Amefican Mineralogist, Volume 59, pages lI05-III2, 1974
CrystalHabit of SyntheticGhalcanthite (Copper Sulfate Pentahydrate)as Relatedto Positionand Orientation in GrowthSolution
Eurn CnesnN, Departmentol Geologyand Geography,Hunter College ol The City Uniaersityof New York, New York, New York 10021
nNn C. W. WornE
D epartment ol Geology, Boston U niuersity, Boston, M sssachusetts02 2 I 5
Abstract
The habit of a crystal of CuSOn.5HrO can be controlled during growth under refrigeration by varying the depth of the crystal in the host solution, its crystallographic orientation during growth, and the maximum size to which it is allowed to grow. Crystals were grown in solution 30 mm deep. Those which were grown at the bottom of these solutions rarely produced the form' {100}; where that form did occur, it was little more than a line face. Seedswhich were set 18 mm up from the bottom yielded crystals with both {100} and {010} forms which were roughly equivalent in size. Those crystals which grew just below the surface irroduggd {l0O} forms but no {010} forms, the opposite of crystals which developed on the bottom. {111} was usually predominant among the terminal forms, but when crystals grew to sizes greater than 0.82 cm" in size, atthe 2 mm and 18 mm level of the solutions, {021} and {121} were almost as large as {ilt}. Crystals which were grown to intermediate size at all levels in the solutions developeda new form, {211}, when either the edge between (010) and (tZt), or that between (010) and (021) was set uppermost and parallel to the solution surface during growth. This new form generally was equal in size to the {121} form. The experimentation demonstrates that as crystals grow, the nuinber of forms diminish in favor of those forms with minimal summation of indices.
Introduction Experimental Method Wolfe (1960) has suggestedthat crystal habit is The refrigeration method of crystallization is based influencednot only by such factors as crystal struc- on the fact that most salt solutions which are satu- ture, impurities included during growth, and varia- rated at room temperatureswill be supersaturatedin tions in the nature of the growth medium,but alsoby a refrigerator. A crystal, e.9., seed,will neither grow crystallographic orientation during growth and by nor dissolveif placed in a solution which is saturated crystal ldbation in the growth medium. To test this for refrigerator conditions and capped to eliminate premise,crystals of CuSOr.5H2Owere grown rlnder evaporation. If drops from a room-temperature satu- refrigeration conditions, where positive controls on rated solution are introduced into the refrigerator orientationand locationin solutionscould be main- solution, precipitation will occur, preferably on any tained.Copper sulfatepentahydrate was chosehfor seed crystal already in the refrigerator solution. The the experimentationpartly becausecrystals of that seed crystal is usually placed on a small raised plat- compositioncan be grown so readily by the refrigera- form or pedestal in order to keep other seeds,which tion techniqueand partly becausethe experienceof might form nearby, from interfering with the perfec- Tutton (1922) as Well as our own had indicated tion of growth of the control seed crystal. The seed that variations in its crystal habit were frequent, crystal is thus being fed at such a rate that it can notable,and apparentlyalmost random. take on additional ions sufficiently slowly to develop a homogeneous crystal. In order to keep the crystal 'Form indices are referred to the conventional settine from growing in only one direction and frorn growing (Palache,Berman, and Frondel,1951). around the pedestal, the crystal was turned over each I 105 I 106 E, CHASEN, AND C. W, WOLFE
day on the pedestal to expose all surfaces to the 5. The b axis was oriented perpendicularto the precipitatingions in the solution. solution surface.
