MECHANISM

Topotoxy has been variously defined. Essentially it designates the mutual orientation of crystals of two different crystalline species, either difierent chemical compounds or pol;'rnorphic forms of one chemical composition, when this orientation is the result of a chemical or physical reaction. Phenomena of mutual orientation have long been studied from the crystallographic viewpoint more than from the paragenetic one

THE AMERICAN MINERAI, OGIST, VOL, 56, JANUARY-FEBRUARY, 1971 AMERICAN CRYSTALLOGRAPHIC ASSOCIATION Ottazaa Meeting, Augwst 20, 1970 SESSION ON MINERALOGICAL CRYSTALLOGRAPHY As announced in the Amer.M'inerol. 55, 1080 (1970) the summer meeting of the A.C.A. included a Special Session on Mineralogical Crystallography.Fifteen papers were given in a full-day session; abstracts are printed below.In a brief discussion at the end of the day the participants, who included the presidents of the A.C.A., M.A.C., and M.S.A., voted unanimously that the Session on Mineralogical Crystallography should be made a permanent feature of the A.C.A. summer meeting.A mineralogical field trip in the region north of Ottawa on Saturday, August 22nd, 1970, was conducted by Dr. D. D. Hogarth.TOPOTAXY J. D. H. DoNr.lv,The Johns Eopkins Unhersity, Bal.timore, Md.21218.
Topotoxy has been variously defined.Essentially it designates the mutual orientation of crystals of two different crystalline species, either difierent chemical compounds or pol;'rnorphic forms of one chemical composition, when this orientation is the result of a chemical or physical reaction.Phenomena of mutual orientation have long been studied from the crystallographic viewpoint more than from the paragenetic one, and their nomenclature stresses the different types of reticular control: tbree-dimensional in syntaxy (H.Ungemach) and two-dimensional in epitaxy (L.Royer);one-dimensional control is unknown.Twinning deals with related phenomena (Mallard) where the mutually oriented crystals belong to the same crystalline species (1.a., to the same form in case of polymorphism).Most twins obey three-dimensional control, whose degree of perfection forms the basis of their descriptive classification (G.Friedel); two-dimensional control has not been reported; one-dimensional control is known (in quartz, J. Drugman), but requires two preexisting faces.Topotactic reactions may lead to syntactic or epitactic intergrowths; such a reaction may go to completion or not (partial topotaxy).Pseudomorphosis, which is independent of mutual orientation, may be involved.Deciphering the crystal morphology of a pseudomorph while heeding crystal growth, in case of total topotaxy, is the only way of determining directly what the original species was.Skeletal growth may simulate twinning and lead to erroneous conclusions regarding topotactic pseudomorphs, as the speaker has Iearned to his dismay.The high-quartz phase of LiAISi:Oo composition reconstructively transforms into the keatite phase at elevated temperature.The transformation matrix was first derived from the powder data and then confirmed by the single crystal data.During the transformation, each independent high-quartz reflection transforms into one, two, or three corresponding independent keatite reflections, depending on the symmetry of each particular high-quartz reflection.(Si,Al)-tetrahedra form 6-and 8-membered rings in the high-quartz phase but form 5-, 7-, and S-membered rings in the keatite phase.All the 6-membered rings and haif of the S-membered rings transform into 5and 7-membered rings, or a combination of both types of rings of the keatite phase.The other half of the S-membered rings remain unchanged linkagewise throughout the transformation.Transformation starts when either one common edge of two neighboring 6-membered rings is broken or the trvo adjacent edges, one at each ring, of the particular common edge are broken.During the transformation, most atoms undergo no change in linkage and little change in position.For example, only two out of tu'elve (Si,Al) atoms per enlarged high-quartz cell are involved in the bond-breakage and only four out of forty-eight (Si,AD-O bonds are broken.The two (Si,AI) atoms which break away from the old framework both undergo a dispiacement ol 2.6 |t, while the displacements of the remaining ten (Si,Al) atoms range only from 0.01 to 0.35 A. This study of the transformation mechanism makes it possible to follow the movement of each atom during the transformation.To the writer's knowledge, this is the first time that a phase transformation is studied in such a great detail.Four sets of data have been analyzed for these three nearly isostructural cyrstals.lThe space group is R 3c, Z :7 ,withlattice parameters of o : 14.09, 14.12, 13.67 A, and a :45.95',M.95", 44.35" for Ca3(AsOa)2, Cas(VOa)2, and the mineral respectively.The unit-cell contents are formulated as CarsM:B(XOn)u with the M ions, Mg for the mineral, Iying on the three-fold axis and B a disordered Ca in the former two structures and2H, according to Keppler, in the mineral.Small difierences in the mineral structure are probably related to the fI position.These structures are related to that of Bas(POa)z and the changes arise from the shorter cation oxygen bond lengths in the calcium salts.The reaction of stannous fluoride with hydroxyapatite is of interest in determining the mechanism by which stannous-fluoride-containing toothpastes are useful in the prevention of cavities.This reaction, in ti,tro, yields a crystalline product, containing Sn, with a rhombohedral unit cell with a:7.030A, a:115' 23'.Equi-inclination Weissenberg data l The difiractometer data for Car(VOu)z were provided by Mr. J. Rowland ilnd Dr. E.

