American Mineralogist, Volume 66, pages 1221-1232, 1981

Cation ordering in lepidolite

SrBpnBN GucceNFIetNI Department of Geological Sciences University of lllinois at Chicago Chicago, Illinois 60680

Abstract Three lepidolite-lM and two lepidolite-2M2 mica structures from three localities have been refined using single crystal X-ray data to determine cation ordering schemesin both ideal and subgroupsymmetries. The lM (Rr = 0.035)and 2M2 Gr : 0.048)crystals from Radkovice, Czechoslovakiaare ordered in their respectiveideal spacegroups so that M(l) : Li6.e1(Mn,Mg)s0efor lepidolite-1Mand M(l) : Lir o for lepidolite-2M2.In contrast,the lepidolite-lM from Tanakamiyama,Japan (R1 : 0.062)is similar topologically to zinnwal- dite in subgroup symmetry C2. The octahedra related by the pseudo-mirror plane are significantly different in size (mean M-O,F,OH: 1.88A) and electron count (11.5 and 6.0). The difference in electron count between these two octahedral sites is more substantial than in zinnwaldite. The previous 2M2 refinement of Sartori et al. (1973) is confirmed but the lM structure (Sartori, 1976)is better describedas similar to that of the Tanakamiyamalepidolite, althoughdue to systematicerrors in the data an ordered model is not unequivocally established.Cation ordering similar to that found in the Tanakamiyama lepidolite is promoted by a high fluorine content, but parametersof crystallization other than fluorine content are important.

Introduction several octahedral ordering schemes. The lepido- Three recent refinements of layer silicate struc- lite-3T structure(Brown, 1978)crystallizes in space tures have shown that additional cation ordering group P3l2 and has two sites that are large and may be present when symmetry constraints are lithium-rich and a small aluminum-rich third site. relaxed from an assumedhigher order spacegroup This type of ordering scheme is analogousto the to a lower one. Lower order space group refine- zinnwaldite structure. In other lepidolite structures, ments have shown that margarite-2Mr(Guggenheim when the ideal symmetry has been used in the and Bailey, 1975,1978) has an ordered arrangement refinement procedure, one large site is located in of tetrahedral cations while zinnwaldite-lM (Gug- the trans arrangement at M(1) and two smaller genheim and Bailey, 1977) and a dioctahedral lM equivalent octahedra in cls orientation. This order- mica (Sidorenko,et al., 1975)showed both tetrahe- ing pattern with M(1) larger than the two M(2) dral and octahedral ordering. In lM polytypes of octahedra appearsto be adopted even in structures ideal space group (CZlm) symmetry, octahedral where the octahedral composition might suggest ordering is possiblebetween the M(1) site on the alternate ordering models. Fluor-polylithionite-lM mirror plane and the two equivalent sites related by (Takeda and Burnham, 1969), lepidolite-lM (Sar- the mirror plane (both designated as M(2)). In toi, 1976),lepidolite-2M2 (Takeda, et al., l97l; zinnwaldite, the spacegroup has been shown to be Sartori, et al., 1973) and lepidolite-2M1(Sartori, C2 and the two M(2) sites are not symmetrically- 1977;Swanson and Bailey, 1981)are all lepidolite related by a mirror plane as in space group C2lm. micas that appear to have such an ordering scheme They are, therefore,designated as M(2) and M(3). where the M(1) site contains the larger lithium ion The M(2) site was shown to be occupied by alumi- and the two smaller symmetry-related M(2) sites num whereas lithium, iron and vacancies are dis- have an averagecomposition near Lis.5Als.5. tributed randomly over the M(1) and M(3) sites. The novel ordering pattern for lepidolite-3T is The lepidolite micas have been shown to have significant in that such an ordering schemeindicates 0003-004x/8l/l I I 2-t 221$02.00 1221 1222 GUGGENHEIM : ORDERING IN LEPIDOLITE there is no a priori reason why a similar scheme tetrahedra in the supergroup refinement (A ": should not be found in the more common lepido- 0.0374) and in the subgrouprefinement (A : 0.054) lites. Experience has shown that some ordering appear unreasonably large for chemically similar schemesmay not be observedbecause of refine- atoms in an identical chemical environment. These ment in the incorrect space group. Alternatively, results suggestserious systematicerrors in the data crystallization history and environment may affect and therefore ordering cannot be unequivocally cation ordering. The purpose of this study is to established in C2 symmetry. Two ordering models examine cation ordering as a function of both are possiblein Cm symmetry,but were not investi- possibilities.In addition, coexistinglepidolite poly- gated because the 1:3 ratio of Al to Si is not types (1M and 2M2) are re-examinedbecause sys- compatible with one Al ion per tetrahedral site tematic errors exist in data reported previously. (maximumpossible ordering is Als.25Sio.zs). All possible octahedral ordering models were Preliminary refinements considered for the subgroup refinement in Cc sym- Initially, Weissenbergfilm data (Sartori, 1976and metry for lepidolite-ZMz and involved varying the Sartori et a1,,1973)were used to refine the lepido- size of the M(2) site so that it was larger than its lite-lM and 2M2 structuresin their respectivecen- pseudosymmetry-relatedM(3) site and, in an alter- trosymmetric space groups and noncentric sub- nate model, smaller than the M(3) site. Each refine- groups. Starting parameters were obtained for the ment produced a large number of parameterinterac- lM structure from the refinementby Sartori and for tions with correlation coefficientsranging from 0.80 the 2Mp from Takeda et al. (1971). The scattering to 0.99, which clearly indicate a centric structure. factor tables were from Cromer and Mann (1968). In addition, bond lengths involving the octahedral Each refinement in the ideal space group agrees cations indicate that the coordination polyhedra with the results of Sartori (1976)and Sartori et al., were more highly distorted than is reasonablefrom (1973); however, the isotropic thermal parameters a crystal chemical viewpoint. The R values for the of several atoms difer and the R values are consid- isotropic refinement for Cc symmetry were Rl : erably lower, presumably becauseof the effect of 0.143and Rz : 0.188and R1 : 0.136and R2 : the different scattering factor tables. 0.200. The refinement procedure in subgroup symmetry procedures in each case followed the method given by Guggen- Experimental and refinement heim and Bailey (1975,1977)and is reviewedbelow. .Because of apparent systematic errors in the For lepidolite-lM, startingmodels in C2 symmetry lepidolite-lM data and the importance of an accu- were obtained from zinnwaldite (Guggenheimand rate comparison of coexisting lepidolite structures, Bailey, 1977) or derived from the distance least- intergrown lM and 2M2lepidolitepolytypes (R1-43 squaresprogram oprDrs written by W. A. Dollase in eerni et al.,l97O) from nearRadkovice, Czecho- of the University of California at Los Angeles.Each slovakia were examined. Microprobe analyses of model was then refined by using the least-squares flakes of each did not show significant chemical refinementprogram oRFLs(Busing et aI.,1962). differences. The resulting formula unit (Table 2) is The model with the smallerM(3) site was rejected assumed to be the same for both. In addition, a becauseit has more than double the R value of the lepidolite-lM (Genth and Penfield, 1892)obtained alternate model. In addition, octahedralsite compo- from the F. A. Genth Collection at The Pennsylva- sitions, as determined from bond lengths and scat- nia State University was examined. The electron tering power, differ from the chemical analysis and microprobe analysis (Table 2) is an averageof nine those determined in the parent spacegroup. How- individual analysesfrom an energy-dispersivesys- ever, convergenceappeared successful for the mod- tem (from an ARL microprobe) and a wavelength- el analogousto the zinnwaldite structure (Table l). dispersive system (from a MAC-5 microprobe), Calculated octahedral compositions based on bond both using the correction procedures of Bence and distancesare consistentwith those determinedfrom Albee (1968)and the alpha values of Albee and Ray bond lengths in the parent space group, but bond (1970).In all casesthe electron beam was broad- lengths from the subgroup refinement are inconsis- ened and the sample current kept as low as possi- tent with the chemical analysis(as was also noted in ble. the supergrouprefinement by Sartori,1976). Differ- The three lepidolite samples were examined ences in the T-O(2) bonds from within individual (Horsey, 1979, personal communication; Bish, GUGGENHEIM: ORDERING IN LEPIDOLITE t223

