T h e first atteinpt to poiiit out :uid treat tlie factor5 u.1iicIi determine what n-e kiion. as crJ-stal lialiit 1 I'. e . , tlie relati\-e size aiid frequeiic!. of occiirreiice of the ixrioiis faces wliicli are possible 011 any giJ.eii cr!-stal) seeiiis to lia1.e 1)eeii iiiade h!. Gihlis' i r i that reiiiarl~ahlecoiitriljutioii \rhicli lins served a5 tlie startiiig poiiit for so inucli of oiir present pli!.sical clieiiiistr!.. He there de\.oloped tlie fiiiidaiiieiital ecjiiatioiis f o r tlie eyiiilibriiim of a crystal i i i its saturated soliitioii iiicliidiiig tlie terms due to surface teiisioii of the differeiit inceb, aiid poiiits out that for coiiiplete eciuilihriiiiii Z(v.v) iiiiist 1ia1.e its i i i i i i i i i i i i i i i value : S. being tlie total area of all the faces of a :,.i\-eii s b f o r i i i , " rr tlie surface teiisioii for tliat forill i i i coiitact \vitli saturated solution, aiid the sumination liein:,. extended to iiiclutle all tlie possible foriiis Tvliicli ilia!. appear oii tlie cr!.stal. T h i s is tlie direct aiialogue of the principle that a drop of liquid teiids t o reduce its surface to n iiiiiiiiiiuiii and liecoiiie a qiliere. I'racticall!, the saiiie idea was later put forlvard iiidepeiideiitl!. aiid n-ithout kiiowledge of Gihbs' work 1 ) ~ . Curie' and has found its \ray the ii ce i ii to t li e ge ii era 1 c r >,st a 11ogra p 1i i c I i t era t 11re, \vli i 1 e t li e iiiore coiiiplete theoretical treatiiieiit of Gililis seeiiis to have aliiiost wholly escaped recognition. .kcording to this 1-ien of crystalliiie habit those face5 n h i c h are developed 11). the crystal in greatest esteiit should have, in coiitact with the solutioii, the loivest snrface teiisioii. 111 q r e e irieiit n.ith this are ail interesting set of iiieasiii-eiiieiits 11). Berent" on sodium a i d potassiiuii chlorides tlioiigli liis inethod as lie points oiit does iiot furnish a real proof. ~~
J . I V . Gibbs : T r a n s . C o n n . Xcad., 101. 3 , 4S9 e t 8.i .l})ril, iS:S , 1'. C u r i e : Bull. S o c . JIiii., 8, I J j ( rSSg). .\list. i i i Zeit. KrTst , 12, 6jr. i S. B e r e n t : Zeit. K r y s t . , 26, j 2 9 (1395 I . See also A. R o t a , Relid. A C C . Lincei (j),7, 12j-129 ( iSgS , , a n d 13:ibl., 23, r j : . ir-ho \vorke(l w i t h alurii. .A, P o c k e l s , Naturwiss. Kurrtisch.. 14, 3'3; ( 1 S 9 j I , an11 I k i l ) ! , , 24, 1 3 , Ilas. h o w e v e r , called tlie results of lmth autliors into q u e s t i ~ ~ i i . I
T h a t this tendency for the decrease of total surface energy must teiid to establish the particular cr!.stal habit predicted by the equations of Gibbs aiid Curie when a crystal is left qtiietly in its saturated solution seeins incontestable. Beyond this, howecer, certain qiiestions arise, ;siz.: ( I ) Tlirougli what channels a n t b!. what inecliaiiisiii woulcl the necessary traiisfer of material he lirought alioiit? ( 2 ) H o w long \vould this take? (3) During tlit. growth of tlie cr!.stal (a dynainic process) n-ould these conditions (derived froni coiisideratioii of a s!.steiii almost i n equilibrium) still lie the deterinining factors ? -As to question (\I1) iiiider isotlierinal conditions the onl!. \va!’ open to transfer of material from one face to another seems through an actual difference ill solubilit!, on the two faces ill question and a stead!. diffusion which may he aided by artificial convection. T h a t surface-tension can actuallj- cliange the solubilitj. of a solid to a I-er). appreciable extent lias been coiiclusiI-elJ-slion-11 11~.the work of Hulett’ and others 011 fiiie powders; but it has lieen likewise deliionstrated that this effect ceases to be appreciable to oiir methods of measurenient long before tlie bodies reach aii!.tliing like tlie diiiieiisions wliicli m-e usiiall!. have to deal with iii the cr!.stals whose habit is iinder discussion. This point i\-as cleai-l!, recogiiized b!. Gihbs and discussed by liiiii. Thus referring to the equation (666) of his origiiial text \Yliicli gil-es for eqiiilibriuai the ratio of the areas of different faces in terms of their surface-tension and angles of intersection, lie sa!.s, “ T h i s coiiditioii will not be affected 11~7 :1 change in the size of a cr!