Preparationof Seeds Depth Placementof Seds In the researchdescribed herein, a stock solution To achieve the location at various depths small was prepared on the basis of the solubility curve of pedestalswere contrived. After disappointing trials CuSO+'5HzOin water. The most satisfactorysolu- with red universalwax, we finally settledupon plexi- tion proved to be 100 g of water and 16 g of the glass pedestals.This material is easily shaped, and salt; sucha solutionis unsaturatedat room tempera- slots of various sizes can be cut in it to keep the ture (26-27"C) but is supersaturatedin the re- crystalsin any chosenorientation as they are grow- frigerator(6-7"C). To obtain seeds,30 ml of stock ing. Pedestalheights were cut at2 mm, 18 mm, and solution in 150 ml beakers.covered with watch 28mm. glasses,were placed in the refrigerator.Before there was wholesaleprecipitation, the solutions were de- Growth Procedures cantedinto other beakerswhich had been sitting in the refrigerator. Crystallization proceededin these The saturated(at about 6.6'C) host solutionsin beakers, and another decanting took place after the refrigerator had a depth of 30 mm in 150 ml many seedshad formed. This processwas continued beakers.Seeds were placed on plexiglasspedestals at until the host solution came to equilibrium with re- the three depths in the five previously referred to frigerator conditions, and no more seedingor crystal orientations. Several crystals were grown for each growth wastaking place. of the fifteenconditions listed. Crystal growth was induced by introducing drops Orientationof Crystalson Pedestals of the room-temperaturesaturated solution with a In order to testthe hypothesisthat crystalhabit is medicinedropper three times a day. Care was taken dependentupon the orientation of the crystal during not to overfeedthe host solution becausethe crystals growth, seedswere selectedon the basis of freedom which developedunder too rapid feeding were ir- from flaws and on the degree of geometrical per- regular in form, rough, and included some of the fection. Many more crystals were measured than mother liquor. The faces on such crystals did not were subsequentlyused for growth seeds.Axono- yield good goniometric measurements.Too slow a metric projections (Wolfe, 1953) of the crystals feeding, on the other hand, produced impractically were made in order to have a rigorous picture of the slow growth. Consideration of these factors and starting habit of each crystal. Careful two circle observationof growth rates led to an optimum rate goniometricmeasurements of the phi and rho anglesz of f ml of sourcesolution per feeding. were made and recorded. and the indices for each The crystals were turned over on the pedestals face were determinedin the Dana setting (Palache, once a day to exposeall surfacesuniformly to the Berman,and Frondel, 1944). With thesedata avail- sourceof precipitating ions. Occasionally,additional able, it was possibleto orient the seedin the host seedsformed on the growing crystals, although this solution for growth in any preselectedorientation. effect was minimized by use of the pedestals.The The following orientations were finally adopted as randomly oriented and undesiredseeds were scraped the most usefuland readily obtained: off manually before becoming embeddedwhen the crystalswere being turned. l. The edge betweenfaces (100) and (ll0) was setuppermost and parallel to the surfaceof thesolution. Final Crystal Sizesand Habits 2. The edge betweenfaces (010) and (021) was setas above. It was not possible to maintain a steady rate of 3. The edge betweenfaces (010) and (i2l) was crystal growth. Therefore, the crystals were simply setas above. fed daily until they reachedthe desiredsize, at which 4. The c axis was oriented perpendicularto the time they were measured,drawn, and photographed. solution surface. The ultimate sizesselected were somewhatarbitrary, but they fell into three sizeranges. The starting seeds 'Azimuth and polar distanceof a face normal are called weighed between 0.2 and 0.8 g, with a maximum phi and ry'ro,respectively (Wolfe, 1941). volume of. 1.4 cm3. Crystalswere consideredlarse CRYSTAL HABIT RELATIVE TO POSITION AND ORIENTATION IN GROWTH SOLUTION IIOT for this work when they weighed between 3.4 and A crystal drawing was preparedfor each possible 4.4 g, with a maximumvolume of 2 cm3.The same combinationof variables.These were consolidated crystals at various stagesof growth and in various into a few drawings of representativehabits which orientationswere measuredon a two circle goniome- developedfor many crystals grown to a particular ter and checkedfor habit development. size, at a certain level, and with a particular orienta- A.total of 46 crystalswere grown on which con- tion. These composite drawings are representative trol measurementswere made. Three variables ex- of what could be expectedif the experimentwere to isted in the depth in the solution,five different orien- be duplicated. Small variatiolts from the general tations were used. and three different ultimate sizes habit, of course, are likely. Ten basic habits are were attained. These variables yield 45 possible shown in Figures 1 and 2. The orientation of all of combinations.Since the same crystals were used to the drawings, unless otherwise noted, is with the produce different sizes, fifteen crystals would have positive end of the c axis upward, the normal to face embracedall of the variables.Thus, the 46 crystals (010) to the right and the normal to face (100) which were grown and measuredshould be suffi- quasiperpendicularto the paper. The face symbols ciently great to prove of statisticalimportance. The employedon Figures I and 2 are those listed in the experimentsextended over a period of 12 months, angle table for chalcanthitein Palaehe,Berman, and although singlecrystals reached maximum growth in Frondel (1951), an abridgedform of which is given about three and a half weeks. here in Table 1 for convenienceof reference.