Table l. Summary of residual values for the lepidolite models

Total ***Goodness- Goodness- Reflections Parameters *& **R^ of_fi t Parameters R, R^ of- fi t

Ideal c2ln Syrmetry Subgroupc2: Zinnwaldite-type orderinq model

Lepidolite - lM (reflection data from Sartori, 1976)

i sotropi c 400 27 0.067 0.068 2.57 44 0.056 0.058 2.69 ani sotropi c 400 52 0.0s4 0.0s7 2,22

Lepidolite - lM (Radkovice)

isotropic I 164 23 0.062 0.074 1.38 ****40 0.043 0.052 LI I ani sotropi c I 154 JJ U.UJ3 0.043 0.08

Lepidolite - l,v (Tanakamiyama)

i sotropic 807 25 0.131 0.142 4.70 42 0.084 0.082 2.00 ani sotropi c 807 53 0.t00 0.106 2.84 92 0.062 0.064 1.74

Ideal cZlc Symetry

Lepidolite - 2rv, (Radkovice)

i sotropi c 2764 40 0.082 0.078 5.5/ anisotropi c 2764 93 0.048 0.050 3.42

* R,= (rllrol-lrci |)/rlro1 2 2L ** = \ {trw(lFol-lFcl)l/6ylFol 12 = #* Goodness-of-fit: [xwllfol-lrcll'/r(n-m)]t whe.ren = numberof independentdata and m numberof parameters **** based on a partial data set of 838 reflections

1979, personal communication) with a neodymium 0.35 x 0.03 mm size fragments. Ten specimens glass laser to observe second harmonic signals were examined before choosing one for study. The (SHG). A SHG signal was obtained for only the cleavageflake is transparent light brown. Tanakamiyama sample which indicates acentricity No streaking was observed in precessionphoto- and, therefore, a reduction in symmetry from the graphs of the Okl net of the Radkovice crystals ideal, centric space group to either C2, Cm or Cl indicating that they have regular stacking. Howev- symmetry.However, the lack of a SHG signaldoes er, in contrast to the Radkovice samples,the Tana- not always indicate a centric structure if the cause kamiyama crystal does show some streakingparal- of acentricity is subtle. Therefore, all three samples lel to Z* indicating partial stacking disorder. The were studied in the reduced space group symme- streaking was notjudged serious enoughto prevent tries. a structure determination, although it was clear that Approximately fifty crystals of the Radkovice the sample was of marginal quality. material were examined by the precessionmethod, Data were measured for the 2M2 sample on a from which a2M2 and lM polytype were chosenfor Syntex (Nicolet) P2r autodiffractometer and for further work. Both crystals are transparent light both lM crystals on a Picker FAcs-l difractometer. purplish red flakes with the lM rectangularin shape Unit cell parameters were detennined for each of and measuring0.31 x 0.22 x 0.075mm and theZMz the Radkovice crystals by least-squaresrefinement irregular in shapeand measuringapproximately 0.5 offifteen high angle reflections. In the lM case, the x 0.5 x 0.05mm. The lM polytype was a cleavage reflections were centeredby hand. Unit cell param- fragment from an associated2M2 crystal. The Tana- eters for the Tanakamiyamasample were calculated kamiyama sample was cleaved and cut to 0.30 x by the least-squaresrefinement of twenty-five mod- 1224 GUGGENHEIM: ORDERING IN LEPIDOLITE

Table2. Chemical analysesof the Radkoviceand Tanakamiyama nature of the material. The 5363 non-zero reflec- lepidolites tions were symmetry averaged into two indepen- dent quadrantsto produce a total of2783 reflections Radkovice Tanakamiyama Radkovice Tanakamiyama after seven reflections were omitted because the lJeight Percent Cations basedon: ll oxygen lwet 2wet intensity differences with their dependent counter- oxide probe best ( anhydrous ) parts were greater than 512o(D.

