ee C Binary Systems Involving the atatectic"

Reaction Solid 1 Cooling Solid 2 Liquid Heating

SIGURD WAGNER AND D. A. RIGNEY

cooling The name "catatectic" is proposed for the reaction solid 1 ~ solid 2 + liquid, and a

heating simple thermodynamic analysis is presented to aid in predicting the existence of this fea- ture in binary phase diagrams. In addition, a survey of available phase diagrams shows that the reaction may occur much more commonly than has been suspected.

IT is common practice in introductory text books on phase diagrams to examine the various types of three- phase equilibria which may be evident in temperature- composition phase diagrams. ~'s For binary systems involving combinations of liquid and solid phases, 12 such three-phase features are possible, each of which is related to a reaction of the type

cooling phase 1 ~ phase 2 + phase 3,

heating

or

cooling phase 1 + phase 2 .------* phase 3.

heating

Six of these are well-known reactions having generally accepted names, such as eutecttc, peritectic, and so forth. Of the remaining six, some have no recorded cases in metal systems, and some may not occur at all. One type, however, may deserve more attention than it has received. It is the main subject of this paper.

NOMENCLATURE

At first sight, the reaction

cooling solid 1 , solid 2 + liquid

heating

may appear rather peculiar, because it indicates that a solid phase decomposes upon cooling into a liquid and a second solid phase. In effect, the solid can partly "melt" when the temperature is lowered, and it can solidify again when the temperature is raised. This kind of topsy-turvy behavior is allowed thermodynam- ically, and indeed, examples of this reaction do exist in metallic systems. 4"e

Gordon states that "This invarlant reaction has as yet no generally accepted name but the designation 'metatectic' is sometimes used. ''2 Rhines provides no name for the reaction, but he points out that the

SIGURD WAGNER is Member of Technical Staff, Bell Telephone Laboratories, Holmdel, N.J. 07733. D. A. RIGNEY is Associate Professor, Department of Metallurgical Engineering, The Ohio State University, Columbus, Ohio 43210.

Manuscript submitted November 12, 1973.

term "metatectic" has been used to describe the peri- tectoid. 1 Prince uses the term "metatectic," and he also notes that "Peritectoid reactions are occasionally referred to as metatectic reactions. "s He also points out that the word segment " - tect ic" is unsuitable for use with a reaction involving only solid phases, since it has to do with melting.

Since "mete - " means '%etween," "with," "after ," or " later ," the term metatectic might be a sensible choice for the reaction under discussion, since "after" initial freezing a material can partly remelt " later ." However, since the term metatectic has been used, perhaps unwisely, for another type of reaction, it might be better to abandon it altogether and use a new term to minimize confusion.

A suggested new term is "catatectic." This is based on the Greek word "kate," which means "down." The term would then literally translate as "down melt" or "down melting," which would be reasonably descrip- tive, and the word would continue the tradition of using Greek roots for phase diagram features. The term "catatectic" will be used for the remainder of this paper.

The solid phase coexisting with the liquid at lower temperatures generally has a relatively close-packed structure, frequently fcc or hcp. It will be called the 3/phase. The single solid phase which exists at equi- librium above the catatecttc temperature is frequently bcc, or some other structure which is not as closely packed as 3/. It will be called the 5 phase.

In binary systems, three kinds of catatectics can exist. If both solids 3/and 5 are solid solutions based on allotroplc modifications of the solvent, a terminal catatectic exists. This is the type most frequently en- countered; it is shown in Fig. l(a). The corresponding free energy versus composition diagram at the cata- tectic temperature is shown in Fig. l(b). An example is the Fe-Zr system. When the 3/and 5 phases are both compounds or intermediate phases, the system will be labelled a compound catatectic (Figs. 2(a) and 2(b)). An example is the Cu-Sn system. The third type would involve a terminal solid solution 5 and an intermediate phase 7, as shown in Figs. 3(a) and 3(b). The only known example of such a mixed catatectic system is Ag-Li, in which the a and ~ solid phases are involved.

For all three types of catatectic systems, the single temperature at which the phase Y transforms directly to the phase 5 shall be labelled T tl.

METALLURGICAL TRANSACTIONS VOLUME 5. OCTOBER 1974-2155

Tml

Tr

!

x S x c x L

(a)

G,Io(L)

T=T c

G~o(B ) 9

Gto ( ) ' )

Y

! !

x s x C x L

(b) Fig. 1--(a) Part ia l binary T-x diagram showing a terminal catatectic. (b) Free energy diagram for the three phases in equilibrium at Tc.