Gabe.
were collected, with CuKa radiation, with the axis of rotation parallel to the 3-fold a-xis.A total of 160 reflections were observed.Identification of this compound was achieved by means of a complete structure determination.
A three-dimensional Patterson map showed the location of the tin atoms.With the heavy atoms located, difference electron-density maps were used to indicate the presence and location of a phosphate ion and three fluoride ions.The structure was refined by least squares to a value of R of 7.6 percent.The stoichiometry was identified to be SnaPOeFs.The space group is acentric, R3 and the calculated density is 4.49 g cm-a.
The phosphate ions are aligned along the 3-fold axis.Each Sn atom has three nearest neighbors (one O and two F) at an average distance of 2 15 A, arranged in a trigonalpyramid.This geometry is similar to that observed in compounds containing the SnCl3-group.The crystal structure of apophyllite, (Nao.roKo.so)Car(SLOro):F.8H:O, with a:8.963(2) , c:15.804(2)4,P4fmnc, Z-_2hasbeen refined by least-squares (R:.05a) with 546 independendent intensities collected with a difiractometer.
Apophyllite is a sheet structure with the bridging Si-O bond lengths 1.619(4), 1.626(4) , and 1.630(4) A, while the non-bridging bond length Si-O(3) is 1.589(4) A. The two independent Si-O-Si angles are 139.9(2)and 140.6(2) degrees.The mean Si-O bond length is 1.616 A. The interpretation of the role of the water in the structure is based on the charge balance approach of Donnay and Allmann (1970).Assuming that the fluorine ion is bonded to calcium, the sum of the cation valences for O(2) and O(3) would be 1.96 and 1.66 v.u.respectively.The water oxygeq therefore would be hydrogen bonded to O(3) and O(2).The oxygen-oxygen distances are 2.75 and 3.17 The crystal structure of apophyllite, KCa+(SLOro)zIr.8HrO,was refined by X-ray diifraction by Colville and Anderson (above).On the basis of the positions of all of the atoms heavier than hydrogen, and using the valence-summation technique of Donnay and Allmann (1970), they have proposed positions for the hydrogen atoms.A further refinement of the structure by neutron diffraction has been carried out.A least-squares refinement, using 671 independent reflections and anisotropic temperature factors, led to an R index of .046.The structure contained a water molecule with a reasonable configuration hydrogenbonded to the silicate framework.Ilowever, a difierence Fourier revealed a region of significant negative scattering density in the vicinity of the fluorine atom.A model in which 1/8 of the water molecules were replaced by OH-ions, with the remaining proton attached to fluorine to form an HF molecule, was therefore tried, and the structure quickly refined down to an R index of .037.This result suggests that the double peaks in DTA and TGA curves may be erplained by the evolution of water and HF at different temperatures.The structural formula should therefore be written KCar(SLOro)z.HF(7HrO.OH).