sio2 51.45 53.34 57.92 57.92 A 0.79 I .01 Data were collected for both lM crystals in A1203 22.62 17.76 16.04 16,04 Rb 0.07 0.03 similar fashion using the moving-crystal, stationary- -na? Gu203 0.0098 na 0.03 counter method (Lenhert, 1975)with an a, scan rate CrZ03 0.0005 na 0.0 0.0 Na 0.03 0.01 limiting sphere Fe203 0. I 6 3.25 0.01 of l'lmin. Intensities for the entire 40.05 Feo 0.036 na 0,65 were collected to 20 ( 60' and in addition, for four Ti02 na na 0.013 0.013 quadrants from 60o < 20 < 90ofrom k : 0 to 26. Mno 0.51 2.77 0.96 0.96 Li ].48 l.4l Three reference reflections were used to monitor fi90 0.53 0.05 0.0 0,0 Fe-' 0.002 0.07 5s.zs ?+ Li20 5.42 4.60 na FC 0.008 the crystal and diffractometer system after every Cao O.20 o.37 0.015 0.0r5 Mg 0.05 fifty observations. The standard deviation of an Na20 0.26 r .55 0.04 0.04 Mn 0.03 0.05 intensity measurementwas computed from o{I) : K20 9.09 10.90 11,9011.90 AI I .30 + (t"/6)2(Br + 82) + (pl)211'twhere CT is Rb20 1.69 na 0.787 0.787 tCT 0.25 Cs20 0.94 na 0.176 0.ri6 AI 0.51 0,13 the total integrated count in time t", 81 and 82 are Tl20 0.0071 na na si 3.49 3.87 the background counts in time t6 and p, the estimate F, 7.4O 7.78 9.08 9.08 of the standard error, is equal to 0.03. Reflections H20 2.36 na na H^0- 0.65 na were considered observed if the intensities were ' 0.84 '103.02 103.52 97.58 deviation. The data -0=2F -3. I I -Tii4--3.28 -3.82 more than twice the standard Total 100.41 6:16- were colTected for Lorentz-polarization and ab- sorption effects following similar procedures as from fernj et a7.. (1970), P. Povandra,analyst z given above. For the Radkovicedata set, the 5151 from Genthand Penfield (1892), F. A. Genth,analyst 3 not analyzed reflections were symmetry averagedinto two quad- 4 all iron assumedFeo rants resulting in 1165non-zero, independentinten- 5 value basedon refinenent sities from which one reflection was rejected be- causethe equivalent reflections ditreredin excessof 512o(I). erate to high angle reflections that were centeredby Equipment failure during the Tanakamiyamadata computer. Cell parametersare given in Table 3. In collection required the use of two scale factors all cases, graphite monochromatized MoKa radia- since the voltage applied to the X-ray tube was not tion was used. identical throughout. A third scalefactor was intro- The data for the 2M2 refinementwere collected in duced for strong reflections collected with a scan the 20:0 variable-scanmode in four quadrantsof the width of 3.5'instead of the 2.5"used for the weaker limiting spherefrom / : 0 to 40 and from 0o< 20 < reflections. For these data, 5485 reflections were 90'. Crystal and electronic stability were checked by monitoring two standard reflections after every fifty measurements.The standard deviation, o{I), Table 3. Cell parametersof the lepidolites studied was calculated from o\I) : T. [S + (Br + B2)/B3+ lM polytype zMz Polytyqe q(D2lrt2,where S is the scan count, 81 and Bz the *Sartori Radkovice Tanakamiyama *Sartori, Radkovice background counts, B. the ratio of backgf,oundtime ( 1e76) et aL. 11973) to scan time, T, the 20 scan rate in degrees per minute, and q is an estimate of the standard error aS) 5.20(2)** s.209(2) 5.242(31 e.o4(2) s.o23l2) squared, 0.003. Reflections were considered ob- bs) e.or(2) e.ol1 (5) 9.055(6) 5.22(2) 5-1s7(2) lo.l49(5) 10.097(7) 20.210(i) 20.17i(3) served if 1 > 2o(4. Intensities were corrected for .$) ]o.oe(r) B(") ee.3(3) loo.7i(4) 100.77(5) 99.6(3) 9e.48(2) absorption by comparing to ry'scans taken at 10' intervals in for selectedreflections at 2d intervals f * specirenfron Elba, Italy deviations (esd) of approximately 5" and for Lorentz-polaization "* pirentnesized figuies re-presentestimated standard in terms of the ieast units cited for the value to their imediate effects. A maximum intensity decreaseof 4lVo was left, thus 5.20(2) indicates an esd of 0.02. observed for some ry'scans because of the platy GUGGENHEIM: ORDERING IN LEPIDOLITE 1225

symmetry averagedinto two independentquadrants sufficiently describe the structure to allow conver- to produce 986 non-zero reflections. However, av- gence. In contrast to other usesof computer model- eraging was not done between reflections with ing to obtain starting coordinates prior to testing different scale factors. Final averagingwas accom- with X-ray data (see Baur,1977 for i summary), thi plished after the reflectionswere put on the same problemof testingaspacegroupoflowersymmetry scale at the end of refinement. A total of 807 without involving a changein the Laue symmetry is independent reflections were produced._ particularly difficult. A successful approach Las The refinement procedures were simifar to those been to move atoms away from their fseudosym- used for the data of Sartori. Both Radkovice and the metrically-related positions by calculating new po- Tanakamiyama crystals were first refined in the sitions based on an ordering scheme. All possible ideal space groups and then refined in all possible models are generatedfrom a distance least-iquares subgroups compatible with octahedral ordering program and the X-ray intensity data are then used schemesas derived from computer modeling. Only for each model in afull-matrx least-squaresrefine- the Tanakamiyama sampleproved to be acentric in ment program (see Guggenheimand Bailey, 1975, agreementwith the SHG results.ResultantR values 1977,1978). Caution must be exercisedin develop- for each refinement are given in Table 1. For the ing trial structures since unrealistic casescan forie Tanakamiyama sample, the R values represent either a coupling or uncoupling of parameters symmetry averaged data with reflections scaled (Geller, 1961). Likewise, few reflections or data appropriately at the final stage of each refinement. containing large systematic errors may also couple No significant correlation effects for the subgroup or uncouple parameters, possibly explaining the symmetry refinement for the Tanakamiyama sam- ordering pattern establishedwith the lepidolite-lM ple were indicated. The largest parameter interac- data set of Sartori. Since this refinement procedure tion of 0.92 was between the y positional coordi- has now been used several times for centric as well natesof T(1) and T(11), but most interactionswere as acentric cases,difficulties regarding its use are considerablyless. describedhere. Tables 4-61 list observedand calculatedstructure The most difficult aspect is in determining suc- amplitudesfor lepidolit e-2M2,Radkovice lepidolite- cessful convergence. Some problems that may re- lM and Tanakamiyamalepidolite- I M, respectively. late to the determination of a successfulrefinement Final atomic coordinates are given in Table 7 and include (a) oscillations in parametersfrom one cycle the calculated bond lengths and anglesfor the 2M2 to another (b) strong parameter interaction and (c) polytype are given in Table 8 and the lM polytypes large shifts of parametersrelative to their associat- in Table 9. The correlation matrix was used as input ed errors at the final stage of refinement. Trizinc in the calculation of bond lengths (Busing, et al., diorthoborate (Baur and Tillmanns, 1970)proved to r96q. be an example illustrating such problems when refined in space group l2lc and Ic.In Ic symmetry, Subgroup refinements:review and suggestions many parameters oscillated around mean values For space groups that have pseudo-inversion and most x and z parametersrelated by the two fold centers, Ermer and Dunitz (1970)warned that a axis had large correlations. Typically, becausein- simple expansion of the parameter set over the teracting parameters become increasingly indeter- questionableinversion center leads to a singularity minant, refinements with correlations between in the resulting normal equations matrix. Nor can atom pairs show correspondingly large estimated the problem of symmetry reduction prior to the standard deviations for those pairs. The higher refinement be solved by introducing small, random order space group was determined as the correct shifts in atomic positions to make the starting one in this case because bond lengths and angles acentric model only approximately centric, because conform to more reasonablyacceptable values, the the resulting set of normal equations does not R value was nearly the same as that of the lower order space group but with half as many varied 'To parameters, and there was an obvious lack of receivea copy ofTables 4-6, order Documentnumbers convergencein lower symmetry becauseparameter AM-81-178,AM-EI-179 and AM-EI-180,respectively from the BusinessOffice, Mineralogical Society of America, 2000Florida shifts were generally larger than one half the esti- Avenue, N.W., Washington,D.C. 20009.Please remit $1.00in mated standard deviation. In this particular in- advance for each table for the microfiche. stance the lack of convergencein subgroupsymme- t226 GUGGENHEIM: ORDERING IN LEPIDOLITE