CONDITIONS FOR THE EXISTENCE OF CATATECTICS

The most complete discussion of eatateetic (meta- teetic) systems ts in the book by Pr ince. 3 He presents a ser ies of free energy d iagrams of the type given in Fig. l(b) and he descr ibes the sequence of events which occurs during sol idif ication for alloys involving the eatateetie reaction. However, further analysis does not appear to exist tn the l i terature.

In this section, some simple thermodynamic re la - t ionships will be discussed and applied to termina l eatateetie systems, and simple guidel ines will emerge which can be used to predict the presence of a terminal eatatectie react ion in a given b inary al loy system.

At the eatateettc temperature T c < T t ~, liquid L and sol ids y and 5 are tn equi l ibr ium, as shown in Figs. 1, 2, and 3. Even with a cursory examination of a phase diagram, one tan see if the liquid is stable below Ttx. It will not be stable at T < Tt i if

a) The 5 solid solution is more stable than the liquid L at T < Tt~ at all composit ions where 6 and L coexist, or, the melt ing point of 8 is not suff iciently lowered by the addition of solute. This ease of high stabi l i ty of the 8-solut ion with respect to the liquid often occurs when the 6 modif ications of solvent and solute form a contin- uous ser ies of solid solutions, as in the Ba-Ca, Ce-La, Fe-Cr , Fe-Co, and Gd-La systems;

I--- L

I--

COMPOSITION x (a)

>- r n~ t~ Z W

W W

b~

nn nn

T 8 L

T :T c

COMPOSIT ION x

(b)

Fig. 2--(a) Partial binary T-x diagram showing a compound catatectic. (b) Free energy diagram for the three phases in equilibrium at Tc.

b) An intermediate phase in equi l ibr ium with the 8 solid solution is more stable than the liquid phase L at T < T t~. Examples are Fe-Nb and Fe-Hf.

Once a liquid phase L has been found to exist in equi- l ibr ium with a termina l solid solution at T < Tt,, then the pr incipal requ i rement for a catatectic to exist is a lowering of Ttl upon addition of solute. The y phase can then be In equi l ibr ium with the liquid phase except for the special ease of y- loop formation, i .e. , when a low temperature phase exhibits a structure identical to that of 6. This occurs for several solutes in Fe, e .g . , Fe-A1, Fe-Be, Fe-Cr , Fe-Si, and so on. For sys - tems not forming y-loops, the required lowering of T t x will occur if, at T = Tt, and near x = 0, the Gibbs free energy for the 8 phase, C 6, is more negative than that for the y phase, G~/, as shown in Fig. 4(a).

There is some advantage to plotting the function G + TS id (Fig. 4(b)) rather than the free energy G itself, s ince the revised function has a finite slope at x = 0. The term TS id is the magnitude of the entropy contr i - bution to the free energy for an ideal solution. It is then possible to compare the slopes of (G + Ts id)6 and (G + Ts id )7 to see which is smal ler (less positive or more negative).

2156-VOLUME 5, OCTOBER 1974 METALLURGICAL TRANSACTIONS

B L G.IO ()")

GtO (8)

COMPOSITION x (a)

T = Ttt

G(8)

0 X (a)

G20 (),')

G2o (B)

o

>- (.9 n~ h i Z IJJ

LU

I=.

( /) m m

T=T c

I -

I -

8

L

COMPOSITION x (b)

Fig. 3- - (a ) Partial binary T-x diagram showing a mixed cata- tectic. (b) Free energy diagram for the three phases in equi- l ibrium at T c.

If one uses the most s imple model for nonideal solu- t ions assuming regular solid solutions, then the condi- tion for catatect lcs is

G 5 - Cy = (1 - x)[G,o(5) - G,o(),) ] + x [G2o(6) - C2o('Y)]

+x(1-x ) [Bs -By]

If Tt i is the temperature for the ~ - - 6 t rans format ion fo r pure component i, and if hHt i is the entha lpy change for th i s t rans format ion , then it can be shown s imply that

G2o(5) - G2o(Y) ~ AHt2(1 - Tt , /T t2 ) . [5]

Thus , if Tt2 is less than Tt~ , a catatect i c might be ex - pected . Th is s imp le cond i t ion shou ld be usefu l for p re - d ic t ing catatect i c react ions , espec ia l l y if AHt2 (1 - Tt~/ Tt~) is s t rong ly negat ive , s ince it would then be more l i ke ly that [B 6 - B~,] cou ld be sa fe ly neg lec ted .

