Metastable Structures in Alloys Rapidly Cooled from the Melt Citation Klement, William, Jr. (1962) Metastable Structures in Alloys Rapidly Cooled from the Melt. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HHG6-AY94. https://resolver.caltech.edu/CaltechTHESIS:08192011-104507587 Abstract Small amounts of liquid alloys are cooled to the solid state very rapidly by means of a technique which is described in detail. Procedures for studying the resultant thin, irregular foils are discussed; most of the results are obtained from x-ray diffraction experiments. Among the nonequilibrium structures found in various alloys are cited the metastable solid solutions in silver-copper and gallium antimonide-germanium alloys, the extended primary solid solutions in some silver-base alloys, and the metastable hexagonal close-packed structures in silver-germanium alloys. The quenching technique is discussed and tentative criteria for the prediction and rationalization of certain metastable structures in alloy systems are inferred from an analysis of the process. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Engineering Science) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Duwez, Pol E. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1962 Record Number: CaltechTHESIS:08192011-104507587 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08192011-104507587 DOI: 10.7907/HHG6-AY94 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 6605 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 19 Aug 2011 20:32 Last Modified: 21 Dec 2023 19:24 Thesis Files Preview PDF - Final Version See Usage Policy. 19MB Repository Staff Only: item control page

J.!EI'ASTABLE STRUCTURES IN ALLOYS RAP IDLY COOLED FROM THE MELT Thesis by William Klement Jr. In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy Californ ia Institute of Technology Pasadena , Calif ornia 1962 Professor P. E. Duwez conce1ved much of the techn1que here1n developed, suggested several exper1ments and superv1sed the research. R. H. W111ens contr1buted many valuable suggest10ns concerning the exper1ments and des1gned the low temperature camera. Professor F. S. Buff1ngton carefully read the manuscr1pt . H.-L. Luo ass1sted w1th much of the work . Also con- tr1but1ng to the exper1ments were A. Abu-Shumays, C.-C . Chao, R. Curt1s, M. Malcolm, W. L. Shanks and F. Youngk1n . Fellowsh1ps from the Nat10nal Sc1ence Foundat1on were held dur1ng the academ1c years 1960-1 and 1961-2. Small amounts of 11quld alloys are cooled to the solld state very rapldly by means of a technlque whlch ls descrlbed ln detal1. Procedures for studylng the resultant thln, lrregular folls are dlscussed; most of the results are obtalned from x-ray dlffractlon experlments. Among the non- equl1lbrlum structures found in varlous alloys are clted the metastable solld solutlons ln slIver-copper and gal11um antlmonlde-germanlum alloys, the extended primary solld solutlons ln some slIver-base alloys, and the metastable hexagonal close-packed structures ln sllver-germanlum alloys. The quenchlng technlque ls dlscussed and tentative crlterla for the predlctlon and ratlonalizatlon of certaln metastable structures ln alloy systems are lnferred from an analysls of the process. TABLE OF CONTENTS Page r. Introduct1on 1 II. Exper1mental Procedures 2 A. Perspect ive 2 B. Quenching Techniques 5 a. Model I 5 b. Model II 8 c. Discussion 8 C. Alloy Preparation D. X-Ray Procedures 25 25 E. Miscellaneous Techniques 29 III. Experimental Results A. Introduction 32 32 B. Elements 38 C. Alloys 41 a. Complete SolId Solutions 43 1. 2. 3. Ag-Cu Cd-Zn GaSb-Ge and other materIals 47 49 b. SolId SolutIons in Silver-base Alloys 50 c. Metastable Hexagonal Close-Packed Structures In Ag-Ge Alloys 57 Various Data for Ag-Cu and Cd-Zn Alloy Systems 62 d. D. DIscussion 43 70 References 86 AppendIces 90 I I. INTRODUCTION Th1s thes1s 1s concerned w1th the study of the very rap1d cool1ng and sol1d1f1cat10n of molten mater1als, espec1ally metal11c alloys, by means of newly developed techn1ques. S1nce th1s work 1s to be cons1dered as ex- ploratory, some effort 1s expended to del1neate the 1mportant phys1cal factors 1nvolved in the quench1ng techn1que. Of spec1al 1nterest 1s the atta1nment of metastable phases, wh1ch here means those phases wh1ch do not ex1st at equ1l1br1um at any temperature for the g1ven compos1t10n, wh1ch tend to equ1l1br1um suff1c1ently slowly to perm1t study, and wh1ch are not read1ly obta1ned w1th ord1nary methods. Although these metastable phases are of cons1derable 1nterest, little d1scuss10n of the1r broad s1gn1f1cance 1s g1ven 1n th1s thes1s. Rather, an attempt 1s made to eluc1- date the cond1t10ns necessary for their formation so as to develop criteria for their occurrence in other alloy systems. This goal necessitates an examination of the solidification process beginning with the melt and ending with the solid specimen at ambient temperature. Examples of the different classes of metastable structures obtained with the present techn1ques are presented and discussed. 2 II. A. EXPERIMENTAL PROCEDURES PERSP]x;TIVE So11d1f1cat1on 1s most assuredly a rate-dependent process, with the structure and propert1es of the resultant so11d sens1t1ve to the t1me var1at1on of temperature. At low rates of temperature change, equ111br1um thermodynam1cs usually suff1ces for an adequate descript10n of the process. The extensive collect1on of exper1mental facts ava11able perm1~a reasonable understanding of the s1tuat1on, desp1te the var10us theoret1cal d1ff1cult1es. At somewhat h1gher rates of cooling, additional factors enter the p1cture; 1n addition to the expected theoret1cal shortcom1ngs, data are scattered and often contradictory. The speculat10n 1n- creases accord1ngly, w1th this trend continued 1nto the area of yet higher coo11ng rates where the experimental data are scanty. This field of yet h1gher coo11ng rates is of 1nterest not only for the sake of curios1ty but also in the hope that elucidation of some of the phenomena occurring under normal cond1t1ons might result. The effects of such great cooling rates on the liqu1d to solid transformation have not been much 1nvest1gated prev10usly because such coo11ng rates are diff1cult to obta1n. Only small amounts of the 11quid can be cooled rap1dly, mak1ng measurements dur1ng the solidificat1on more diff1cult. 3 One must , 1n general , be sat1sf1ed w1th study1ng the resultant so11d (wh1ch may be quite tolerable because of 1ts own interest1ng features) and trying to work back to ga1n some 1ns1ght 1nto the so11d1f1cat1on mechan1sms. The problem of obta1n1ng h1gh coo11ng rates 1s that of promot1ng heat transfer between a small amount of l1qu1d and a med1um at a lower temperature . The poss1b1l1t1es for several med1a are exam1ned. Rad1at1ve heat transfer 1s usually much too small at the temperatures of 1nterest . Convect1ve heat transfer 1s greatest 1n a stream of rapidly moving gas . The diff1- culty here 1s that the liquid droplet diSintegrates 1nto globules too small f or convenient exam1nation after be1ng subjected to the gas blast . For l1quids which are common- ly used as quenching media, eff1cient heat transfer is lim1ted by the vapor layer which builds up around the sample. Liquid metals with very high boiling pOints and consequent low vapor pressures at the temperatures of interest, e.g ., gal11um, prove to be react1ve chem1cally and thus inappropriate . Aqueous solutions seem to be the most eff1c1ent l1qu1d coolants(l). If the l1quid of 1n- terest 1s Shot 1nto a l1qu1d 1n an effort to min1m1ze the l1rnit1ng effects of the ub1qu1tous vapor layer, the project1le d1s1ntegrates. 4 To utlllze the hlgh thermal conductlvltles of approprlate sollds, the 11quld must be malntalned ln lntlmate contact wlth the solld and spread lnto as thln a layer as posslble . Thls prlnclple ls the ralson d'etre for the technlque descrlbed ln thls thesls and has been also reallzed by at least two other groups, Falkenhagen and Hofmann (2), and Salll and hls coworkers at Dnepropetrovskl State Unlverslty (3). Falkenhagen and Hofmann (2) constructed a small conlcal copper chamber wlth a tube leadlng lnto the vertex and a vacuum connectlon in the base. Nlth a fol1 stuck wlth wax onto the external end of the tube, the chamber was evacuated, and often cooled ln 11quld nltrogen. The end of the tube was put lnto a pot of the molten alloy of lnterest and the wax melted, allowlng the molten materlal to shoot up agalnst the base of the conlcal chamber and solldlfy. Falrly large amounts of alloy were lnvolved (e.g., ~ 20 g of alumlnum) and lt was then posslble to follow the temperature change wlth tlme vla thermocouples and a fast recordlng osclllograph. Coollng rates up to 29,OOOoC/sec were clalmed. The solldl- fled materlals were then examined by standard technlques such as x-ray dlffractlon, metallography, etc. Salll (3) experlmented wlth a devlce in which the alloy of lnterest was melted on the end of a catapult by reslstance heatlng. #hen the catapult was sprung, the molten materlal 5 was flung into the crotch of two converging copper plates where films of varying thickness (down to ---' were obtained. rot for iron) Cool1ng rates of ~ l05 °C/sec were claimed. Sufficient quantitites of the quenched alloys were available for metallographic examinations. Recently discovered was a patent (4) for a device designed to produce very thin filaments from molten alloys. It is probably superior to the two devices just described and may even be equivalent to the present technique insofar as the rapid cooling and solidification of molten alloys is concerned, although not primarily intended for such a purpose . B. QUENCHIDC TECHNIQUES The present technique requires that a small amount of the material of interest be melted in a nonreactive environment, then ejected onto a substrate of high thermal conductivity held at a lower temperature so that the liquid spreads into a thin layer which cools and solidifies very quickly. a. Model I For the first model to be put into extended operation, "Model I" (Fig. U, alloy charges were melted in graphite or alumina within graphite. The crucibles or "nozzles," as . shown in Fig . 2, were designed and machined with a minimum of stress concentrations to avoid failures from the shock waves used to eject the molten alloy. With hellum as the driving gas, shock waves were generated by the ruptures of 6 Figure 1 . Photograph of Model I . 7 !L _1r--=---_ ___ _ (C) (A) WIRE ALUMINA INSERT o I 2 I I I I I I INCHES (8) Figure 2 . o I I I II I I INCHES Scaled drawings of graphite nozzle (a), graphite nozzle with alumina insert (b) and alumina insert (c) . mylar diaphragms. Nozzles were heated to l400 0 c by eddy currents from rf current supplied to the watercooled induction coil. The criteria (5) for optimum conditions for induction heat1ng were considered in the design of the nozzle. Strips, onto which the alloys were shot, were mounted on the inner periphery of a rotating wheel. Copper and aluminum were used, with the surface treatments described in ILB.c. b. Model II The second model (Fig. 3) was mounted in a dry box to allow the substrate to be maintained at low temperatures without ice formation. Liquid nitrogen was pumped into the box and used for cooling the wheel; the low temperature camera (ILD.)was shuttled through an interchange box mounted below. The apparatus is closely related to Model I, except that a quick-opening solenoid valve which generated gas pulses was used instead of the diaphragm arrangement. Also, additional cooling was required since temperatures to 18000 C were possible. c. Discussion Consider first an alloy wire loaded into a crUCible, either graphite or an alumina insert within graphite. As the nozzle was heated by Joule losses from eddy currents 9 Figure 3. Photograph of Model II . 10 induced by the rf field, the alloy was heated by conduction and radiation. Upon melting, the charge was assumed to move into a stable configuration at the intersection of the holes, completely filling the cross-sect1on. The temperature of the molten alloy was taken to be sensibly that of the surround1ng media for graph1te crucibles but somewhat lower for the alumina 1nserts. Temperatures were determined near the hole-surface 1ntersection for graphite nozzles and near the hole for alumina inserts to within + 150 C with an L & N optical pyrometer . Stirring by convection currents should have been sufficient to attain sensible bulk equilibrium within the molten alloys. It was assumed, 1n general, that the 11quids did not wet the cruc1ble, 1n the sense of spreadlng along the 1nner surfaces. Both graph1te and alum1na have relat1vely low surface energies and it was unlikely that any wetting took place, in the absence of definite chemical reactions. Only tellurium showed any tendency to wet graphite, and its surface energy 1s very low compared to the other materials 1nvest1gated. In the absence of wetting or chem1cal reactiOns, it was reasonable to assume that all of the charge was expelled during the shot. Only for tellurium was it observed that some mater1al was ejected during the flush of the gas after a shot. Operations with reactive liqu1ds and solids at elevated temperatures are subject to contaminat1on. However, in 11 exploratory work, it is useful to proceed in such a way as to determine what further measures, if any, must be taken to obtain results of the desired quality. Reasonable pre- cautions were taken throughout this work to avoid contaminants and it is believed that the results obtained were not dependent upon such agents. Assuming that the alloys were not contaminated during preparation, attention must be directed primarily to their melting in the crucibles prior to a shot. For those ele- ments known to react appreciably with carbon, alumina inserts were used. Reactlons wlth nltrogen and oxygen were ever present posslblllties but the quenching procedure, especlally the meltlng and flrlng of the alloy charge, was conducted with reasonable speed and at temperatures no greater than deemed necessary ln order to minlmlze the deleterious reactions. It may be argued that a layer of CO from the eroslon of the nozzle partially the more reactlve gases. shlelded the melt from For reactlve metals, such as lron (however, see App. I), the downstream slde of the Model II shock tube was fllled wlth hellum by repeatedly dlscharglng the solenold valve and the nozzle, the insert , and surroundlng area were thoroughly doused wl th argon. For Model I I operat- ing in a closed dry box, the oxygen was soon consumed. Conslderable varlatlon ln the mode of expulsion of the molten droplet ls possible. The maximum dynamlc pressure assoclated with the shock wave in Model I may have been about 12 20,000 pSi, as crudely estimated from the nozzle geometry, elastic constants of graphite and the occasional failures in shear. The choices of driving and driven gases probably were not critical. No measurements of the velocities of the moving droplets were made, but estimates of a few hundred ft/sec. may be reasonable. The dynamics of the moving droplet are rather obscure and all that was absolutely clear was that, under certain condit1ons, the droplet d1sintegrated before it h1t the target. Th1s situation was read1ly 1dentified by the incoherence of a specimen in which several droplets impinged and solidified at different times. There is some ev1dence that 1t was more d1fficult to obtain coherent specimens for droplets ejected from graph1te nozzles w1th badly eroded holes. It would seem to be advantageous to have a well def ined edge to the hole. S 1mllarly, coherent spec 1- mens were more d1ff1cult to obtain for alloys shot from the inserts. The length of the hole through wh1ch the droplet was accelerated is probably more important here. D1s- integration of the speeding droplet may have been due to unstable osc1llations 1n1t1ated by the propell1ng shock wave or gas pulse and abetted by the cruc1ble geometry and roughness of the hole. 1mportant. On the other hand, air friction may be A mod1f1cat1on of the techn1que to operate 1n vacuo would be useful 1n assessing the relat1ve importance of the a1r as well as for some of the spreading effects 13 descr1bed below. The 1nterest In prevent1ng d1s1ntegrat1on of the droplet 1n fl1ght ar1ses from a des1re to obta1n good spread1ng and h1gh cool1ng rates, slnce there 1s some ev1dence that coherent spec1mens were th1nner than 1ncoherent ones, for the same alloy. The nozzle and rotating wheel were arranged so that the molten droplet would str1ke the substrate at a grazlng angle w1th the respect1ve veloc1t1es approx1mately add1tive, 1.e., the alloy charge was shot nearly tangent1ally agalnst the rotat1ng wheel. The rat10nale beh1nd th1s geometry was that the molten alloy would be spread 1nto a thinner layer, w1th consequently h1gher coollng rates, and th1s seemed to be borne out In pract1ce. D1stlnction between two more or less1ndependent mechanlsms must be made for the droplet 1mp1ng1ng on the target; v1z., spreading of the molten layer and adhes10n to the substrate after solld1f1cat1on. The former seems to be related to the surface energ1es of the molten mater1als and a br1ef summary of the pert1nent knowledge 1n th1s area, gathered mostly from the rev1ews of Taylor (6) and Bond1 (7), 1s glven first. The llqu1d-gas surface energ1es, ~ , and the1r var1- atlons w1th temperature have been measured or estimated for many pure metals near the1r melting po1nts; F1g. 4 shows approx1mate plots of ~u vs temperature, w1th extrapolat10ns for the undercooled llqu1ds. Upon alloying, 14 CU o - -- __ ,AU SI o -.