American Mineralogist, Volume 59, pages 974-984, 1974

Trolleite, A|,(OH),[PO*],: A Very Dense Structure withOctahedral Face'Sharing Dimers

P,q,ur BnrAN Moonr, lNp TarAlr,tnu Anarr

Department of the Geophysicat Scien:ces, The Uniaersity of Chicago,Chicago, Illinois 60637

Abstract

Trolleite, 4Al4(OH)elPO.l', a 18.894(5) A, b 7.161(r) A, c 7.162(2) A, P 99'99(2)', sPacegroup I2/c, is a valid species. For 2010 independent reflections, R(hkl) converged to 0.036.Estimated standard errors in distances are Me-O r- 0.002 A and O-0 -t- 0.003 A. Its crystalstructure consists of Al-O octahedral face-sharing dimers which link by corner-sharing hydroxylgroups to form an infinite double-chain wbich runs parallel to the [001] direction. The [PO.]tetrahedra bridge these chains to produce a very dense three-dimensional structure.

The structure is topologically related to that of lazulite, MgAL(OH),[PO.],. This is par-

ticularly evident if the orientations of the [PO,] tetrahedra are noted: the lazulite tetrahedraand the oxygen packing can be approximately superimposed upon those of trolleite.

Severe distortions occur on account of the face-sharing and result from the cumulativeeffects of cation-cation repulsion and deviations of the anions from local electrostatic neutralityby the coordinating cations. The octahedra are distorted into elongate trigonal antiprisms withthe A1-O distances toward the shared face longer (1.9+2.A9 A) than those to the opposingfree face (1.79-1.96 A). Average polyhedral distances are Al(1)-O 1.915, Al(2)-O 1.905'P(l)-O 1.528, and P(2)-O 1.528A. Differonce synthesis provided locations of the hydrogenatoms. The proposed hydrogen bonding scheme involves bifurcated hydrogen bonds from theoctahedral groups to phosphate oxygens.

fntroductionThe peculiar mineral trolleite has recently been

characterized by Sclar, Carrison, and Schwartz(1965), who proposed the formula Alb.ss(OH)4[POrJ+. According:to these authors, it is an unusuallyhard substance, about 8.5 on Mohs scale. Originallynamed by Blomstrand ( 1869) from a small iron oredeposit at Westani nsar Kristianstad in Sk6ne,Sweden, it occurred with a host of unusual phos-phate minerals such as attacolite, cirrolite, augelite,lazulite. and berlinite. What remains of the old minedump was visited by the senior author in 1968; thephosphates occur rarely as lenticular masses andblebs associated with qtrartz, pyrophyllite, rutile,etc. A similar paragenesis has been recently notedfrom the White Mountains, Mono County, Cali-fornia, where trolleite has been found (C. B. Sclar,private communication). Specimens of the Californiamaterial are appearing in mineral dealer's catalogues,but a detailed characteization-including singlecrystal study-is evidently lacking. Most systemsand compendia of mineralogy place the mineral ina dubious position or group it with lazulite as avariety of that mineral. Sclar e/ al (1965\ propose

a structural kinship with lazulite MgAl2(OH)2['POr1z.Our continued interest in the systematics of Al-O

clustering, phosphate crystal chemistry, and densestructures in general prompted a detailed investiga-tion on trolleite, and this study not only reveals theunique status of the mineral but also provides evi-dence for Al-O octahedral face-sharing dimers.

Experimental

A specimen of trolleite from California was kindlydonated by Mr. A. L. McGuinness. It consists of acompact and dense mass of small pale green trol-leite grains, blue-black prisms of scorzalite, whitecleavage surfaces of augelite and minor amounts ofan unidentified granular pale orange phase. A por-tion of the sample was crushed and trolleite grainswere hand-picked. From these, a small crystal frag-ment was examined by rotation, Weissenberg, andprecession photography. Some grains were groundwith silicon standard (a = 5.4301A), and a chartdiffractogram was prepared. These data were in-dexed on the basis of the strong intensity singlecrystal data and are listed in Table 1. The crystalcell parameters in Table 2 were derived by least-

974

TROLLEITE 975

squares refinement from twelve high angle reflectionson a PrcxBn automated diffractometer. These resultsand the density calculation for Alr(OH)s[pO+]gagree well with the original analysis, specific gravitydetermination, and description of the material byBlomstrand (1869), and with the results of Sclaret al (1965). Although we bave not examined a typespecimen, we are confident that the Californian andSwedish trolleites are in fact the same mineral andconclude that trolleite is a valid species, distinct fromthe lazulite group of minerals. The powder data inTable 1 match those published by Sclar et aI (1965).

It immediately became apparent that the structureanalysis would prove a difficult problem since about80 percent of the reflections were relatively weak.This explains the rather simple powder pattern de-spite a cell of considerable complexity.

The crystal originally selected was a small chipabout 60 microns in average dimension. From thiscrystal, the structure was eventually solved but thedata were of such poor quality that a search for asuperior crystal was undertaken. Over 20 crystalfragments were examined by film techniques until asuperior roughly equant crystal of O.2 mm size wasfound. Detailed restudy was undertaken on the su-perior crystal. Two-thousand and eighteen inde-pendent reflections to sin 0/X = 0.80 were col-lected on a Parrnep automated diffractometer of the0- to lO-layers with b as rotation axis. We utilizedMoKc radiation, graphite monochromator, scanspeed of 1.0'/minute, with half-angle scans of 1.6o,widening to 3.9o at the high levels. Strong reflections

Tesrs 1. Trolleite. Powder Data*

I / Io d (obs) d(calc)

6 . 6 8 35 .025u 6 q 2

4 .2093 . 5063.3r123 . 2 0 33.10I3 .0792.5232.2261 .986L .9861 .803f . 8001 .6101 .60 II q q ?

I q q l

1 .5+0L .399I . 39 3

*Cu,/Ni radiation, chart diffractogram, VZj2O/

ninute scan, Si standard.

Terrn 2. Trolleite. Crystal Cell Parameters

Trol lei te Lazul i te"

et$lbrA)sGeiv ri.3rF '

1 8 . 8 9 4 ( s )7 .161(1)7 .L62(2)

95 t l .399 .ee (2 )

I .LO

t -zo

7 . 2+

120.670

Pzy'c

MsAl^ (Ol0 ̂f PO,.'l ^- a - ' e - 9 ' z

3 , I 23 . 1 +

16 .2s ? - 6

3520251010q0

r009 050451035

15

I51030 brd

201010

6.6675 . 0 1 64.6 r+94 . 1 9 73 . 5 0 23 . 3 3 63 . 2 0 83 . 0 9 5

2 . 5 1 92..22LI q c ?

1 .79 I

1 .6071 .598I . 547

L.5371 .396I.392

fi 'tro011-l+002lt2022201r260040252I) 4 1

9r0I3280e32382?2z+2+2.

L 2 . 0 . 0804134+1S

space grcup iUc

fomla Ar4(olD3[po,+]3

4 l l

specif ic gnavity ^ S.OSId q s i t y ( c a l c . ) , g n c n - r 3 . 0 8volme,/oxygen atom, AJ 15.9.hardness 8.5r

ts" Iuo g 4. ( r96s).

- Lindberg md Christ (1959).

with a wide scan range (and the very low anglereflections) were obtained manually. All but eightreflections were accepted for the ensuing study.These rejected reflections were of very low angle andeventually revealed differences resulting from ourscattering curve for Po and the scattering profile of Pin the crystal.

Solution and Refinement

The data were processed by conventional corn-putational methods to obtain jF(obs) | from whicha Patterson synthesis, P(uuw), was prepared. On ac-count of many overlapping y-coordinates of theatomic species situated at y - O, lf4, solutionproved difficult but successive B- and y'-syntheses(Ramachandran and Srinivasan, 1970) led to theresolution of all cations and anions (except hy-drogen) on the final Fourier synthesis.

Likewise, refinement of the structure provedrather slow and tedious. Full-matrix least-squaresatomic coordinate and anisotropic thermal vibrationparameter refinement led to the results in Table 3.Unobserved reflections with 1 < 2o(I) were set aso(1). Reflections were weighted based on countingstatistics, long term intensity fluctuations, and theefiect of 0.1" mis-setting of the p-angle for our dif-fractometer.

Trnrr, 3. Final Refinement of Trolleite

B11BD = qlF(ob-qI:-. lI(carc)l lE l r (obs) |

Relative lf1ou") | Nurnber of refLections R(hk})

AboveI

| l

il

0 . 04 .2

L2.625.2

2010L7841364

873

0 . 0 3 6.031.o2+.o2L

976

For the refinement, we employed a local version(Inu 360 computer) of the familiar Onnrs pro-gram of Busing, Martin, and Levy (1962); and thescattering curves of Cromer and Mann (1968) forAl2*, Po and O1-. Table 4 provides the atomic co-ordinate and isotropic thermal vibration parameters,and Table 5 lists the structure factor data. Tables6a and 6b provide the anisotropic thermal vibrationparameters and the orientations of these ellipsoidsrespectively.

Description of the Structure

Topology and Geometry

Trolleite is a most fascinating structure since itsunderlying principle is a face-sharing dimer of alumi-num-oxygen octahedra. The dimer has composition

[Alz(Op)e(OH)3], where Op is the phosphate oxy-gen, but further polymerizes to equivalent dimersby corner-sharing hydroxyl groups to form an in-finite double-chain with composition [Al4(Op)12(OH)rl. Thus, all oxygen atorns in the unit cell canbe associated with the octahedral fraction of thestructure. The octahedral double-chains run parallelto [001] and are linked to equivalent chains (relatedby the 1-centering) by the PO+ tetrahedra in generalpositions. The result is a very dense three-dimen-sional framework of octahedra and tetrahedra. Theunusual hardness is attributed to a rather uniformdistribution of strong AI-O-P-O bonds.