RESULTS AND DISCUSSION

Table I is presented as a test of Eq. [5]. It lists the known binary terminal catatectic systems for which enthalpy data are also available. Only the prototype transformation 6(bcc) --- y(fcc) is considered. The temperature and enthalpy of transformation for stable modifications, including all solvents and several sol- utes, were taken from the reference work by Hultgren and coworkers, 7 or from the book by Kubaschewskl et al. s For transformations involving metastable solutes, Tt~ and AH~2 are the values calculated by Kaufman and Bernstein. With the exception of Mn-Cu, the values for AHt2 (I - Tt,/Ttz ) show an acceptable spread. Though the Ce-Mn value has the wrong sign, it is small, and one might still predict a catatectlc if, for i ns tance , AHt2 (1 - Ttz /T t2 )

Table II. Terminal Catatectics, Known and Possible 4"6

Ca-Cd La-Ag +1600 Mn-P Ca-Li La-AI +4500 Mn-Y* Ca-Na La-Au Mn-Si Ca-Zn +420 La-Cu +2500 Mn-Pu - 1700 Ce-Ag + 1900 La-Ni Mn-U* - 1500 Ce-AI +5200 La-Pb Sr-Li Ce-Au La-Pu -1000 ThAI + 1700 Ce-Fe* -2000 La-Sb Th-Be -5400 Ce.Mn* +540 La-Sn Th-Bi -125 Ce-Ni La-TI - 1000 Th-Ce -2000 Ce.Pu -650 La-Zn +90 Th-Cu +650 Ce-T1 -860 Mn-Ag* +1050 Th-Hf -2000 Fe-Gd Mn-As Th-In Fe-La* -1450 Mn-Bi -350 Th.Pd Fe-Pb Mn-Ca -850 Th-Pt Fe-Pu* -2300 Mn-Cu +1580 Th-Rh Fe-S Mn-Gd* Th-Ru Fe-Zn -350 Mn-ln Th-Ti -5300 Fe-Zr -5300 Mn.La* Th-U -2300

Mn-Li* TI-As

*More than one catatectic possible. The value for AHr2(1-Ttl/Tt2) in J/mole is given where sufficient data are

available.

where the requ i red data a re ava i lab le . Most data were taken f rom Ref. 9. It is in te res t ing to note that, us ing Ref. 9, the e lements Cu, Ag, and A1 a l l lead to re la - t i ve ly la rge pos i t ive va lues . It should be apparent that even if some of the sys tems l i s ted in Tab le II p rove to have no cata tect i c , th is type of react ion may be much more common than has been assumed prev ious ly .

Table III inc ludes the smal le r number of b inary sys - tems in which a cata tect ie invo lv ing a compound ap- pears to ex is t .

APPENDIX

1. St ra in Energy and the 5 ~ 7 T rans format ion

Since a so lute a tom wi l l genera l ly have a d i f fe rent s i ze f rom so lvent a toms in a so l id so lut ion, an e las t i c s t ra in energy contr ibut ion should be inc luded in ex - p ress ions for the f ree energy of so l id phases . For a mo le of hos t c rys ta l , th is e las t i c energy is g iven by

W= ~G1V, (V a /v , - 1) 2= ~ClV ~((r~/rz) s - 1) 3

[A l l

per mo le of so lute at inf in i te di lut ion, z~ G, is the shear modulus of the host c rys ta l and V,, r , and V2, r 2 a re the molar vo lumes and the a tomic rad i i of the so lvent and of the so lute respect ive ly .

In o rder to determine whether the s t ra in energy te rm favors the c lose -packed phase 7 or the less c lose - packed phase 6, W 7 and W 5 should be compared . If W 6 - Wy < 0, the s i ze e f fect tends to s tab i l i ze 6 with respect to 7. The express ion to examine is there fore

W 5 - W 7 = [~ G IVz (V 2 /V z - 1)a] 6 - [~ G zV~ (Y z Iv, - z )~]~ [A2]

Darken and Gur ry *~ ment ion that G,V, does not vary much f rom meta l to meta l or with temperature . They ass ign an average va lue of 250 k J /mo le (60 kca l /mo le )