Carletonite, a new mineral from Mt.St. Hilaire, is tetragonal with a:13.178A (3), c:16.695(4), space group P4/mbm, Z:8, D":2.426,D-:2.45 (l).1220 s],'rnmetry non-equivalent reflections were measured on a Supper manual single crystal diftractometer, using MoKa radiation.A cleavage fragment in the shape of a cube (0.08 mm) was used.The structure was solved by three-dimensional Patterson synthesis and refined by full matrix least squares method.Occupancy factors for the cations are also included as least squares variables.The final agreement index R is 0.050.
In carletonite the SiO+ tetrahedra share three of their Iour oxygen atoms to form sheets consisting of 4 and 8-membered rings, similar to the sheeets in apophyllite.However, the structure of carletonite is unique in that pairs of such sheets are cross-Iinked by half of the oxygen atoms not shared in the single sheets, forming "double sheets" of the composition SieOrs.Thus half of the SiOr tetrahedra share all four oxygen atoms and the other half share only three.K, Na, Ca atoms arld the COs groups are sandwiched between the "double sheets".The ideal composition of carletonite is estabiished as KNarCarSisOrs (COB)4(OH,F).HzO in contrast to that calculated from the analytical data, (K,Na,Ca)s SiOre(CO:,OH,F)u.HrO.The mineral is non-stoichiometric, being deficient in Na (-13 atomicf) , Ca (-6.57; ,K (-13%) , COz (-gok) and (OH,F) (-30%) .The least squares occupancy factors agree with the analytical values within 5/6.
The Pn3n cellhas been refined to R:0.16 with Ga in 8(c) and OH in 24(h) (r:0.0877) .The isotropic B of the oxygen, however, diverges to very large values and the shortest O-O bond approaches 1.55 A. A similar situation pertains in the centric orthorhombic derivative of this cell (Pmnm).
The correct space group is Pm.n2t with an almost centric arrangement of Ga in 4(b) general positions, very slightly displaced about ], ], t, and |, |, i.The oxygen atoms form distorted octahedra about the gallium, which octahedra share corners to form an infinite framework.Two of the oxygen atoms lie near z:0, |, the other four atoms forming a rough plane centered on s :0.30.The present R index is 0.09 for 2 13 observed planes.Spherulites (up to 2mm in diameter) and single crystals of CaWOr have been synthesized at ambient conditions by reacting CaClz.2HzO and NaWOr.2HzO within acetic acid-NazSiOa.9HzOgels.High calcium concentrations favored the growth of clear spherulites, r,vhereas high tungstate concentrations resulted in almost opaque spherulites.The clear, highly translucent spherulites consisted of radiating single crystals.On the other hand, the nearly opaque CaWO4 spherulites seemed to have formed by both radiating single crystals (in the inner part), and concentric banding or an agglomeration process in the outer half.After withdrawal from the gel, most of the spherulites developed crack patterns which, in general, divided the spherulites into halves or quarters.The addition of NI{rCl to the gel system led to the formation of single crystal needles (up to 2mm in length) of CaWO4.
Lavender-colored rhombic plates ({001}, {ZtO}, {101} forms), dendrites, and spherulites of Ndz (COa)a ' SHzO were also synthesized in a silica gel by reacting NdCls.6HzO with NasCOr.Utilizing low pH HCI-NazSiOe.9HrOgels the crystals formed by recrystallization from an initial precipitate (perhaps Ndz(COr)r'Na:COs.nHzO) or at gel-gel and gelbubble interfaces.Single crystal X-ray diffraction studies demonstrated that the crystals are orthorhombic with o:8.88 it,b:9.+3A, and c:16.8S A. f]ne diffraction symbol mmmPecn uniquely determines the space group as Pccn.These data are consistent with those determined for Laz(CO:)a.8H:Oby Shinn and Eick (Inorg. Chem.,7, 1340).Observation of the crystals with a petrographic microscope revealed that they consist of a domain structure and a resulting strain birefringence.Difierential thermal analysis on the material showed that six waters of hydration are lost beginning at77'C and the last two beginning at 121'C; infrared and visible absorption spectrawere also obtained frorn selected single crystals and compare favorably with the spectra for other neody'rnium and carbonate compounds.