Table 7, Final atomic parameters

Brz Btg Bzg "l l "22 "33

Radkovice Lepidol ite-avz 'r.73(r) -0.00il6(1) K 0.5 0.4097(2)***9.25 o.oos49(7)o.or52(2) 0.0 0.00033(2) 0.0 M(1) 0.25 0.25 0.0 0.82(9) o.oo3o(5) o.oo7(l, 0.00049(9) 0.0003(7 ) 0.0004(2) 0.0005(3 ) M(2) 0.58561(9) 0.2437(2) o.oooos(4)0.67(r) o.oo2ro(7)o.oo57(2) 0.00050(l ) -0.0002(1) 0.00018(2) -0.00001(4) T(l) 0.794?6(6)0.4078(r 0.',r3397(3)0.572(e)o.0or82(4) 0.0044(r ) 0.000439(9)-0.00024(6) o.oool 5( l ) -0.00003(3) ) -0. r(2) 0.r2556(5) 0.4136(r ) 0.r3394(3) 0.562(9)o.oor64(4) o.oo49(r) 0.000436(9) -0.00008(6) 0.00017( l ) ooooo(3) o(r) 0.7676(2) 0.3937(3) 0.05266(7)r.r3(3) 0.0057(2) 0.0085(4) o.o0o42(2) 0.0006(2) 0.00007(s) -0.000r3(8) (4) 0.00003(e 0(2) 0.0905(2) 0:4261(3) 0.05283(7)'1.e0(4)1.l2(3) 0.0040(r) 0.0132(4) 0.00043(2) 0,0023(2) 0.00007 ) 0(3),F0.4468(2) 0.429r(4) 0.04e23(8) 0.0060(2) 0.0334(s) o.0006r(3) -0.0083(3) 0.00037(6) 0.0002( l ) 0(4) 0.7058(2) o.r7i4(3) 0.16634(9)1.29(3) 0.005r(2) 0.00e8(4) 0.00090(3) -0.0032(2) 0.00043( 6) -0.0000(1) o(5) 0.2380(2) 0.r785(3) 0.',r62re(8)1.27(3) o.oo54(2) o.ooe8(4) 0.00073(3 ) 0.0028(2) 0.00007(6)-0.00026(9 ) 0(6) 0.971e(2) 0.3787(4) 0.l66l l (8) r.27(3) 0.0024(r) o.0r8s(6) 0.00086(3) -o.o0o3(2) o.0oo4o(s) 0.0002(I ) RadkoviceLepidol ite-lM 'r.99(2) K 0.0 0.5 0.0 'l 0.0r90(3) 0.00595(8)0.00519(7) 0.0 o.ool5(l) 0.0 M(l) 0.0 0.0 0.5 .8(l) 0.0r9(2) 0.00s0(5) o.oo52 (5) 0.0 0.0033(8) 0.0 M(2) 0.0 0.328e(r) o.s 0.73(2) o.0062(2) 0.oo23r(8) 0.002r3(7) 0.0 0.0005(r ) 0.0 T 0.0810c(8)0. r6860(5) 0.23203(4)o.i3(l) o.oo6s(r) o.oo2o9(4)0.oo22r(3) -0.00012( 6) 0.o0os8( 4) -0.0000r(3) 0(1 0.0218(4) 0.0 0.1750(2) r.42(4) 0.0]ee(7) 0,0029(2) 0.003r(r ) 0.0 -0.000r(2) 0.0 ) -0.0003(1 o(2) 0.3252(?\ 0.23r9(2) 0.1680(r) r.46(3) o.o1l3(4) o.0056(l) 0.0038(1) -0.0028(2) 0.0016( 2 ) ) o(3) 0.r418(3) 0.r768(1) 0.3e45(r) r.26(3) o.or70(4) o.oo37(l) 0.00223(8 ) -0.00r2(2) 0.0004(r ) -0.000r0(8) F 0.1076(3) 0.s 0.40ri(2) 2.il(5) o.ol2s(5) o.0l4t(3) 0.0030(l ) 0.0 0.00r'r(2) 0.0 TanakamiyamaLepidol i te-lM K 0.0 0.5028 0.0 2.21(5) M(l) 0.0 -0.006(2) 0.5 0.3(l) M(2) o.o 0.323(r) 0.s 0.66(8) M(3) 0.5 0.r 6'l (2) 0.5 r.3(2) T(t) 0.0756(i) 0.1704(8) 0.2309(4) 0.85(6) T(il ) 0.s863(7) 0.3338(8) 0.2302(4) 0.87(6)

0(l) 0.041(l) 0.002(?', 0.1708(5) 1.53(e) 0(2) 0.31s(2) 0.243(l) o.',r6e(l) 1.6(2) o(?2) 0.813(2) 0.260(l) 0.'r62(r) r.4(2) 0(3) 0.il4(2) 0.175(r) 0.3e4(l) l.r(r) o(33) 0.663(1) 0.328(r) 0.391',I(9)o.e(r) F 0.110(l) 0.4729(9\ 0.3e8s(s) r.0('r)

* Isotropic temperaturefactor as reflned ** Theanisotropic temperature factor formis exl (-xtIrBtrh,h,)' *** parenthesizedfigures representestimated standard Oevilt]ois (esd) in termsof the least units cited for the value to their irmediateleft, ihus 0.409i(2)indicates an esdof 0.0002.