The trolleite structure is topologically and geo-metrically related to the lazulite arrangement, con-firming the proposal of Sclar et aI (1965). Figure 1reveals the octahedral double-chain in trolleite; thestippled octahedra in this chain coincide nearly

Tenrs 4. Trolleite. Atomic Coordinates and EquivalentIsotropic Thermal Vibration Parameters*

B (i2)

0.320s9 (8 ).r+urq (8).2s000.08r09 (6)

.32611 (2r)

.oes7e (22)

. r6861 (21)

.00803 (22)

.23708 (21)-.07ssr+ (2 2)

.2500

.06e66 (20)

"Estinated. standardl errcrs refer to the last digit. The hydrc-gen atom positions were located on the tl i fference slmthesis.

P. B. MOORE, AND T. ARAKI

a1(1)Ar(2)P(I)P (2)

o (1)o (2)o (3)o (4)

o (s)o (6)ox(1)oH(2)

H(1)H(2)

0.16778(3) - .00654(8).07s70 (3 ) .27r r8 (8 ).00000 .88269 (9 ).1681+r+(2) .36728(7)

.064s8 (8) .0rr73 (2r.)

.02061+(8) .76272(22)

.23738 (8 ) .46488 (22)

.Ir1r4(8) .so8+4(2r)

.1r+191(8) .245sr(20)

.18216 (8) .23sr6 (2r)

.0000 .36'+28 (28)

.L61r+I(8) .87e00(20)

.000 .tlgl+

.L90 .809

0 .38 (r).43 (1).3s (r).3 6 (r)

.60 (2)

.7 ' ] (2)

.7 3 (2)

.7 3 (2)

.s6 (2)-7s(2).62 (3).s3 (2)

exactly with the loci of the stippled octahedra of thelazulite structure in Figure 2. The structure data of

lazulite were obtained from Lindberg and Christ(1959). To derive the octahedral dimers from thelazulite structure, the MgAl octahedral pair is re-placed by AlAl.

The relationship between the two structures can

be better visualized on the basis of the packing of

the [PO4] tetrahedra. Figure 3 shows the dispositionof the tetrahedra in lrolleite projected down the

b-axis. At b/2 from each tetrahedral center is an(OH)- group. The tetrahedra are oriented on a

checkerboard such that their pseudo-lf axes areparallel to b. If thg tetrahedra in lazulile are pro-jecte{ down the lazulite b-axis (Fig. 4a), all tetta'

hedr4 poincide in the two structuros. An identical

arra4gement of tetrahedra occurs in the structure of

lipscombite (Fig. ab). These tetrahedra were plotted

from the results of Katz and Lipscomb (1951). The

difference between the lazulite and lipscombite struc-

tures evidently involves the degree of ordering of the

octahedral cations: in lipscombite these are dis-

ordered leading to partly occupied chains of face-

sharing octahedra (see Moore, 1970, for the rela-

tionship of lazulite and lipscombite to the large

family of "5.1A fiber structures"). The density of(OH)- groups and [PO+] tetrahedra are identical in

the trolleite and lazulite structures. Thus we can

write a general crystal-chemical relationship between

the two structures, ulz.'

lAl,l(oH)ulPo"lu ttu'o\JjSSJulPOnlo

and conclude that on the basis of 30 oxygen atoms,

lazulite contains nine occupied octahedra and trol-

leite cpntains eight. Hence, although the oxygen

packing gfrpiency of trolleite is greater than that of

lazul i te ( t5 .91i . /O2 us 16.2A1O*) , the la t ter

specie,s is denser (3.08 os 3.14 gm cm3-). Trolleite,

in effect, is an ordered derivative structure of lazulite.

Although the oxygen packings are topologically

identical, the octahedral sites occupied are distin-

guishable. Since the isotropic temperature factors are

0.38 and 0.43 A-'z for A1(1) and Al(2) respec-

tively, we conclude that these sites in trolleite are

fully occupied.

Analysis of Potyhedral Distortions and Distances

The existence of a shared octahedral face for each

of the tWo non-equivalent octahedra in trolleite re-

sults in severe polyhedral distorfion' we examine

977TROLLEITE

Taerp 5. Trolleite. Observed and Calculated Structure FactorsF O F C l o F c F o f c H x L F t f c H r L E o E c i r l t u t c

- 3 a o . a a l . 6 L t - L o a L . 2 2 . r- 6 2 2 . 9 2 5 . 0 0 3 I I A . r l o . r- a 3 0 . r - 2 a t o 3 I o r . r - . r . o- z 1 . o 4 . 3 0 3 5 r d . a a a . 3

o 35 . I - r1 . . o 1 t 20 .5 -22 .42 13 .4 3 t .L O 1 9 t . .A 25 .94 1 5 . 2 a 5 . O 2 3 4 0 t r . ! 1 6 . 0a 19 .5 11 .2 26 . -2 0d .6 59 .6a 6 . 9 - t . 9 2 7 a - 5 J . o - t . 2t 22 .1 -2 t .6 27 4 -3 ' . . 5 . t5 71 .O t9 . t 21 . -L 12 .2 La .9r 5 5 . 6 5 l . O 2 7 4 | 2 . e - ! . 2r 2 1 . 5 2 2 . O 2 6 4 2 t L . i 6 9 . 2

- l 1 2 . . 5 - r 2 7 . a 2 5 . 0 a . 9 - t . a-a 23 .L -21 .5 26 . -2 13 .6 31 .0- 5 3 . . 3 - 3 5 . 9 2 6 a { J ! . r - 3 6 . 0-1 72 .4 ?L .a 26 . -6 2 r .O -2 r .2- 9 r 9 . . 2 2 . 1 2 5 { - 5 t 5 . e l 5 , d- le 2o .s 2o .1 25 . -3 16 .2 L ' .a- 3 5 0 . . - a 3 . 2 2 5 a - L a ! . . - 2 1 . r-6 2 .5 - t .O 25 1 L- 4 4 9 . 2 5 G 9 2 5 + a- 2 3 2 . 1 3 r , r 2 1 4 . 2 5 . 1 - 2 2 . 5

o 5 6 . 5 5 ? , r 2 4 4 2 9 . 1 - 1 I . 2a 24-1 24 .A a . . 0 cc .O -65 . {( 6 3 . 4 - 6 a . 1 2 . . - 2 2 . . - t . Za 1 6 . 3 I 5 . 9 2 4 4 - a 5 . . - I . a3 1 0 . r . l o , r 2 a . - 6 6 9 . t 6 9 . 2

? . o? l f . . - t c a 2 ! 4 - 5

2 t a - 3 2 . a2 t { - l z . a - 2 . 2

I 2 9 . 2 t l . 2 2 . ! - 2 . 5- 1 2 . 5 2 3 . 3

4 . 3 ? 2 a 4 r e . o - 3 t . 5-5 25 .2 -2A.O 22 { 2 .6 . d -a6 .0

3 .9 22 . O a5 . . - . . . t-9 22 .6 -20-5 22 4 -2 LJ2 .9 re? .g

a 5 z . l - 5 2 . € 2 2 4 - a 6 . 06 l t . 4 - I 2 . 5 2 2 1 - 6 2 . e. 3 6 . 5 1 6 . 5 2 2 { - 3 r r . . - 5 1 . 62 a l - t - 1 9 - o 2 l . - t r I 9 1 2 . 3o 57 .6 59 .5 t .5

2 L 4 - a t r . , - 2 t . a- 4 l o r . 9 - 1 0 9 . . 2 1 . - r 2 ! . i - a 9 . r-6 22 .9 24 .2 2 r a I- 3 1 o . O - 1 . 3 2 l { 3 r o . r l t . l

- l o 1 2 . 4 - I 5 , 2 z l { 5 l t . o t r . r1 . 0 z o 4 6 / t . d 2 b . 2

- 7 a l . o - t 1 . 7 2 0 . { z J . ) - 1 9 . 9- 5 l 4 . O - r a . 2 2 0 . 2 d J . L t t . t- 3 r € . 0 l a . o

20 I -2 2A. t -28 .2L 21 .2 2 t . t aO . -1 25 .2 L t . t1 2 . 6 - t . 1, 29 .e -29 .5 l . t1 29 .4 -23 .2 Ie . -99 € . t l o . a l e 4 - ? r t . t t 5 , 6a t 2 - 6 a r . 6 1 9 4 - 5 r u . r - 1 3 . ra 2 0 . 1 - 2 2 . t 1 9 . - 3 r d . 2 - l r . t4 r { . 0 1 4 . 6 1 9 { - r l o . 7 - r ! . 22 t3 . l la .9 19 a Io r 3 r . 0 - I 7 . - o

- 2 r d , r 1 3 . 2

3 - a t a . 3 l 6 . a l 3 . 6 1 2 d . 6 1 r 9 . o) - 6 a 5 . 9 - 2 1 . 4 l 3 a . I r . { I i . ?a - a a t . 2 t a - a r 3 ( z r l . e I 2 . I3 - l o r 8 . a - 2 1 . e L a 4 0 t a . 5 - 1 2 . 2t - 9 2 a . 5 - 2 9 . 3 1 3 { - Z . l . t - { t . l

5 . 2 l d . - . r f . 2 _ t { . 93 - 5 2 9 . 6 - 2 9 . 9 r r . - 6 r 2 0 . r r J o . 53 -a 42 .9 46 .5