§A "-- IN SN CD GE o 0- --0_ ~8 -"",or, - - , - - _ TL---'::::::: 81 Figure 4. TJ S8 "'--- Liquid-gas interfacial energies, ~s I and approximate variation with temperature -- for undercooled and equi11br1um 11qu1ds. 15 generally there ls a marked decrease ln surface energy lf the solute has an appreclably lower ~i..G' whl1e only a small 1ncrease ln surface energy occurs lf the addltlon ls ln the opposlte sense. Few data exlst; devlatlons from thls be- havlor may result lf molecules or extenslve short range order are present 1n the 11quld. Of 1nterest ln the wet- tlng of sollds by 11qulds are the lnterfaclal energles as well as the 11quld-gas and solld-gas surface energles but the former are rarely known. In these clrcumstances, lt ls customary to use the necessary but not sufflclent condltlon as a crlterlon for spreadlng. It has been noted that the contact angles for 11qulds advanclng on sollds are usually greater than those for a recedlng 11quld and thls may be related to surface roughness or surface reactlons (8). Hlgh surface energy materlals are chemlcally reactlve wlth absorptlon and/or gas reactlons tendlng to lower the surface energy. Because of the conslderable 19norance concernlng spread1ng phenomena, even under more or less controlled condl t1ons, one cannot expect that much of an understandlng ls posslble for the technlque at hand and thls ls 1ndeed so. There ls, for lnstance, the posslbl1lty of a gas layer 11mltlng heat transfer. As for the consequences of the rotatlng target, lt ls known that lt ls not lndlspensable, s1nce some metastable structures were obtalned ln alloys quenched onto statlonary plates. It ls belleved that the prlmary effect of the rotatlng substrate was to contlnually present a fresh surface to the lmplnglng droplet. That ls, lt ls advantageous that molten materlal lncldent on the coollng surface at a glven lnstant not be deposlted on the materlal lald down prevlously. It may be argued that the centrlfugal forces on the molten layer produced more Intlmate thermal contact wlth the substrate but an approximate calculatlon shows that the effective pressure due to rotatlon was only about 2 psl. The greater contrlbutlon to efflclent heat transfer between molten layer and substrate was probably due to the radlal component of momentum of the lncldent droplet. However, another compromlse had to be made here slnce lt seemed that grazlng lncldence favored spreadlng. Slnce an important consideration was convenience, the surface of the substrates were prepared In ways whlch admltted wide variatlons. Copper strips, used for most of the work, were treated thus: pol1shlng with 320 or 400 grl t emery paper of the strlp ln the wheel rotatlng at a few hundred or so rpm untl1 bright, followed by app11catlon of an acetone-soaked wlper to the rotat1ng strip to remove the dust, etc. Because of the tenac lous oxlde coat, aluminum could not be dealt wlth thls slmply and etches ln var10us nltrlc acid solutions were necessary. Also, both alumlnum and copper strips were lightly sandblasted and used without 17 further treatment. Some copper strlps were pollshed in the usual way, carefully cleaned wlth acetone, reduced a few mlls ln thlckness ln a rolllng mlll and cleaned with acetone again. These smooth strlps were not satlsfactory slnce molten droplets appeared to bounce off wlth only a small portion adhering. Balley and Watkins (8) concluded from thelr experlments on the spread1ng of solders that surface roughness ls an important factor in the rate of spreading of mol ten metals on solids. Parker and Smoluchowskl (9) studled. the spread- lng of some molten metals on substrates whlch had been carefully sanded or po11shed ln dlfferent ways and concluded that the caplllarlty assoclated. wlth a system of flne, interlacing grooves and strlat10ns was of considerable importance 1n promotlng rapld, effectlve coverage of the surface . These studles were restrlcted to rather slowly spreadlng llquld metals on clean surfaces, sans superlmposed. rotation, gas afterblasts, etc., but seem to agree wlth the present observatlons. Also in reasonable qualltative agreement wlth exlstlng data are observatlons on "spreadablli ty" from alloy to alloy. As seen from Fig. 4, copper, gold, and silver have markedly higher liquid-gas surface energies than the other elements cited. The experience was that copper and. gold spread rather poorly and thin, coherent foils were rarely obtalned (however 18 see below for dlscusslon of a corollary effect); slIver was a borderllne case whlle the other elements spread nlcely. Addltlon of an element of slgnlficantly lower ~G dld seem, ln general, to lmprove the spreadablllty of high surface energy materlals; for lnstance, quenched Au-Ge alloys were obtained as coherent, thln speclmens, as most easlly observed for folls on resln blocks (cf. II.E.). The overall coollng rate ls, of course, critlcally dependent upon the thlckness of the molten layer lnltlally lald down as well as upon the heat transfer to the substrate. Glven in Appendlx II ls an ldeallzed calculatlon of the coollng rate for a one-dimenslonal array of wall, poorly conducting layer and materlal of lnterest. Bulk thermal par~ meters are assumed, thlcknesses of the solldlfled materlals are obtalned from experiment and the poorly conductlng layer, simulatlng elther an oxlde coat or a layer of gas, ls allowed to vary ln thickness and thermal diffuslvlty. As computed ln thls crude way, the overall time for the process ls IO-4t1 sec. for cooling to room temperature. Another estlmate of the tlmes involved was obtalned by considering the circumferential extent of the spreadlng on the lnner periphery of the rotatlng wheel . The lengths of the specimens were , typlcally, rv 1 In. although much longer when the holes in the nozzle did not lntersect cleanly and molten material was sprayed out and not discharged in a 19 coherent lump. For a motor speed of 5000 rpm, /"--' 2 '10 -4 sec. would have elapsed as the molten alloy was being deposited on the target, assumlng no circumferential spreading afterwards . Thickness was measured with a micrometer for some coherent, ductile foils which were stripped off intact. For these specimens, which were among the thickest encountered, values of 15-25jA were typical for the maximum thickness. Of course, thickness ranged all the way down to nil, as was eas1ly seen from the cast specimens. X-ray measurements (10) suggested that 5-10~ were typical for some alloys. No systematic study was successfully made of the effects of the several variables on the resultant quenched specimens. The results of such an effort for Ag-Cu alloys are given in III.C.a. In a general way, it appeared that, the higher the initial temperature (1.e., the "superheat"), the more eas1ly a given material spread on the substrate. This may be rationalized by the decrease in surface energy with temper~ ture and the increased fluidity. Opposing this was the possibility that the molten layer laid down on the substrate was energetically unstable and, 1n an effort to reduce its surface area, attempted to clump and form "lenses." These hummocks were somewhat thicker and would not cool as rapidly. If the clumping proceeded far enough before solidification, the foil would be incoherent and discontinuous. Tendencies 20 11ke thls seemed to have appeared, e.g., gold, although the phenomenon was not unquestlonably lsolated from the other spreadlng effects. The free surface of the speclmens, ln general, was irregular and hl11y whl1e the surface cast against the substrate falthfully reproduced the scratches and strlatlons of the wall. In Flg. 5 ls a sketch of a typlcal speclmen whlch 111ustrates some of the spreadlng effects now dlscussed; approx1mate contour lines are sketched. At what seemed to be the 1n1tlal p01nt of inc1dence, the mater1al was defin1tely thlcker and had started to cool f1rst but probably not most rapldly because of the adJ01n1ng add1t10n of yet more molten mater1al as well as because of 1ts greater th1ckness. Lens format10n, espec1ally in the h1gher energy materlals, seemed to occur randomly on the surface. There were also r1pples and valleys due, perhaps, to surface waves set up at impact, propagated outward and then sol1d1f1ed. As suggested by the contour lines, the thlnnest port10ns seemed to be near the edges although, perhaps, not at the edge because of the p11eup of mater1al wh1ch m1ght be expected as a consequence of the larger contact angle of advance. The portlon usually taken for x-ray examlnatlon was that so marked because 1t was la1d down at a somewhat h1gher temperature and could spread well, wlth perhaps more lntlmate thermal contact and posslbly some lateral heat transfer to the adjacent 21 SUBSTRATE-....... DIRECTION QUENCHED SPECIMEN OFROT7 TAKEN FOR X-RAY EXAMINATION Figure 5. Sketch of speCimen quenched onto substrate. 22 solidifying material. It is important to realize that all of these observations were made on specimens subjected to the inevitable afterblast of gas. The dotted lines indicate roughly that section of the foil which might have been ripped off by this blast, i.e., the thicker section which had been laid down first. The factors affecting adhesion of a given solidified alloy to a given substrate are poorly understood. It is known that the surface had to be roughened or striated so that, after the flow of the melt, there was solidification with sufficient mechanical adherence to resist the blast of gas. Brittle materials, such as germanium, silicon, and some ionic salts, adhered much better to lightly sandblasted strips. There is some evidence that foils which adhered firmly to the substrate were cooled more rapidly than those which were partially or completely blown off. This criterion was used for selecting those portions of the quenched alloys which were to be examined further. The observations and experience of Pond(4) are reviewed. Molten alloy was supplied to a tube, one end pressurized with gas and the other terminating in an orifice through which the stream of metal was ejected onto the polished inner surface of a rotating bowl. Low melting point alloys were used with gas pressures of /V 15 psi and ejection velocities controlled in the range of a few hundred ft/sec; for appropriate geometries and target velocities, filaments of various 23 th1cknesses were obta1ned 1n great lengths as they were thrown out of the bowl after so11d1f1cat10n. Mater1als, ejected ob11quely onto the coo11ng surface, flowed more eas11y with increased superheat. As target velOCity was increased relative to ejection velOCity, filaments became thinner, then discontinuous and, finally, were obtained only as flake or powder; conversely, for given target velocity, this sequence occurred as ejection velocity was decreased. To produce the thinnest possible filaments, it was claimed that very great superheat, minimum ejection velocity and very high surface speed were simultaneously required. The filament surface contactlng the target was smooth and reproduced the chill block marks, while the other side featured ripples, valleys, etc. It was claimed that co- herent filaments down to f"'J 1/ thickness could be produced. Since Pond was unaware or uninterested in the pOSSibilities of producing metastable phases by rapidly cooling certain alloys from the melt, there is no experimental baSis for comparing his cooling rates with those obtained in the present work. That is, there is the question, resolvable only by experiment, as to whether the metastable structures, such as described in this theSiS, can be obtained with Pond's device. In the meantime, other improvements have suggested themselves in the course of the present work. Reproducibility 24 of the Shot 1s a des1rable goal and some progress in th1s d1rect10n can be made, 1t 1s bel1eved, by s1mpl1fying the geometry of the cruc1ble as well as by carefully control11ng the man1fold factors -- dr1v1ng gas, cruc1ble d1mens10ns, temperature, etc. Also bear1ng on this is the problem of contam1nat10n, which 1s ever cr1t1cal for several rather react1ve alloys. Such a problem can never be completely solved but the use of more nearly non-react1ve crucibles, an 1nert atmosphere or vacuum and a cruc1ble wh1ch can be heated more rap1dly w111 certa1nly be improvements. Clean, h1gh surface energy, yet nonreact1ve substrates of high thermal mass and conduct1v1ty are des1rable and, for eff1c1ent spread1ng and adherence, a network of str1at1ons seems to be necessary. V l'hlle a more powerful dr1v1ng force m1ght be of some advantage, it is of more 1nterest to m1n1mize the atterblast of gas . To get the target further av~y from the hot cruc1ble and yet have coherent droplets 1mp1ng1ng on the cooling surface is a problem obv10usly 1nterrelated w1th those c1ted above. It 1s bel1eved that a longer, more care- fully f1n1shed hole would m1nimize the dynam1c 1nstabilities of a mov1ng droplet. As 1mpl1ed 1n the forego1ng statements and 1n the absence of contrary results from, say, Pond's dev1ce, 1t 1s believed that the highest cool1ng rates w1ll be obta1nable only w1th small quantit1es of mater1al. 25 C. ALl/JY PREPARATION Alloys were usually made up ln 1.5 to 5 g. quantltles, wlth errors ln the welghlng-out of the components ~ 1.5 mg . The flrst melt was made under hydrogen ln quartz, alumlna or graph 1te cruc 1bles wl th lnduct lon heat lng. The slug was remelted under argon and cast 1nto 1 mm wlres by sucklng lnto quartz or alumlna tubing (Fig. 6). From the sl1ght welght loss lncurred ln the lnltlal melt and wlth the assumptlon that s1mllar losses occurred during castlng, estimates of the precislon of the alloy composltlons were made; analyses of the flakes obtalned after quenchlng were not feaslble because of the mlnute amount of material. Alloys were prepared ln thls manner only for convenience. Alloys prepared by other technlques were, of course, sultable for use in the rapld quenching apparatus wlth the sole crlterlon belng homogenelty over the dlmensions of the charge, typlcally r v 1 mm 3 • D. X-RAY DIFFRACTION PROCEDURES Qualltatlve work was done ln a Norelco gonlometer wlth large flakes pasted onto a glass sllde or sample plus substrate clamped flat ln speclmen holders (Fl g . 