try is obvious;however, this is not alwaysthe case. However, a similar case is conceivable when the A particularly disturbing aspect of the lepidolite procedure is used to test for the ordering of two ions IVSi subgroup refinements involving the Radkovice of similar scattering power, for example and IvAl. specimensis that each model appearedto converge; If the refinement behaves similarly to that parameter shifts were less than a tenth of the described above, only the correlation matrix and a associatedestimated standarddeviations at the end comparison of R values will be particularly useful' of the refinement process.In this case,high correla- Such a circumstancewas noted for margarite (Gug- tions between symmetry-related pairs suggested genheim and Bailey, 1978),and one must arguethat that the parent space eToupis the proper one. In the case for an acentric structure from X-ray data addition, difference maps showed that the two alone is less compelling for such examples. Alter- "pseudosymmetry-related" octahedral sites in the nate methods of determining centricity such as by subgroup refinement were identical in scattering infrared spectra or by SHG, in addition to diffrac- power, which is in contradiction with results ex- tion data, strengthensthe case considerably. Scho- pected for ordered models. Such inconsistencies maker and Marsh (1979) suggestthat weak reflec- allow one to choose one spacegroup over another. tions should be carefully examined in a non-centric GUGGENHEIM: ORDERING IN LEPIDOLITE 1227

subgroup refinement since these are the most sensi- Table 8. Calculated bond lengths and angles for Radkovice tive to the small imaginary component of the struc- lepidolite-2M2

ture factor. Of course, the size of this component Bondlengths e) Bondangles (') dependson how closely the structure approximates centricity and the need for a close inspection will TetrahedronT(l) *0(1) 1il.77(e) vary depending on the problem. 0(4) 1t, o

Table 9. Calculatedbond lengths and anglesfor Radkovice and Tanakamiyamalepidolite-lM (") Bondlenqths eA) Bondanqles (') Bondlensths m) Bondanqles (Tanakamivama) Tetrahedron T: (Radkovice) Tetrahedron T( l ):

0(t L6342(8)* 0(t 2.629(2) 0(r 107.02(s)0(l) r.64(l) 0(I )--0(2) 2.62(?) o(r)--o(2) 105.7(5) ) )--0(2) )--0(2) o(22) l06.I (5) o(2) r.635(l) 0(2) 2.620(2) c(2) 106.43(8)o(2) ',I.64(lr.66(l ) 0(2?\ 2.62(t) 2 71q(t\ 0(3) l l2.ee(8) 0(22) ) 0(3) 2.7r(1) 0(3) r 12.7(5) o(2) 1.637(r) o(3) **0(3) **0(3) 1.62?(1) 0(2)--0(2) 2.625(rl o(2)--o(2) I 06.69(7) r .62(',r) o(2\--o(?2) ?..64(2) 0(21--0(22) r06.6(6) 1.ta\t) o(3) I 14.2(s) Mean T.63- 0(3) 2.695(?) 0(3) 'il1.63(6)lll.68(6) l4ean 1.64 o(3) 0(2)--0(3) 2.695(2)0(2)--0(3) o(22)--o(3) ?'99-(2)o(22)--o(3) 110.9(6) Mean ?.663 Mean roq-T- Mean z.ol Mean 109.4 TetrahedronT(.1 I ): (Tanakamivama) r05.8(5) 107.1(5) (s) '106.0(6)113.',r 'il 3.8(6) r10.6(6) Io-t:f-

Interlayer cation K Radkovice TtoT Interlaver cation K Tanakamivama o(l\xz 2.956(2) 3.319(2) around0(l ) 136.7(l) 0(l)x2 3.036(6)3.205(6) 0(2)xa 2.9a7(l) 3.246(?) around0(2) 132.02(7) 0(2)x2 3.03(l) 3.19(r) Mean 2,952 3.283 Mean r34-:a-- 0(22)x23.01(l ) 3.13(l) i nner outer Mean 3.03 T:T6...- I nner ouEer

Tanakamiyama octahedron M(l ) : Radkovice 0ctahedronM(l): 2.820(2) 0(3)--0(3)x283.01 (4) 0(3)x2 2.ll(2) 0(3)--0(3) ?.64(2) o(3)--o(3) z.s(8) 0(3)x4 2.127(l) 0(3)--0(3)x2 FxZ 88.7(4) Fx? 2.100(l) Fx4 ?.741(2) Fx4 80.82(5) 0(33)x22.]3(l ) Fx? 2.95(l) o(33)--o(33) 3.02(?\ 0(33)--0(33) eo.s(8) Mean 2.114 Mean 2.781 Mean 81.92 Fiz z.il7(5) ?E t a?\ 2.59(r) Fx? ry ( shared) (shared) Mean TjT- FxZ Mean Tffi- Mean 83.0 (shared) (shared) --0( 0(3)--0(33)x2 e6.2(2) 0(3)--0(3)xz3.186(l ) 0(3)--0(3)x2e6.ee(4) 0(3 ) 33)xz 3.r52(8) Fx4 99.I 8(5) Fxz 3.22(i) Fxz ee.3(4) Fx4 3.2]9(2) --Fxz e7.5(5) Mean 3:n-3- Mean 98.09 0(33 ) 3.r9i(9) o(33)--Fxz 3lT9- Mean 97.7 (unshared) (unshared) Mean (unshared) (unshared)

0ctahedronM(2): Radkovice octahedronM(2): Tanakam'ivama (8) a(3)x2 I .966(l o(3)--o(3) 2.820(?\ o(3)--o(3) e1.62(6) o(3)x2 1.88(l) 0(3)--0(3) 2.64(2\ 0(3)--0(3) 89.0 ) 8e.3(4) 0(3)x2 1.971(l ) 0(3)x2 2.587(l) 0(3 )x2 82.I 7(5) 0(33)x21.901 (8) 0(33)x22.660(7\ 0(33)x2 1.853(8)0(33)--Fx2 2.5e(l) 0(33)--Fxz q7.r (4) Fxz 'lI .9i4(1) F--0(3)x22.741(2) F--0(3)x?88.02(6) Fx2 Mean .970 F 2.464(3) F 77.27(6) Mean T]66- F--F 2.s3(r ) F--F 60.Z tC,, Mean Z:ltTI-- Mean $:Tf- Mean T:87- Mean 87.9 ( ( shared ) ( shared) ( shared) shared) 0(3)--0(3)x2?.920(2) 0(3)--0(3)x2es.73(5) o(3)--o(33)x22.7a(1 ) 0(3)--0(33)x2 e2.6(4) FxZ 2. 919('l ) FxZ 95.63(5) Fx? 2.70(1) FxZ 92.4(3) F--0(3)x2 2.892(?) F--FxZ 94.31(6) 0(33)--Fxz 2.67(1) 0(33)--Fxz 90.9(5) Mean 2.910 Mean 95.22 l"lean 2.70 Mean 92.0 ( ( unshared) (unshared) (unshared) unshared) octahedronM(3): Tanakamivama