Frc. 1 Crystal drawings of Habits A-E. Habit A is oriented with to0il axis up, (0i0) to the right and ( 100) out from paper. All bar scalesrepresent 5 mm' I 108 E, CHASEN, AND C. W. WOLFE
\ T
11
I v.a H
1 I
t-l Frc. 2. Crystal drawings of Habits F-J. All bar scales represent 5 mm.
ResulS sized crystals at all levels in the solution when the (010) In addition to those forms listed in the Dana edge between(010) and (021) or that between and (i2l) was at the top of the crystal and oriented Systemangle table, one new form lZtt| is included here. This form occurred on all of our intermediate parallel to the surfaceof the solution. The new form was usually equal in size to ltztl (see Figure l, Tlsrp 1. Angle Table of Forms Obtained* habits C and D). All of the forms listed in the angle table were observedin this study. The ten distinctive Foms Letterslndlces 6 P A habits that wereobtained by varying seedorientation, depth in the solution, and size to which the crystals b 0r0 0'00 90'00 r00'54.5 85'45,5 a 100 100 54.5 90 00 100'54.5 73 46.5 grew are tabulated in Tables 2 arrd 3 and are shown 7 130** 33 54 90 00 57 01 33 54 76 49 i\ 120 47 08.5 90 00 47 08.5 74 22.5 in Figures I and 2. il 110 69 49 90 00 31 05.5 69 49 1t 11 major M 110 126 59 90 00 26 04.5 78 48.5 Tables 2 and 3 and the figuresreveal some k 011 25 45 35 5I 8L 22,5 58 10 of depth of im- t 02I t4 23 51 38 87 16,5 40 35 45 I0,5 variations in habits as functions q ofl 147 38 30 23 11517.5 mersion, orientation, and size to which the crystals r 02I 163 37.5 48 04 70 03.5 49 47.5 @ 111 -rL2 49 37 33 L20 27.5 103 40 were allowed to grow. Habits A, E, and H are those o r31 39 56.5 64 20.5 64 03,5 50 30 of small crystalshaving, respectively,eight, ten, and Jt JO 06 J).) 70 48 57 01.5 r33 26 6L 29 42 7L.5 127 LO 53 07 elevenforms. Habits C, D, and F are intermediate e tzr -r40 52.5 4a 26.5 IIO 43 t25 29 63 26,5 -153 52 58 07.5 102 53 139 40.5 10 28.5 sized crystals with nine, fifteen, and thirteen forms. 6 211*** -93 19 59 56 r47 05 87 08 77 5L crystals * chalcathite, C\SO4. 5820, is EticliDic. pinacoidai f. with a:b:c = Habits B, G, I, and J are for the largest 0.5715:1:0.5575; a= 97o44t, B = J.07o26','t=77020', po:2to:ro= grown in theseexperiments and have eight, nine, ten, 0.9907 : 0. 5452 : I ; | = 85045. 5' ; v = 76o46.5' s | - 70Oo54. 5' i Pot 1.04L3' qo'0.5730, xo'0.3f39, go'0.0778. ETerents fton Palache, EtMn, anil number of forms for FEondef (1944). and nine forms. The average ,r Indicates this forn not presenX on Figptes 7 ild 2 dte to lbor crystals less than one gram in size was just under quality ot rate occuttence. ten; for those crystals which were between 1.9 and CRYSTAL HABIT RELATIYE TO POSITION AND ORIENTATION IN GROWTH SOLUTION IIO9
3.2 gthe averagenumber of forms was twelve, while TesLB 2. Variations in Growth with Orientation, Depth in for crystalsbetween 3.4 and 4.4 g,the averagenumber Solution, and Size to Which Crystal Was Grown of forms was nine. These empirical results are in Hebtr klatlonshlD.