? . 3 - 9 . 3 ) . ' - 1 . 2i I 2 4 . 0 2 6 . 9 r 7 . - 7 1 6 . r _ 1 3 . rt a 41 .1 -4 ) -2 L l 4 -5

t t 2 5 . 2 - 2 5 . 4 l t . - l r t . d r r . t1 9 r 2 . 9 L z . r 1 7 a I ' . r 3 { . t3 t o 5 - t l r . 3 l r . o - r c . 6

l ? . 5 r { . . - r ' . 2i 6 1 1 . 6 ) o . 4 L 1 4 7 t . c - 7 . I3 1 3 4 . 5 - 3 4 . 1 1 6 a 6 r r . r - l t . {3 2 l 5 . l - 1 6 . € r o 4 . 4 i . I - 1 e . 2t o 2 4 . 6 - 2 2 . 1

5 . 1 - 6 . ' 1 6 < A l r . / l r . tr - . 5 2 . 1 a 6 . t 1 6 4 - 2 r r o . i r r 2 . l3 - 6 l l . r l t . 2 1 6 r - 4 , e . t - 4 r . 33 - 3 3 3 . 2 - 4 C . 0 1 6 { - 6 l r . e I r . 7

6 . t a . 2 1 6 . - A d . d - 6 9 . 01 -9 13 .2 -15 .L 15 { -9 2 .9 -4 .43 - r t 6 , 4 - r t . o

3 - 3 1 6 r - ? 1 6 0 . 2 1 5 . - l r l . 2 r I . 9L5 . - l 26 . B 25 .9

r I 3 0 . 1 - 2 9 . 9 t 5 t r r r , o - e - .l , . 1 l . o

! 5 r 5 . 5 - 1 6 . 3 l t 4 53 1 t A . O 1 1 . r r 5 a ? l d . 7 - 1 6 . 3

2 . 4 O , f l { { 6 1 6 . r - 1 6 . 3r 3 l l . 9 - 3 2 . 6a 6 t z - t r 2 . 2 r a 4 z r 7 . 2 3 5 . 91 4 61 .1 62 .0 l . . 03 2 6 9 . 9 6 7 . 4 l { 4 - 2 I c . r - r 5 . 0I O 21 .1 25-9 14 a - . ?6 . t -7e .3t - 2 2 a . 9 - 2 4 . 2 1 4 a - 6 D e . r - ? r . l

3 - 6 4 6 . 0 ( r . r 1 4 . - l O r 9 . 9 . e . 0; - 3 r e - . t s . 7 l 3 { - 9 I t , . - r t . lr - 1 0 : { . 4 l e 6 2 . t - 5 . 6r - 9 1 5 . 5 - 1 7 . 5 1 3 . - t r i . r 1 6 . 03 - t 3 L t 4 1 . 3t - 5 4 . . ' . 1 . A r i { - r r r . 7 - r 7 . 2

3 . 6 - 1 1 . 6 I f 4 3 I o . . - r ? . 23 I r r a . 2 - r f o . a l a . 5a 3 a o . ' - { r . a r J . 7 a l . o l r . 0I 5 a 3 . 7 { 9 . 3 1 2 a 3 J o . Y - J z . oa t 2 f - o 2 e . 2 1 2 4 5 d l . t r u . 6

3 . 1 1 2 . . 5 d . 9 - t c . 63 r O 1 9 . 5 - 1 4 . 0 r l 4 2 r I . 7 - . 1 . 03 a 2 o . 4 2 l . o 1 2 a o 2 9 . 6 - 2 ) . 1t t 20.3 20.t L2 4 -2a a t2 -Z 5a .5 l2 . - . 2d . t -3d .6t 2 l l . 1 1 5 - 6 1 2 4 - 6 1 5 . 2 , e . t3 0 5 . . ? - 5 9 . 9 1 2 ( - 3 r r . v - { l . r

5 . 2 t 2 6 - r C r z . l l l . r3 - 4 6 . t r l { - 9 l z . 2 - 1 . . r

r l 4 _ t3 -A .2 .2 42 .1 L r . -5 r5J L5r2

2 . 0 - r . l t l 4 - a t a . 2 a a . eI - 9 r 2 . 3 l l . . I l 4 - r 1 2 . 6 - 9 . 3t -1 15 .5 31 .5 l I { I . . . r -43 . t3 - 5 1 9 . 2 I 9 . 2 r r a 3 r g , d - r 9 . 33 - l 1 3 . 6 - 1 3 . 5 l l 4 5 I . l3 - r 5 9 . A - 6 6 . 6 r t a 7 1 . 1 5 . 13 I 9 . 5 3 . t t l 4 9 l t . r r r . ta a t ' -o aa .6 Io ( 3 r l .2 r . .91 t a 2 . 4 1 9 . 6 l O . 6 i 9 . r - 3 t . 4

3 . O r 0 4 . C ' . s - 6 r . 0r o 4 2 5 Z . ) - 5 2 . 6

2 . 9 - 2 . O r O . O l r . 2 - 3 r r t2 . , - 7 . 1 l 0 4 - 2 1 2 3 . 9 1 1 6 . 0

r 6 29 .O 2e,O l0 4 - {3 { t 4 r . 5 - r { 5 . 0 l o r - 5 l J . t r 5 . 53 2 t . . r l t .o ro . -3 t5 . I -72 .13 -2 ro3 .5 - ro t .2 ro 4 - ro { r ,3 - . . - tI - . r t . 2 t 9 . .J - 6 1 3 . 5 - r r . 2 9 4 - t 2 r . 5 2 r . lI - 0 a o . 9 - 9 c l 9 . - t r g . t 2 t . l

2 0 l t . t - I t . tI l 0 l a . l 1 3 . l

2 r z l . o 2 0 . 32 r I 2 C . 9 l r 6 . a2 ) a a . r - t 5 . 12 I 1 9 . 0 l 6 . az - r r 9 l . r - l 9 t . t2 - t 2 t . t -26 .12 - 5 l ( . ' t o . t: - r 3 6 . 1 e 3 . 6

2 - l l t l . 3 t a . t2 - I O 3 r . e - 3 9 . 92 - 3 I 2 . r - 1 5 . 4

2 - a 4 . 3 - 1 . 92 -2 59 .2 -56 .aa o 5 . 6 - 5 . 12 2 a5- ' -a1 .3

2 6 5 6 . t - 5 1 . 12 6 l5 .L L r .g2 r o2 e f s . a . e . t

2 I 1 4 r . t - l ( r . ?2 | 2a .9 -24 .22 - r l 3 . l - t 3 . 22 - 3 l a a . I 1 6 7 . 52 - l l c . t r 0 . l2 - 1 2 1 . 6 2 r . 12 - r 6 r . r - t q . i2 - r r t : . r - r l . l2 - l o 1 6 . r - 1 2 . 7

r . | - 1 . 52 - 6 l { . C - 1 t . 9a { l s 6 . t 1 4 7 . 3

z 3 r 3 . l r . . 4e , t r . l - r e . o, 6 r r - 2 1 6 - 52 3 { r . a r a . .? I 0 1 5 . 5 - r ? . rr l r l : . 0 - 1 t . 52 e 21 t2 -2 r . t

2 5 Z t . g 2 6 . 12 r r 9 . 2 t 6 . 32 | 2 ? t . l 2 1 4 . 2

2 - t ao . t -4o .22 - t t l 6 . l - r r 9 . 52 - 1 4 . 32 : 9 2 . 1 - 6 . 12 - l l t l . 8 5 l . e2 2 nq .2 -a2 .d

? 6 l 3 ( r t t a r . ?I 3 r 7 . . - t 3 . 'I t 0 { . 3 - 4 . 4

1 r : ? - 2 r 5 . ?3 r f 1 2 . 5 : l r - t

- 5 1 0 9 . 2 - 1 1 7 . 6 2 t 2 - 5 t o . o- . 6 . 4 6 . 2 2 1 2 - r 2 . a - 1 . 0-z !2 . r a . .2 z t 2 -9 5a .a - t9 .1

o t 2 J . 9 - I l ? . 9 2 0 2 - € r O . 9 - t 2 . 22 2 4 . 6 2 l . l 2 0 2 - 6 a r , 6 - a 3 . 9

2 0 2 - a r . l 4 . t5 r 0 6 . f - 1 0 3 . 9 t o 2 - 2 7 . 3 - ? . t3 J { . O i , . 6 2 0 2 0 2 4 . 2 2 a . 5

2 0 2 2 9 € . 5 l O O . t9 2 5 . 6 - 2 5 . 6 2 0 2 ( 4 6 . 3 - a t . g

3 .9 20 2 6 16 .0 -aA.C5 a ! . u . 5 . ? t j 2 1 f r . 5 - a 7 . s

t . 6I z z . t - 2 t . 2 1 9 2 3 1 0 . 2 - 1 1 . 3

- | 4 3 . t - . A . 5 1 9 2 r 6 9 . 3 r O . 2- l 0 6 . 0 - t 0 . 0 r l 2 - r- 5 r . I 7 - Z 1 9 2 - 3 l g . t 1 9 . 6- 7 t o . . , a . 4 l s 2 - t ? 1 . 9 - ? 6 . 0- e z 6 . a 2 5 . a 1 9 2 - ? 9 , 1 - 7 . 3

1 . 5 - 5 . 2 l e 2 - 9 i ? . 0 - r 5 . t- L O 2 2 . e 2 . - 2 r a 2 - 1 0 a , a- 3 1 6 . 5 l b . t r a 2 - 0 3 r . 5 - 1 2 . 3- 6 r r . o - 1 3 . 6 l 3 2 - 6 9 . ? t 2 . 3