7). Speclmens mounted on resln blocks (II. E.) were sllpped 1nto the rotary head. 26 INDUCT COIL """~"L.UMINA Figure 6. CRUC IBLE Casting of liquid alloys into wires . 27 Figure 7. Specimens as quenched onto copper substrate, clamped in holder , and mounted on resin block. 28 Quant1tat1ve work was done with Norelco 114.6 mm d1ameter Debye-Scherrer cameras. Spec~ens were stuck onto 2-5~ d1ameter quartz f1bers w1th celvacene. Flakes» 0.3 mm 2 1n area could be pos1t10ned normal to the 1nc1dent beam and exposures made w1th the specimen stat10nary. Information about gra1n size and preferred or1entat10ns thus was often read1ly obta1ned. Most spec~ens were rotated dur1ng the exposure, however. The pos1t10ns of the d1ffract10n l1nes on the f1lms were located to wlth1n 0.05 mm for sharp lines; less precision was possible for broad and diffuse lines. A l1near correc- tion was applied for f1lm shrinkage, which was less than 0.4%. Spacings were obtained and visual 1ntenslties es- timated for the several reflections. For cubic structures, spac1ngs were plotted aga1nst the Nelson-Riley function and the parameter and errors estimated from the extrapolation to ~ = 90 0 • For hexagonal and tetragonal structures, an axial rat10 was assumed and the £, ~ parameters calculated and plotted separately against the Nelson-Riley function. Ex- trapolations were made and a new axial ratio estimated, etc. unt1l a good fit was obtained. as computed relative to All spacings are in Angstroms f (CuKP() = 1.54l78~, f (CoKo() = 1. 79020 ~ for the unresolved lines and f\(CuKO(, ) 1.54050 ~, r- (CoK P\1 ) = 1. 78890 for the resolved doublets. All work was done at room temperature, 26 + 30C. 29 To examlne speclmens at lower temperatures, a vacuum holder for the GE ~5 dlffractometer was used (Flg. S). E. MISCELLANEOUS TECHNIQUES To remove the quenched specimen more or less lntact from the substrate, nucleated resln was poured lnto a greased teflon-llned mold (Flg. 9) and allowed to set. Wlth the fol1 cast lnto the face of the res1n block, the gross varlatlons ln thlckness were evldent and many areas were transparent to vlslble llght. For speclmens cast onto blocks, the type of electrlcal conductlvlty (p or n) was determlned wlth a thermoelectrlc tester(ll) wlth copper lead wlres . estlmated wlth an ohmmeter. Reslstlvltles were Attempts to determlne the slgn of the reslstance change at 11quld nltrogen temperatures were usually unsuccessful because of the cracklng of the fol1 and/ or resln blocks. Specimens were glven anneals and the resul tlng transformatlons followed by x-ray dlffractlon. Most of the samples studled were merely heated for glven times at glven temperatures in ovens or furnaces ln alr whlle on the copper or alumlnum strlps clamped ln the spec1men holders. For estlmates of the effects of severe deformatlon on the decomposltlon of the nonequl1lbrlum phases, spec1mens quenched onto the substrates were cooled ln llquld nltrogen and reduced ln thlckness ln a rolllng ml1l or ground to powder ln a mortar. Figure 8. Low temperature vacuum holder for diffractometer. "camera" -- 31 SPECIMEN COPPER Figure 9 . Cutaway v1ew of mold for mount1ng quenched spec1mens onto res1n blocks . 32 III. A. EXPERIMENTAL RESULTS INTRODUCTION The concept of equ1l1br1um has had farreach1ng consequences in the phys1cal sc1ences; equat10ns of great genera11ty are used to describe matter 1n the un1que state of equ1l1br1um. The understand1ng of nonequ1l1br1um states, however, 1s at a somewhat more pr1mltive level. ~ne nonequ1l1br1um phenomena of 1nterest 1n thls thesis are those metastable phases and structures obta1ned by so11d1fication at rather h1gh rates of coo11ng. Here spec1f1c reference ls to structural relat10ns between atoms, crystalline and otherw1se, as detectable by x-ray d1ffraction and not to the morpholog1cal macro-structural relat10ns between grains, phases, surfaces, etc. The structures obta1ned w1th the usual cooling rates are, 1n general, not too d1fferent from the equ1libr1um structures and have usually not been systemat1cally investigated. In the hope of uncovering systematic relatlonsh1ps among the nonequ1librium phenomena, 1t 1s preferable to restr1ct efforts to those systems where cons1derable data havebeen accumulated for the equ1l1br1um states. Th1s thes1s 1s l1mited to phenomena in metals and metal11c alloys, lon1c sal ts and s1milar h1gh surface energy substances. A survey of the l1terature on nonequ1l1br1um structures obta1ned upon so11d1f1cat1on has been attempted and some of the observed 33 phenomena are d1scussed 1n the following. ith the knowledge from thermal analysis that solid thallium undergoes a phase change, Sek1to(12) attempted to determ1ne the crystal structure of the h1gh temperature polymorph. HaV1ng only room temperature x-ray apparatus, he attempted to reta1n the h1gh temperature form by quench1ng the so11d from above the transformat1on temperature. Since the phase obtalned was the usual low temperature form, hexagonal close-packed (hcp) , he quenched from the liquid and found a new phase -- face centered cubic (fcc). Later work with a high temperature camera showed the high temper~ ture polymorph to be body centered cubic (bee), although this finding seems to be disputed also. The history is re- capltulated ln more detall in III.B., where the present experiments, which do not resolve the confusion, are described. Cech(13) found that small particles of iron-nickel alloys melted and then slowly cooled 1n a hydrogen atmosphere solidified in the bec structure when a fcc or tetragonal structure was expected. Further investigation showed that the bec particles came directly from the melt and that no solid state transformations were involved. The details are given in App. I, with the results of the present work for the same alloy system. The most important conclusion was that the occurrence of the bcc phases could be related to the Fe-Ni equilibrium phase diagram. Cov lngton , Groenwolt and Howlett(l4) have found a metastable compound upon anneallng blsmuth-rlch Cu-Bl melts at varlous temperatures and coollng rather slowly untll solld. Only small needles of the compound could be obtained; mlcroanalysls suggested a compos1tlon tV C~B12 and the crystal structure could not be determlned although lt was not of cublc symmetry. No new structure was obtalned by rapldly quenchlng 33 at.% Bl;Cu melts wlth the present technlque. Covlngton, et al. suggested that a surface energy contrlbutlon to the free energy may cause the compound to become the stable phase ln the absence of copper nuclel. They also commented that "a dlstlnct flattenlng ln the l1quldus curve ln the range of the probable composltlon of the compound suggests assoclatlon ln the l1quld" but thls ls hardly the case, slnce such flattenlng infers instead lmmlnent unmlxlng in the undercooled liquid. The dlscovery of Covington, et al. thus lacks explanatlon and seems to be lsolated in the sense that it does not polnt to the way for further work. Pawlek(15), solidlfylng zlnc-base alloys ln a devlce which was a forerunner of the Falkenhagen-Hofmann model (II.A.), found that several complex perltectic phases could be suppressed. Schramm(16) proposed that these solidl- fication phenomena be interpreted in terms of a "metastable phase dlagram" in whlch all the usual features of equ1l1brium phase diagrams were to be preserved in spite of the 35 inapplicability of Gibbs' phase rule. Such concepts have also been proposed elsewhere; viz, on rapid solidification of germanium-rich melts, the crystallization of the 5 -phase (FeGe 2 ) was suppressed and a metastable eutectic, ~ (Fe Ge) + Ge, formed(17) and, also, on solidification of 2 Cd-Sb melts, a metastable Cd Sb phase was formed in pre3 2 ference to the equilibrium configuration which featured, rather, a CdSb phase (17) • Falkenhagen and Hofmann(2) carried out a somewhat systematic investigation on the extension of solid solubilities in some alloys by rapid solid1f1cat1on (cf. II.A.). The1r results are presented 1n the following table: Solvent Solute ~ Al Al Al Al Pb Pb Pb Cu T1 V Cr Mn Fe Na Te Ca Cr maximum solid solub11ity (at.% solute) equilibrium rap1d so11d1ficat1on 0.09 0.18 0.45 0.7 0.026 10.1 0.16 0.52 0.9 0.19 0.55 2.85 4.7 0.082 23.8 0.32 0.95 1.8 Except for ~-Mn (cf. App. III), there was no attempt to verify or extend these results 1n the course of the present work. Among the 1nterest1ng results of the F- H work were the measured undercool1ngs. For the alum1num-base alloys, under- coo11ngs of 100°C were cons1stently observed, w1th even 200 - 300°C no ted f or t he manganese and chrom1um alloys 1n whlch the greatest lncreases ln solld solubl1lty were obtalned. From the limlted number of alloy systems studled, F-H concluded that slgnlflcant extenslons of solld solubl1lty may be expected for blnary systems characterlzed by rlslng 11quldus curves (due generally to the occurrence of lntermetalllc phases wlth hlgh meltlng polnts) near the solvent. They also polnted out that, for those alumlnum- base alloys contalning 0.1 at .% solute where the "ablosearbeit" was mown; vlz., Mg - 27 kcal/mole, 81-32, Cu-42, Mn-79, extended solld solublllty was obtalned only ln the latter. 8alll has been actlve ln thls area slnce 1952 and two of hls papers(3) (18) were avallable ln translatlon. These papers are qulte dlsconnected and verge on lncoherence (due posslbly to dlfflcultles ln translatlon), but, nonetheless, a summary of hls observatlons ls attempted. In the 1958 paper(3), lt was stated that extrapolatlons from the equl1lbrlum phase dlagram were sometimes val1d, when made ln accord wlth the Clauslus-Clapeyron equatlon. A consequence of the analysls was that sllghtly supersaturated solld solutlons decompose more rapldly than more strongly supersaturated ones. It was stated that nuclel of metastable and stable phases are lnitlally present and that "the separatlon ••• takes place, as it were, dur 1ng the 'compeU t lon' of the two phase dlagrams" (l.e. stable and metastable). That ls, lt was assumed that 37 the metastable s1tuat1on can also be character1zed by a phase d1agram. At large undercoo11ngs, 1t was postulated that "diffus1onless" transformat1ons occurred. From ex- amlnat10n of success1ve layers of some quenched samples, 1t was found that, for the mater1al d1rectly 1n contact w1th the substrate, a supersaturated metastable solut1on of compos1t1on close to that of the 11qu1d was formed; in the next layers, the usual mult1phase structures, more or less, were found. It was concluded that the relat1ve rates of growth from the undercooled 11qu1d were most tmportant in determining wh1ch phase, metastable or stable, predomlnated. In the 1960 paper(15) by Sal11 and M1roShn1chenko, some features of the crystal11zat1on of eutect1c-type alloys were d1scussed. The tendency to form supersaturated prtmary solid solut1ons in systems w1 th intermed1ate phases was aga1n noted. Also ment10ned was the poss1b1l1 ty of obtaining lightly supersaturated solid solut1ons by "crysta1l1zation w1thout diffus1on." For the simple b1nary eutect1c systems (w1thout intermetal11c phases) AI-S1, Pb-Sn and B1-Sn, prtmary so11d solut1ons w1th concentrat1ons less than the ma.xtmum equil1brium solid solub1llty were found, wh1ch was related to the undercoo11ng and 1ndeed taken as a measure of 1t. Aga1n, d1stinct Itmetastable phase d1agrams" were postulated and parallels w1th the equ1l1br1um phase d1~ grams drawn. Little further systemat1c thought of value has been fO\llld in the llterature. The treatment by Jackson (19) of the k1net1cs of so11dificat1on was of some 1nterest though because 1t cla1med to descr1be the dev1at1ons from equ111br1um for d1fferent growth rates of the so11d from a melt. Th1s expos1t1on 1s based on the interfac1al k1net1cs descr1Pt1on(20) of the 11qu1d-so11d transformat1on, an approach wh1ch 1s cons1dered complementary to the usual v1ewpolnts that emphas1ze more heav11y the nucleat10n processes 1n solld1f1cat1on. Foremost among the latter are the theor1es developed by Turnbull and coworkers (21) (22) for heterogeneous and homogeneous nucleat1on. Although the latter seems to be 1n reasonably good shape, the former has been ser10usly challenged, espec1ally by the exper1ments of Sundqu1st (23) • The scope of th1s thes1s 1s 11m1ted to the so11d1f1cat10n processes and matters d1rectly related to the atta1nment and retent10n of metastable so11d structures. So11d state transformat1ons are dealt w1th only to the extent necessary to explain the observat1ons and to eluc1date, 1f poss1ble, the so11d1f1cat1on mechan1sms. The s1gnif1cance of metastable so11d structures thus obtalned can only be g1ven br1ef comment here. B. ELEM1iNrS Several exper1mentally conven1ent pure elements were quenched and the follow1ng poss1b111t1es, or some combinat1on 39 thereof, exlsted; (1) the equlllbrlum crystalllne structure would be obtalned, (11) a crystalllne structure, stable at hlgher temperatures, would be retalned, (111) a nonequlllbrlum structure, not necessarlly crystalllne, would be gotten. The close-packed elements magneslum, alumlnum, copper, nlckel, slIver and gold were quenched to room temperature from a few hundred degrees cent1grade above the1r meltlng polnts and, as expected, only the usual crystal structures were observed. S111con and german1um were also quenched to room temperature and only the character1stic d1amond structure noted. The h1gh temperature fcc structure was the predom1nant phase detected 1n cobal t f 11ms, al though some hcp lines were detected, wh1ch was not unusual (24) • Manganese was quenched from 13000C to room temperature. Most of the 11nes 1n the Debye-Scherrer f1lm can be correlated to the ~ -Mn structure; other l1nes, mostly fa1nt, probably 1nd1cated some contam1nat1on. The x-ray results for quenched 1ron are d1scussed 1n App. I. Quenched to 11qu1d n1trogen temperatures, as well as to room temperature, w1th only the usual crystalline mod1f1cat1ons detected, were ant1mony, zlnc, carlrn 1um , blsmuth, lead, mercury, and indlum. In tin, the body centered tetragonal structure was retalned because of slugglshness of transformat1on to dlamond structure(25). Thal11um was lnvestlgated more intens1vely than the above mentioned elements because of the conslderable confus1on concern1ng the crystal structures. Seklto(15), working in 1930 when neither the crystal structures of the high temperature form (stable from 230 0 C to 3030 C, the melting pOint) nor the low temperature form (stable below 23O oC) were known w1th certalnty, undertook to determine these structures. The low temperature form was found to be hcp and this has been verified by L1pson and Stokes(26). Because his x-ray equip- ment was limited to room temperature operation, Seklto attempted to retain the high temperature phase by quenching into ice water, with specimens coated with glycerol to avo1d oxldat1on. It was not possible to obtain anyth1ng but the hcp phase by quench1ng the solid from above 230 oC. By quenchlng the liquid, a fcc phase was obtained if the watertank was not too shallow or the quantity of metal not too great, (say, not more than 5 g). Under these latter con- ditions, wh1ch lmply too low a cool1ng rate, the hcp modification was formed. Seklto then concluded that the high temperature phase was fcc. Lipson and Stoke~26), working with a high-temperature camera, found that the structure at 262 0 C was bec although some hcp 11nes were noted. The purity of their thal11um was ~99.995% whlle Seklto dld not state the purlty of hls materlal. Schneider and Heymer(2 7) de- termlned the lattlce spaclngs of thalllum at temperatures wl thln the f leld of the h1gh temperature polymorph and found the structure to be fcc, as Seklto had suggested but ln 41 contrast to the results of Llpson and Stokes. In view of this unsatlsfactory sltuatlon, an attempt was made to reproduce the face centered cublc structure of Seklto wlth the present technlque, whlch is capable of much greater coollng rates. Thall lum of purlty ;> 99.99% was quenched from various temperatures onto copper and aluminum at room and liquid nitrogen temperatures. Only the hcp structure was ever observed. C. ALLOYS From equilibrium phase diagrams, working hypotheses were developed to predict the occurrence of some metastable structures ln alloys rapidly quenched from the melt . Some of these working hypotheses are now descrlbed, followed by a presentation of the experimental results and the attempts to develop adequate criteria. Chemically similar components possessing the same or similar crystal structures generally form complete solid solutions when they are not too grossly different in vOlume/atom. As the dlfferences become greater , lt is generally found that eutectic systems with l1mited solid solublllties and then monotectlc systems with very limited solid solubilities and some liquid immiscibility occur. It was initially expected that metastable solid solutions might be obtained, for these alloys, by quenching from a region of liquid miscibility. Metastable solid solutions have 42 1ndeed. been found for the eutectIc system Ag-Cu, 1n whIch the components crystallIze 1n the fcc structure, and also for the pseudo-bInary eutectlc system GaSb-Ge, In whIch the components crystallIze 1n the closely related. zlncblende and dIamond structures respectIvely, but not for the eutectIc system Cd-Zn, In whIch each component crystallIzes In dIstorted. hcp structures wIth simIlar axlal ratIos. For the relatIvely well-studIed Ag-Cu and Cd-Zn alloy systems, the avaIlable data are examlned for clues to thIs dI~ metr1cally oppos1te behavIor, whIch was not expected from an elementary cons1deratlon of the phase d1agrams. For metals and 1nterrnetalllc phases, lt was expected. that the solld solubIlItIes mlght be extended beyond those found at equlllbr1um, regardless of the crystal structures of the components. For thIs very large class of problems, no systemat1c results have emerged. 