-stal n-hile its proportions reiiiain the same. But tlie teiideiicies of similar cr;jstals towards the form required b!. this coiiditioii as ineasiired b y the inequalities in coiiiposition or the temperature of the surrounding fluid \vliicli n-ould coiinterbalaiice them will be iiiI-ersel!, as the linear diiiieiisions of the crJ-stals as appears froiii the preceding equation. ’‘ In order to tliron. soine light 011 question ( 2 ) as regards eve11 fairl:. siiiall cr!.stals, the follon-ing esperiineiit was carried out, soine three >.ears ago, i u t h e PliL-sical Clieniistr!- Institiite at I
G. A . Hulett : Zeit. phys. Cliem., 37, j8j i 1901:.
L e i p i c . -1glass rod clra\vii out to a point and hearing a t its apex, ceiiieiited with was, a iiiiiiute fragiiieiit of sodium chloride \vas iiitro:luced into a saturated solution of t h e saiiie salt plus something over I O perceiit of urea, the whole v a s placed i n a large tlieriiiostat at 25' C.(l-nriatioii seldoiii esceediiig 0.01 O C.) aiid allo\ved to iiudergo .;pontaiieous evaporation until a crj-stal of soiiie 2 to 3 millimeters across was developed 011 t h e eiici of the rod. I\Ieann-hile, a saturated soliitioii of the saiiie salt without the urea lint1 beeii pi-epared, a sinal1 test-tube filled with it aiicl a few uiidisolI-ed crL-stals added, tlie xyliole tightly stoppered and placed iipoii one of tlie rotating ase.5 below the surface of the water i n tlie thermostat aiid left there a couple of claj-s to ensure saturation at that teiiipcrature. T h e rod aiid crj-ita1 ivere iioiv reiiioi-ed fi-oiii tlie urea solution riiised with a little of the piire saturated sodium chloride solutioii aiid the free elid of the rod fastened into tile rubber stopper of the tube of piire solution, so tliat tlie crJ-stnl \vas held at about the center of tile t u b e . fen- loose crystals of piire salt aiid an air bubble wei-e left in the tiilie which facilitated stirring aiid tlie whole. after sealing with \ m x 3 ivas returiied to the rotating axis aiid reiiiaiiiecl therc, iiiakiiig aboiit fi\-e revolutions per iiiiiiute for oT-er t\vo months. TT71ieii taken from tlie solution with urea tlie salt cr?.stal was a perfect octalieclroii (as is al~vaj-sobtained froiii such soliitioiis). I t ~ v x sesaiiiiiied tlie next d a y (without reiiioT-a1 froiii tlie tube) and 1))- the aid of a hatiti leiis a barely perceptible truncation of the octahedroii corners li?. cubic faces conld be detected. This m a y liave been produced l ~ ? .solution aiid recrj-stallizatioii as a whole, due to fluctuntion of temperature atteiidaiit upon its transfer from oiie solutioii to tlie other. or it iiiay have been due to the causes disciissed b!. Gibbs aiid Curie. The fact that although tlie truiication n-as 1-ei-J.slight, still decided cliff ereiices co!ilcl lie obser\.ed betweeii the different corners leads me to favor tlie foriiier of tliese esplaiiatioiis, as, if it were due to tlie secoiid c a m e , vie sliould expect greater uniformity. During the reiiiaiiider of the two iiioiitlis and more that the cq-stal was under obseri-atioii n o further growth of tliese faces could be detected.