13 2 -a 10 . I 33 .4- 2 6 A . ! - r t . d t a 2 - 2 9 . r l o . r

o z a . r 3 l . l l 3 2 0 l o t . 3 r t 2 . 02 z i - t 2 . . 1 t s 2 2 t 4 . O - 3 1 . A

1 6 2 1 2 a . 1 - 2 5 . a7 . 4 l 8 2 6

€ l D . o - I r . t L l z 1 9 . ? 1 2 . €r o . 1 . 5 - e . 2 t 7 2 5 ' . . 2 f 1 . 4e 5 . 4 - 1 . 2 L f 2 3 t 1 . 2 - 1 2 . 5t l t . ) - r 9 . e l r 2 r 2 . 5 0 . 65 l t . l r r . l r 7 2 - l 1 0 6 , 6 - r r r . 4

L f 2 - 1 t . e - 6 . 9I o r . , d u . I L 1 2 - 5 7 . 5- r . 5 . . - 3 a - 3 , L 1 2 - 1 1 a . 2 r t . j

- r r r o . 3 - 1 r . . 2 L 7 2 - 9 a . l 3 . 4t5 2 - ro ,5 .O -36 .31 6 2 - 3 l I . 3-9 J r . . J l .e L6 2 -6 2O.5 22 .1- r r r 3 . 9 t z . 3 1 6 2 - . 1 . 2

- l o 1 3 . 6 - 1 6 . 0 1 6 2 - 2 l t . 6 r 3 . 9

1 6 2 2 a i . ' - a O , 2- . 6 9 . d 7 1 . 7 L 6 2 4 a . 6- Z 2 a . 5 a t . ) 1 6 2 6 6 . 2

o 1 6 . 9 5 6 . r t 6 2 3 l 9 . l 1 6 . 92 L r . 5 r t 2 ? 1 5 . 6 - 1 4 . 24 2 . . d 27 .5 l5 2 5 6 .26 5 . 7 l t 2 , 7 6 , t - 7 9 . 66 J J . r l r . I L 5 2 L S . t - A . 6

l o r i . t 1 . . 0 L 5 2 - r9 2 . t -5 . ' L5 2 -1 99 :5 tAz-Or r r 7 . r - I t d . 4 1 5 2 - 5 2 . t - 0 . 6

15 2 - t 22 .6 24 .1a 1 . t 2 . t L 5 2 - 9 5 s . 6 , 5 9 . 2I 2 6 9 . + 2 5 0 . 1 1 4 2 - r O 2 . 3 - 5 . 3

- r i . t ? 5 . € t . 2 - 6 0 . 3 a , 5-a 2 r . L -21 .2 L4 2 -6 5 .A -6 .2-5 l J r . c - r le .9 t4 2 -4 1 . r -LO.5- t 2 2 . 9 - 2 ! . A L 4 a - 2 t 2 . 5 - t 1 . 1

l { 2 0 1 6 . 3 - 7 0 . 0i l r + 1 . 9 5 o . 2 l t 2 2 I € . { 2 2 . 1

e 4 . ,

l 1: a a a . t t e . 2 t (- 6 . . . 5 - 5 6 . 3 l a

J 2 6 0 . d 5 r . 0 t lo r 0 . . 2 ? . e

6 5 l - r - 5 r . 6

3 r 2 . ! r Z . 9 t ll 0 5 . cl I ? . .

l l, 1 2 . \ - t L . 5 1 25 2 ) . 4 - . ! . 1 1 2

I J C . + 1 6 . 9- r r 7 . r - r t . l t 2

l 2- 5 1 2 . 2 - L a . A t 2

l ?- 9 l d . I - I € . 2 1 2

- t r t 2l ll ll ll r

- 2 2 . . . L - 2 4 4 . 6 t rr l

4 3 5 . 2 - a { . t

6 r 7 . f { o . . l l6 ) . e - l . t

r lI 5 7 . 1 - r b . o

3 Z o . r r o . d l ol o

? r e . c l e . e l o9 t 2 . t i t . t l o

r r r r . o l { . 0 l 0t 0

- 3 2 . 9 - 1 . ' t 0' 0

- 2 t o . l 5 r . 2 l 0o 2 r . e - 2 { . { l o

- , 2 . 9 - O - 1- 6 5 . t - 5 . 9 9- a 2 . d

- L z . d - 3 . 2- f l o . 5 1 0 . 6- 5 6 r . ? - 6 3 . e

- 6 r l . 3 - e . i

3o 2 ! . L 2 2 . '

1 7 . a1

l . t

- 3 6 . r - a . l 1- t L L . 2 - 1 4 . 5

- a r 5 . c J . . l I- a z d . l - 2 1 . 1 1

- 2 r e . 5 r 3 . 9o 2 2 . V - 2 a . 1

2 l . o

5 l o . l - l o . l

1 1 r . a - 1 . . f

I 9 , r 5 . 2- l 2 . 6

I X I F J f C

to 0 -2 4 { .9 -4? . r 26 L -3 27 .6 2 r .62 S 0 - 6 r 3 . r - 1 9 . 6 2 6 L - 5 2 . 62 s 0 - 1 2 1 . 1 - a L . O 2 6 | - 1 2 . 9 - I . 626 a -2 1 t . r -a6 .5 25 | -a 23 .5 aa .Zza a o a ! . r 25 .1 25 L -6 20 .9 -2 t .2

2 t r - 4 1 0 . 6 l r . 9: .0 -10 . r 25 L -2 a6 .9 -16 ,A

2 5 t 0 2 . 1 - 2 . 12 6 0 0 2 . 3 2 . t 2 5 I 2 r e . 9 1 9 . 62 6 O - 2 1 Z - t 1 2 . 1 2 5 r 4 1 6 . 5 t 6 , 62 6 0 - 4 t 1 . 0 r 9 . 3 2 { r 5 1 9 . 6 t 9 . 52 6 0 - 6 I € . 3 - 1 6 . 6 2 4 I 3 5 t . 4 - 6 1 . 72 4 0 - A t t . 6 - t 2 . 5 2 4 r r 4 0 . 9 - 4 r . 324 0 -6 44 .2 -4a-7 2a L -L 14 .1 -11 .6z . a -4 zc . r t6 .6 24 | -a 62 .5 6a . l2 4 O - 2 0 . 3 2 4 | - t 3 { 2 a A . .za o o 6 t .J 62 .e 24 | - l a6 .2 26 .22 . 0 2 l r . 2 - r 5 . 9 2 3 I { r 2 . 9 l t . f2a o 4 20 .4 -20-O 2a L -e 36 .4 32 .322 0 6 2q .5 -26-5 2a L -4 9 .1?2 0 4 )9 . { 30 .3 23 L -2 2 .6 - t . t2 2 0 2 6 1 . 1 - 6 1 . 1 2 3 I 0 r e . r l c 722 a a aa .2 - r5 -5 2 ! I 2 39 .2 - .O.02 2 A - 2 2 r . O - 3 a . ' 2 ) L I t 2 . O ) 1 . 9t2 0 -4 2 .1 -o -9 22 | 5 4 .12 2 0 - 6 r : . 0 - 1 f . 7 2 2 L ) t . t 2 1 6 . '

2 2 r I r G 52 0 0 - 3 2 r . r 2 5 . 0 2 2 | - t 5 . t - ? . 620 c -6 tL .5 12 .1 22 I - t r r .6 - l { .o2 0 0 - { r 9 € . . ? o 0 . 5 2 2 r - 5 l r . 5 - 1 3 . 02 0 0 - 2 t o . l - 5 0 . 3 2 2 L - I a . S2 0 c 0 4 9 . 2 - ? 1 . 5 2 2 I - e r O . 1 9 . 1z o o 2 6 4 . 4 - 6 1 . 2 2 t L - 6 a 5 . O 2 a . 520 0 4 21 .0 -26 .1 2 r r -a 6 r .L -a9 .o2 0 0 6 t 9 . t z t . r 2 r ! - 4 3 1 . 3 3 2 . 3l 3 0 6 r { . 4 r 7 . 5 2 t | - 2 4 1 . 9 4 t . lr 0 0 4 l r . ! 3 ? . 2 2 r t o 1 . . 3 - r 2 . 31 6 o 2 l r . c r ? . 2 2 I r 2 3 2 . 5 3 C . 6l 0 0 0 r 0 : . 2 1 o . . 5 2 r L 4 t . 3LS O -2 4 t .5 -49 .4 2 r I 6 53 . t -5 r . r

20 I 7 r3 .d . -12 .56 . 5 - ? . 3 2 0 | 5 ! r . a 2 a . a

2 0 r 3 l o . o 2 9 . tl 3 0 - r o r : . 6 r t . e 2 0 I t 2 1 , 2 2 t . 51 6 0 - r 0 l c . ? r r . 5 2 0 I - l 2 0 . 3 - I 3 . 91 6 0 - e t { . 9 6 2 . 5 2 0 I - 3 . r . t - . t . 9

2 . 6 - 4 . t 2 0 I - 5 t 7 . 6 - t 6 . 91 6 0 - { 6 ( . t - 6 a . r 2 0 I - l 1 2 . 9 r 4 . a1 6 0 - 2 3 S . 0 - 9 3 . 4 2 0 | - 9 2 a . L 2 a . 21 6 0 0 2 r . ? 2 6 . r 1 9 I - l o t r . 5 1 3 . 6

r e r - 3 t ' , r - t 8 . t1 6 0 4 r r a . o l t a . 6 1 9 I - a r r . 7 - 1 6 . 6