1n the course of the present work. However, for some slIver-base alloys of con- s1derable theoret1cal Interest, latt1ce parameter measurements of multiphase quenched alloys suggest metastable extended. solubllltles. It was also expected that new structures, hltherto unknown ln the particular alloy system, could be obta1ned. These new structures mlght be merely the suppresslon of a compllcated equI1lbrlum phase; they also should not be restrlcted to beIng crystalllne, although noncrysta1l1ne 43 solld structures are not found ln bulk metalllc systems. Dlscussed ln thls thesis are the metastable hcp structures obta1ned ln Ag-Ge alloys. a. Solld solutlons among components of s~llar crystal structure. 1. Ag-Cu Sllver and copper are slmilar chemically and structurally, both crystalllz1ng ln fcc lattlces. The silrrple eutectlc alloy system has been wldely studled and there ls good agreement on the equlllbrlum phase dlagram(17) (Flg. 10). Pert1nent experlmental and theoretlcal lnformation is dlscussed, especlally ln conJunctlon with the Cd-Zn alloy system, after presentatlon of the present experlmental results. Alloys were prepared ln quartz cruclbles from elements of purlty> 99.9%. The alloys were usually quenched onto copper from graphlte nozzles heated to rvl3000c although dlfferent temperatures, substrates, etc. were also used. From many films, est~ates of the lattlce parameters of the metastable solld solutlons obtalned were made and are presented below; also glven there are the est~ated accuracles of the alloy compositlons and the characters of the other phases detected. 44 1200r-------------------------------~ w a:: ~ 600 «a:: w a.. ~ ~ 400 200L-~ o Ag Figure 10 . __ ~~ 20 __ _ L_ _L_~_ _~_ _~~_ _~ 40 60 80 COPPER (ATOMIC PER CENT) 100 Cu Equllibrium phase diagram of Ag- Cu system . o Alloy (at .%Ag) a(A) o 3.6153+3 3.6860+10 11.5+0.2 25.0+0.4 Comments 3.759+3 falnt s11ver- rlch phase detected, hlgh angle llnes unresolved. 37.1+0 .2 falnt sllver-rlch phase detected 50.0+0 .3 3.8815+20 falnt copper-rlch phase detected 60 .0+0.3 3.9250+15 falnt slIver-rich phase detected - - falnt copper-rlch phase detected 77 .0+0.3 100 3.9980!15 4.0853!3 Grain slzes were est1mated as ~ It from the broadenlng of the diffractlon lines. Fllms of statlonary speC1mens did not suggest any preferred orlentatlons . It ls to be emphaslzed that the results tabulated above represent the best of much work; the falnt, nearly equlllbrlum phases Just could not be suppressed ln the lndlcated alloys, at least not to a level below that detectable by the present technlques. In thls respect, the lesser scattering power of copper may allow it to go undetected relatlve to the same amount of slIver wlth a few percent as the approx1mate threShold of detectlon here. The presence of the other phases may be ratlonallzed ln terms of the competltlve growth 46 or precipitation processes (III.D.), but also may be due to other factors more nearly within control of the investigator. For instance, hesitation in pulling the rotat- ing wheel away from the hot nozzle after a shot may result in some annealing out of the metastable solid solutions. Mechanical working during the removal of the spec1men from the substrate may also result in decomposition. The posSibil- ity exists that certain areas have cooled at much lower rates than adjacent material and hence are not essentially all metastable solid solution; indiscriminate choices of the spec1mens to be further examined would then result in detection of the nearly equilibrium phases. Attention was paid to these possibilities here insofar as was possible. Considerable effort was expended with these alloys in an attempt to separate the effects of the sundry variables involved in the quenching technique. This approach was far from successful, although some tentative conclusions were possible. Used as a qualitative indicator were the relative intensities of the metastable and nearly equilibrium phases, under the plausible assumption that the conditions under which a good deal of the nearly equilibrium phases formed were somewhat less stringent. Copper substrates, treated in the usual way (II.B.c.), seemed to be somewhat better than the other materials, although the latter were occasionally adequate. The pressures of the driVing gases in both Model I 47 and II were varled over a few hundred psl wlthout slgnlflcant dlfferences. As expected, alloys .1n thls system quenched from graphlte nozzles and alumina lnserts were much allke. Contaminatlon seemed to be un1mportant except for the occaslonal oxldatlon noted for some of the copper-rlch alloys. Exper1ments wlth dlfferent wheel speeds were in- conclusive and, occasionally, metastable solid solutlons were achleved even wlth a statlonary wheel. By followlng the surface temperature of the nozzle wlth an optlcal pyrometer , it was found that nearly single-phase solid solut10ns could often be obtalned at superheats of as llttle as 25-500 C. It was also of interest to test the posslbi11ties of quenching these alloys lnto llqulds. To thls end, a charge of the 60 at.% Ag;Cu alloy was flred from a graphlte nozzle at l3000 C into a 10 mol.% NaOH;H 20 solution wh1ch had been chllled wlth lce. The molten projectlle easlly penetrated the Saran wrap holdlng back the lnclined coolant and then dlsintegrated into many spherical part1cles of a few f dlam. Only the copper- and sllver-rlch phases were detected ln these partlcles . 2. Cd-Zn Cadmlum and zinc are very slm1lar chemlcally and crystalllze in dlstorted hcp structures of s1mllar axlal ratl0. The equ1llbrlum phase dlagram of the binary alloy system (17) -u - 350 o W 300 - 0: :::> ~ 250 0: W a.. ::E 200 W ~ 150 ZN Figure 11. Equilibrium phase diagram of Cd-Zn system. 49 (F1gure 11) 1s well determ1ned. Prepared 1n quartz cruc1bles, w1th no apparent segregat10n, were the following alloys: 15, 27, 50, 75 and 85 at.% Zn;Cd. Shots were made from graph1te nozzles heated to 500 0C and h1gher (desp1te volat1l1zat10n) onto copper at room temperature and aluminum at l1qu1d n1trogen temperature. Debye-Scherrer f1lms of quenched alloys ind1cated two phases in all cases; latt1ce parameters were not computed because of the v1ew that only neg11g1ble extens10n of the equ1l1br1um so11d solub111t1es had been obtained. In the low temperature camera, the d1ffract10n peaks were rather broad and d1ffuse and only the strong low angle 11nes could be unamb1guously separated from the background. There was no ev1dence that metastable so11d solut10ns were obtained for the quenched alloys lnVest1gated at low temperatures. 3. GaSb-Ge and other mater1als The work done by the present invest1gator and prev10usly reported (below) 1s yet va11d and no emendat10ns are necessary. Because of the lack of other exper1mental data for th1s alloy system, no further analys1s 1s attempted. 50 Metastable Solid Solutions in the Gallium Antimonide-Germanium Pseudobinary System* 1\)1. nI IWE?. H. II. \\'11,1.1'::-; 5, ,\:-;11 \V. r.: ....:;\I1·::-H. jl( . HI / ·:III:,;"r("";II ;:. ,'" :i/ /I,,,;(I /II .•til/ll,. II/ "I',rllllol"KY, J)il'i .,jrlJ/ /'<1 \./.1,'''''' ( '.,Iij urll;,J (l(nTiwtl "' prjl 14, I'}(,C) ilER E seems to be a dearth of published work on the Ga·Sh- Cc ternary system despite the great interest in the !'cmiconductors CaSu and Ce. However, unpu hlished work ' ind icates tha t g:1.l1 iu Ol ant imonide and germanium may be regarded as the components oi a simple eutectic pscudobinary system. The ~u1l"Clic is cstimated to occur a.t 35±lO at. % germanium at a temperature of 648±:4-°C. The maximum solubility of germanium in ga llium antimonide is probably less than 2 at. % under equilih rium condit ions. The proced ure hy which small amounts of liC]uid a lloys can be 'l ucnchcd rapidly enough to forestall the normal nucleation and g:rowth procc!'scs has been previously rcpor te(J.2 A series of alloys was prepared from stoichiometric galli um antimonide «(I =6.097 A) and zone refined germanium (11=5.653 A) . The alloys were cooled rapidly and t heir resultant structures studied by means of x-ray (liiiraction . :\ single phase-with the d isordered zincblcnde structure- was ohserved in all of the aHoys investigated. The plot of lattice pa rameter vs composition ( Fig. 1)3 does not indicate signitican t or systematic deviation from Vegard's law. These results were not unexpected. The zincblende structure of gallium antimonide and the diamond structure of germanium arc hot h lJased upon the necessity of each atom having four nearest neigh hors which. in turn , is demanded by the covalent bonding. ]f the conventional valancics are assig ned to the clements, the number oi valence electrons/ atom remains four throughout the pscudobinary system . Furthermore. the germanium atoms seem to be of such a size as to fit substitutionally into the lattice 1)'ithout causi ng undu e distortion. From a qualitative study oi the intens ities of the diITraction lines on the Debye-Scherrer films and the ahsence oi any detecta.ule splitting of these lines, it is hypothesized T .. ~~o~~-,k-~-.k-~-.k-~-.~-L~ Go 50 G. GERMANIUM 'ATOMIC PER CENT) FIG. 1. Lattice parameter vs composition in the germanium-gallium antimonide Dsuedobinary system. that germanium substitutes randomly in the lattice, and docs not destroy the cubic symmetry. Acknowledgments are made to J. O. McCaldin for providing the alloys and for his continuing interest in this investigation. • This wo rk was jointl)· sponsoreti by the •. S. Office of :-':a\'al Research and the C. S. Atomic Energy COlllmis.."!ion. 1 J. O. ~'tcCaldin (Ilrh'ate communication). I Pol Duwez . R. H. Willens. and W . Klement. Jr .• J. A pp1. Ph)'s. 31. 1136 (1960). I The granh of Fig. I is based on the no minal composition of the alloys before melting. It has not been possible to obtain reliable chemical analyses thus far. Maximum deviation between nominal and ac tual compositions might be as large as 5 at. % germanium. Perhaps the most important consequence of thls work ls that the rapld quenching technlque ls also appllcable to covalently-bound materlals. There ls no § prlorl reason why metastable solld solutlons between approprlate lonlc salts Should not be obtalned wlth thls technlque although no posltlve results were obtained ln a serles of experlments. b. Solld solutlons ln slIver-base alloys In the work on Ag-Ge alloys (III .C.c.), lt was dlscovered that the lattice spacings of the metastable fcc structures 51 appeared to increase linearly with germanlum content up to 13.0!1.0 at.% Ge. Desplte the lnabllity, ln general, to obtaln s lngle-phase alloys, it was suggested that the prlmary solld solubl11ty had been extended beyond the maximum equ111brium value of 9.6 at.% Ge. According to the vlew(28) polnt of Hume-Rothery, et ale , the equlllbrlum solld solub1li ty of germanium in s1lver is "restricted"; however, the metastable solublllty limlt corresponds to an electron concentration of 1.39!3 -- a value glven conslderable emplrical support. Other slmilar slIver-base alloys, with re- strlcted solubillty limits, were then investigated in order to determine the metastable primary solid solubilities attalnable with the present technique. The experimental procedures and results for Ag-Ge alloys are presented ln III.C.c. Simllar methods were employed for the antlmony, bismuth, lead, tin and sllicon alloys except, for the latter, lt was necessary to melt in alumlna crucibles as well as to use alumlna lnserts ln the graphite nozzles. To minlmize volatl1lzation, the antlmony, lead and bismuth alloys were quenched from 1200oC. All elements were of purlty;> 99.9%. ~.l Composltions were believed accurate to or 0 .2 at.% for the tin and antimony alloys; composi- tions for the other alloys are only nominal. Some equilibrium data on the silver-base alloys of lnterest are given ln the following table: 52 (17) equilibrium solid solubility (17) Solute 1~imum Ge at.% solute 9. 6 Sl ? small Sn 11.5+0.2 1.3%+6 intermediate phases Sb 7.2 1.29 intermediate phases Bl 2.7 1.11 simple eutectic Pb 2.B LOB simple eutectic electron concentration 1.29 ? Comments simple eutectic system Simple eutectic Despite much effort with the Ag-Si alloys, it has not been possible to obtain lattice spacings which are sufficiently critical to establish either the variation of lattice spacing with silicon content or the limits of solid solubillty.The Si (Ill) diffraction line was not detected in any alloy containing less than 16 at.% Si. For alloys in the range 10-25 at.% Sl, faint low angle lines were detected which could be indexed as the (10.0), (00.2) and (10.1) reflections of an hcp structure with a = 2.B75!25 ~, c = 4.520!30~, cia = 1.572!20. In contrast to Ag-Ge, there was no range in which the hcp phase predominated at room temperature. The 16 at.% Si alloy was quenched to and ex- amined at liquid nitrogen temperatures but no predominant hcp phase was found. 53 The Ag-Bl and Ag-Pb systems(17) are qulte slinl1ar ln that the eutectlc composl tlons are at rV 5 at.% Ag and the maxlmum solld solubliltles ln slIver occur above the eutectlc temperatures. N For electrodeposlted alloys, 4 at.% Pb can be held ln supersaturated sol1d solut lon (29) • Lattlce spaclngs from the 11terature(3Q) (31) (32) and from the present work are plotted agalnst Bl, Pb content ln Flgure 12. Metastable solubliltles have been estlmated from the extrapolatlons of stralght 11nes fltted to the equlllbrlum data. Single-phase alloys could not be obtalned; falnt 11nes correspondlng to the Bl(102) and Pb(lll) reflections, respectlvely, were detected. were lnvarlably dlffuse. Hlgh angle dlffractlon 11nes No crystal structure other than those present at equl1lbrlum was found although the hcp structure dlscovered by Heldenrelch(33) was searched for ln many quenched Ag-Pb alloys, lncludlng some rlch ln lead. Thus, the 11mlts of metastable solld solubillty under these condl tlons appear to be IV' 4 at . % Pb and "-" 4.5 at.