The structural parameters of buergerite (ideally NaFeaBrAloSisOroF) have been refined, using three-dimensional single-crystal neutron difiraction data.The occupancy factors in the cation sites have been refined and provide confirmation of the substitution of Fe for AI in the 18c sites of space group R3zr.Because of the differences in scattering amplitudes, somti of the bond distances have been determined to slightly higher precision than in the X-ray study (Barton, in press)2 In general the position and thermal parameters agree extraordinarily well with those of the X-ray study.The most significant result was the location of a partial hydrogen atom from a difference map; the occupancy factor of 0.083( 11 with Z:3, D,:3.07 g.cm-3.Of 1600 independent reflections measured, ll42 were significantly above background; the residual R for the observed reflections is 0.058.Eibaite is a species of tourmaline of ideal composition Na(Li,AIh BeAleSioO:z(OH,F)r.This investigation was conducted because an earlier study of elbaite (Ito and Sadanaga, 1951) is now thought to have been performed on a tourmaline of dravite-schorl composition, and a detailed knowledge of the structure of elbaite might explain why no solid solution occurs between eibaite and dravite.The results of the refinement show that the atomic coordinates of elbaite are very similar to those of dravite (Buerger, Burnham, and Peacor, 1962) and also to those of buergerite (Barton, 1969), so much so that no explanation of the lack of solid solution presents itself Tourmaiines free from iron and manganese can only be paramagnetic, whereas those tourmalines containing magnetic ions can be expected to show evidence of magnetic exchange interactions.Magnetic susceptibilities of three iron-rich tourmaline crystals of different, known, chemical compositions have been studied from 8' to 300'K.
'fhese are specimens on which careful checking showed the absence of ferromagnetic inclusions.One sample studied is a ferric-oxytourmaline or buergerite (Barton 1969), which may be described from a magnetic viewpoint as having isolated triangles with Fe3+ ions at the corners.Its exchange constant I/h:7.5'K may be derived from the measured susceptibility data.The susceptibility measurements are also consistent with the X-ray and spectral evidence that, in spite of the presence of just enough aluminum to fill the Al position, a small fraction (-Sok) of Fe3+ ions are substituting for aluminum.From the other two tourmaline samples, an iron-rich, aluminum-deficient specimen from Madagascar, and a magnesium-iron specimen from Pierpont, N.Y., it is possible to estimate the exchange interactions between the iron atoms substituting for aluminum atoms.Our results are again consistent with the optical spectral evidence that there is considerable deviation from octahedral s1'mmetry at both the 9(b) and 18(c) positions of space group R3m' The distortion is most pronounced for the general position.
. lvsn, Department oJ Energy, Mines and, Res our ces, Ottaw a, C anada.Electron micrographs are presented which are interpreted as evidence of the surface decomposition of Al:Ni to AINi during electropolishing of directionally solidified Al-AlsNi eutectic alloys.This efiect occurs for a wide range of polishing conditions.Lt, Owens-Ill,inois TechnicaL Center, Toled.o,Ohi,o.
CRYSTAL STRUCTURES OF Ca:(AsOo)2, Cae(VOD, AND WHITLOCKITE.C. C,c.Lvo aNo R. Goe,lr,, Institutefor Material,s Researclt M c M a s t er U nil er si'ty, H ami'l ton, O ntar'i.o. 7l A,b:3.67A, c:632L) o:9Q"2', 9:92"35', z:90'51'; cell triclinic, CI, a:140.37L, b:3.67 it, c:37 .92A, a: B:pQo, r:90'51'; layers SnS2 are ofiset again by -1.1 A, ofiset parts have the same length as in A. Step regions accommodate Sb and Fe atoms.Many difierentpairs of Iattices, such as the F1 and C1 triclinic ones given above, are observed for,4 and B. Step regions face each other and have opposite formal charges.Several cylindrite subtypes with difierent Sb contents in the step regions exist, with Sb-content increments equal in the two iayers.The relative position of the two sets of layers in the cylinder-axis direction, perpendicular to the steps, is fixed.Cylindrical growth is