19 I -4 ra .o l s . I1 5 0 s i . 9 c . 9 1 9 r - 2 e s . 9 - r o r . 51 4 0 s t g . o 6 r . 2 1 9 r 0 ? 6 . . 1 6 . Il . c 6 { 4 . r - 4 2 . 6 L C | 2 t 9 . 2 2 0 . 2L 4 0 4 2 r , 4 - 2 2 . . L 9 | 4 2 t . 2 - 2 a . Ob o 2 t l r . o - t 2 r . 3 l 9 I 6 1 3 . 4 I t . 21 4 0 0 1 . 1 1 3 r r a . ? - 3 . e1 4 c - 2 t o . z - 2 t . 5 r 3 I t 2 - t1 4 0 - 4 l l l . l r r ? . 5 l 3 I . ! a . , - 3 4 . 91 4 0 - 6 6 r . r - r c . 7 r a I I 2 5 1 3 2 3 . 6r a o - 3 r r . 9 1 5 . 5 l 3 r - r t . r - t 0 . 1

r a r - f l 2 . d l t . t

1 2 c - r 0 l 3 I - 5 3 2 . 9 - 3 2 . ?1 2 0 - 6 r e . t - r t . 6 r 3 t - ?1 2 0 - 6 l o 2 . L - 1 0 5 . 7 r t r - 9r z 0 - r t a . { - r 9 . { l r l - 1 0 2 d . . - 2 3 . 01 2 0 - 2 l l . o r 0 . 7 l l r - € r 2 . 9 - r { . at2 a a 26 \ .s 255.4 t l | -6 22 .9 23 .61 2 0 2 1 \ - 1 - \ 1 . L1 2 0 4 6 l - 0 - 6 4 . . 1 7 r - 2 r l . 3 - r 3 . 31 2 0 6 r r . 6 - 6 t , {t 2 0 3 4 4 . 4 - 4 t . 6 l r I 2 s l . z - a ? . ?l o o l 0 t . 2 l t . 4 t 7 I a ? . 2 r o . ll 0 0 3 { 4 . t a 4 - r r a r 6

1 7 I 3 2 . 9 4 . 0I O 0 a r r { . r l l r . r 1 6 t r 4 7 . c - 4 a . sr o 0 2 3 ! . 3 - 9 2 . ! t 6 I 5 4 3 . O - 4 e . 0l o 0 0 5 t . r - 5 2 . 5 1 6 r 3 r 5 . r - 1 6 . rl o 0 - 2 t : : . 9 r ' f . rl 0 0 - 4 i , 5 - I . 9 I 4 I - l 1 3 . 6 3 C 7l o 0 - 6 l 0 . B - 1 o . 4

1 6 I - 5 9 4 . 4 - 9 5 . .1 6 I - ? 4 0 . t - . 1 . 4

3 o - I 0 r ( . 2 - t 3 . 2 1 6 r - 9 r 5 . e - r 5 . r3 0 - a a c . g 2 2 - 6 I 5 r - 1 0 r e , 7 - ! 3 . 20 0 - 6 r r . l r o . o r 5 | - a 2 0 . o 2 2 . 23 c - . 2 r q . o 2 e r . ? t 5 | - 6 2 2 . L - 2 2 . '6 C - 2 L a . n - r 2 . 2 r t I - 4 r 3 . 5 r 4 . 43 0 0 t z . . - 5 5 . r L 5 L - 2 4 5 . 1 a 3 . O3 0 2 1 6 1 . 2 - 1 5 3 . 4 I t I O 3 r . 7 3 : . t3 0 4 : l . r - 1 2 . 3 r t I 2 1 6 . 0 - 1 6 . 3s o 6 2 6 . a 2 6 . t 1 5 I . 2 - 5

1 5 L 6 r . . t - 3 4 . 63 0 l o I ? . t - l J . e I r I € t 6 . l l t . 66 0 l o 1 6 . r - i 6 . r6 0 6 a c . l - l a . r l { I r 2 . 4 2 . 66 0 6 6 0 . l - 6 2 . 5 1 . I 5 2 7 . o - t o . o

r { r l 2 t . r - 2 6 . 35 0 2 2 0 . 3 - 2 0 . 6 1 4 I I l . . O - t r . 56 0 0 2 2 t . ) 2 1 4 - 2 r a r - l 5 5 . r 5 9 . 06 0 - 2 6 r . 6 - 7 5 . 9 1 4 I - l f r . a a o . r6 0 - 4 2 C . d 1 r . 0 1 4 r - t 6 . 2 t . 56 o - 6 r r s . t - 1 2 4 . 3 I { I - r 2 I . r - 2 I . t6 C - 3 l : . r - 1 . . 2 l . I - 9 1 4 . 6 - l r . f

{ o - 1 0 t . l

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4 0 2 r 0 . 1 - r l . l. o . 9 i . , 9 r . s 1 3 I 6 2 3 . 4 2 9 . r

2 . 6 - a . 5 l r I 3 2 . 6 2 . 6a 0 s 1 0 . . - 9 . r 1 2 L 9 5 4 . a t 5 . .. o r o t g . r - 6 0 . 6 1 2 I 7 ' 2 . C t l . I2 C l 0 r r . r - ' { . 6 1 2 r t 1 6 . r r ? . 22 0 3 e . . 9 S 6 . 6 1 2 L a 9 2 . A - 9 2 . 12 o 6 4 3 . d - t 0 . 7 1 2 r I 4 5 . 5 - . 9 . 12 0 a t e - 6 - 4 1 . \ 1 2 r - l l ' . a - 1 3 . 42 0 2 1 2 r - 3 6 l . 1 6 6 . 32 O - 2 1 2 . 2 - r 2 . a 1 2 r - 5 l 9 . l 4 2 . 0

r z r - r r o . 9 1 0 . 9? o - 6 t : . 6 - 5 5 . O 1 2 r - e 2 a . e - 3 0 . ,2 o -a ta . t t5 .22 0 - t o l s . a I r . 7 r l I - l o 5 4 . 2 - 5 9 . 2

r r I - ao 0 4 2 e , 2 - 2 f . 2 t t I - 6 . { . 2 . 6 . 6o o 6 l r r . ! - r l r . 4 r r I - 4 6 0 . 6 - 6 { . f

L l | - 2 2 r . t Z a . 60 c r 0 r : . 6 l l . 5 r r I o 3 1 . 6 3 . . 1

3 0 r - I t . 7 l l I ? ! 1 0 . 6 - 1 3 2 . 03 0 I - 3 1 5 . 6 3 5 . 3 l t I 4 6 4 . 6 6 { . t2 9 r - { ? . 1 - 4 . 2 l r I 6 1 6 . 6 l ? . 52 9 L - Z

t . a 5 .5 t -o2 3 r I r : . t t l . o l o I 7 2 6 . r - 4 9 . 52 3 I - l 1 6 . ) 3 6 . 2 l O I t l l . 9 I t . I? 3 I - r l r . ! 1 4 . 9 r o t 32 S I - t l 0 . r - r 0 . 9 r o r r r l r ? r . tz ? I - 6 l 0 . l - 1 2 . o l o I - l , . . 2 - 3 5 . I2 7 | - 4 ; . r - t . A l O I - 3 1 6 . 0 l r . t2 7 I - 2 t a . . r 7 . 9 r O t - t t 0 . 2 - t 1 . ,

r .a -3 . r ro L - t 21 .6 24-a2.6 -2 .6

2 6 r l r l . r - r r . , r o r - r r 2 5 . r 2 5 . 52 6 I r 9 r - r 0 r o . 3 - r l . a? 5 I - t t l . a - 1 0 . 4 9 r - 3 , G 6 3 1 . 9

F O a C

3 9 5 2 r . ? - 2 0 . 12 9 5 r o . l l a , ?2 9 1 2 t . 1 2 1 . 42 9 1 d . 2 - 6 . 0

0 . t3 . 6

2 e - t t4 .z !2 .1I e - 6 5 . c - r , lr 9 { 1 2 . > t 3 . 0| 9 - 2 . 4 . 1 - . 2 . OL 9 2 1 2 . 2 - 3 1 . 2

r 9 6 r { . 9 1 5 . 6o 9 L 2 6 . 2 - 2 ? . 5o 9 3 r 5 . { - l r . to 9 5 1 5 , f - l z . ao 9 7 I 2 . 5 l l . 7

r . r o - 2 l 3 . e - 1 r . 9B r o - 31 3 l o - r 1 5 . r - 1 3 . 1r l l o r o o . o 5 5 . 91 2 L O 2 , 4 . 5 - i t . 9l 2 r o oL 2 t O - 2 2 t . ) - 2 t . O

L t t o - 3 2 0 . 3 - r 9 . 5r r r 0 - l 5 3 . o - 4 9 . 5r r l o r 2 5 . ? 2 4 . rl o l o 2 l o . s - I 1 . 7l 0 r 0 o l l . ot o t o - 2 l 2 . o l l . 5t o l 0 - 4 2 . 3 - 1 . 3c l 0 - 1 6 3 . 9 6 0 , 19 l o - l 3 2 . 6 3 2 . O9 t o L 2 2 . 9 2 t . 29 r o I 6 { . 4 - 5 0 . 63 l o a 2 - 13 r 0 2 5 3 . O t 3 . 3

3 r o - 2 I . ?3 l o - a 7 . o? lo -5 le .6 -19 .4? l 0 - r 3 4 . e t . . o7 t 0 - l 6 . 2? l o r 5 0 . r . 3 . 9? l 0 3 2 . 1 - O - 2

