005 fl22 0.0011

fl33 0.0016 fl33 0.0027fl12 - 0.0006 flu - 0.0012flI3 0.0012 fll3 - 0.0003

fl23 - 0.0003 fl23 - 0.0002

Al3 06flu 0.0012 0.25 flu 0.0031 0.66

fl22 0.0012 fl22 0.0020

fl33 0.0007 fl33 0.0026fl12 - 0.0004 flI2 - 0.0011fl13 - 0.0002 fl13

I

0.0002fl23 I - 0.0002 fJ23 - 0.0001

102 HILDA OID-DRESDNER

Table 5. Anisotropic temperature coefficients

AtomI

Pil B AtomI

Pi!I

BI

I

07 OnPn 0.0037 0.86 PH 0.0054 0.66P22 0.0012 P22 0.0018P33 0.0041 P33 0.0021

P12 - 0.0016 P12 - 0.0016P13 0.0014 P13 0.0008

P23 - 0.0005 P23 - 0.0001

Os

I

012

PH 0.0075 0.74 PH 0.0016 0.61

P22 0.0037 P22 0.0026

P33 0.0013 P33 0.0025

P12 - 0.0040 P12 - 0.0003P13 - 0.0003 P13 0.0012

P23 0.0001 P23 - 0.0010

09 013PH 0.0048 0.61 PH 0.0025 0.59

P22 0.0033 P22 0.0038

P33 0.0009 P33 0.0015

P12 - 0.0025 P12 - 0.0026

P13 0.0006 P13 0.0009

P23 0.0001 P23 0.0003

010 014PH 0.0043 0.95 PH 0.0007* 0.41P22 0.0016 P22 0.0042

P33 0.0043 P33 0.0002*P12 - 0.0011 P12 - 0.0015P13 0.0002 P13 0.0024

P23 0.0001 P23 - 0.0008


Table 5. (Oontinued)

Usually an arbitrary change of approximately half of the standarddeviation will give a positive character.

In regard to the fact that the absorption correction was notaccurate enough, no attempt was made to interpret the vibrationellipsoids of the atoms. The only remark that can be made is that theCu vibration is in the direction of the longer bond (Cu-H20) whichis approximately perpendicular to the plane of the square arrangementof OH radicals.

Table 6 gives the hydrogen coordinates unrefined, as obtainedfrom the last three-dimensional electron-density difference functionusing F

0 - Fe as coefficients. An arbitrary isotropic temperature

Atom x y Z

HI 0.8667 0.0333 0.7533

H2 0.1500 0.1567 0.1500

Ha 0.6333 0.1433 0.5900

H4 0.3933 0.0833 0.2900

H5 0.1433 0.1167 0.5933

H6 0.6500 0.1433 0.1000

H7 0.9800 0.3500 0.9000

Hs 0.4500 0.2767 0.4233

Oi-Hi ... Ok I Oi-Hi Ok-Hi Oi-Ok

04-H1 '" O2 0.869 A 2.067 A 2.871 A04-H2 ".Oa 1.150 0.901 2.950

01o-Ha . . . 01a 1.172 1.567 2.688

010-H4 . . . 012 1.004 1.881 2.780

°5-H5 ...01 0.743 2.292 2.883

°6-H6 . . .014 0.716 2.062 2.670

09-H7 . .. On 0.844 2.220 2.970

012-HS . . . 07 0.725 2.173 2.862


Table 6. Atomic coordinates of the hydrogen atoms in turquois

coefficient of 2.0 was assigned to all hydrogens when included in therefinement, but no attempt was made to change it.

The largest O-H distance is 1.17 A and the shortest 0.72 A.Taking the average value 0.95 A as the normal O-H distance, a stand-ard deviation of the hydrogen coordinates can be estimated in 0.2 A.All 8 hydrogen atoms seem to be involved in hydrogen bonding.Table 7 gives the relation between them and the atoms they contributeto bind.

Table 7. Distances in hydrogen bonds

Interatomic distances and bond angles were computed withSHOEMAKER'Sprogram DISTAN25. Interatomic distances are listed onTable 8 and bond angles on Table 9. In both tables the atoms designat-ed with a single prime represent the centrosymmetrical equivalentof the unprimed atom whose coordinates are listed on Table 4, plusor minus a cell translation. The short distance 05-06 correspondsto the share edge of the All and Al2 octahedra.