* RelattoashtPsr Orlentatlm of DePth of Critt.l aFbol of frce 6lzea of face slzet cryalals oo cryatel 1[ llzc ln gr@ close agreementwith natural crystals of different tn rcne [0oll lor teElnel pedes!.lo lolutr.on mineral species.Very small crystals and very large tacee 30n deGP b>a large Edge (1Oo)- 2 6 .bove 0.2-0.8 crystals usually show few forms, but intermediate f>r>q (1I0) up end boltil paiallel to crystals usually have a multiplicity of forms. It is eolutlon aurface interestingto note that the new form {Ztt} occurred o'7-(, all Sue as for A 2 m .bove 3,4-4,4 'on r< tr sul-l but equl bott@ only thesecrystals of intermediatesize. 10 slze The dominant form among the forms is {l,k0l t and @ large Edte betvee! 2 @ abovc ,.9-t.2 usuallyM but the importanceof 100 and latg€r than (qlo) and _ bortoD [ii}l , [ ] , {010} , trb o Iatge sue a. for c 18 d above 1.9-3'2 doesnot occur on habits obtainedat 28 mm bott@ {010} I< ! t>qandt depth; {ll0} doesnot occuron habit A, and {120} f'8 o lalg€ s&e aB for A 18 d s$ovs 0.2-0.8 doesnot occur on habits B, G, and J. H mch Sreatar bottoo lhrn other z > q >k Among the terminal forms {ttt} is usually the {hkol s >b @ elmat equal + 9 rp 18 o cbovc 1.9-3.1 dominant form, although in habits B, C, and F, E position. was developed on I and Piwtes I ild 2' theoretical The form * Rltrn ad Grcek letterc aEe face sgtuols qiEn in nable crystals grown at all depths where the orientation during growth was with either the edge (010H021) or the edge(0l0Hi2l) up and parallel to the surface attitude which would encouragethe developmentof of the solution. The striking conformity between this form; or, perhaps, they were never examined observed and calculated angles and the frequency upon reachingthe intermediatesize. of this form is remarkable,since the form had never Discussion before been recognized.The best explanation for such lack of observation in the past must be that The appearanceof the new form is a strong argu- during previous experimentation the crystals of ment in favor of the conclusionthat habit is a func- synthetic chalcanthite were never positioned in the tion of crystal orientation, during growth, relative to Tasle 3. Habits Developed by Crystals with Different Orientations, Depths, and Sizes* Edee(100)-(u0) Edee (010)-(021) Edge (010)-(121) up and parallel up and parallel up and parallel c axlg: b axls to surface to surface to surface vErtlcal v6rtical Iteight in mm above botton 28E J JE DJD CCFFIIIII 18E JrE JD DCD DCFFIHHG 2A E BD ccD CCHFIHHI Welght in grams 0.2 1.9 3.4 0.2 1.9 3.4 0.2 L.9 3.4 0.2 1.9 3.4 o.2 1.9 3.4 3,2 4.4 0.8 3.2 4.4 0.8 3.2 4.4 0.8 3.2 4.4 0.8 3.2 4.4 0.8 x See Figures I and 2. 1110 E. CHASEN, AND C. W. WOLFE Tegre 4. Reciprocal Lattice Vectors of Chalcanthite Forms ing of planesin terms of their reciprocal lattice vec- tors. Reciprocal Reciprocal If importance of form, is directly Theoretlcel Lattice Theoretical Latt lce the a {hkl}, lnportance Vectors Inpor!atrce Iotn Vectors proportional to its interplanar spacing[usually indi- 1 010 I1 11t 1.3598 proportionalto 2 100 .9907 5l II2 2.5984 cated as d(hkl)1, it is inversely the 3 001 I.0000 Il2 8 110 L.2r79 2a 2.0318 length of the reciprocal lattice vector L*[hkl]. A test 4 1r0 1.0364 30 II2 2.0529 of the validity of this approachto the importanceof 17 120 1.6060 32 2.0722 l0 r20 2T r2l L.7759 forms in terms of size and frequency of occurrence 31 130 2.0663 12]. 1.5391 19 130 t.7444 l8 T2I L.6925 can well be madehere in this triclinic substance. 