Table III. Catatectic Systems Involving a ~ompound 4"6

Ag-Ga Cu-Sn Ag-ln Fe-Zn Ag-Li Li-Sr Bi-Mg

to G,V,. Kaufman and Bernste in ~ use the propor t iona l - ity

G1 cc HI,s/V1

to e l im inate V, (~-/ , ,s is the heat of sub l imat ion of the so lvent) :

2 Hl ,s(Vz/Vl_ l )Z Wcc~

The magni tude of H~,s is indeed of the order of that of G,V, . Th is leads to a useful approx imat ion for W,

W ~- ~ H,,s(V2VI-1) 2 [A3]

The s t ra in energy contr ibut ion to the regu lar so lut ion te rm in Eq. [5] is then

[B6-BT]s t ra in : W 6 - WT-~[~H,,s(~-~21 -1 ) ' ]6

)'] - L ,skv - 1 [A4]

7

L i t t le in fo rmat ion is ava i lab le about the molar vo lumes of high temperature modi f i cat ions , in par t i cu la r of the metastab le phases . There fore it is most expedient to assume that the ra t io of the molar vo lumes remains constant dur ing the 6-7 t rans format ion , i.e.,

Vz

With H z,s (6) - H,, s (7) = -AHt l we obtain

, )' [B 5 -BT]s t ra in -~ - ~ - 1 7or 6at T 1

[A5]

This resu l t suggests that the s t ra in energy contr ibut ion to nonideal so lut ion behav ior tends to s tab i l i ze the 5 with respect to the 7 phase, and there fore favors the occur rence of ca ta tect i cs .

2. E lec t ronegat iv i ty

D i f fe rences in the e lec t ronegat iv i ty behav io r of so l - vent and so lute, - contr ibute to a negat ive dev ia - t ion f rom ideal i ty . The resu l t ing port ion of the regu lar so lut ion parameter is z*

B e = - 96,500 n ( - 2 J /mo le . [A6]

n is the number of bonds per a tom formed between 1 and 2. The e lec t ronegat iv i ty contr ibut ion to the regu- la r so lut ion te rm in Eq. [5] is

[B 5 - By] e = - 96,500 ( - 2 (n 5 - n 7) [A7]

There are two approaches to es t imat ing n. 11 In one, n is set equal to the max imum va lency of the const i tuents , which makes it independent of c rys ta l s t ruc ture . In the o ther approach, the number of bonds per a tom is not

METALLURGICAL TRANSACTIONS VOLUME 5, OCTOBER 1974-2159

on ly determined by the va lency , but a l so by the coord i - nat ion number wh ich i s h igher fo r denser pack ing . S ince an a tom in 5 has a lower number of neares t ne ighbors than an a tom in 7, n 6 - n~, < 0, and [B 6 - B3,]e > O. Thus the e lec t ronegat iv i ty cont r ibut ion may s tab i l i ze

w i th respect to 5, and there fore d i s favors cata tec t i cs .

RE FERENCES

l. F. N. R/fines: Phase Diagrams in Metallurgy, McGraw-Hill, New York, 1956. 2. P. Gordon: Principles of Phase Diagrams in Materials Systems, McGraw-HiU,

New York, 1968. 3. A. Prince: Alloy Phase Equilibria, Elsevier Publishing Co., Amsterdam-

London-New York, 1966.

4. M. Hansen and K. Anderko: The Constitution of Binary Alloys, McGraw-Hill, New York, 1958.

5. R. P. Elliott: Constitution oflh'nary Alloys, First Supplement, McGraw-Hill, New York, 1965.

6. F. A. Shunk: Constitution of Binary Alloys, Second Supplement, McGraw- Hill, New York, 1969.

7. R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley: Selected Values of Thermodynamic Properties o.f Metals and Alloys, Wiley, New York, 1963, and Supplements.

8. O. Kubaschewski, E. LI. Evans, and C. B. Alcock: Metallurgical Thermo- chemistry, 4th ed., Pergamon Press, London, 1967.

9. L. Kaufman and H. Bemstein: Computer Calculation of Phase Diagrams, Academic P~ess, New York, 1970.

10. L. S. Darken and R. W Gurry: Physical Chemistry of Metals, McGraw-Hill, New York, 1953.

11. B. W. Mott: Phil. Mag., 1957, vol. 2, pp. 259-83.

2160-VOLUME 5, OCTOBER 1974 METALLURGICAL TRANSACTIONS