25 DAVID P. SHOEMAKER, DISTAN, crystallographic bond distance, bondangle and dihedral angle computer program. Internal publication of theChemistry Department (1963) Mass. Inst. of Technology, Cambridge, Mass.

Multi- Dis-

I

MUlti-I Dis-Atom pair plicity tance Atom pair plicity tance

Cu pseudo octahedron

12.422 A05'-01a 1 2.676

Cu-04(H2O) 2 06-0U 1 2.669Cu-06(OH) 2 1.915 06-012 1 2.725Cu-09(OH) 2 2.109 OU-012 1 2.75904-06 2 2.748 Ou-01a 1 2.75204-06' 2 3.420 012-01a 1 2.72004-09 2 3.420

04-09' 2 3.029 Ala octahedron

06-09 2 2.690 Ala-01 1 1. 903

06-09' 2 3.025 Ala-02' 1 1.893Ala-Oa 1 1.904

All octah edron Ala-O/(OH) 1 2.164AI1-05(OH) 1 1. 858 AIs-012(OH) 1 1. 906AlcOo'(OH) 1 1. 963 Als-Ou 1 1.878AI1-07 1 1.812 01-02' 1 2.734All-Os 1 1.817 01-0a 1 2.593AI1-09'(OH) 1 2.011 01-09 1 2.811AI1-010(H2O) 1 1. 943 O2-09 1 2.79705-06' 1 2.340* 09'-014' 1 2.70205-07 1 2.623 09'-Oa 1 2.70205-09' 1 2.808 012-01 1 2.64705-010 1 2.668 012-0S 1 2.73006'-OS 1 2.699 012-02 1 2.73006'-010 1 2.722 012-014 1 2.72906'-09 1 2.690 014-0a 1 2.70907-0S 1 2.834 014'-02' 1 2.66707-010 1 2.67507-09 1 2.875 P 1 tetrahedronOS-010 1 2.704 P1-0a' 1 1.541OS-09 1 2.584 P1-OS 1 1.521

P1-OU' 1 1.539Al2 octahedron

P1-014 1 1.556AI2-O/(H2O) 1 2.084

Oa'-Os 1 2.458AI2-05'(OH) 1 1.844

Oa'-Ou' 1 2.489AI2-06(OH) 1 1.963

Oa-014 1 2.501AI2-Ou 1 1.805

Os-Ou 1 2.504AI2-012(OH) 1 1.899

OS-014 1 2.531AI2-Ol3 1 1.832

Ou' -014 1 2.59104'-05' 1 2.681

04'-00 1 2.748 P 2 tetrahedron04'-OU 1 2.606 P 2-0t' 1 1.53404'-01a 1 2.815 P 2-02 1 1.53305'-06 1 2.340* P2-07' 1 1.54305'-012 1 2.752 P2-01a 1 1.550


Table 8. The interatomic distances in the turquois structure

Multi- Dis-

I

Multi- Dis-Atom pair plicity tance Atom pair plicity tance

0/-02 1 2.527 O2-07'

I

1 2.507

0/-07 1 2.524 O2-013 1 2.4 70

01'-013 1 2.528 07-013 I 1 2.538

Atoms Multiplicity Angle

Cu pseudo octahedron

Os'-Cu-04(H2O) 2 77.4°

°s'-Cu-04'(H2O) 2 102.6°Og'-Cu-04(H2O) 2 96.7°Og'-Cu-04'(H2O) 2 83.3°Os-Cu-Og' 2 96.5°

°s'-Cu-Og' 2 83.5°

All octahedron

I

(shared edge)°5-All-Os' 1 75.6°05-AIl-07 1 91.4 n

Os-All-OS 1 90.8°07-All-Os 1 102.2 °05-All-Og 1 93.3°

°s'-AIl-09 1 85.2°°7-All-Og 1 97.3°Os-All-Og 1 84.6°

°5-AIl-OlO(H20) 1 89.0°°s'-AIl-OlO(H20) 1 88.0°07-AIl-Olo(H20) 1 90.3°Os-AIl-OlO(H20) 1 91.3°Og'-AIl-OlO(H20) 1 172.0 °o s'-AIl-O 7 1 166.9°

05-All-Os 1 166.4 °

Al2 octahedron

°4-AI2-05' 1 85.3°04-AI2-0s 1 85.2°05-AI2-0s 1 75.7° (shared edge)

°4-AI2-011 1 83.2°

Os-AI2-011 1 90.0°

°5'-AI2-Ol2 1 94.4 °Os-AI2-Ol2 1 89.9°



* Shared edge.