% B1. The sllver-rlch ends of the Sb, Sn systems(17) are quantltatlvely qulte slmllar when the phase boundarles are plotted on a temperature vs electron concentratlon dlagram . Narrow two-phase regions separate the fcc phases from the ~ -phases, whlch are hcp wlth nearly ldeal axlal ratlos(24) at the solublilty llinlts. Lattlce spac1ngs of fcc structures 1n the equlllbrlum reglon(34 ) are plotted 1n Flgure 13 wlth - 4.140 o<{ - ~ / / / / ~ <{ 0:: eCHISWIK 8 HULTGREN / \-j RAUB 8 ENGEL ~/ o PRESENT WORK / /1 / 0:: W w o RAUB 8 POLACZEK-WITTEK / / 4.120 b: w 4.100 u ~ ~ --1 4.080'-----'-----'----'---'-----'-----'----'---'---'-----'----'---' AG 2 4 6 ATOMIC PERCENT SOLUTE Figure 12 . Lattice parameters plotted agatnst solute concentration for face centered cubic solid solutions of bismuth and lead tn silver . 55 o<{ o 5 OWEN a ROBERTS PRESENT WORK 10 15 ATOMIC PERCENT SOLUTE Figure 13 . Lattice parameters plotted against solute concentration for face centered cubic solid solutions of tin and antimony in silver . the present results. Hcp dlffractlon llnes were detected ln the 11.1, 12.7 and 12.95 at . % Sn and 7.1, 8 .4 and 9.5 at.% 5 Sb alloys; thelr relatlve lntenslty increased wlth hlgher solute content. The metastable solubl1lty limlts appear to be"""" 8 at.% Sb and"'" 13 at.% Sn. Assumlng that the measured lattlce spaclngs correspond to supersaturated solld solutlons, the metastable solld solubl1lty 11mlts for the slIver-base alloys are (in terms of electron concentratlon); Ge, 1.39f3; Sb, 1.32; Sn, 1.39; Bl, 1.18; Pb, 1.12. For the Ag-Sn and Ag-Sb alloys, the vlewpolnt taken ls that the free energ1es of the fcc and hcp phases are nearly the same as are the nucleat10n and growth rates upon solld1ficat1on. Thus the admiXture of these phases ln the quenched alloys reflects the compet1t1on between these structures wh1Ch, w1thin certain 11mlts, are of nearly the same compos1tlon. Sim11ar1y, the metastable hcp structures 1n Ag-Ge alloys have free energles, etc. close to that of the fcc structures. These matters are dealt w1th more fully 1n III.D. The Ag-B1 and Ag-Pb alloys seem to requ1re d1fferent 1nterpretat1on. As noted for apparently the flrst time from a survey of pub11shed equ111br1um phase d1agrams(17), retrograde so11d solub111ty generally occurs in b1nary metal11c alloys whose components are markedly d1fferent 1n s1ze w1th the larger element as solute. Thls retrograde so11d 57 solubility is usually accompanied by a flattening in t he l1qu1dus curve and, often, some 1mm1sc1b111ty 1n the l1quld . Such flatten1ng presages unm1xing 1n the undercooled 11qu1d. Pronounced flatten1ng in the 11qu1d1 of the Ag-B1 and Ag-Pb alloy systems are found(17) and the expected separat10n or tendency thereto 1n the undercooled 11qu1d 1s suggested as the reason that the so11d solub111t1es cannot be apprec1ably extended w1th the present techn1que. c. Metastable hop structures 1n Ag-Ge. Nonequ111br1um hcp structures have been obta1ned 1n Ag-Ge alloys quenched w1th the present technique. The ex- per1mental procedures and results are adequately presented 1n the following repr1nt. Lattice Param.e ters of the Metastable Close-Packed Structures in Silver-Germanium Alloys By W. Klement, Jr. , B. S. The lattice spacings of the metastable face-centred cubic and hexagonal close-packed phases in the silver-germanium system have been determined for alloys of various compositions which have been quenched rapidly from the melt. The quenching and X-ray difIraction techniques are discussed in detail. Results of some cold-working and annealing experiments with the quenched alloys are presented. Difficulties-both experimental and of interpretation-are briefly noted. The lattice parameters of the recently discovered 1 nonequilibrium hexagonal close-packed (h.c.p.) phase in silvergermanium alloys have been obtained by means oT the DebyeScherrer technique . Similar measurements imply that the solid solubility of germanium in the face-centred cubic (r.c.c.) silver lattice is extended beyond the reported equilibrium value. At equilibrium, silver and germanium form a simple eutectic system.' The limit of solubility is 9·6%' germanium,' and is to be considered as restricted,' since it corresponds to a value of e/a = 1'29, where e/a, the electron concentration, is defined as the ratio of all valence electrons to the number of atoms. This investigation was undertaken with a view to determining the properties of the metastable structures so as to provide information which may eventually lead to a clearer understanding both of the metastable structures in this system and of the equilibrium close-packed phases in allied systems such as silver- tin, silver-antimony, and copper-germanium. Experimental _Procedure Alloys were prepared from chemically pure silver (ca . 99'95% pure) and zone-refined single-crystal germanium Paper No. 2089. Manuscript received 14 February 1961. Mr. Klement is in the Division of Engineering, California Institute of Technology, Pasadena, Cal. , U.S.A. • Compositions are expr sed in atomic per cent. (';3:99·999% pure). Weighed quantities of the elements were melted by induction heating in a quartz crucible under hydrogen . The alloys were then reweighed . The estimated TABLE I Diffraction Intensities of Phases in Quenched Alloys Alloy Com· posi tion . I f.c.c , h.c.p. b .c.p : Ge d·spadngs, intensities of unidentified lines, A Ir 4-10 vw al.- % Ge 9·0 9·6 10'3 11 ·9 IH 15·0 16·8 18·1 19 -9 21-6 23·2 25·9 s s s m w w Ir Ir Ir Ir w S S s s s s = stro ng, m = medium, Ir Ir w W = weak, 3·76 VW, 4· 14 VW 3·75 W, 4-13 m v = very, tr = trace. compositions (accurate to better than :rO-\ at.-% Ge) are given in Table I. The alloys, remelted in the quartz crucible under argon, were cast by sucking the liquid up into preheated l-mm-inside-dia . quartz tubing and immediately quenching 59 28 Klelllmt: Lattice Parameters of the Metastable into \\ater. Because of the stirring action of the eddy currcllls and the speed of the quench. the cast alloys were of homogeneous composition throughout. (This conclusion was writied by noting that the data obtained from different portions of a gi,'cn casting were reproducible, within experimcntal error.) Finally, the quartz tubing was broken away and the alloy, in the form of short lengths of I-mm-outsidedia. wire, was ready for usc in the rapid-quenching apparalus . The principles of this rapid-quenching technique have been described elsewhere.' Graphite nozzles (i.e. crucibles) were used in air throughout the investigation. Reactions with carbon. oxygcn. and nitrogen should be negligible in the tcmperature range involved; also, the vapour pressures of the clements should be so low as 10 be safely neglected. To obtain a suitable spccimen, approximately 25 mg of the alloy was loaded into the nozzle, which was then heated 10 1300 ± 25 ' C by means of eddy current s. The molten alloy was [I..(CTIiiON The lines on the Debye-Schcrrer films were, in all cases, continuous and of uniform in tensity. T his ind icatcs that there is no obvious preferred orientation and that the crystallite size is less than, say, a few microns. Broadening of the lines was noted but was not considered 10 be pronounced. Further investigation (to estimate the minimum crystallite size) did not seem to be justified. since the effccts of residual strain (and possible stacking faults) must also somehow be taken inlO consideration. In this connection, it was observed that , at high angles, the K, doublet was resolved in the predominantly f.c.c. alloys but not in the predominantly h.c.p. alloys. Consequently, the uncertainty in the determination of the lattice spacings of the h.c.p. structures was much grea ter than that of the f.c.c. spac in gs. The positions of the sharp diffraction lines were read to within 0·005 cm; when diffuse high-angle lines were encountered, the films were reread a number of times 10 obtain (O .. (U. T" .. TIO .. ...o,~,·t~'-2-----r---~r----T""---T---.....,..----4"'----,----T-----,--"" &. OWE"" • ..., IIDWL.""'DS EI ""ESENT STUDY .. Ag Fig . 1 Louiee p(Irometers of f.c.c. structu res plotted against cOmpO$ilion. Uncerta;nlif>s in the spacings are indicated by the vertical Jines on 'h e squorcs enclosing 'h c points obtain ed by 'h e best extrapolations again$l the Nelson - Riley function. The 114..'0 sets of dOlO It'er e rccl)rdecl at diffrrel1l temperatures (see t ext). ejected on 10 a polished copper strip held on the inner periphery of a rotating wheel. Heat was extracted very rapidly from the alloy, assisted, in part, by the centrifugal forces on the droplet which ensured good thermal contact with the substrate. The time necessa ry for the alloy 10 reach the temperature of the copper conductor is estimated to be a few milliseconds. (A lower lim it for this time may be estimated by noting the speed of the wheel and the extent of the spreading along the circumference; this lower limit is about a halfm illisecond .) The thickness of the specimen was 15 ± 5 fl. A flake (ca. 0·7 ± 3 mm') was ca refully removed from the substrate, stuck on 10 a quartz fibre with Celvacene, and mounted in a Norelco Debye-Scherrer camera (radius = 5·73 cm) so that the incoming beam of filtered CuK radiation was normal 10 the plane of the specimen. Exposures were made for a few specimens both rotated and stationary; comparison indicated only a negligible difference in d-spacings, while the lauer technique often yielded sharper lines as well as very fai nt lines otherwise absent on the film obtained from the rotated specimen. Thus, the procedure of not rotating the specimen was adopted . Typical exposures were for 3 h at 35 kY and 15 m .amp, using Kodak No-Screen film. good averaging. Corrections were made for film shrinkage. Extrapolations to 0 = 90° by means of the Nelson-Riley function yielded the lattice spacings of the f.c.e. and h.c.p. st ructures. For the latter, various values of the axial ratio were assumed until the best- extrapolated values of c and a could be obtained. Errors were estimated from the extrapolations. All spacings are given in Angstroms with A(CuK•• ) = 1'54050 A. Results By visual comparison of the intensities of the strong lowangle lines, e.g. the h.c.p. (10.0) and (10.1), f.c .c. (200), and Ge (Ill), rough estimates were made of the quantity of each phase present in the quenched alloys (Table 1). Also included are the d-spacings and intensities of the several unidentified lines. The accuracy of these spacings is, of course, limited by the difficulties inherent in reading faint or diffuse lines. The lattice spacings of the f.c.c. alloys are plotted against germanium content in Fig.!. (In anticipation of its possible pertinence, an electron-concentration scale has been included .) 60 Close-Packed Structures ill Silver-Germanium Alloys Th~ results of Owen and Rowlands' are also presented, after com"Crsion from kX to A units. Since their work was done at IS · C (cf. 16 ::: 4 ' C in the present work), a correction must be applied for the temperature difference. The "'ttice parameters and axial ratios of the h.c.p. alloys arc plotted against germanium content and electron concentration in Fig. 2. Within experimental error, the h.c.p. strucELECTRON 29 Specimens of this alloy were quenched upon copper strips in the usual way so as to produce the metastable phase. With TABLE \I Variation of Intensities of H.C.P., H.C.P.' Diffraction Lines with GcrJllaniurn Content CONCEHTJIATIOH Germanium. at.- X Indices 18 19 21 22 (h •. l) 17 (10.0> (00. 2) • (10. 1) (10.2) .n15 •.. ••• .• •• . •• . •••••.•••.•• 5 ••.••.•.•.. . •••••••. 20 2) .. \'5 . • . . _.......... . .................. . .. . ......... . . . . n . .. . 5 diff ... . .. .. .. ..........•..... .. .. . ...... . . \' \ '5 . . (absent) vw diff ms ..... . .... . . . ..... .. s .. .. (11.0) • . s ... ...••....... . .. .. •. . .•...........• • • • • . .••....... S .••. (to ..1) (absent) vw difT ms ..... . ..... . . _ ....... s. (~O .O) . vw ..•............. .. •.. . ...... .. ....•• • • .. • •• . .. . ... \·w •. (l1.~) • . nlS ....•...... .. ..... .• .... . ..... .... • • • • .• • •• ... .. .. Ins . . CO.I) .nl •••••••••• ••••• • ••••• ••••••••••••••• • • • • • •• • ••••••• 111 •• • ((10.4) .w ............ . . . . . ... . .......... . .. . . ... . .. .. ..... w .. . t20.:!) (ahscnl} vw ...... . . ... ... .. ..... w . •• (ab~nt) vw .....•• •. . . • • . ... .... w .•. . ••••••• .. vv.- di lT Ill . . • . . • • •• • ••• •• •• . . • . • 1" (12.0) .. •...... . vw . ....... ••• • .. .. . w .•.... •••••• ••• •• ..•.• w ••• (12.1) . m .. . ... .. .......... ••.. .•... . •• ..• ••••••••••..•.• n1 ••• (11.4) • .m . . ... . ... . ........ . • • ... .. ......... • ••... •• ........•n . .. ( 10.5) ....... .. . vw diff m ..•..••.• ••• •••....•.• n1 ••. (20.4) . (absent) vw .......... . ....... .. . vw .. ()O.O) • . mw difT............ . . •• . .... . ... . . ••..... n1W difT. (12.) . ........ . w diff ms difT ...... .. ....... ms difT.. (00.6) • . m diff ........... .. ...... .. ....... . . . .............. n\ dilT. ( 10.4) (20.3) ··., > . The position of a symbol (e.g. vw diff) along a horizontal cor(esponds to the alloy whose composition is given directly above. Continuous variation of intensity from alIoy to alloy is to be inferted from the connecting series of docs: abrupt changes are emphasized by absence of dots. For a lloys containing thc h.c.,,: phase (high Ge content) there is lin le variation in relati\'c intcnsit y : for alloys of somewhat lower Ge content the intensities are altered by the o\'crlapping f.c.c. reflections (marked by an asterisk). > oj CIIII COPPER Fig.2 Lau;ce parameters Qfh.c.p . ~ h.c.p.' structures plotted against composition. The meaning of the vertical lines, squa res. and (OO.2IHCP· IIII)FCC enciasc(I points is the same liS in Fig. 1; for a given composition. points enclosed by squares with vertical lincs on the right (or Jeft) lire obtnined from th e same specimen. For similar valu es of the spacings. the number of squares about the points denot.es the number of indepenc/ent dala considered. In the absence of vcrtical lines, uncertainties in th e parameters are indicated by the si:e of the S(jlwres . The relatively large errors are discussed in the text. ture (denoted h.c.p.') found in alloys containing ;;:22-23% germanium seems to be invariant with composition. The I'lllice spacings of the h.c.p.' structure in a quenched alloy containing 49·7% germanium are: a = 2·898 ± 3 A, c = 4·723 = 3 A, cia = 1·630 ± 3. Lines at d = 4·14 A (mw) and 3·72 A (vvw) were also observed. Typical intensities for the diffraction lines of the h.c.p., h.c.p .' structures are given as a function of germanium content in Table II for the alloys of Table I ranging from 16·8 to 23·2% germanium. These may be useful for qualitative comparisons, but should not be incautiously considered as absolute measurements. Changes in the intensities, plus the appearance of the extra low-angle lines, leads to the distinction between the h.c.p. and the h.c.p.' phases. J PARTIALLY OfCOMPOSEO .. ze, OEGREES Fig. 3 Diffractometer traces of the angular region con raining the strong lou}·angle diffraction peaks of th e fc .c. ami h.c.p.' structures. The upper trace is that of th e 25·9 % germanium alloy shortly after quenching; th e lower trace rep resent.s th", degree of decomposition referred to in th e isoth ermal·ann ealing and cold.working experiments. The eu (111) peak is clue to the substrate; it is of no interest and has been truncozed. Other Observations Some work was done with the h.c.p.' phase in the 25·9% germanium alloy to obtain semi-quantitative estimates of the effects of temperature and mechanical working upon the transformation (i .e. decomposition) to the equilibrium phases. a Norelco diffractometer, continuous scans were taken over the angular region containing the strongest lines. Then the specimens were isothermally annealed in air until a given stage of decomposition was attained (Fig. 3). Typical times 61 30 Lallice Parameters of Ihe Il/felastable Close-Packed Structures ill Sih'er-CerlllalliulII Alloys and temperatures corresponding to this degree of transformalion 3rc: Time. min ± =:O o;.