0(3)x2 2.116(8)0(3)--0(33)x2 2.660(7) 0(3)--0(33)xz 77.3(4) 0(33)x22.14(2) FxZ 2.e5(r) Fx2 88.s(s) Fx2 2.12(1\ 0(33)--0(33) 3.02(l) o(33)--o(33) 8e.6(8 ) Mean T:IT- F--F t Eelll F--F /J.JtO,, Mean 2.79 Mean 8?.? ( shared) ( shared) o(s)--o(as)xzs.zoIt 0(3)--0(33)x2 ] 31:i{31 fl(33)--Fx2+HL fl(33)--Fx239#1) (unshared) (unshared)

* deviations (esd) in tems of the least units cited for the value to their Darenthesized' f.iqures represent'l.6342(8) estimated standard imnediate leit, thus indicates an esd of 0.0008.

** apical oxygen

only are the mean bond distances consistent with reflect the greater scattering power of manganese the respective chemistries,but the R values also and magnesium. Difference maps for both final improved for the lM refinementwhen the scattering structures were featureless' The full complementof factor for M(1) was increasedby 0.75 electronsto lithium to the M(1) site of the 2M2 form appears GUGGENHEIM: ORDERING IN LEPIDOLITE 1229

---) +Y

Fig. 2. Octahedral ordering pattern of Radkovice lepidolite- lM.

1.634, respectively. Apparent differencesin tetra- hedral composition as derived from average bond lengths are not significantbecause of high estimated standarddeviations. It is interestingto note that the apical O(3) anion of the apparently larger tetrahe- dral T(1) site is more closely coordinated to the aluminum-rich M(2) site in contrast with the apical O(33) anion of the T(11) tetrahedron. A similar o(D oil) I topology exists in lepidolite-3T and zinnwaldite. An +x Al concentration in T(1) would causethe apical O(3) anion to be undersaturatedand would favor a more Fig. l. Octahedral ordering pattern of Radkovice lepidolite_ highly charged cation in M(2) and a closer M(2)- 2Mr. O(3) approach. In addition, two (F,OH) anions are in the cis orientation along a shared edge between M(2) and M(3) and, becauseof the smaller fluorine unique for the lepidolites. All previous lepidolite radius, may approach each other more closely than refinements show minor substitution for lithium in any other anion pair along the shared edge around M(1) similar to the lM refinementresults. M(1). The combination of both effects probably For the Tanakamiyamalepidolite, the mean octa- contributes to the accommodationof A1 in M(2). hedral bond lengths for the cation-anion distances areM(1):2.lZA,tt(Z):I.88 A andM(3):2.13 A, and The Radkovice structures the scatteringpowers are 6, 11.5and 6 electrons, There are major diferences between the struc- respectively. Even with the large estimated stan- tures of the lM and 2M2 polytypes caused by the dard errors, there is no doubt that M(2) and M(3), which are related by the pseudo-mirror plane, are quite different in both size and scattering power. Within the estimated standard elrors, M(l) and M(3) are identical in both size and scatteringpower. The size and scattering power of the M(2) site are consistent with complete or nearly complete order- ing of alumium into this site. The remaining ele- ments and vacancies may be allocated equally be- tween M(1) and M(3). However, the estimated standarderrors and the large number of substituting elements prevent a unique solution from being determined. For the Tanakamiyama lepidolite, the mean T-O Fig. 3. Octahedral ordering pattern of Tanakamiyama bond lengths for T(1) and T(il) are 1.64A and lepidolite-lM. t230 GUGGENHEIM: ORDERING IN LEPIDOLITE fundamental variations in stacking. This variation Table 10. Important structural features around accounts for the differencesin coordination Radkovice TanakamiYama the interlayer cations and has been discussed in Paraneter tuz lM 1M detail by Takeda and Burnham (1969)and Takeda, -tet^ 1o\ 6.57 7.25 et al. (1971).Takeda et al. (1971)suggested that the " octahedral coordination around the potassium ion (Ll tzo'-mean ob-ob-ob anglel ) in the lM form produces an energetically more *ta"r(') T(l): I 12.14 ll2.l0 T(l):112.6 stable structure than the 2M2 form, which involves (meanoapical-T-obasal angle) T(2):ll2.l5 T(il):112.5 a trigonal prism coordination about the interlayer Bideat(') 98.58 99.85 99.97 cation, because of the staggered arrangement of (d,/3c)l oxygens. However, they suggestedthat the 2Mz ll80'-cos-l **{ (.) K: 52,36 56.7 polytype may be stabilized at small tetrahedral 60.4 rotation angles, o. The tetrahedral rotation angle, [cos 1,= lt4(l): 6l.07 61.34 oct. thickness/2(11--0,F,0H)l14(2): 58.54 58.96 56.1 which is a measureof the deviation of the tetrahe- M(3): 60.5 dral ring from hexagonal symmetry, is 7.25oin the Mean 59'38 59.75 59.0 lM polytype and 6.57'in the 2M2form. The potassi- Sheet thickness (q) tetrahedral 2.254 2.259 2'26 um coordination reflects this difference also with octahedral 2.052 2.032 2'10 mean inner K-O distancesof 2.9524 for the lM and Interlayer separation ('A) 3'387 3.420 3'32 2.9614 for the 2M2 form and mean outer K-O Basaloxygen azuu" (1) 0.080 0'007 0'08 distancesof 3.283Aand 3.251A,respectively. Since the tetrahedral-octahedral sheet misfit and the size * ideal value:109.47" and charge of the interlayer cation are similar in ** ideal value: 54.73" both structures. such differencesmust be attributed to the variation in stacking and the resulting envi- ronment about the interlayer cation. contribution to the temperature factor from posi- The smaller angular rotation of tetrahedra in the tional disorder caused by differences in Al-O and 2M2 structure accounts for the larger inner and Si-O bond distances and the lack of tetrahedral smaller outer mean K-O distances of the 2M2 cation order. However, unlike these other struc- polytype when compared to the lM form. Conse- tures, there is no appreciable difference between quently, the hole formed in the ditrigonal ring is the vibration ellipsoids of the apical and basal slightly larger in the 2M2 structure allowing for a oxygens. Although the M(1) site of the 2M2 poly- small decreasein interlayer separationwhen com- type is more elliptical than that of the lM form, its pared to the lM form (see Table 10). magnitude is considerably less. Any positional dis- Tables 11 and 12 list the magnitudesand orienta- order of cations in M(1) of the lM polytype must tions of the apparent atomic vibration ellipsoids. conform to the 2lm point group symmetry of that The ellipsoids of the two structures are remarkably site, thereby producing a larger ellipsoid. The large similar. The r3lr1ratio for the cations vary from 1.05 magnitudes of the (F,OH) ellipsoids for both poly- to 1.22 indicating their nearly spherical shape.The types also suggestpositional disorder' The orienta- only exception to this trend is the M(1) cation in the tion of the major axis of the vibration ellipsoid for 2M2 polytype which is elongate as indicated by a this site is similar in both structures, each perpen- ratio of 1.48. The ratios for oxygen atoms range dicular to the plane establishedby the M(1) site and from 1.49 to 1.74 with the averagevalue of 1.63, the shared edge between the M(2) octahedra. The whereas the hydroxyUfluorine sites have values of elongation of the ellipsoid is not directed along 1.98in the lM and 2.35 in the 2M2 polytypes.The bonds to the nearby cations. However, the three major axes of the ellipsoids for all anions in the 2M2 octahedral cations around the (OH,F) site and the polytype are oriented approximately parallel to the Al + Li disorder in M(2) would be expected to layers. The trend is also approximated in the lM influence the (OH,F) position in a complex way. polytype although to a lesser degree' Conclusions Similar to zinnwaldite (Guggenheimand Bailey, 1977) and phlogopite (Hazen and Burnham,1973), It is apparent that not all lepidolites have similar the magnitudes of the oxygen vibration ellipsoids octahedral ordering schemesand some may differ are quite large and may suggest that there is a slightly in tetrahedral ordering patterns. Based on GUGGENHEIM: ORDERING IN LEPIDOLITE r23l crystal chemical arguments, high fluorine content Table 12. Magnitudes and orientations of thermal ellipsoids for may promote the ordering of aluminum into either Radkovice lepidolite- lM M(2) or M(3). Such a conclusionis consistentwith Atm Axis rms F) Angle (') with respect to the ordering observedin the Tanakamiyamalepido- displacement X Y Z lite, lepidolite-3T (Brown, 1978) and zinnwaldite o"l 0.r56(r)* 90090 (Guggenheim and Bailey, 1977). Ilowever, high z 0.r58(r) 142(8) eC il7(8) r^ 0.r64(r) 128(8) e0 27(7) fluorine content cannot be the sole cause for this J phenomenon. 0. l 43(8) 90090 The Radkovice lepidolites are nearly "r as fluorine-rich as the Tanakamiyama sample and 0.146(8) 38(14) e0 139(14) 0.17i(7) 52(14) e0 4e(i4) more fluorine-rich than either the Sadisdorf zinn- M(2) 0.09r(2) 17(6) 90 84(6) waldite or lepidolite-3T. "i Parametersof crystalliza- o.097(2\ 90 180 90 0.105(2) 107(6) s0 6(6)

