Crystal Structures and Mineral Chemistry of Double-Salt Hydrates: I. Direct Determination of the Crystal Structure of Tamarugite
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THE AMERICAN MINI]RALOGIST, VOL. 54, JANUARY.FEBRUARY, 1969 CRYSTAL STRUCTURES AND MINERAL CHEMISTRY OF DOUBLE-SALT HYDRATES: I. DIRECT DETERMINATION OF THE CRYSTAL STRUCTURE OF TAMARUGITE P. D. RosrNSoNAND J. H. Feuc, DepartmentoJ Geology Southern I llinoi.s Llniaer s,ity Carbondale, I l,linois 6290 I . Assrnlcr The structure of tamarugite, NaAI(SOa)r.6HzO,has been solved by reiterative applica- tion of sayre's equation using three-dimensional photographic and counter data. The final R value is 7.3 percent (hydrogens included). The coordination polyhedra of sodium and sulphur are joined to form infinite chains parallel to r. The perfect (010) cleavage traverses only weak hydrogen bonds. The mean distances are: Na-O:2.415 A, Al-Ow:1.8$ A, S-O: 1.488A, and Ow-O : 2.65 A. The A1(H2O)6octahedron and the two independent SOa tetrahedra are regular but the Nao6 group deviates considerably from a regular octahedron INtnooucrroN This study is the first of a seriesdesigned to elucidate the mineral struc- tural chemistry of the double sulfate hydrates. Tamarugite was chosen because(1) optical and preliminary X-ray data have been reported by us (Robinson,Fang, and Bloss, 1967) and (2) tamarugite is a dehydra- tion product of Na-alum whosedehydration mechanismwe plan to inves- tigate in our laboratory. Analysis by the direct method was desirablebe- causethe atoms are near enoughin atomic numbersto make a Patterson approach difficult. The crystals,from Alcaparrosa,Chile, were obtained from the U. S. National Museum, SmithsonianCat. No. R 9117. Cnvsrar, Dare a:7.353+.002A Space group P21/o b:25.225+.N5 i\ Z:4 c:6.097+.002A D (calc):) 066g/cml A:95.2+ l" D (meas):2.06f .01 g/cm3 INroNSrty MnesunBunNTs AND ConnBcrrorqs The crystal used in the analysis was a singly terminated prism, with dimensions0.32X0.14X0.13 mm., mounted normal to its [001] elonga- tion direction, the b axis coinciding with the axis of crystal rotation. Ini- tially, intensities were collected by the standard multiple-film Weissen- berg technique and were correctedfor a1 a2 separation, Lorentz pola:iza- tion and absorption. At a later date,data collectionwas carried out usinga 0.01incrementing Buerger automated diffractometerand CuKa radiation. Crystal orienta- P. D. ROBINSONAND J. H. FANG tion and system stability was monitored by measurement of a standard reflection before and after each level. The reflections thus collected were then corrected for Lorentz polarization and absorption. A.ry reflection which did not meet the condition (C-Bkgd) )3.0 x (C+ntga;+ was rejected. During finai refinement 3 sigma weighting was applied where o: F2/2.0* (C - Bkgd) * {Cl (r)(Bkgd)+ (0.03[Cf Bkgdl)': F2 : Intensity correctedfor Lorentz polarization and absorption Bkgd: (BL+ B)*t I : Scan time/2.O x Bkgd time C : Total integrated counts during scan Bt, Br: background DorBnlrrNerroN ol rup SrnucrunB The structure was solved by reiterative application of Sayre'sequation (Sayre, 1952). First, observed structure factors F6 are normalized to E2r,: 1, where i": pi/,Et?,,^ J:I For the primitive monoclinic cell, e:2 for 0k0 and h)l reflections and e:1for other reflections(Hauptman and Karle, 1959), and the sum of the squares of atomic scattering factors fi extends over the Iy' atoms of the unit cell. Second,the En are ordered in decreasingmagnitude of lEol t I ar,I I 1++r',1, and the three largest normalized structure factors which are Iinearly in- dependent (Woolfson, 1961) are arbitrarily assigneda positive value in order to determine the origin. Third, the next n (n rsually 4) strong reflec- tions are given assumedsigns. Fourth, the Sayre's equation is reiterative- ly applied to each of these starting sign sets, yielding 2" solutions. The signsare calculatedfor reflectionswith E>1.5 (in our case,the number of reflectionswith -E>1.5 is 161). The statistical averagesfor the nor- malizedstructure factors are listed in Table 1. Fifth, when eachiterative processgives no more sign changes,then consistencyindex, C, defined as (Long, 1965). STRU C7'U RE OI1'T A M A RUGI TL) 2l ':(] EnEEn'En+n'l> / (l' \; I"'I l'r.,'l) where the sums are all pairs of h' and h!h', and where ( ) means the averageover all values of h' . The highest index usually indicates the true solution. Using a starting setof sevensigns (three origin-determining signs which are arbitrarily assigned as positive) and four other reflections, sixteen Teer-n 1. Expnnrlmr,mar, ano Tuoonr:uc,a.r Vlr,uns ol Nonua.r,rzno Stnucrunr Fecrons Experimental Centrosymmetric Non-Centrosymmetric 0.809 0.798 0.886 