~ Temp .. ~ C ± 10'" C 5 40 200 350 300 250 Oth~r. rather cursory diffractometer work indicates that, initially, the nucleation and growth of the equilibrium phases proceed very rapidly, as a result, presumably, of the abnormal number of lattice defects retained during the quench. Since the qualHity and type of defects cannot be controlled (or even estimated) at present, further work on the kinetics has been postponed. To obtain order-of-magnitude estimates of the effects of cold working, specimens of the alloy were again quenched upon copper strips. Both specimen and strip were then cooled in liquid nitrogen. By means of a small rolling mill. the ltHalthi<.:kncss was rcducl!d in 10'% decrements. ever, Barrell's work 7 on stacking faults may be of pertinence here. He argues that the faulling tendency should be high for supersaturated phases in a two-phase (equilibrium) field in which twO close-packed structures coex ist. The stackingfault energy of the alloys considered here should be very low, perhaps of the order of I erg.'cm'. ' Pronounced faulting is thus possible. Barrett further suggests that the plastic deformation accompanying the (s<) lid-state) quenching may initiate the faulting. For alloys quenched from the liquid state, growth" mistakes" during solidification a rc probably also involved. Experimental verification of the hypothesized faulting could most readi ly be obtai ned by transm ission electron microscopy. Attention is directed to the 16'8% germanium alloy; uncombined germanium has been detected in the quenched alloy, as well as a low-angle unidentified line. However, a change in intensities, as noted for alloys containing the h.c.r .' structure. has not been observed. Possibly. decomposition has pro- UClwccn ceeded further. at roolll tcmpcraLUrc. in this alloy tha n in passes, the specimen and strip were kept at - 190" C. Upon examination (at room temperature) in the diffractometer, it was found that decomposition had indeed occurred; a reduction in thickness of ~50% was responsible for roughly the same degree of transformation as shown in Fig. 3. the adjoining alloys. If so, this might suggest that the unidentified lines are associated with the decomposition. As mentioned above, the h .c.p: structure appears to coexist with germanium throughout the region ca. 20 - 100% germanium . The exact nature of this st ructure, taking in to account the change in intensities and extra diffraction , lines, has yet to be determined. The situation is further complicated by the lack of knowledge concerning stacking faults, vacant lattice sites, and possible intermediate decomposition products. Discussion For metals not forming continuous solid solutions, it is predicted 6 that the primary solid solubilities should be increased under non-equilibrium conditions. The question arises: What factors limit t he metastable solubility of one component in the other? T he data cogently suggest, in the author's opinion, that the metastable primary solid solubility of germanium in silver is limited by the same facto rs operative at equilibrium when restrictions due to, say, disparity in the size of the atoms are unimportant. 1f it can be assumed that the lanice parameter varies linearly with composition through the whole region (and this relation holds empirically for the majority of other, similar alloy systems), the" terminal" composition is found to be 13·0 ± 1'0% germanium (Fig. 1). For alloys of slightly greater german ium content, the lattice parameter of the f.c.c. structure is, within experimental error, the same -4,09 10 ± 4 A-as that of the .• terminal" alloy. Assigning the conventional valences, this limiting composition would correspond to an e/a = 1·39 ± 3, a value which has been given considerable theoretical foundation.' The inability, in general, to obtain specimens containing only a single structure (Table 1) is to be emphasized. How- AclmowlcdgemenlB Professor Pol Duwez contributed some useful suggestions, as did R. H. Willens. Support was jointly provided by the U .S. Office of Naval Research and the U.S. Atomic Energy Commission. References 1. Pol Duwez, R. H. Willens, and W. Klement, Jr., J. Appl. Physics, 1960,31, 1137. 2. M. Hansen and K. Anderko, .. Constitution of Binary Alloys ". 1958: New York and London (McGraw-Hili). 3. E. A. Owen and V. W. Rowlands,J. IllS/' Melals., 1940,66.361. 4. W. Hume-Rothery and G. V. Raynor, .. The Structure of Metals and Alloys ". 1956: London (Inst. Metals). 5. Pol Duwez. R. H. Willens, and W. Klement, Jr., J. Appl. Physics, 1960,31, 1136. 6. See, e.g. L. S. Darken and R. W. Gurry, .. Physical Chemistry of Metals" . 1953 : New York and London (McGraw-Hil I). 7. C. S. Barrett, .. Imperfections in Nearly Perfect Crystals ", p. 97. 1952: New York and London (John Wiley). 8. P. R. Swann, private communication. © The Institute of Metals. 1961. 62 The statements made thereln remaln yet valld. In addltlon, low angle hCp/ dlffractlon 11nes were detected wlth the germanlum-rlch phase in alloys contalnlng as llttle as 5 at.% Ag. As reported in the preltmlnary cornmunlcatlon(35), the solld solubl1lty of slIver ln germanlum appears to be very small. Proceedlng from the results obtained in the Ag-Ge system, (17) the homologous alloy systems Ag-Sl, Au-Ge and Au-Si were investlgated. For Ag-Sl, it could not be established whether the primary solld solubl1lty could be extended and there was some indlcation of a metastable hcp phase (cf. III.C.b.). For Au-Ge, lattlce spacing measurements did not seem to indlcate any appreclable extenslon of prtmary solid solubility; however, very complex nonequilibrlum structures, as yet unravelled, were found in quenched alloys. For Au-Si, equally complex nonequillbrlum structures were found ln many alloys but, more tmportantly, noncrystalline structures were occaslonally obtalned(3 6 ). This seemed to have been the first ttme that noncrystalline structures were obtalned in metaillc alloys by cooling from the melt and the results have already been used by Cohen and Turnbull (37) (38) ln thelr theory of glass formatlon. d. Various data for Ag-Cu, Cd-Zn alloy systems In order to attaln any semblance of understanding of the solldlfication process, the properties of both the 11quid and so11d state must be cons1dered, espec1a11y 1n the v1c1n1ty of the meltIng po1nts . Much of the avaIlable data of pertlnence 1s here assembled; where experlmenta1 results are lack1ng, estlmates of the quant1t1es of Interest are made. Some data for the component elements In the Ag-Cu, Cd-Zn alloy systems are g1ven in the fo1low1ng tabl~39)(40)(7). Cu Nt. Cd Zn At melting po1nt : T(oK) 1234 LJ Hf heat of fusion (kcal/mole) 2.69 2.84 1.50 1. 74 (cal/moleOK) 2.18 2.09 2. 53 2.51 change (%) in volume 3.8 4.15 4.7 4.2 8 at 3.06 11 at 2.94 l::, Sf entropy of fus10n ~V Coord1nation numbeA at distance 1n )t liquid solid Self-diffus1on (solId) Do (crn 2/sec) Q (kca1/mole) 594 8-11 4 at 4.0 12 at 2.89 12 at 2.55 6 at 2.97 6 at 3.29 6 at 2 .66 6 at 2.90 0.40 0.10 (1) 0.20 0.05(1/) 44.1 47.1 18.2 (//) 19.7(1) 0.58(l) o .1 3{/t) 21.8 (II) 24.3(1 ) 64 Lumsden (41) has given a thorough discussion of the rather high quality thermodynamlc data aval1able for the Cd-Zn system. Slnce lt ls of interest to attempt an estlmate of the miscibility gaps in the undercooled liquid alloys , the pertinent informatlon for Cd- Zn is that the excess heats of solution are: 2 2000 N Zn in cal/mole, with Nl the atomic fraction of 1; there does not seem to be any excess entropy. For Ag-Cu, Edwards and Downing (42) have published some data which apparently differ considerably from that in a preliminary report; the latter was used by Kubaschewski and Catterall (43), who arrived at somewhat different estimates for the various quantities. According to the later results(42), both positive excess heats of solution and excess entropies exist but diminish with decreasing temperature. Despite con- siderable scatter in the data , the excess heats of solution at l42S oK are crudely estimated by the present investigator as : 2 HCu;:::::: 3400 N Ag, and from the Gibbs-Duhem equation, HAg -::::::::. 3400 N2Cu An overestimate of the temperature of unmixlng results if the temperature variation and excess entropy are neglected but th1s 1s done. Nakagawa (44) Accord1ng to the model employed by , the temperature at the boundary for com- pos1 tion N 1s: T= ~ rl10g ~ -J 1_N1 N with '!! ~ 1000 for Cd-Zn and 1700 for Ag-Cu. The (sym- R metr1c) values obta1ned are: Cd-Zn N T(OK) T(OC) 0.5 0.4 0.3 0.2 0.1 0.05 oo a 94 470 277 221 197 158 91 32 t 41 3 4 305 Ag-Cu 0.5 0.4 0.3 0.2 0.1 0.05 ~ag 799 133 619 519 Temperature dependenc1es of the v1scos1t1es of 11qu1d metals have been shown to be descr1bed qu1te well by express10ns of the form 1 = A exp ( ~) 66 Gebhardt and coworkers(45) have measured the v1scos1t1es at d1fferent temperatures for a number of elements and some alloys. To est1mate D, the Stokes-E1nste1n relatIon may be a faIr approx1mat10n (46), v1z. D = kT G-r(~r where r 1s taken to be the 10n1c rad1us(47) and lInearly The measured interpolated values are used for the alloys. and est1mated quantItIes are collected In the followIng table: -rr. (centipoises) .till at at Q(kcal/mole) 10520K 841 0K 8.6 cu .36 .55 D(cm 2/sec) at at 941 0K 102 20K 0.96 2. 22xlO- 4 1.16xlO- 4 23 at. %Ag;Cu 5.5 .31 .43 1.03 2.40 1.39 35 at.%Ag;Cu 5.4 .29 .40 1.06 2.50 1.45 63 at.%Ag;Cu 4.9 .28 .37 1.14 2.41 1.46 84 at.%Ag;Cu 4.9 .27 .36 1.21 2.36 1.41 Ag 4.9 . 26 .36 1.26 2.34 1.35 at 539°K at 431 0K Cd(4S) .29 .43 0.97 Zn .27 .37 0.74 1.96 at 5390K at 4310K 1.40xlO- 4 0.76xIO- 4 1.15 There have been no systematic studIes of the undercooling possIble in these alloy systems with, say, the standard small droplet technique. Turnbull (22) has obtained under- coolings of 227°C for Ag and 236°C for Cu. Sundquist (23) found undercoolings to 726°c and 750 0C for 36 at.%Cu;Ag and 43 at.%Cu;Ag alloys, respectively. Undercooltngs for Cd-Zn alloys on both sides of the eutectic seemed to be small (49) • Turnbull (22) est1mated the liquid-solld 1nterfaclal energy, <7i!:; , as 128 ergs/cm 2 for Ag and 189 ergs/cm 2 for Cu; slmllarly, the present investlgator obtalned 60 ergs/cm 2 for Cd and 91 ergs/cm 2 for Zn. Estimates of the free energy vs composltlon curves for the solld alloys are made at the eutectic and 0.8 eutectlc temperatures wl th Hardy's" sub regular" model (50). Uslng experimentally determlned phase boundarles and assum1ng no en trop les other than those of m1xing, the model employs equatlons of the form: where x 1s at.% solute and ~ = 6620 ,A2 = 4640 cal/mole for Ag-Cu and Al = 3800 , A2 = 4540 cal/mole for Cd-Zn. The dlfferences ln free energy between solid solutlons and stable two-phase alloys at the eutectlc and 0.8 eutectlc temperatures are plotted vs compos1t1on ln F1g . 14. These estlmates may be wl thln 20% s1nce the " subregular" model allows only for asymmetrlc solld solublllt1es but not for 68 W500~---r----~--~---.----'----.----.----.----,---~ ....J o /"'- ~ 400 /' ....J <{ U ~ ~ <.!) / / 300 /~CD-ZN / / 158°C/ /' -266°C/ / I a::: ~ 200 I w / w a::: / / IL. / / w x w u F1gure 14. / / / / -.... .................. '- '- "- "- "- ,, ~~ ~ / I / w en en ---- /' / / / / / r CU ZN D1fference 1n free energ1es between metastable so11d solut1ons and equ111br1um phases for Ag-Cu and Cd- Zn alloys at eutect1c and 0 . 8 eutect1c temperatures as funct10n of compos1t1on according to the model of Hardy . excess entropies, which may be present. Gross errors are to be expected from this model at temperatures far removed from the eutectic. Neglectlng excess entropies, temperature dependencies of entropies of fusion, excess enthalpies, and specific heats as well as the lim ited solid solubilities , the driving free energies for solidification for equiatomic Cd;Zn and Ag;Cu melts are obtalned at the eutectic and 0.8 eutectic temperatures from the above data. For the Cd-Zn alloy, the negative free energy for solidification lnto the equilibrium two-phase configuration is approximately twice that for the metastable solid solution; for the Ag-Cu alloy, the relative differences are ~10% and ~20% at the eutectic and 0.8 eutectic temperatures, respectively. There exist no reasonable approximations f or the various diffusion-related phenomena in non-dilute solid SOlutions(40). However , diffusion coefficients may be within a few orders of magnitude of the self-diffusion coefficients (bulk) computed at the various temperatures of interest, viz.: 70 D(cm 2/sec) meltIng point eutectIc O.B eutectIc room 10- 32 6 x lO- B Ag 3 x 10- 10 10- 13 10- 34 4 x 10- 10 10- 14 Cu 5 x lO- B Cd 10- 9 Zn 2 x 10- 9 D. DISCUSSION 2 x 10- 10 2 x 10- 11 3 x 10- 12 10- 12 liquid nitrogen 3 x 10- 16 10- 53 10- 17 10- 63 Ideas In the following areas are reviewed wIth respect to their possIble pertInence and valIdIty In the present work -- liquId alloys, especially undercooled lIquIds; homogeneous and heterogeneous nucleation of solid phases from the melt; growth of the nucleated phases; solid state reactIons, especially precipItation . The speculations and ideas of previous workers in the present area of rapId solidification, as presented in III .A., are dealt with. In- terspersed throughout are other results from the present experiments; conclusions are tentatIve and designed to encourage further experIments, as is approprIate for a frankly exploratory investigation. From the few measurements (51) that have been made, many propertIes of undercooled liquId alloys seem to be smooth extrapolations of those propertIes In the equilIbrium region. AssumIng no appreciable excess entropIes, the multlcomponent 71 11qu1ds tend to unm1x or order accordlng to whether the enthalpy of mlxlng ls posltlve or negatlve, respect1vel y. Unmlxing of undercooled 11quld alloys has been observed by Nakagawa (44) (Cu-Co and Cu-Fe alloys) under nearly statlc condltlons. Whether unm1xlng or the tendency thereto, 1.e., clustering of llke atoms lnto small groups, can occur under more dynamlc cond1t1ons -- such as 1n the present experlments -- has not been dlrectly determ1ned. Crltlcal in thls matter are the d1ffusion rates 1n the llqu1d alloy. Accord1ng to Nachtrleb(46), the sUnple picture of atoms Jumplng fram place to place, wh l ch sufflces to descr1be d1ffus1on 1n the crystall1ne sol1d, 1s not valld for the l1qu1d state 1n wh1ch a rap1d, collect1ve sh1ft1ng of groups of atoms is a preferable 1deal1zat1on. Such a model has not proved particularly amenable to calculat1on; measurements suggest(46), however, that the Einste1n-Stokes relation prOVides a fa1rly good connect1on between D and the read1ly measured~. As est1mated for the Ag-Cu and Cd-Zn alloys (IILC. d. ), D var1es between I and 2 x 10- 4 cm 2/sec over the temperature range of interest. < dlffusion length I> -;::::. sec, \./" 10- 4 em or 10 4 R. Thus the mean -J4Dt is, for times of order 10- 4 Thus it seems that the m1cro- scop1c d1ffus1on processes in the liquid are not sensibly affected by the present rates of cooling. Therefore, in- s1de or near a solubil1ty gap in the undercooled liquid, it is diff1cult to see how clustering on at least a microscopic 72 scale can be prevented. It has not been posslble to obtaln extenslve metastable solld solutlons ln those systems ln whlch a reglon of 11quld lmmlsclblllty occurs at