7 . 6 - a , 06 l o 2 l ? . 1 - 1 t . 36 I O 06 r o - 2 l o . ? - r r . r6 l 0 - 4 2 . 45 7 0 - 5 2 3 . r 2 4 . .5 l o - l 1 5 . 3 - 1 6 . 25 t o - l 6 1 . 6 - 6 r . 25 I O I5 t o 3 2 A . 2 - 2 1 . a{ r o 4 1 3 - r 1 5 . 34 ro 2 z6-e -21 . t4 I O O4 L O - 2 A . t l O . 4+ l o - 4 2 - 1 3 . o

z . t

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a

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l o - r e . 2l o - 3 5 o . l { 9 . 3l o - I 1 2 . 7 - 1 3 . 2l 0 r l o . 9 - 2 9 . 1r 0 3 5 3 . 3 - 5 r . 2r 0 5 l 5 . o r 2 . 5l o 4 r ? . 7 - 1 7 . ILO 2 24 .4 22 .2LO -2 2 r .5 -26 .2LO -4 !2 -6 31 .2ro -5 t4 -5 -52 . rt o - 3 ) 2 . 2 - ) 2 . 4t o - r 2 1 . 7 - 2 3 . 1r 0 I t 3 . 7 5 a . ?I 0 3 1 r . O 2 3 . Iro 5 22 .2 21 .5r 0 2 l 7 . r - r t . 6l o { t 3 . 7 t 3 . t

- l 35 .6 l? .0 7I 2 o . 5 - 2 1 . r 13 r r . l - 1 2 . 25 l 6 . e - 1 6 . 31 2 . 6 1 . 66 l 9 . r 3 5 . 9r 5 . 1 t . )2 20 . r 19 . Io .1 .2 -4 t -o

-2 1a .5 -15-7- 4 1 6 . 0 l l . .- 6 2 a . t : t . 9 5- a 2 0 . r 1 3 . 0-1 42 .2 - ta .o 5- 5 3 6 . 7 3 9 . 0 5

- l l o . 2 - ! 0 . 3I 1 0 . 5 - l o . I ,a 1 9 . r - I t . 35 40 .4 -40 .9? ro . l ao . f3 2 0 . r I ? . O6 { . . 3 a r . o4 5 1 . 0 5 3 . 62 4 4 . O - 1 r , 6o 21.4 -26.4

- 2 r t . t - 1 5 . 3- . 1 6 . 1 1 3 , , t- 6 6 t . l 5 6 . 4 a- 3 I 9 . 3 l 9 . a- ? ? . 1 l l . 6- r a ? . 5 5 5 . 3 a- 3 E . a - t o . 6- l 2 6 . 4 3 1 . I 1

I 9 5 . 5 - 9 r . ?t 3 . 1 - 1 . 4 25 21 .1 26 .4 27 4 9 . 9 4 9 . S3 2 . 9 - I . 3a 1a .L -47 .5a l ? , 5 1 3 . 4z s l .a aa . f

- 2 4 . 6 I-a 16 .1 -11 .e- 6 5 9 . 7 - ! 9 . O I- 3 l € . 3 l e . 4

I-5 20-A 23 .4- 3 2 l . r - 2 0 . r

| 24 .2 -22 .2- t 1 6 . 1 1 6 . 2

3 !6 .0 34 .35 t3 .6 -1 .3 l !1 22 .1 22 .1 !B2 3 t - O - ! 2 . 16 2 1 - 6 2 ) . o l :. 1 9 . 5 - 1 5 . 7 : :

-2 e6 .2 -e . .2 1 :l 9i :- 6 ? . 5 - 9 . 3 i :

I A-9 -9.1

- l 5 . 1 , . 1

- 2 2 5 . 2 - 2 1 - 9

P. B. MOORE, AND T. ARAKI

Tarrt 5, Continuedf o f c t u F c x ( l t 0 f c f o F c

- 1 . 2 1 2

L T

r . 5 1

t l o t . 5 - 1 0 0 . 52 4 . 7 1 . 6

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I 25.1 -24.1- I a o - e e- 5 7 . 1 ? . I-4 3 .1 -4 .6

o 2) .9 25 . )2 3 . O - 2 . 2I l 2 . a r o . 5

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o 25 .6 -26 .02 r € . 3 l s 3 a

5 . 3 3- l 2 r . 9 2 0 . 9 3

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a 5s .9 56 . '4 13 .2 -3 t .9

1 26 .6 -25-e 2| 93 .0 10-5

- r r l . 2 l o . s I

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0 r 3 . r € I . t I2 t l . r - r 2 . 0a 23 .6 -23 .O5 1 t .1 - tU63 a . r - r o . JL 2 - 1 - t . a 2 )

- r 5 2 . e 5 2 . 6 2 3

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2 l

2 r r . s - l r . o ? o{ 1 9 . 2 l e . ?

5 25 .2 24 .5 ZO3 r 3 . l 4 9 . 9 l e| 2 2 . e - 2 2 - 5

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2 l l . 5 1 5 . 5 1 34 l l . 5 - f c . 8 L 76 r 5 . 9 r { . 2 L l1 52 .1 5 r .2 L15 t 4 . 4 - 1 4 . a l ?3 te .5 16 .2

- r 2 r - 2 - 2 2 . t 1 6

- 7 7 . 1 6 . 4- e 2 r - ) 2 6 - 9- 3 r r . 2 - 1 1 . 6 1 6- 6 5 1 . 6 5 0 . 5

0 1 9 . 5 t 9 - 2 1 5

L '5 r 5 . 3 r 5 . r 1 5

a 22 .9 22 .2 L4I 2 9 - I 2 9 . 0 I a

- I 9 3 . 0 9 i . 3 l a- 3 9 . 6 - I t . 4 l .-5 a6 .e -a6 .1 l (

L '

l 3- 6 3 . 2 t 1

4 l o 3 . ? r o t . l L 26 r 9 . 3 - 1 9 . r L 2

3 6 5 . t 6 3 . 4

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2 l f t . 6 r 0 1 . 9 I o4 21 .5 - 22-L

2 . 6 l O7 7 f . l r 0 . l t ot 3 r . 5 - 3 r . ?

I r r 5 . l - 1 1 3 . 95 . 5

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978

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o r r . d 1 9 . ? I- 2 2 t . 9 4 2 . 2-4 ao-6 -aL . r I- 6 ? 0 . 0 r 9 . r- 6 { : . r - . 4 . 3 I4 LC.1 -20 .2 I- l ? . 9 - r . o I- 5 l ( . ? - r o . q I-3 t t .2 - t7 .1- l 3 1 . 9 3 r . a

I 3 . 7 - a . 6 03 2 0 . 6 - 4 0 . o5 2 - 3 0 . 47 ( . 1 r . t z ,6 24-6 21 .1

2 t . t - . - 5 2 1c t r . 6 - 5 s . r 2 4

- { t6 . t 16 .4 2a- a r r . s ! 5 . a 2 1- 3 ( . r a . l- 9 l a . { - r 1 . 3 2 }- 1 c a . a - 4 4 . 6

2 2- l 9 I . { 9 r . r

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- 2 9 . r - r . r- 4 3 0 . 1 r 9 . 3- 6 ( r . J . 2 . 0 2 0- a 2 c . 6 - 2 0 . ?- 9 i 1 . 2 Z t - 4 l 9- 7 l r . { r o . t 1 9- t 1 . 3- 3 l e . 2 - 1 9 . 7- I a . r - 1 . 5

r r . 33 2 . e5 t 3 . 9 1 5 . 2

B '4 .2 -52 .16 r . r I 0 . 3 l 34 r a , J 1 6 . 1 1 6? l r . r - r 2 . 1o l i - a r 2 . 2 l a

-2 2A.O 21-s- { t c c . { - r 0 2 . a l 7- 6 : t , 9 l s . 6

- 1 0 ! . 0 - r . 5 1 7- 9 : . e - 0 . 7 1 7

t r-5 24 .9 29 .9- 3 t 3 . t z 0 . r- L 5 1 . 5 . r 0 . . L b

t 2 . 2 l 5

- 1 . 9 1 3

2 . 2 L 3

1 7 . 3 1 2

-2 23 .2 21 .O

2 I . r 2 t . 2

3 , 1 - 5 . r

TROLLEITE

Tlsrs 6a. Trolleite. Atomic Anisotropic Thermal Vibration Parameters (x101)*

Atom Fu Fzz Ezz Ftz 6rs Fzz

979

A1 (r)A1 (2)P (1)P (2 )

o (1)o (2 )o (3 )o (+)

o (s)o (6)oH(1)oH (2)

2 . 8 ( 1 )3 .4 (1 )2.r+ (1)2 .8 (1 )

3 . r ( 3 )6 . r ( 3 )2 . s ( 3 )4 . 7 ( 3 )

s . 0 ( 3 )8 . 8 ( 3 )4 .0 (4 )3 . 6 ( 3 )

13 .4 (8 )16 .7 (8 )12 .8 (e )L2 .2(7)

2 2 . 2 ( t . 6 )r + 0 . 6 ( 1 . 9 )4 r . 1 ( 1 . 8 )2 2 . r ( L . 7 )

22 .3 (8 )22.7 (8)2 2 . r ( e )2 1 . 3 ( 8 )

4 2 . 6 ( 1 . e )3 e . 6 ( 2 . 0 )4 s . 3 ( 2 . 0 )s r . 0 ( 2 . 0 )

-2 . '+ (5 )-1 .0 (s )0 . 01 . 3 ( 4 )

e . 0 ( 1 . 2 )- 1 1 . 7 ( 1 . 3 )

0 . 00 .1 (1 . 2 )

- 0 . 3 ( 2 ) o . s ( 2 )- 0 . 6 ( 2 ) o . 7 ( 2 )0 . 0 0 . 0 ( 3 )

-0 .0 (2 ) -0 .0 (2 )

- r .6 (s) - r . r+(s) -11.1(1.3)2 .6 (6 ) 7 .1 (6 ) l e .2 ( l - . 4 )