49 r40 2.5602 3.3178 We shall use as the three basic vectors in the 36 210 2.7523 212 3.t4!2 54 230 2.7978 ,r, 2.4002 reciprocal lattice the valuesfor pe, qs, and 16,which 5 0rl 1.1738 212 2.5013 5 011 t . r029 2.8300 are listed in Table 1. The three basic reciprocal lat- 13 o2r 48 t22 2,5585 72 021 t.4239 r22 2.2308 tice angles are ),,,st, v, also listed in Table 1. Since 34 0L2 2.III5 38 2.2693 29 012 2.O337 I3I 2.4628 the approachhere is morphological,it sufficesto use 27 031 r.9790 23 131 22 031 1.8528 r3t the reciprocal (polar) lattice constantsderived from 39 041 2,3308 r41 2.9036 goniometric measurements,rather than the X-ray 15 101 7,5922 50 2.5443 7 101 1.1949 2II 2.6115 structural ones. The generalformula for the square 44 20t- 2.4563 42 2rt 25 201 r.9542 24 21r L,9462 of the length of the reciprocal lattice vector for any 16 r02 33 2II 2.t082 26 LO2 r.9683 40 22r 2,3800 form {ftkl} is: 20 rll 53 2.7347 l' 5959 9 lll 1.2654 lL*(hkDl' : h'po' -f k'qo' -f l'ro" * 2qoroklcos tr * 2rspslhcos p * 2poqohkcosv. the major source of ions. One of the well known = observationsof crystal synthesis, which has been The fact that ro 1 simplifiesthe calculation. The strikingly confirmed in this work, is that as crystals values for the calculatedlattice vectors for various grow larger, small facesdisappear in favor of larger permutationsof indicesbetween O and 2 (with a few ones.As ions are depositedon any crystal face, that more complicatedones added) are given in Table 4. face is extendedfurther from the crystal center; and The computed theoretical importanceof each form, if the starting size is maintainedfor that face, it be- basedon the magnitudeof its reciprocal lattice vec- comes relatively smaller in comparison with the tor, is also given for the 58 forms listed. The im- other faceson which no ions precipitate.In practice, portanceof a form, from a geometricalpoint of view, continuedprecipitation of ions on small crystal faces should be inversely proportional to its reciprocal ultimately results in the disappearanceof the small lattice vector. face from the growing crystal. Small faces receive Table 5 indicatesthe observedimportance of the more ions becausethe energy of crystallizationcan forms which developedon the ten habits shown in be releasedmost readily on faces which approach a Figures 1 and 2. Under each of the habits (Habits point in dimensions;that is, small faces are better A-J columns,Table 5), the size irnportancefrom l, heat sinks than larger ones simply becauseof their geometry, and precipitation of ions on small faces Tenre 5. Size and Frequency Rating of Forms growsthem out of existence. The Law of Haiiy, which states,in effect,that the Inportance Ratlng Slze trequency Size Ratlng importance of a form is directly related to the sum RatinBFomABCDEFCH I J Ratlng Frequency Retlng of its indices,does not difierentiate betweenvarious b0t0 I 4 64 0.6 9.0 'possible aI00 5 - 1tt 1 0.8 2.8 forms with the samesum of indices.Bravais n100 - 2 22 4 0.8 4.0 M1l0 4 L ll L22 I 1.0 7.7 suggestedand G. Friedel demonstratedthat the im- I120 3 - 4l I0.0 portance of a form is directly related to its reticular q0.ll 6- -Il 6 9 9I0 6 0.8 10.1 k 0lr -13r011 -1110 7 0.6 L7.2 density (or its interplanarspacing). In the triclinic t02I 7 5 512 -10 4 6 9 6 7.9 7.O 702L - I 784Ea75a 0.9 system we do not have to be concernedwith the otll 2 3 35327 424 1.0 effectsof group et2L a 7 86-65919 0.9 8.0 space symmetrieson the spacingsof 9.0 