equl1lbrlum, e.g., AI-In, Cu-Pb, and also those systems ln whlch unmlxlng of the sllghtly undercooled 11quld ls expected, e.g . , Cu-Bl, Ag-Bl, Ag-Pb and Cd-Zn. It ls, therefore, suggested that a necessary but not sufflclent condltlon for the extenslon of solld solublllty by rapld solldlflcatlon (and concomltant undercool1ng) be that the 11quld ls not cooled or undercooled lnto an equl1lbrlum or metastable solubl1lty gap. Because dlrect measurements are lacklng and perhaps imposslble, lt ls necessary to estimate the magnltudes of the undercoo11ngs sensibly possible 1n given alloy systems. The slowest step 1n crystallization from the metallic melt is the nucleation of the solid phase(s) and not the subsequent growth from the liquid . As the process of nucleat1ng (21)(22) a homogeneous solid phase is usually visuallzed , the bulk free energy driving force for crystallizatlon below the melting po1nt is opposed by the work necessary to create the surface between the solid and the liquid. At large under- cool1ng, the rate of creatlon of nuclel of critlcal radll is very great. Experimentally lt has been Shown(22), under nearly statlc conditlons, that ~20% undercoolings were the approxlmate limlts for metallic elements. For aluminum solidified under dynamic conditlons, Falkenhagen and 73 Hofmann (2) found stmI1ar limIts, and lIkewIse for the Cu_NI(22) alloys whIch exhIbIt cont1nuous equilIbrIum solId solub1llty. Except under very refined statIc cond1t Ions , e.g., the small droplet technIque (22) , homogeneous nucleat10n 1s rarely observed. Usually nucleatIon takes place on an 1mpurlty and It has been stated(22) that as 11ttle as 1 part 1n 10 16 of impur1ty can cause perceptIble heterogeneous nucleat10n under the typIcal statIc cond1t1ons. The formal theory of (21) (22) heterogeneous nucleat10n assumes the formatIon of one type of nucle1 and then presumes to delineate the cond1tIons for the nucleation of the other phase(s) upon the (23) inItIally formed solId. SundquIst ,studying heterogeneous nucleatIon in binary alloys wIth the small droplet techn1que, has recently shown many of the assumptIons of the theory to be Inadequate. Reta1nIng the orIgInal assumpt10n of the In1t1al formatIon of one class of nucleI, he proposed a "nucleation serIes" to rat1onal1ze hIs observatIons. Elements hIgh In the series (see below) are readIly nucleated by those elements lower in the ser1es and pronounced undercoolings are not possIble . The elements h1gh in the ser1es (low entropy of fus1on) are poor nucle1 for those below. Some ambiguIt1es were noted, though, and the general- Ity of the conclusIons 1s uncertaIn. 74 ElE'IIlent not necessarily 1n th1s order Entropy of fus10n (cal/moleOK) Tl Pb 1.78 1.81 Ag Au Cu N1 Co Fe 2.18 2.28 Ge Sn 5.93 3.32 2.51 4.83 5.25 2.~ 2. 2.12 2.01 Zn B1 Sb Other exper1mentJ5 2 ), under nearly stat1c cond1t10ns, suggested that the in1t1ally formed nucle1 may reproduce themselves rather than be solely occup1ed w1th nucleating the other phase(s). Thus, the formal theory of heterogeneous nu- cleat1on, wh1ch 1s rather successful in descr1b1ng aspects of other transformat10ns, 1s not adequate 1n the case of the 11quid-so11d transformat1on. The present results, e.g., Ag-Cu and GaSb-Ge, suggest, further, that the assumption of one class of nucle1 form1ng or1g1nally may also be quest10nable, at least 1n the l1m1t of very h1gh cool1ng rates. The nucleat10n phenomena in the present work are poorly understood but, nevertheless, some essent1ally qual1tat1ve ideas are advanced. Fundamental to the developinent 1s the prev10us conclus10n that, desp1te the rap1d rate of coo11ng, the d1ffus10n processes are much faster in the liqu1ds and equ1l1br1um 1s more nearly approached at all temperatures. 75 It 1s assumed that the s1tuat1on 1n the undercooled l1quid 1s descr1bable by the class1cal theory of homogeneous nucleation (22), v1z., a sharp 1nterface ex1sts between the liqu1d and solid nucleus, wh1ch are taken as unifonn 1n compos1t1on; recent suggest1ons(53)(5 4) of nucle1 w1th diffuse 1nterfaces and compos1t1onal grad1ents are presently being subjected to experimental exarninat1on(55) and do not now seem to be preferable to the class1cal theory. For nuclei of cr1t1cal rad1i I*, -2 CJlS r* = 6G v where <ts 1s the liquid-solid interfac1al energy and Ll Gv 1s the bulk free energy dr1ving force for solidif1cation. Few measurements ex1st for cts • is ~ G*, Another important quantity the free energy barr1er for a nucleus of cr1t1cal radiUS, which is K G* crt:s 3 = where K is a geometr1cal factor. Furthermore, a free energy of act1vation, 11 GA, 1s postulated, wh1ch determ1nes the rate of movement of atoms across the 1nterface through the usual expresslon from absolute rate theory . The rate of formatlon of nuclel , I, ls then log I = log K - ( D. G* + t1 G ) v A kT where K ls an almost tanperature-lndependent factor Inv volv1ng, among other quantltles, the slze of the nuclel. Un- known here ls iJ G whlch ls, however, usually taken as r v kT. A Unfortunately, the frequency of movement of atoms across the lnterface and consequently the trans lent rates of nucleatlon are exponentlally sensltlve to A G . that b. G* >;> ~ G . A Translents Usually , lt ls assumed (22)A are probably not of lmportance slnce nuclel of ~ 10 7 atoms are requlred at the ..:6 GA r--.../ kT and 1t does not seem llkely that such large nuclel are lnvolved . Jackson and Chalmers (20) have developed an alternatlve model of the solldlflcatlon (and nucleatlon) processes ln whlch the net rate of the process ls obta1ned from the dlfference ln the rates of freez1ng and meltlng, as consldered lndependently. For undercoollngs of rv 20%, lt was estimated that crltlcal nuclel contalned only ~ 103 atoms. Jackson (19) , ln a further elaboratlon of thls approach, speclflcally sought to treat the Ag-Cu system. Although the appllcablllty seemed somewhat forced, lt was suggested that 77 the equl1lbrium conflguratlon was a good app roxtmatlon up to growth rates of 100 cm/sec. Thls does not seem to be so (as dlscussed below) . Conslderlng the Ag-Cu results flrst , lt ls not clear where ln the nucleatlon process outllned above the metastable solld solutlons galn a clear-cut advantage over the equlllbrlum phases as a result of the present large coollng rates. It ls expected that phase and, of course, conf 19urat 10n. OLS ls less for an equillbrlum \ ~ Gv I ls greater for the equillbrlum From the prevlous est 1mates of L::, G v equlatomlc Ag-Cu alloys, lt ls suggested that perhaps for r* (metastable solid solutlon) ~ 1.15 r* (equillbrlum) for Ag-Cu. It thus appears lnescapable that many nuclel of the copper- and sllver-rlch phases are formed together wlth the nuclel of the metastable solld solutlons. For Cd-Zn, the dlfference ln free energles may be so great that only a negllglble number of metastable solld solutlon nuclel are formed. For the Ag-Ge alloys, lt ls temptlng to suggest that there ls some tendency for short range order ln the undercooled llquld, resultlng ln a QLs sufflclently lower than that of the equlllbrlum phases to compensate lor the dlfference ln b G and thus ln a reasonable nucleatlon probabil lty for v the metastabl e hcp phases . Also demandlng attentlon here are the coexlstlng fcc and hcp phases ln Ag-Ge, Ag-Sn and Ag-Sb alloys. It has been 78 suggested (56) that the free energy differences between fcc structures and hcp structures of stmilar dtmensions and nearly ideal axial ratio must be small in the (equilibrium) two-phase region. Accordingly, faulting requires energies of only a few ergs/cm 2 • Although there seems to be a compositional limitation to the prtmary solid solution, the close packed structures are much alike in other ways, perhaps with nearly the same ~. On this basis, nucleation of the two phases (with usually the same composition) in proportions as detected is a real possibility . Tacitly ignored thus far are the effects of the impurities inevitably present . In contrast to the stat ic under- cooling techniques , dynamic expertments such as the present work and that of Falkenhagen and Hofmann -- seem to be little affected by extraneous matter . For a reasonably dilute amount of impurities of perhaps low nucleating power (a' la Sundquist) , 1t is 1mprobable that enough nuclei could be produced to materially affect the situation before the temperature had decreased suff1c1ently so that an avalanche of nucle1 was brough t about . It is necessary to consider the dispos1t10n and effects of the release of the heat of fus10n . In the static ex- pertments(22) it has been found that the small droplets were heated up to the so11dus temperature during th1s per10d of recalesence 1n the initial stages of solid1ficat10n; Falkenhagen and Hofmann found s1m11ar behavior . It 1s not 79 clear how much the undercooling persists as solidification proceeds. The rough estimate (App. II) suggests lO-6.5!O.5 sec for the release of heat and solidification; a more realIstIc number is perhaps 10- 5 sec. As estimated from the equilibrium bulk diffusion data, <1), at the Ag - Cu eutectic temperature, is then only /V 10~ for the latter time interval, although, in reality, it must be somewhat larger due to the excess vacancies, etc. Movements of simIlar magnitude may be expected In the solId as It cools on the substrate. However, these matters are inextricably bound up with the processes of growth of the solid phase(s) from the melt. To make connections between the present work and the body of experIence (57) (58) amassed for growth under more leIsurely and controllable condItions, It seems to be necessary to understand the morphologies of the solIdIfIed materials . The graIn sIzes are, however, usually too small to allow optical examInatIon and electron mIcroscopy is clearly required. It has been long realIzed that the growth rates of solId nucleI in undercooled lIquId metals are very high and, Indeed, may vary as the square of the underc001Ing(59) • DifficultIes In measurement have prevented the establishment of any sensible upper lImit, save that implied by the need for a supply of atoms by dIffUSion In the lIquid. The model 80 of Jackson and Chalmers (20) suggest s /V 200 cm/ sec as an upper lim1t for the present temperature range. Macroscop1cally 1t 1s expected that the growth rates 1n the present exper1ments are rv 10 2 em/sec. Gra1n s1zes are relat1vely small because of the abundance of nucle1 produced homogeneously 1n the undercooled 11qu1d adjo1n1ng the substrate or produced heterogeneously (but not ep1tax1ally) by the substrate. Gellar and Garbeck(60) have undercooled l1qu1d metal11c alloys encapsulated in slags and found that f1ne gra1n s1zes were associated with pronounced undercoo11ngsj this was also apparent from the microstructures presented by Sundqu1st in his thesis (23) • Desp1te the quant1tative deficienc1es in the understand1ng of the growth processes, some qua11tative arguments are poss1ble. For the Ag- Cu alloys, it seems inescapable that a good many nucle1 of the equi11brium phase(s) are created along with those of a compos1tion approximately that of the 11qu1d. However, 1t is plaus1ble that the growth rates of the metastable nuclei are much greater than those of the nuclei of nearly equilibr1um compos1tion s1nce the latter are selective in the choice of atoms supp11ed by the liquid while the former accept atoms ind1scr1minately. The process 1s thus visualized as a compet1tion between the var10us spec1es. For the Ag-Ge, Ag-Sn and Ag-Sb alloys, 1t seems l1kely that the growth rates of the fcc and hcp phases are 81 about the same. Because of the low faulting energies ex- pected, it is not improbable that "mistakes" during growth are also involved. Thus different, but s1milar structures of the same composition can be rationalized in this way, with implications perhaps of applicability to other pairs of closely related structures. For the structures in Ag-Ge alloys, it is likewise reasonable that the growth rates of the metastable hcp phase are much greater than those of the equilibrium phases. Upon further cooling of the solidified alloy and its subsequent examination and maintenance at room (or liquid nitrogen) temperature, there is the possibility that the metastable structures thus far retained might anneal out and decompose to some transition structure or to the equilibrium structures. With the present technique, it is r eason- ably expected that many latt1ce defects, such as vacanc1es and perhaps 1nterstitials, have been retained in the quench. Thus diffusion rates are enhanCed(6l); also the relatively large proportion of gra1n boundar1es and the possib111ty of mechanical deformation during the quench would tend to promote diffus10n over and above that expected from the equilibrium bulk parameters. Because of the uncertainties in these quantities due to the inability to sufficiently control the quenching technique, it is difficult to assess their participation in the solid state reactions. An attempt to study the kinetics of decomposition of quenched 60 at.%Ag;CU 82 alloys was unsuccessful because of the tnab1l1ty to obta1n reproduc1ble results due to the var1able 1n1t1al cond1t1ons. The 1n1t1al stages of the decompos1t1on were more rapid because of the hypothesized abundance of latt1ce defects . It was expected that precip1tat1on would occur more read1ly at the grain boundaries although nuclei of the equilibr1um phases, reta1ned 1n the quench, would have been fa1rly potent in the transformat1on . Until the cond1t1ons of the quench can be controlled, k1net1cs work w111 rema1n qual1tative. The results obta1ned for the Ag- Gu alloys (III.G.a.) apparently require 1nterpretation both in terms of the competit10n in nucleation and growth and in terms of precip1tat1on . With the bulk of the present exper1ence and ideas now set forth, it is appropr1ate to attempt to make the connections between it and the previous work referred to in III .A. Gech's results, which could not be obta1ned with the present techn1que, are indeed striking but do not seem to be compatible w1th the present experience. In no case of structures of h1gh ~etry has it been possible to obtain a given (adjacent) phase by quenching into the equilibr1um single- phase field of another phase. As outlined above, the thermodynamic disadvantages in nucleation must be overcome by a sign1f1cant dispar1ty 1n growth rates 1n order to obta1n an apprec1able amount of the metastable phase. I n general, one has to quench into (equilibr1um) multi-phase regions to 83 accompliSh this. Pawlek's success in suppressing complex, peritectic phases opens readily two avenues of investigation; although peritectic structures are unambiguously defined, notions of complexity are less restricted. The peritectic compound Auzal was almost completely suppressed in one rapid quenching experiment and there is promise that many peritectic phases can be prevented in this way. With respect to com- plex structures, it dld not seem that the e -phase in Cu-Sl alloys (76 atoms/unit cell) was completely suppressed by rapid quenchlng; on the other hand, the congruently melting AuTe 2 compound dld not form upon rapld solldlflcatlon(62). No clear cut crlterla have emerged thus far . The use of metastable phase dlagrams is perhaps Justlfled ln terms of convenlence in the approxlmate represent~ tlon of nonequl1lbrlum situations under clearly understood conditions. There is no firm physical basis for such representations and indiscriminate use can (and has(l8» lead to absurd interpretations of data. Nothing in the course of the present work seems to have indicated or Justified representation by means of a metastable phase diagram . Three 1nterestlng suggestions have come from Falkenhagen and Hofmann (2) • First is the observatlon that solid solu- bilities were extended most appreciably in those alloys in which extensive undercoollng was noted. This theme