- 3 . 3 ( s ) 0 . r ( s ) - 8 . r + ( r . s )- 3 . 0 ( s ) - 0 . 8 ( s ) - 1 4 . 3 ( r . 4 )

2 0 . 7 ( 1 . 6 ) 2 e . 7 ( 1 . 8 ) r . 8 ( s ) 4 . 7 ( s )2 2 . 2 ( I . 7 ) 3 2 . 2 ( 1 . e ) - 2 . 3 ( s ) 6 . 3 ( 6 )2 L . 7 ( 2 . 5 ) 3 8 . 4 ( 2 . 8 ) 0 . 0 - 3 . 8 ( e )2 s . 0 ( 2 . 0 ) 2 s . 0 ( r . e ) - 1 . 2 ( s ) - 1 . e ( 6 )

*coefficients in exp-flBrrnz * Brrt2 * 0:s1' + zgrrnx * 4r:i l + zSrrkrl .

the consequent distortions in considerable detail be-cause trolleite is an extreme example of anisotropicpolyhedral distortion for ionic structures containingAl3-. The analysis of the distortions in trolleite shallinclude comparisons with similar shared faces inlazulite and corundum. For trolleite, the estimatedstandard errors in atomic distances are Me-O :L0.002 A and O-0 i 0.003 A. The structure oflazulite was approximately refined by Lindberg andChrist (1959). They did not state errors and, as thestructure was refined on the basis of two two-dimen-sional projections, uncertainties in error estimatesarise. We feel, however, that the effects of distortionsare so great that the errors would have to be severe(above Al-O + 0.1 A) to eliminate their resultsfrom consideration. Consistencies in their P-O dis-tances suggest that uncertainties in their study arenot serious, probably not over -+ 0.06 A in Al-Odistances. Corundum, o-A12O3, has been refined byNewnham and DeHaan (1,962) and their estimatedstandard errors are i 0.02 A in Al-O distances.

For comparison among structures, we utilize con-gruently oriented Schlegel diagrams (cl Moore,1970) showing Al-O and O-O'distances as well asthe O-AI-O' angles. The following statements areessential in comparing distortions among these struc-tures.

l. The topology ol the neighborhood about thepolyhedron. Al(1) and A1(2) in trolleite andAl in lazulite are the same; each polyhedronhas one shared face, all other shared topo-logical elements being corners. Corundum dif-fers in having three additional shared edges.

2. The nature ol the cations ecross the share'd

faces. For trolleite and corundum, these areAl-Al cations. In lazulite, they are Mg-Al. Dis-tortion of the Al-O polyhedra should be moresevere for the former two structures.

3. The deoiations of the aniorw lrom electrostatic

TlsI-E 6b. Trolleite. Parameters for the VibrationEllipsoids"r

p i (x ro2) 8 ia O ib o ic

A1(1) L 7 .82 s . 73 7 . O

f 8 . 12 6 . 4a 7 L

1 7 . 82 5 . 83 6 . 3

L 7 . 92 5 . 63 6 . 6

1 I I . 32 5 . 63 8 . 1

] . I2 .82 6 " 93 8 . 1

I l l . 52 6 . 43 1 0 . 2

L L Z . J

123

L23

5 . 6

] 0 . 36 . 2a l

f 2 . 66 . Io u

1 1 . 66 . 9

al(2)

P (1)

p f r \

0 (r)

0 (2)

0 (3)

0 (+)

0 (s)

o (6)

or{(r)

oH(2)

12208 2

I+6

L4775

1r9

LzI9 0

149

t3r8 8

138

tr054

L37

6 7110r48

9 2296 0

1t066

148

509 +40

9 46 4

t3l409 0

looo 25ot8 7574 109

85 472L 7869 135

90 2L0 9 0

90 lII

8 3 3 2I70 81

97 120

109 2I48 68+7 8rt

5 U 5 J

12+ 3758 8r

L28 3969 79

134 I27

IO7 203 5 6 96 0 9 0

o o 5 t

I4s 55llq 128

101 763 6 5 355 140

90 3090 59

.180 90

r 9 . 7 1 3 9 7 5 4 32 6 . 5 4 S 7 6 5 23 8 . 0 8 7 1 9 1 0 9

, j i = r .m.s. ampl i tude of . i=th pr incipal axis. The 0 values are

th"e angles between the i - th axis and the crystal axes a, b ad 9.

980

neutrality when compared on a congruent basis.Calculating the deviation from neutrality onthe basis of the bond strengths, the oxygenenvironment about Al(1) in trolleite and Alin lazulite are similar, with Al(2) in trolleitesignificantly different and Al in corundum verydifterent.

Geometrically, the Al-O octahedra can be brokeninto three regions: the shared face, the opposite un-

Ftc. 2. Octahedra in lazulite which correspond to theoctahedra in trolleite of Figure l. Similar octahedra arestippled. Inversion c€nters are shown and the lazulite cellis outlined.

P. B. MOORE, AND T. ARAKI

Frc. 1. Octahedral double chain in the trolleite structure. The cell is outlined and inversions,rotations, and 2-fold screws are placed appropriately. Labelled atom positions correspond to

Table 4. Heights are given as fractional coordinates y. The cell at and ct refer to the origin

for lazulite. Octahedra which are identical in position to those in lazulite are stippled.

J

shared face (the back face), and the remaining six

linking edges. Starting with an undistorted isolated

neutral dimeric species with local electrostatic neu-

trality of anions about cations, repulsion across the

shared face would result in a foreshortening of the

edges on the shared face, a lengthening of the Al-O

distances toward that face, and O-Al-0 angles to-

ward that face which are considerably less than 90o.

The opposite face in turn will reveal lengthened

edges, shorter Al-O distances, and O-A1-g angles

greater than 90o.In Figure 5, we present the interatomic distances

and deviations from local electrostatic neutrality(with OH- treated as a single negative ion) for the

Al-O octahedra in trolleite, lazulite, and corundum.

Table 7 presents a tabulation of the O-Al-0 angles,

Sf A6<isAG r SjeVFrc. 3. Orientation of the tetrahedra in the trolleite cell.

Heights are given as fractional coordinates in y'

TROLLEITE 9 8 t

listed according to the three geometrically distinctregions. For trolleite, in all instances but one, theAl-O distances toward the shared face are lengthenedand those opposite are shortened. The exception isthe bond to the severely oversaturated OH(2) anionon the back face of Al(1). In addition, the O-AI-C[angles toward the shared face are less than 90o,rangtng between 73" and 79'. We, note anotherimportant feature among the structures. In corun-dum, the anions are all formally neutral. In trolleiteand lazulite they are over-saturated (severely in theformer) about the shared face and two of the threeanions on the back face are undersaturated. Thisresults in a "double-distortion," first by cation-cationrepulsion and second by additional lengthening ofthe Al-O bond due to oversaturation or shorteningdue to undersaturation. This results in long Al-Odistances to the shared face (1.94 to 2.09 A) introlleite and very short Al-O distances to the op-posite face (rangrng from 1.79 to 1.96A). Themean O-Al-0 angles to the back face deviate onlymoderately from 90", ranging from 88" to 97o. Incorundum. the differences betwe.en the two facesare 79.5" and 101.0o for the shared and back facesrespectively. These distortions affect edges linkingshared and back faces (herein called the antipris-matic edges) in trolleite and lazulite: the correspond-ing O-Al-Or angles are all greater than 90". Theresult is an elongate trigonal antiprism whose direc-tion of elongation is parallel to the cation-cationaxis.

The severe oversaturation of OH(2), since it isbonded to three Al3* cations. makes the trolleite

a

FIc. 4a. Orientation of the tetrahedra in lazulite. The cellaL and. cL refers to lazulite, arr and cr to trolleite. Heightsare given as fractional coordinates in y.

b

Frc. 4b. Orientation of tetrahedra in lipscombite. Thelipscombite cell is outlined by c and ln(=[110]) with 4Land cr referring to lazulite. Exact correspondence to Figure4a occurs if + 0.13 is everywhere added to the heights.

structure rather queer and creates more assym-metrical distortions. This deviation of * 0.50 foran (OH)- group, disregarding the hydrogen bond,is unusually high for a mineral structure but it isknown to occur in the basic ferric phosphate mineralleucophosphite (Moore, 1972a) and the basic ferricarsenate mineral pharmacosiderite (Buerger, Dol-lase, and Garayocochea-Wittke, L967); both struc-tures show long Fe3.-(OH)- distance averages (2'16and 2.08,A, respectively). The A1-OH(2) averageis 2.03 A, about 0.1 A greater than the AI-OH grandaYerage of 1.93A (Moore, I972b).

Hydrogen Bonds and Location of the HydrogenAtoms

Hydrogen bond formation in trolleite and in lazu-lite is severely limited by the spatial restrictions ofthese rather dense structures. Since the (OH)-anions are displaced b/2 away from the tetrahedralcenters which are located above and below the locusof the (OH)- anions (Fig. 1), it is not possible togeometrically predict whether the hydrogen atomspoint up or down. Thus, we can conceive the hydro-gen atoms pointing toward the O(1)-O(1)"' or

Ws

\

N

1

6@

)

@e@

/^ve

e./^v>

oX.

@s

o@I

o6I

"'i5t[-.2s]

982 P. B. MOORE, AND T. ARAKI

b

Flc. 5. Schlegel diagrams of (a) the A1(1), Al(2), P(1), and P(2) octahedra and tetra-hedra in trolleite; (b) of Al in lazulite and A1 in corundum. For trolleite, atoms are labelledaccording to Table 4, with superscript' = x, -y, 1/2 * z; " - l/2 - x, l/2 * y, l/2 - z;"' = -x, y, 1/2 - z. For lazulite and corundum, atoms are labelled according to the refer-ences (see text). Shared edges are drawn bold. Me-O distances are included parenthetically,local electrostatic deviations (based on OH- -X-) are in brackets. Me-O averages are under-lined once and O-O' averases underlined twice.