rl 0.0915( 9 ) sr(il) 40(12) 8e(3) Table ll. Magnitudes and orientations of thermal ellipsoids for 0.0944(9) 42(il) r30(r2) 88(3) Radkovice lepidolite-2M2 0.r062(7) ro3(3) e0(3) 3(3) 0(l) "r o.r0e(3) 90090 Atm Axis ms (fl) Angle (') with respect to 0.122(3) ro4(3) e0 155(3) d i spl acement XYZ '3 0.r70(3) r4(3) e0 ils(3)

tl 0.r06(2) 2s(2) 6r(2) e8(3) K"r 0.1440(9)* 90 0 90 0.r38(2) 83(3) 100(3) l6e(3) ,2 0.r476(9) r4e(7) 90 |i r (7) 0.r 63( 2) il8(2) 3o(2) e7(3) '3 0.r539(9) r2r(7) 90 21(7) o(3) tl 0.r0s(2) 83(2) 80(6) 2r(4) M(1) r.l o.08(r) 109(18) r25(r8) (',r 38 4) ,2 0.121(2) 105(3) 160(4) 7s(6) '2 0.r0(l) t r37(25) 4e(24) J\41 ) o.r56(2) 17(2) 107(3) ro4(2) '3 0.r18(9) q?t24\ 6t (22) 58(l4) J tr 0.122(31 e6(re) eo s(re) 0.087(2) se(r0) 3r(r0) e3(5) "I '2 o.r2e(3) r74(r9) 90 85(19) 0.0e4(2) 149(r0) 5e(10) 82(10) t3 0.24r(3) 90090 '3 0.r00(1) er(e) el(i) 8(e) tr 0.077(r ) 22(5) eo(3) * parenthesizedfigures represent estimated standard deviations (esd) ,2 0.087(r ) lqolql 82(6) in terms of the least units cited for the value to their imediate 0.093e(9) ieft, thus 0.156(l) indicatesan esdof 0.00i. J e2(6) e3(4) 8(6) I(2) r, 0.080(I 3r(8) se(r8) ee(4) I ) 0.083(r ) r2r(r8) 3r(r8) '3 0.0935(9) 8e(3) eo(4) il (3) tion other than fluorine content may be important in 0(l) r. 0.091(3) 88(2) 7e(8) l6(5) I determining cation ordering patterns in the lepido- r. 0.108( 2 ) 82(2) l6e(6) 8r(7) '3 o.I s4(2) 8(2) 83(2) r03(2) lites and zinnwaldites. The conclusion that zinnwal- dite is 0(2) r, 0.0e2(3) 80(5) (51 (6) not ordered in A symmetry reached by I s7 2t '2 0.r09(3) 43(3) r3r(3) r0e(i ) Levillain et al., (1981)from Mdssbauerspectra of '3 0.r51 (2) 48(2) 42(2\ 98(2\ Zinnwald and Madagascarspecimens suggests that 0(3).F r, 0.102(3) r28(6) l i2(3) 38(7) cation ordering schemes may variable I be in zinn- r^ 0.r l8(3) t?7(61 (7) a ilr(3) 127 waldite as well. 0.240(3) se.5(8 ) r4s.5(8) 9s.0(e ) A comparison of octahedral sizes and scattering 0(4) r, 0.0e2(3) q7l2\ 33(2) e8(3) I power between the Radkovice lM and 2M2 poly- '2 0.r34(2) 86(4) e6(3) r 72(3) types indicates very small differences that cannot '3 0.159(3) 33(2) t22(2) er(4) greatly affect the limits of lepidolite stability. Octa- 0(5) r, 0.oee(3) 117(2) )al t\ 8l(5) I hedral and ,2 0.I 20(3) r0r(4) er(5) i 5e(3) tetrahedral sheet units are remarkably 0.r63(2) 30(2) 62(2) 109(2) similar and, as suggestedby Sartori Onq, structur- 0(5) r, (2) al unit variations do not apparently control the I 0.092(3) 6(3) 87 r05(3) z 0.r32'(2) YD(J' 84(4) r64(3) stacking sequence. 0.r60(3) e3(2) 7(4\ 83(4) Acknowledgments