0.894 0.968 0.736 0.29o/a o.30k 4-0'/o s.0% 30.6o/a 32.0% possiblestarting sets were consideredso that each possiblesign combina- tion of the remaining four signs could be tried. The first seven reflections used were; I 3 -l 2.53 q 2 3 3.01 I 6 0 1.88 I 3 | -2.64 1 5 -2.92 8 I -J tt n 7 -4 3.18 An E map (a three-dimensionalFourier map with .E values rather than F values for the coefficients)was made using the 161 signed values of E from the set with the highest consistencyindex. The peaks which ap- pearedin this map, however, were not at all meaningful.Although the true solution WiIlusually be the most consistentone (i. e.it will have the highest consistencyindex) this is not always the case (Karle and Karle, 1964).Therefore, severalmore maps were calculated in the hope that the true solution would reveal itself. Our efforts proved fruitless. We then recalled that our previous space group determination of Ph/m (Robinson, Fang, and Bloss, 1967) was based on several very faint reflections (h01,hl2n) which appearedonly on the longest exposure films (96 hrs). Assuming those reflections to be the result of Renninger P. D. ROBINSON AND J, H. FANG T,ter,n2. A CoupenrsoNol'rrrr Srxrrpr Sor,urroNs Signs of the First Seven No. of Cycles Consistency Index L +++++++ 0. 54606 2 +-+++-+ 7 .58606 J -+-++-+ 7 38s55 A ---++-+ 5 .49047 5 ++++--+ 7 40548 6 +-++-++ l4 .57018 7 -+-+--+ 5 .+4438 8 ---+-++ 12 .39839 9 ++++++- 5 .56505 10 +-+++-- I .38448 11 -+-+++- 6 52119 12 ---++-- 7 .57154 IJ ++++-+- 5 53848 1A +-++-+- 5 .66262 I5 -T-T--- 3 .853 19 t6 ---+-+- 8 .63047 effect, the spacegroup then becamePh/ a. This assumption was con- firmed by the successfulstructure determinationin P21fa and by the fact that the occurrenceof the spurious reflectionswas found to be dependent on the wavelength and techniquesused in the taking of the photographs. Recalculation of the 16 possiblesolutions in P21/a led to set No. 15 (Table 2) as the most likely choice.Subsequent E map calculation re- vealedseventeen peaks (there are 18 atoms,hydrogen atoms excluded,in the asymmetric cell). The 18th peak was later found to be very closely associatedand almost maskedby the highest peak. Table 3 gives the coordinates and relative heights of the peaks and identifies the correspondingatoms. The R factor using all reflectionswith the coordinates given in Table 3 wa"s27 percent. RBUNBITBNToF THE Srnucrune The structure was then refinedusing the atomic coordinatesobtained from the E map. The film data wereinitially used,and when the counter data becameavailable, the refinementwas carried out with this new set of data. The various stasesin the refinementare tabulated below. Film Data CounterData No. of reflections:1179 744 Weighting scheme:unit weight Prewitt and Burnham(1966) R factor,fo: 27 8.9 17.5 79 16.0 7.3 15.9 13.9 STRUCTURE OF' TAM ARUGITE 23 Tenla 3. PosrtroNer,PARAMETERS OgrerNno rRoM TrrEE MAp Peak height 0.640 0. 184 0.210 269 s(1) .7ro .016 . / .).) 25r s(2) . IJJ .145 .680 231 AI .620 .051 .190 IM Na .385 130 " 640 r22 Ow(3) .820 . ro/ .140 tt7 o(2) .730 .043 .560 lt7 o(6) .910 .151 .73s to7 Ow(4) .150 .104 .925 101 Ow(6) .530 .039 .800 99 o(7) .680 .2t7 .430 96 o(4) .840 .040 .910 95 o(8) .070 .095 .510 93 Ow(2) .515 .r4l .230 92 o(3) .220 .204 .840 9r Ow(s) .570 .228 .065 84 o(1) .120 .r94 .425 82 Ow(1) .290 .042 .245 (80) o(s) The scalefactors and the positional parameters were varied in the first 3 cycles (film data). In the last cycle, (film data) the individual tempera- ture factors were also varied. When the counter data were employed, the R factor was improved by nearly 5 percent. AII parameters were varied in the two cyclesusing the counter data. No hydrogen contributions were included. At this stage Fourier and difierence Fourier syntheseswere cal- culated with the signs given in the last cycle (counter data). The electron density map showed clearly rpsolved non-hydrogen peaks with correct relative heights. However, the positions of the hydrogen atoms were not apparent in the difference electron density map. Therefore the expected hydrogen positions were calculated by placing the hydrogen atoms 0.97 A away from Ow on the line Ow-O. Using the hydrogen positions thus ob- tained, another cycle of least-squaresrefinement was carried out in which all the positional parameters, including those of hydrogen, were varied. However, the shifts of some hydrogen atoms were so large as to give un- reasonableOw to H distances.At this stage, we returned to the Fourier method, and a difference map was recalculated using only those reflec- tions with sin 0/I(0.36, as there is very little or no hydrogen contribu- tion above this value. Again, the hydrogen positions could not be ascer- tained from the differencemap.