caused by the flexibility of bond adjustments on interlayer boundaries along the step direction, the b axis, which is tangent to the cylinder.The o dimension is related to the thickness of one cylindrite growth layer.Cylindrical growth starts from a minute straight-Iayered nucleus.Central parts of cylinders have complicated structures showing a series of nuclei.Phases departing from the cylindrite A: B ratio are not cylindrical and vary in composition.ORDERING OF CATIONS IN OLIVINE.' L. W. Frxcen, Geophysical Loboratory, Carnegie Institut'ion of W ashi.ngton, W ashington, D.C. 20008.The crystal structures of olivines from rock 10020 of the Apollo 11 Iunar sample and a volcanic rock from Australia have been refined to determine if there is any cation ordering in the two octahedral positions.After intensity collection, the crystals were analyzed on the electron microprobe and the octahedral occupancies were constrained according to this chemistry.The refinement converged satisfactorily with the conventional R equal to 4.$ I Research partially sponsored by NRC through Prof .A. J. Frueh. 2 This research was partially supported by N,A.S,A.eqnlract NAS 9-9988, and 2.6 percent for the lunar and terrestrial samples respectively.The refined values of the occupancies indicate partial ordering of iron into,41l despite the smaller size of this octahedron.The efiect is consistent and more pronounced in the terrestrial sample which probably has a slower cooling history and a lower temperature of equilibration than the lunar sample REFINEMENT OF THE CRYSTAL STRUCTURE OF APOPHYLLITE Ar,erv A. Cot-vtr-m, ColiJornia State Col.lege at Los Angdes, CaliJorni,a arn Cuenr,ns P. ANounsow, Unhtersity of Cdi,fornia at Rirersid.e,Riters i.d.e, Cdi.fornia.
A respectively and the final sum of the cation valences reaching O(2) and O(3) would be 2.03 and 1.93 v.u.Preliminary results from a neutron-diffraction study by E. Prince indicate that the fluorine may be bonded to an H+ ion.This would eliminate fluorine from the calcium polyhedron and lead to a formula of KCa+(SLOro)z HI-(OH) .THzO for apophyllite.THE HYDROGEN POSITIONS IN APOPHYLLITE E. PnrNce, Center for Radiati,on Reseorch, National, Btweaw oJ Standards, W ashington, D.C. 20234.
CRYSTAL GROWTH OF CaWOr AND Ndr(CO3):'8H,O BY SILICA GEL TECHNIQUE J. W. McCeur.rv,.Lltn I{.M. Gnnnnlnor, Army Material's and.M ec kanic s Re s ear e k C ent er, W al er t own, M o s s ac hus etts 0 2 17 2.
) implies a substitution of OH for O eight percent of the time in one of the oxygen sites (O(3)) which surround the iron atom octahedrally.3This amounts to 0.75 H atoms per unit cell.A weak hydrogen bond with O-H 0.94(5), H... O 2.46(5) andlO-H... O 154'(2) is formed.The final R(F'?) is 0.034 for 391 independent reflections; the maximum error in the final difference synthesis is 0.4 f A-3, about one percent of the maximum peak height in the observed scattering Censity map; the bond lengths are in general precise to 0.002 A. A comparison of powder diffraction patterns at 300' K and,4.2oK provides no evidence for magnetic ordering or other structural changes between these temperatures.Research Laboratory, Erperimental, Stali.on,E, I. d,u Pont de Nernours anil Co., W'ilmington, Delaua,re, ozd G. DoNNau, Geopkysical Lab or ator y, 280 1 U pton S tr eet, N .W ., W as hin gtron, D. C. The crystal structure of eibaite has been refined by least-squares by use of single crystal X-ray intensity data collected by counter difiractometry.Elbaite crystallizes in I Research performed under the auspices of the U. S. Atomic Energy Commission. 2 Barton, R. (1969) Refinement of the crystal structure of buergerite and the absolute orientation of tourmalines.Acta Cryst.825,1524-1533. 3 OH substitution in this site was predicted by G, f)onnay (private sommunication) on the basis of charge-balance considerations, R3m; the hexagonal cell dimensions for the specimen used ate: o:15.838(1), e :7.1032(2) A' ar 21"C.D-:3.05(1); TsrNc AND ARTEuR N. Tnonra, Howard (Inhersity, Washington, D' C.; Fnall E. SnNrrr-r:, LI. S. Geological Suraey, Washington, D. C.; Gennrar,lE DoNNAY, Geophysi,cal Loboratory, Carneg'ie Instituti'on oJ Washington, Waslington, D. C.