A maximum error of 0.005 can be assumed on all distances

Table 9. Bond angles in the turquois structure




01l-AI2-012 1 96.0°

0~-AI2-01S 1 91.3°

05-AI2-01S 1 93.4 °01l-AI2-01S 1 100.2 °012-AI2-013 1 93.7°

Oo'-AI2-Oll 1 162.4°

0~-AI2-012 1 175.0°

06-AI2-01s 1 168.8 °

Als octahedron

01-AIs-02' 1 92.4 °01-Als-Os 1 85.9°0]-AIS-09' 1 91.8 °02'-Als-0'9 1 89.4 °Os-AIs-09' 1 87.2°

01-AIs-012 1 88.1 °02'-AIs-012 1 92.0°

Os-AIs-012 1 91.5°

02'-Als-Ou,

1 90.2°

Os-Als-Ou' 1 91.5°

09'-Als-Ou' 1 88.0°0]2-Als-Ou' 1 92.1 °O2' -Als-Os 1 176.1 °09' -AIs-012 1 178.6 °01-Als-Ou' 1 177.4 °

PI tetrahedronOS'-PI-0S 1 106.8 °Os'-P1-Oll' 1 107.8°

°s-P1-OU,

1 109.8 °Os'-P1-OU 1 107.7°

°s-P1-OU 1 110.7°

01l'-P1-OU 1 113.7°

P 2 tetrahedron

0/-P2-02 1 110.6 °0/-P2-07' 1 110.7°

°2-P2-07' 1 109.7°

01'- P 2-01S 1 110.0 °°2-P2-01S 1 105.6°

07'-P2-01S 1 110.1°

Oxygen coordination angle

P2'-01-Als 1 143.4 °P2-02-Als' 1 134.1 °P1'-Os-Als 1 133.2°




Cu-04-AI2 1 88.2° (H20 coordi-nation angle)

AII-Os-AI2' 1 108.1 °Cu'-06-AII 1 98.6°Cu'-06-AI2' 1 108.4 °AI/-06-AI2 1 99.8°P2'-07-AII 1 140.1 °PI-Os-AII 1 140.2 °Cu'-09'-AII 1 91.3 °Cu'-09-AI3' 1 130.9 °AII-09' -AI3' 1 129.9°

-Olo-AII 1 (H20 single-coordinated)

PI'-Oll-AI2 1 137.3°AI2-012-AI3 1 138.8 °P 2-013-AI2 1 135.7°

PI-Ou-AI3' 1 139.6 °

Description and discussion of the structure

A final three-dimensional electron-density function was calculatedafter the last cycle of refinement of the turquois structure. A com-posite of sections of the structure which contains maxima, as seenlooking down the a axis, is shown in Fig. 3. If this composite sectionis compared to the minimum function M4(yz) of Fig. 1, a close corre-spondence can be recognized. The false peak on M4(yz), that projectson the inversion center 0, t, is due to the pseudosymmetry 0 I ofthe crystal. In a first approximation turquois can be described asa O-centered structure with a Cu deficiency in the inversion centert, 0, t. Actually the biggest hole in the structure corresponds to thislocation, as can be seen from Figs.4 to 7.

Figure 4 is the interpretation of the three-dimensional electron-density function projected parallel to the a axis. Fig.5 and 6 areviews of the structure represented as linked polyhedra as seen lookingin the direction of the a axis. For simplicity, the structure has beendivided into two parts, centrosymmetrically related. The first halfof the structure, considered from x = 0 to x = t is represented onFig. 5; the second half, from x = t to x = 1 is represented in Fig. 6.

The structure can be described in terms of single and doubleoctahedral groups of oxygen atoms, OR radicals, and water aroundthe aluminum atoms. The double group consists of two Al octahedrasharing an edge. It is linked by four P04 tetrahedra to the two trans-

Det . .

.

ermmatlOn of the crystal structure of turquois 109

latlOnal-equivalent groups in the d' t'

hedra are attached to t h £ fIrec IOn of the b axis. These tetra-

' th

e our ree corners f t hWI the common ed ge as h

. F '

0 e square sections

. . 's own In IgS 5 to 7

Orlgm

. .