is amply 84 explo1ted 1n the 1nterpretat1on of the present results. However, the pauc1ty of data for l1qu1d alloys and the 19norance concern1ng nucleat10n processes do not allow def1n1te pred1ct1ons of undercoo11ngs 1n g1ven systems. Another useful correlat1on 1s that of the h1gh ab18searbe1t" l 1n Al-Mn alloys and the extens10n 1n so11d solut1on there1n obtained. It seems that th1s 1s related to the pers1stence of the metastable phase after nucleat10n and espec1ally dur1ng recalescence. That 1s, 1f the d1ffus1on rates 1n the so11d are low, there 1s less l1ke11hood of the metastable structures annea11ng out 1n the cr1t1cal, h1gh temperature 1nterval after nucleat1on. S1nce measurements and/or es- timates of d1ffus1on rates 1n so11d alloys are generally unava1lable, 1t 1s doubtful whether th1s cr1ter1on 1s of pract1cal app11cab1l1ty 1n the search for metastable structures. Also ment10ned was the tendency for extens10ns 1n so11d solub1l1ty to be assoc1ated w1th the presence of 1ntermetal11c phases of h1gh melt1ng po1nts. Few systems of th1s sort were encountered 1n the present work; also to be rea11zed 1s that the s11ght 1ncreases 1n so11d solub1l1ty, such as formed the bulk of the F-H results (III.A.), were not bothered w1th here. Sal11 and M1rOShn1chenko(18) carr1ed some of the German 1deas somewhat further -- and perhaps too far. diffus10n rates 1nferred from the h1gh II The low ab18searbe1 til 85 results in "crystallization without diffusion," according to the Russians. Also deserving of incredu11ty are the1r statements that the undercoo11ngs 1n several s1mple eutect1c systems were reflected by the less-tban-max1mum so11d solub1l1t1es of the resultant phases. In agreement w1th the present conclusions are the 1deas that nuclei of both the stable and metastable phases ex1st and that the observed structures were a consequence of the compet1tion 1n growth of the var10us nucle1. Suff1c1ent ev1dence 1s at hand from the Ag-Cu alloys stud1ed to refute the content1on(3) that s11ghtly supersaturated so11d solut1ons decompose more rap1dly than more strongly supersaturated ones. Th1s content1on, however, may be va11d for some part1cular systems though, Since fundamental criteria are absent. Of considerable 1nterest in the Russ1an work was the observat1on that a spectrum of structures -- from metastable so11d solut1on to equ1l1br1um phases -- was revealed by exam1natlon of success1ve layers of the quenched mater1als . Th1s 1s hard to be11eve s1nce growth once 1n1t1ated, presumably near the substrate, should be suff1c1ently rap1d to overwhelm the other, d1fferent nucleat10n processes occurr1ng 1n the 1nterlor of the sample. One wonders if the decompos1t1on products noted were not a product of the etch1ng and po11sh1ng prerequ1s1te to the metallographlc exam1nat1on. Th1s pOint, as well as the several others c1ted above, 1s deserv1ng of further exper1mental 1nvest 1gat 1on. 36 REFERENCES 1. A.U. Seyboldt and J.E t Burke, Procedures lD Exoerimental Metallurgy, (1953J. 2. G. Falkenhagen and W. Hofmann, Z. Metallkunde, (1952), !!], 69-81. 3. I.V. Sal1i, Zhur. Neorg. Kh1m., (1958), 3, 4. R.B. Pond, U.S. Patent 2,825,108. 5. L. Brewer, UCRL 653; as quoted in reference 1. 6. J. W. Taylor, Progress in Nuclear Energy, (1959), V2, 398-416. 7. A. Bondi, Chern. Rev" (1953), sg, 417-458. 8. G.L.J. Bailey and H.C. WatkinS, J. Inst. Metals, (1951-2), 80, 57-76. - 9. E.R. Parker and R. Smoluchowski, Trans. ASM. (1945), ,25, 362-373. 10. H. -L. Luo, private communication. 11. L. Marton, Methods of ~er1mental Physics - Solid State Physics, \195 ,6B, 61. 12. S. Sekito, ~ Krist., (1930), A74, 189-201. 13. R.E. Cech, Trans. AIME, (1956), 206, 585-589. 14. A.K. COVington, K. Groenwolt and B.W. Howlett, ~ Inst. Metals, (1960-1), ~, 291-2. 15. F. Pawlek, ~ Metal1kunde, (1944),]2, 105-111. 16. J. Schramm, Ibid., 111-112. 17. M. Hansen and K. Anderko, Constitution of Binary Alloys, 18. I.V. Salli and I.S. Miroshnichenko? Doklady Akad. Nauk SSSR, (196~, 132, 1364-13b7. 19. K.A. Jackson, Can. ~ Phys., (1958), ]2, 683-691. 20. K.A. Jackson and B. Chalmers, Can. ~ Phys., (1956), J!±, 473-490. 142-159. (1958) • 87 21. D. Turnbull, Thermod~am1cs 1n Phys1cal Metallurgy (ASM), (1949), 2 2-306. - 22. J.H. Holloman and D. Turnbull, Progress 1n Metal ~~ Phys1cs, (1953), 4, 333-388. 23. B.E. Sundqu1st, Thesis - Illino1s Inst. of Tech., (1960). - 24. \'1 .3 . 25. G.A. Busch and R. Kern , So11d State Phys., (1960),11, 1-40 . 26. H. L1pson and A.R. Stokes, Nature , (1941), 148, 437. 27. A. Schne1der and G. Heymer, ~ anorg, Chern., (1 956), 286, ll8-l35. 28. N. 29. E. Raub and M. Engel, ~ E1ektrochem., (1943), ~, 89-97. 30. H.H. Chlsw1k and R. Hultgren, Trans. AIME, (1940),1]1, 31. E. Raub and A. Engel, ~ Metal1kunde, (1946),31, 76-81. 32. E. Raub and A.V. Po1aczek-Wittek, ~ Metallkunde, 33. R.D. He1denre1ch, Acta Met., (1955),], 79-86. 34. E.A. Owen and E.'ll. Roberts, Phil.~, (1939), £1., 294- 327. 35. P. Duwez, R.H. Willens and ;'1 . Klement, .is. Ano1. Phys., (1960),31., ll37. Pearson, Handbook of Lattice Spac1ngs and Structures of Metals and Alloys, (1958). Hume-Rothery and G. V. Raynor , The Structure of Metals and Alloys, (1956). 442-446. (1942), ~, 93-96. W. Klement, R.H. Wi llens and P. Duwez, Nature , 187, (1960), 869-870 . 37. M.H. Cohen and D. Turnbull, Nature, (1961), 189, 131-132. 38. D. Turnbull, Trans. AIME , (1961), 221, 422-439. 39. B.R.T. Frost, Progress 1!l Metal PhYSiCS, 96-142. (1954),~, 88 40. D. Lazarus, Solld State Phys., (1960), 10, 71-127. 41. J. Lumsden, Thermodynamlcs of Alloys, (1952). 42. R. K. Edwards and J.H. Downlng, ~ Phys.-Chem., (1956), 60, 107-111. o. Kubaschewskl and J.A. Catterall, Thermochemlcal Data of Alloys, (1956). 44. Y. Nakagawa, Acta Met., (1958), 6, 704-711. 45 . E. Gebhardt and K. Kostlln, ~ Metallkunde, (1958), .!i9, 605-613. - 46. N.H. Nachtrleb, Llquld Metals and Sol1diflcatlon (ASM) , (1958), 49-86. C. Klttel, Introductlon to Solld State Physlcs, (1953 ), 40-41. - 48. K. Gering and F. Sauerwald, ~ anorg. Chern. , (1935), 223, 204-208. 49. B.E. SundqUist, pr1vate communlcatlon. 50. H. Hardy, Acta Met., (1953), 1, 202- 209. 51. G. Urbain; G. Cavaller, The Physical Chemistry of Metallic Solut lons and Intermetallic Compounds, Vol. I & II , (1960):-- 52. L. Benjamin and R. F. Str 1ckland-Constable , Acta Met., (1960), 8, 362-372. - 53. J.W. Cahn and J .E. Hilliard, ~ Chan. Phys. , (1958 ) , 28, 258-267. 54. J. W. Cahn and J.E. Hill1ard, L. Chern. Phys. , (1959) , ]1, 688-699 . 55. B. E. Sundqulst and R.A. Orlani , J. Chern . Phys., (in press) . -C.S. Barrett, Imperfections ln Nearly Perfect Crystals, (1952), 97. 57. K.A. Jackson, Llquld Metals and Solldlf lcatlon (ASM) , (1 958 ), 174=186. - 58 . J. W. Rutt er, Ibld., 243- 275. '39 59. G.A. Colligan and B. J. Bayles, ~ Met., (in press) . 60. ~. Geller and H. Garbeck, Arch . fur Eisenhutt ., (1955), --26, 611-621. A. Le Claire, Progress in Metal Physics, (1953), ~, 265-332 . H.-L. Luo and W. Klement, i..s. Chem . Phys ., (in press). H.S. Carslaw and J .C. Jaeger, Conduction of Heat in Solids, (1959). 64. L.R. Ingersoll, O.J. Zobel and A.C. Ingersoll, Heat Conduction, (1948), 241-246. N.I. Va~ich and K.E. Kolesnichenko , Tsvet . Metallurgt;a( (1960) , ~, 131-137; as quoted in Met . Abstr ., (1 9 I), 28, 715 . 66 . W. Hofmann , Al uminium , (1938), 20, 865- 872 . APP~~IX I: Metastable bcc structures ln solldlfled Fe-Ni alloys One of the more lnterestlng of the nonequi1ibrium phenomena in the Fe-Ni system(17) ls that investigated by Cech(13) who found bcc phases ln alloys containing up to 30 wt.% Ni which had been solidified rather slowly as small spherical particles . Alloys were prepared by the reduction of homogenized oxides which were then heated to above the liquidus in hydrogen and dropped through a vertical furnace, thereby solidifying . For the 30 wt .% Ni;Fe alloy, the powder thus produced was found to contain nearly equal amount s of bcc ( 8 or 0<. ) and fcc ( Y ) part lcl es, the former be1ng smaller and s1ngle crystals and the latter polycrystalline. Further work appeared to 1ndicate that the bcc structures formed dlrectly from the melt and not by t he martensltic transformatlon, y-- ~ It was then suggested that the droplets had been undercooled suff1ciently so that the bec phase was preferentially nucleated with some particles transforming to fcc before reaching room temperature . Th1s transformat10n, 8 - Y , should be favored 1n larger part1cles and seemed to be borne out by the exper1ments. Cech extrapolated the b -11quidus and so11dus 1nto the i -reg1on and cla1med that nucleation of 8 from the undercooled 11qu1d could occur 1n the reg10n thus bounded. The coo11ng rates were calculated to be ~ 100°C/sec for a 13 ! particle, but only lOoC/sec for a ~ part1cle; there 1s 91 some evidence that very small particles would tend to transform to Y because of this relatively slow cooling r ate . It was calculated that, upon release of the heat of fusion, the 13/ part1cle would be held 1/20 sec at the temperature of solidification. To compare results obtained from the present technique with the above , alloys were prepared in alumina crucibles from iron of purity >r 99.9% and nickel of purity ~ 99.95%. The lmmediate vic inity of the nozzles was doused with argon to heating the alloys to l500-1550 oC and quenching onto copper. The effects of contamination were strikingly in evidence for two quenched specimens of pure iron; for one, shot from an insert doused with argon, only the bcc (~) was detected with a lattice parameter, o a::: 2.8685!20A,lTl agreement with others (24) , whUe, for the other shot from an undoused crUCible, a fcc phase was detected with lattice parameters nitrogen contamination. (24) suggestive of conSiderable For the 20, 30 and 40 at.% Ni;Fe alloys investigated, a bec phase was detected only in the 20 at.% Ni;Fe alloy and this was probably due to the martensit1c transformation. were found. For the other alloys, only Y -phases Cech's results thus cannot be obtained with the present technique; further comments are given in III.D. 9? APPENDIX II: Coollng and solldlflcatlon - macroscoplc vlewpolnts - To obtaln rough estlmates of the tlmes involved ln the varlous stages of the cool lng, the process 1s ldeallzed as follows : (a) The geometry ls taken to be one-dlmenslonal wlth a slab of the materlal of lnterest (denoted m for metal) abuttlng a slab of the poorly conducting materlal (denoted 1 for lnsulator) whlch, in turn, abuts the seml-lnflnlte, perfect heat sink (denoted w for wall) . Conductlon ls the only mechanlsm consldered for heat transfer, whlch ls assumed perfect between reglons. Contact reslstance at the lnterfaces, finlte thermal conductlvlty of the wall, etc. ls allowed for by varlatlon of the parameters of the poorly conductlng layer. Typlcal ranges of values for the pertlnent thermal parameters are consldered. (b) The three stages ln the process are: Coollng of the molten layer, inltlally at the superheat temperature, # soh' to 19- , the solldlflcatlon temperature. s Propagatlon of the solld-llquld lnterface through layer m, at 19- , wl th concomitant res lease of the heat of fuslon. Coollng of the solld layer from s to 0' the orlglnal temperature of the wall. J J- Stages (1) and (111) are treated slmllarly, with the pertinent equatlons; 93 where r = 1. ,m k = r ~ thermal dlffuslvlty Crfr thermal conductivity r = Cr = spec if lc heat k Pr = denslty and the boundary condl t lons: J1 (x,O) = t9s (or ,Jo) -1 1 ~ XL ° = kl dd 1 (O,t) Jx Separatlng varlables, {) r t'V (space- dependent functlon) exp fC - K~;rn a.2 t J r a 2 2 with f"rn '" n 11" (n = 1 , 2 •• • ) An exact solutlon can only be obtalned numerlcally; however, from an analogous problem (63) , ~ (1 m (orJ-o ) for Kr t --;2 r /'J 2 - 4 ro, t) ls senSiblY-,J s Estlmates of the times involved ln stages (1) and (111) are gotten wlth numbers(64) collected below in cgs unlts and arranged- -- hlgh > probable> low . 1.5 > 0 .8,/ 0 .05 2 .10- 3 ;> 10- 3 ;> 5-10- 4 6-10- 3 > 5 .10- 6 > 2-10- 7 > 0.2;> 10- 2 2-10- 3 5 _10- 6 > 10- 6 > 10- 7 3'10- 5 ::;> 3.10- 8 > transit t1me for sound wave The poorly conductlng layer does not affect the tlme requlred for coollng to wlthln an order of magnltude . There ls 11ttle dlfference between the t1me requlred ln stages (1) and (111), whlch ls taken as 10- 4. 5±0.5 sec . For stage (11), the propagatlon of a solld-llqUld interface lnto a seml- 1nflnlte 11quld ls consldered. Thls, the so- called Neumann problem, has been dlscussed elsewher~62)(63). A partlcular solutlon ls x =i t! where x ls the dlstance of the lnterface from the wall andYls of order 1-4 for the present sltuatlon . The estimates of the times necessary for the interface to traverse the distance 1m are 4'10- 6 :;> or time required "--' 3 '10- 7 > 10- 8 10- 6 •5:tO. 5 sec. The overall time required for the coolings and solldlflcatlon are then, 95 t overallrv 10- 4+1 - sec assuming the validity of the physical parameters and models chosen. For the latter, approximations have been selected which should yield overestimates of the several time intervals. APPENDIX III: A1um1num-base manganese alloys and very h1gh coo11ng rates Several workers have stud1ed the metastable so11d solub111ty of manganese 1n a1um1num by rap1d quench1ng from the melt. Fa1kenhagen and Hofmann (2) , w1th coo11ng rates to rv 29,OOOoC/sec . , c1atmed to have obta1ned so11d solut1ons conta1n1ng /V 4 . 7 at . % Mn , although s1ng1e-phase alloys were gotten only to /V 3.6 at .%MIl . (65) Var1ch and Kolesn1chenko have clatmed the extens10n of so11d solub1l1ty to ~ 5.2 at .% Mn, w1th coo11ng rates of / V 50 ,OOOoC/sec., although latt1ce parameters were not presented . Alloys were prepared 1n a1um1na cruc1b1es from a1um1nu~ of purity > 99.99% and remelted e1ectro1yt1c manganese of purity ;> 99.9% . We1ght losses were small and the alloy w1res were be11eved homogeneous to ! 0 . 3 at.% . Alloy charges were heated to rv 1300 oC 1n alum1na lnserts and quenched onto copper . X-ray work was done 1n the usual way although, slnce CuK~ rad1at1on was used for the conven1ence of short ex- posures, the background was h1gh and the qua11ty of the f11ms below the usual standards. The results of the present work are g1ven 1n F1gure 16; also plotted there are the data of Hofmann (66) , Fa1kenhagen and Hofmann(2) and Fr1d11ander (as quoted by Pearson(24)). Fa1nt l1nes, with d r'J 2 . 06~, 2.16~, 3.S0~, were detected 1n the mult1phase (shaded symbols) h1gh-manganese alloys of the present work. 97 There 1s d1sagreement between the present work and that c1ted above. The reasons are presently unknown and 1t 1s unfortunate that Var1ch and Kolesn1chenko(65) d1d not present the1r very recent measurements . The present data was f1tted n1cely w1th a 11near latt1ce parameter vs compos1t1on relat1on, of slope -0.00 9 ~/at.% Wn . The extent of the 3 metastable so11d solub111ty was 5.1!O.3 at. % Mn . The fcc spac1ngs 1n the 8.8 at. % Mn;Al alloy suggested a subs1d1ary metastable so11d solub111ty 11m1t at ~ 4.3 at. % Wm , near the l1m1t of Falkenhagen and Hofmann. To br1ng the present results lnto agreement w1th the prev10us work, a loss of alum1num durlng the quench1ng 1s demanded. Th1s could have resulted from react10ns w1th1n the alum1na 1nsert although there 1s no ev1dence for th1s. Other contam1nat1on, p1ckup of carbon, oxygen, etc., may be 1nvolved but hardly to the degree necessary for the gross d1fference 1n latt1ce spaclngs. At the very least, 1t 1s suggested that the coo11ng rates of the present techn1que are equal to those cla1med elsewhere. 4.050 · · a:: w 4.030 Iw o HOFMANN 8 FALKENHAGEN o FRIDLIANDER 8 PRESENT WORK a HOFMAN ~ « 4 .020 a:: « CL. w 4 .010 o I- ~ 4 .000 ....J 3.99 0 !-,-_...L_~_ _±-_~_---= Al Figure 15 . __:!:-_-=-_----;!:--_-;!:-----' Lattice parameters plotted as function of manganese concentration for face centered cubic structures .