0 I I 01 1 st[z//i?i t’ H o b it
55
This experiment together nitli the fact that froiii pure water solution it is aliiiost impossible to crystallize an octahedron face on a sodiuiii chloride crj-stal, make it apparent how verj. slight the difference in solubilit!. on the two faces must be even under the most favorable conditions, such as the above. Hulettl has recently reported siiiiilar conditions i n the case of g j p u i n Finall\- in regard to question (3) : T h e magnitude of the effect of this difference in solubility at the different faces upon their rate of growth. If a crystal is to grow in solution the coiiceiitratioii of the iiiass of the latter must be maintained slightl?. above the saturatioii point while the layers in contact with the crystal will be kept dowii nearly or quite to this point. Material is thus transported to tlie cr!.stal by the process of diffusion a n d ? if other conditions are eqiial, the rate of its growth will be determined by the rate of the diffusion. For our present qnalitative purpose, with crystals of iiioderate size, we may coiisider diffusion as essentiall!. linear and iiorinal to each crj.sta1 face. Its rate will then be proportional to the degree of siipersaturatioii of the bulk of the solution referred to the particiilar solid face. If this degree of supersaturation is of the same order of magnitiide as the differences betvieell the saturation coiiceiitratioii for solution at tlie different faces, then this latter difference n o u l d tindoubtedl!- be ail important factor in determining the rate of deposit and coiisequentl!- the habit. TTere this the case, however, the rate of growtli of a cr!.stal xvould lie of the same order of magnitude as the rate of change from one face to tlie other in the experiiiient on sodium chloride cited abox-e, for the processes would be stricti!. analogous. T h e inore rapidl!. the crj.stals are grown, 11 E . , the greater the degree of supersaturation of the solution, the less pronounced would be the differelice in the diffusion to the different faces and the iiiore nearly ~vouldall possible faces develop to the saine extent. Froiii this standpoint, a moment’s consideration of the exceedingly slon- rate of transformation indicated by the above experiment, will I think convince one that at the rate n.e
’ G . A . Hulett : Jour. Ani. Cherii. SOC., 2 7 , 53 , 1905
I.
j6
F.G. Colt1-cZl
orclinai-ily crJ-stallize substances in tlie lahoratory, even when n-e are seeking t!.picall!- dei.eloped ci-!.stals, for measurement, tliis factor can have little or 110 practical significance. This forces u11oii 11s the conclusion tliat the practical explauation for ci-!.st:il habit iiiust iiot be sought for in any of tlie ternis of the ecliiatioiis siiiipl!- defiiiiiix conditions of qz/il'ihrii/ui of the cr!.stal aiid its ,saturated soliltion, but 011 tlie contrary must be sought in tei-ins (1efiiiiiiE the r n f r ( f C q r o x ~ fof / i the various faccs n-liicli disappear entirelJ- in the filial equations of ec~iiilibriiiiii. TTyorl;ers in this field haye lieen far too hasty in applj.iiig tlie eqiiations of statics to d!-nainic nieasurements. -1paper liy Sclienck' 011 dyiiainics of cr!-stals is a good example of tliis. I t \\.as in the liope of lxiiig able to analJ-ze these \.elocity teriiis and reacli sonic at least of tlieiii 1.! iiidependeiit esperiiiieiit tliat tlie foregoiiix 1ia.s 11eeii ~ritlilieldtiiitil iiow : but dtliougli coiisidernble tiiiie :uid effort has lieen expended, no satisfactor!. iiietliod of attack has been found. \Ye ilia!., of course, consider tlie pi-ocesses at tlie surface of aiicl in the solid phase (i.c,, arrangement of cr!-stal elemelits) as distinct from those in the licliiid pliase (stippl!. of material by diffusioii if from a soliitioii 01clissipatioii of lieat if froiii fusion). Tlie fact tliat crystals separated lj!. cooliiig of a pure melt show a distinct habit, points strongly to the fii-st t!.pe as a responsible factor, \vliile tlic cliang-e of lialit oil atltlitioii of a substatice to the solutioii as in the alxn-e espcriiiients iiiakes it probable tliat the secoiid t!-pe of process must also lie included in an!. general explaiiatioii of cr!.st:il lialiit. 111 concliision, it should be noted tliat t h e forces underl!.iiig processes of the first type have been treated theoretically from oiie staiidpoiiit a t least ljj- Sohncke' aiid tlie receiit \\-ark of Seriist aiid IIruiiner" 011 reaction velocit>- in lieterogeiious sj.steiiis lias enipliasized the utility of clearly separatiiig these tn-o tj-pes of process. 1
I