0(6)( r .861

0(41(r,79)

LAZUL ITE CORUNDUM

TROLLEITE

Taers 7. Trolleite and Related Structures: O-Me-O'Aneles

983

o(s) -41(r)- o(r)J0(s) -oH(z) io(1) - i ' -0H(2) t

0H(2)oH(z) .o io j '

TROLLETTE, At(1)

Shared face

TROLIEITE, A1(2)

Sharecl face

7s .30 o ( s ) -A I (2 ) - o (1 ) 7q .778 .6 O (s ) - ? ' - oH (2 ) i 76 .77s .o o ( r ) - i l - oH (z ) i 73 . s

IAZULITE

Sharetl face

o (3 ) -A1 -o (1 ) r 8 r . z0(3) - i l - or t 79. Io( f ) - " - oH" 78.5

average 79.6

Sack face

oH - " - o (2 ) 86 .90H - " - 0 (4 ) e1 .0

0 ( 2 ) - ' r - o ( r + ) 8 9 . 7

aver:age 89.2

Antiprismatic edges

0 (3 ) - " - 0H e3 . s0H - " -o ( r ) 97 .3

o ( I ) - ' t -s 1a1 . . e4.4o (4 ) , - " - 0H - 96 .5

oH* - f - o (Z ) 96 .8o (2 ) - t r - o (3 ) e3 .6

average 95.+

8 9 . 9

CORUNDUM

Shared face

o(2) -A1-o (3) 7e.s0 (2 ) - " - o ( r ) 7e . s0 (3 ) - t r - o (1 ) 79 .5

average 79.5

Back face

o (6 ) - " - o (4 ) 10L .00 (6 ) - " - 0 ( s ) 101 .0o(4)- " -o(s) lor .o

average 101.0

Antiprisrnatic edgesAntiprismatic edges

average 75"0

Back face

o H ( r ) - i l - o ( q ) + e 6 . 7o H ( r . ) j - n - o ( z ) i e r . 8

0 ( 2 ) ' - i l - 0 ( t r ) ' 9 4 . 9

average 94.5

Antiprismatic edges

average 9+.6

89.7

TROLLEITE, P(2)

110 .4l -08 .8111 . '+Ir.0 .3IO7 .2108 .7

r09 .5

average

Sack face

- ' - o 1 3 ) 1 r-o io t * .

- " -o(s) t .

average

t o . J

9 0 . 68 8 . 893.2

o n o

0 ( 2 ) - " - o ( 6 ) 8 6 . 30 (6 ) - " - 0 (3 ) e0 .e0 ( 3 ) - " - 0 ( s ) 8 6 . 30 ( s ) - n - 0 ( r ) e 0 . e0 ( r ) - n -0 (4 ) 86 .3o (4 ) - n -o (2 ) go .e

average 88.6

e o L

0(s) - ' r -0H(2) 97.7 o(s) - " -oH( l ) e6.s0 H ( 2 ) - " - O ( r ) . 9 8 . 3 o H ( ] ) - i l - o ( l - ) " . 9 s . 8

o ( 1 ) " . - " - 0 ( 6 ) i e 7 . 6 0 ( r ) , - i l - 0 ( 2 ) : e 3 . 80 (6 ) : - i l -OH(z ) : i e4 .2 o (2 ) i - t r - 0H (2 ) ; e2 .e

o H ( z ) : . - " - 0 ( 3 ) - * s s . 6 0 H ( 2 ) i - " - 0 ( 4 ) * e 3 . 30(3)- ' - " - o(s) e3.r o(4)*- " - o(s) 9+.6

o (4) -P(2) -0 (3)o(t l)- " -o(s)o(rr) - n -0(6)o(3) - n -0 (6)o (s) - rt -0 (6)0(s ) - u -0 (3)

aver?age

(shared edge)

( " ' ! )

( t r " )

average

Gnantl average

TROLIETTE, P(1)

o (I) -P(r) -o (4*i+o(1) - " -0( l ) -**o r l ) . . . - n - 0 ( 2 )orzi i i i - " -oizio( r ) i i i - " - o (2 ) ; i ;o( r ) - -* - n -0(2)***

average

96 " t

89 .9

Lr l .80t 0 6 . 9108 .1.l_10.3l f l .8108 .L

I09 .5

O(2)-O(2)"' edges for OH(l) and toward theO(3)-O(4) or the O(5)-0(6) edges for OH(2).

Fortunately, the quality of the data permitted un-ambiguous location of the hydrogen atom positionson a three-dimensional difference Fourier map. Thecoordinates are H(1) 0, 0.484, l/4 andH(2) 0.190,0.809, 0.072. Thus, H( 1) points toward the O(2)-O(2)"' edge and H(2) points toward the O(3)-

Tlsrr 8. Electrostatic Valence Balances of Cationsabout Anions in Trolleite*

Anion Coordinating cations A Deviation

O(4) edge. Calculated distances are O-H(1) 0.86 Aand O-H(2) 0.74 A. The H( 1) . . . O(2) distance is2 . 3 4 A a n d H ( 2 ) . . . O ( 3 ) a n d H ( 2 ) . . . O ( 4 ) a r e2.67 and 2.6I A, respectively.

We propose a bifurcated hydrogen bonding modelwhero H(1), on the 2-fold rotor, provides bonds toO(2) and O(2)"' simultaneously; and H(2) pro-vides bonds to O(3) and O(4) simultaneously.These proposed bonds are in consonance with theelectrostatic balance of cations about anions in Table8; O(2), O(3), and O(4) are all formally under-saturated with respect to nearest neighbor cations.For these cations, we elected the O-H. . . O bond

strength € = *1/6 proposed by Baur (1970), and,accordingly, distributed half this bond strength toeach of the three undersaturated anions.

Acknowledgments

We appreciate continued support through the NSF GA10932-Al grant awarded to P.B.M. and a Materials Re-search Grant (NSF) awarded to The University of Chicago.

o (L)o (2)0 (3)0 (|})

0 (s)0 (6)oH(1)oH(2)

P (1) +AI (I) +A1 (2)P (1) +At (2) +V2H(1)P (2) +A1(1) +V2H(2)P (2) +AL(z) +V2H(2)

?(2) +A1 (r) +A1 (2)P (2) +Ar (1)2Ar. (2) -H(1)2Ar(1) +Ar(2) -H(2)

+0.25 alL +-0.17 alJ- --O.I7 aIL --0.L7 aI I -

+0.25 al l +-0.2s AI(1)- ; P(z) 1-0.17 al l -+0.33 al l +

*A l" th" deviation from l-oca1 electrostatic neutrality.

Under "Deviation'r are Me-o bonds longer (+) or shorterf-l thil polvhedral avemqes.

984 P. B. MOORE, AND T. ARAKI

References !Beun, W. H. (1970) Bond length variation and distorted

coordination polyhedra in inorganic crystals. Trons. Am.Crystallogr. Assoc. 6, 129-155.

BrousrneNo, C. W. (1869) Uber neug schwedische Min-eralien. Neues Jahrb. Minerql. Geol. Palaeontol. 1E69,481482.

BuEncsn, M. J., W. A. Dorrese, AND J. GARAyococHEA-Wrrr<s (1967) The structure and compocition of themineral pharmacosiderite. Z. Kristallogr. 125, 92.

BusINc, W. R., K. O. M,lnr-rN, aND H. A. Lew (1962)Onrls, a Fortran crystallggraphic least-squares program.U.S. NatL Tech. Inform. Seru. Onnr-lrr-305.

CRoMER, D. T., ervo J. B. Meryrq (f968) X-ray scatteringfactors computed fror4 numerical Hartree-Fock wave-functions. Acta Crystallogr. LA, 321-)24.

EveNs, H. T., Ir. (1972) Heteropoly and isopoly complexesof the transition elements of groups 5 and 6. Perspectioesin Structural Chemistry, voL. 4, John Wiley and Sons,2-59.

Ktrz, L., eNn W. N. Lrpscovrs (1951) The crystal struc-ture of iron lazulite; a synthetic mineral related to lazulite.Acta Crystallogr. 4, 345-348.

LrNonnnc, M. L., eNo C. L. CHusr (1959) Crystal struc-tures of the isostructural minerals lazulite, scorzalite, andbarbosalite. Acta Crystallogr. 12, 695-697.

Moont, P. B. (1970) Crystal chemistry of the basic ironphosphates. Am. Minerol. 55, 135-169.

(1972a) Octahedral tetramer in the crystal struc-ture of leucophosphite. Am. Mineral. 57, 397-410.

(1972b) Aluminum-l3A. Handbook of Geochem-istry il-3, Eq. K. H. Wedepohl, Springer-Verlag, NewYork.

NewNnepr, R. E., exo Y. M. DpHleN (1962) Refinementof the a-Al,O'I, Ti.O", V,Or and Cr'O" structures. Z.Kristallo gr. ll7, 235-237 .

RluecneNqneN, G. N., AND R. SRINIVesm (1970). FourierMetho$s' t,,in Crystallography. Yliley-Interscience, NewYork, p. 96-119.

Scun, C.'B., L. C. CrnnrsoN, AND C. M. Scnwlnrz (1965)Syntheqis and properties of trolleite (aluminian lazulite?),a high'pressure mineral from the Westani iron deposit,Kristilinstad. Sweden (abstract). Amer. Mineral. 50,1965.

Manuscript receirsed, April 23, 1973; accepted

lor publication, May 13, 1974.