Fig. 3. Composite of sections from the fin I Ia e ectron-density function

aFig. 4. The structur ft' .

e 0 urquOls projected parallel t o the.a aXIS


The single aluminum octahedron shares the four oxygens at thecorners of a square section with four PO 4 tetrahedra. Of the tworemaining vertices, one is shared with the double octahedral group,and the other is also common to an octahedron of the double groupand to the Cu octahedron. There are only two OH radicals in the asym-

Fig. 5. Polyhedral chains, view parallel to the a axis, sections from x = 0 to x = !

metric unit that are common to the coordination polyhedra of threecations. One is OH(6), in the shared edge of the double group whichalso belongs to the Cu polyhedron. The other is OH(9), common toone single octahedral group, to a double octahedral group, and tothe Cu octahedron.


The Ou octahedron has the expected 4 + 2 coordination predictedby the Jahn-Teller effect 18.The square coordination is formed by twoOH radicals and their centrosymmetrical equivalents. The two longbonds are directed to two water molecules, related by an inversioncenter, which also complete the Al(2) octahedron.

Fig. 6. Polyhedral chains, view parallel to the a axis, sections from x = t to x = 1

The location of the water molecules in the Ou coordination agreeswith the distribution found in eucroite2a and liroconite27. However,

26 GUISEPPE GUISEPPETTI, La struttura cristallina del'eucroite C~(As04)(OH) . 3H20. Periodico Mineral. 32 (1963) 131-156.

27 G. GUISEPPETTI, A. CODA, F. MAZZI e C. TADINI, La struttura cristallinadella liroconite, Cu2AI(As,P)04(OH)4 . 4H20. Periodico Mineral. 31 (1962) 19-42.


the results reported for krohnkite 28place the H20 molecules as complet-ing the square coordination of the Cu.

28 B. RAM A RAO, Die Verfeinerung der Kristallstruktur von Kr6hnkit,Na2Cu(S04)2 . 2H20. Acta Crystallogr. 14 (1961) 738-743.


The values of the interatomic distances and angles for the PO 4tetrahedra agree well with the reported values in related compounds.The single Al octahedron is also regular, the average AI-O distanceis 1.94 A, the longest value is 2.164 Aand the shortest value is 1.878 A.The average octahedral angle for the single octahedron is 90.01 ° withvalues ranging from 85.9 ° to 92.5°.

The largest departures from regularity are found in the interatomicdistances and angles of the double octahedral group. The sharededge 05-06 shows an extremely short bond distance of 2.34 A, coupledwith octahedral angles 75.7° (05-AI2-06) and 75.6° (05-AII-06)'Bonds of 2.43 A had been reported for shared octahedral edges inandalusite21 and in anatase and rutile29, but they are seldom found.A possible reason for this rather remarkable distortion is that thedouble octahedral group also has two edges (one from each octahedron)in common with the Cu pseudo octahedron. These edges ar.e °6-°4of the Al2 octahedron and 06-09 of the Al2 octahedron. One of theOH radicals (06) belonging to the share edge also completes theCu square coordination, thus becoming one of the two anions actuallybonded to three cations. The second negative ion coordinated tothree cations is °9, It can be observed from Table 9, that the oxygen-bond angles which agree the least with the ideal values are the onesincluding 06 and °9, The only exception is the value 88.20 for oneof the water molecules, in the coordination angle Cu-04-Al2.

Acknowledgements

The author wishes to thank Professor M. J. BUERGER of theMassachusetts Institute of Technology for his constant encourage-ment and helpful suggestions and Dr. C. T. PREWITT of E. 1. DuPontde Nemours for making the piezoelectric test. Professor C. FRONDELfrom Harvard University and Dr. G. SWITZER of the U.S. NationalMuseum kindly provided the turquois crystals used in this investiga-tion. This work was done while the author was on leave of absencefrom the Laboratorio de Cristalografia de la Universidad de Chileunder an OAS fellowship. All the computations were carried out onthe IBM 7094 computer of the Computation Center of the MassachusettsInstitute of Technology. The work was partially supported by a grantof the National Science Foundation.

29 RALPH W. G. WYCKOFF, Crystal structures, vol. 1. Interscience Pub-lishers, 2d ed. (1963) 252-255.

Z. Kristallogr. Bd. 121,2/4 8

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