olzL - 6 -10 913 - g 8 - 0.6 15.0 planes(Donnay 9.0 6 211 99-- 0,2 45.0 and Harker, 1937).In the triclinic 13.0 0 131 -14 -12 o.2 65.0 system,in particular, it is easierto considerthe spac- 15,0 s 141 - 15 - - 0.1 I50.0 CRYSTAL HABIT RELATIVE TO POSITION AND ORIENTATION IN GROWTH SOLUTION 1111 largest,to 15, smallest,is indicatedfor eachform in all are found within the first eighteen on the the- relationship to the other forms occurring on that oretical list. Since secondaryfaces usually develop particular habit. The size importance is simply an on the edgesbetween dominant faces, the absence arithmetical rating basedon the size of the form as of {001} as a primary form (third most expectable comparedwith the others on a particular habit. The form, theoretically) makes the lack of development largestface is rated 1, secondlargest 2, and so on. of {iOt } (seventhmost expectableform, theoretically) The column labelled Size Rating is determined by somewhatunderstandable. One of the factors which the summationof the sizeimportances for eachform is impossible to control in the experimentsis the in the varioushabits, divided by the number of habits rather fortuitous nature of the form developmentof on which the form appears.On this basis, the size the initial seed which was employed. If the seeds rating of the lowest magnituderepresents the largest could have formed in an isotropic environment in form occurringon the crystalswith habits that exhibit midsolution, rather than on the bottoms of the that form. TlheFrequency Rating simply indicatesthe beakers, a closer approximation to the theoretical ratio of the number of occurrencesof the form as importance of forms might have been obtained in seen on the ten habits. Thus, a form which is ob- practice. servedeight times out of ten habits has a frequency It is to be expectedthat the larger the crystals rating of 0.8. The Importance Rating of a form is grow, the closer would their form development inversely proportional to its Size Rating relative to approach the theoretical importance based on its Frequency Rating, as shown in the last column reciprocal lattice vectors, since the influence of the of Table 5. initial seed habit would be in part vitiated. From Table 6 gives the sequential importance rating Tables2 and3 we recognizethat habits B, G, I, and J of the forms noted on the various habits, with the were those of crystals which were grown to largest lowest importancerating (for {ll0}) from Table 5 size in these experiments.On these habits, not only set equal to one. These ratings are compared with is the number of faces relatively reduced,but there the expectedimportance based on reciprocal lattice is a somewhatbetter agreementbetween theoretical vectors,from Table 4. and observed importance of forms. The reduced No generalagreement exists. Of particular interest size or absenceof {010} is not expectable,however. is the omissionfrom the form list of {0011, the- The data, at present, do not warrant a more oretical importance 3, and IiOt ], theoreticalim- detailed analysis of the discrepanciesbetween ob- portance 7. Otherwise, it is rather impressivethat served and theoretical importance of forms; these of the forms which do occur among the fust twelve, discrepanciesprobably are attributable to crystal T,rsr-e 6. Comparison of Observed