* parenthesized figures represent estimated standard deviations I thank Dr. P. Chernf of the University of Manitoba for the (esd) in terms of the least units cited for the value to their Radkovice samplesand Dr. D. K. Smith and Mr. R. S. Horsey inmediate left, thus 0.1440(9) indicates an esd of 0,0009, of The Pennsylvania State University for the Tanakamiyama sam- ple. Dr. D. Bish of Los Alamos and Mr. R. Horsey kindly 1232 GUGGENHEIM: ORDERING IN LEPIDOLITE supplied the SHG results. I thank also Mr. P. Terpstra for margarite structure in subgroupsymmetry. American Mineral- locating a suitable 2M2 crystal and Mr. G. Harris for the ogist 60,1023-1029. microprobe analysis. Thanks are due Dr. S. W. Bailey of the Guggenheim, S. and Bailey, S. W.(1977) The refinement of University of Wisconsin-Madisonwho reviewed the manuscript zinnwaldite-lM in subgroup symmetry' American Mineral- and allowed the use of his Syntex diffractometer,and Drs. W. H. ogist62, ll58-1167. Baur and M. F. Flower both of UICC who gavevaluable advice. Guggenheim,S. and Bailey, S. W. (1978)The refinementof the Drs. A. Kato of the National Science Museum (Japan)and T. margarite structure in subgroup symmetry: correction, further Sudo ofthe Tokyo University ofEducation provided information refinement, and comments. American Mineralogist 63' l8G regarding lepidolite localities in Japan. Portions of this work r87. were supported by a University of Illinois Research Board Hazen, R. M. and Burnham, C. W. (1973)The crystal structures Grant, by the UICC Computing Center, and by the National of one layer phlogopite and annite. American Mineralogist 5E' Science Foundation under grant EAR 80-18222. 889-900. Lenhert, P. G. (1975) An adaptable disk-oriented automatic References diffractometer control program. Journal of Applied Crystallog- raphy 8, 568-570. Albee, A.L. and Ray, L.(1970) Correction methodsfor electron Levillain, C., Maurel, P. and Menil, F. (lgEl) Mdssbauerstudies probe microanalysis of silicates, oxides, carbonates, phos- of synthetic and natural micas on the polylithionite-sidero- phates, and sulfates. Analytical Chemistry 42, l40E-1414. phyllite join. Physics and Chemistry of Minerals 7 ,71J6' Baur, W.H. and Tillmanns, E. (1970) The space group and Sartori, F. (1976)Crystal structure of a lM lepidolite. Tscher- crystal structure of trizinc diorthoborate. Zeitschrift fiir Kris- maks Mineralogische und PetrographischeMitteilungen 23' tallographie l3l, 213-221. 65-:75. Baur, W. H. (1977)Computer simulation of crystal structures. Sartori, F. (1977)Crystal structure of a 2Ml lepidolite' Tscher- Physicsand Chemistryof Minerals2,3-20. maks Mineralogische und PetrographischeMitteilungen 24' Bence, A. E. and Albee, A. L. (196E) Empirical correction 23-37. factors for the electron microanalysisof silicates and oxides. Sartori, F., Franzini, M. and Merlino, S' (1973)Crystal structure Journal of Geology 76, 383-403. of z 2M2lepidolite. Acta CrystallographicaB.29, 573-578' Brown, B. E. (1978) The crystal structure of a 3T lepidolite. Schomaker, V. and Marsh, R. E. (1979) Some comments on American Mineralogist 63, 332-336. refinement in a space group of unnecessarilylow symmetry' Busing,W. R., Martin, K. O., and Levy, H. A. (1962)oRFLs, a Acta CrystallographicaB.35, 1933-1934 - Fortran crystallographic least-squaresrefi nement programs. Shannon,R. D. (1976)Revised effective ionic radii and systemat- U. S. National Technical Information Service oRNL-rM-305. ic studies of interatomic distancesin halides and chalcogen- Busing,W. R., Martin, K. O., and Levy, H. A. (1964)oRFFE' a ides. Acta Crystallographica A32, 75l-:7 67 . Fortran crystallographic function and error program. U.S. Sidorenko,O.Y.,Zvyagin, B' B. and Soboleva,S. V' (1975) National Technical Information Service onxr--ru-306. Crystal structure refinementfor lM dioctahedralmica' Soviet eernf, P., Rieder, M. and PovondraP. (1970)Three polytypes of Physics-Crystallography20, 332-335(English Transl')' lepidolite from Czechoslovakia.Lithos 3, 319-325. Swanson,T. H. and Bailey,S. W. (19E1)Redetermination of the Cromer, D. T. and Mann, J. B. (196E)X-ray scatteringfactors lepidolite-2Mr structure. Clays and Clay Minerals 29' El-90' computed from numerical Hartree-Fock wave functions. Acta Takeda, H. and Burnham, C. W. (1969)Fluor-polylithionite: a Crystallographica 424, 321-4. lithium mica with nearly hexagonal(Si2O5)'z- ring' Mineralogi- Ermer, O. and Dunitz, J. D. (1970)Least-squares refinement of cal Journal (Japan)6, 102-109. centrosymmetric trial structures in non'centrosymmetric Takeda, H., Haga, N. and Sadanaga, R. (1971) Structural space groups. A warning. Acta Crystallographica 426,163. investigation of polymorphic transition between 2M2-, lM' Geller, S. (1961)Parameter interaction in least squaresstructure lepidolite and2M 1muscovite. MineralogicalJournal (Japan)6' refinement. Acta Crystallographica14, 1026-1035' 203-215. Genth, F. A. and Penfield, S. L. (1892)Contributions to mineral- ogy, No. 54 with crystallographicnotes. American Journal of Science64, 381-389. Manuscriptreceived, March 12, 1961; Guggenheim, S. and Bailey, S. W. (1975) Refinement of the acceptedforpublication, June 30, 19El'