Importance Rating to Theoretical Reciprocal-Lattice-Vector Rating rsiportance natrng {nkr} Predlcted lmportance based on reciprocal vectors Importance Rathg {1To } Forn (Frcnn Table 4) 11 rTo 4 2 L.6 -r11100 2 3 2.L 11 4 2.4 L10 I 5 4.6 02L 13 6 4.7 gZ1 T2 7 4.8 LzL 18 8 5.3 010 1 9 5.7 011 5 10 5.9 120 L7 11 8.8 Tzt L4 L2 10.1 011 6 13 26 2LL 33 L4 38 131 45 15 88 141 56 rl12 E. CHASEN, AND C. W. WOLFE structural factors rather than to the simple morpho- Structural factors connectedwith bonding strengths logical approach.Donnay (19'72)suggested that in in differing directions in the lattice will control, in somecases it might be well to use a differentbasic large measure,the final habit attained.The extent to morphological cell from that of the structure.As an which habits vary from predicted developmentis a anonymous referee put it "The morphological direct indication of the deviation of the geometryof lattice (insteadof beingrecalculated as a new primitive a lattice from coincidencewith bonding strengthsin one) may be describedas the X-ray lattice centered differing directions. Other controls on habits, which on the C face. . . . the fact that the Cu atoms lie on were not consideredin this paper, would, of course, this C lattice, which is thus both the rigorousmorpho- be variables in the physical-chemicalenvironment, logical lattice and a pseudo-latticefor the structure" such aspH, foreign ions, and rate of feeding. producesa multiple cell which, if used for the cal- culation of reciprocal lattice vectors, would produce References even closer agreement between theoretical and DoNNAy, J. D. (1972) Acceptanceof the Roebling Medal actual importance of the various forms. In general, of the Mineralogical Society of America for 1971. Am. the external geometrycan be expectedto reveal the Mineral. 57, 620-625. internal relationships,and the presentwork indicates eNo D. Hrnxen (1937) A new law of crystal a specialstructural relationship which controls form morphology extending the law of Bravais. Am. Mineral. 22,446-467. development. P.rrecne, C., H. Bnnrr,reN,eNo C. FnoNuer (1944) System It should be mentionedthat the new form observed ol Mineralogy . Dana, 7th ed., John Wiley and Sons, in this study, {211}, is 33rd in expectabilityout of Inc., New York. Vol. l, p.9-15. the 58 forms listed in Table 4, which meansthat its (1951) System o'f Mineralogy Dana, 7th ed. actual occurrenceis consistent with its theoretical John Wiley and Sons, Inc., New York. Vol. 2, p. 4:88492. TulroN, (1922) probability. A.E. Crystallography and Practical Crystal Measurement.MacMillan and Co., Ltd., London. Vol. 1, Conclusionsand Implications p.282-298. Worrr, C. W. (1941) Crystallographic procedures. Am. Crystal habit is at least partially determined by Mineral. 26. 55-91. attitude of the seedduring growth and to proximity (1953) Manual for Geometical Crystallography. of source ions for growth. Habit, also in part, can Edwards Brothers, Inc., Ann Arbor. (1960) be predicted Crystal synthesis by refrigeration. Am Min- on the basisof latticeconsiderations; the eral. 45. 1211-1220. frequency and size of a form (form importance) is inverselyproportional to the reciprocallattice vectors Manuscript receiued,October 23, 1973; accepted implicit in the coordinatesindicated bv form indices, for publication,April 30, 1974.