Stability of amorphous alloys

Solid Sta:e Communications, Printed in Great Britain.

Vo!.43,30.3,

STABILITY

pp.l71-174,

OF AYORWOUS

K.B.J. Philips

0038-lO98/8Z/Z7Ol7l-04SO3.00/0 Pergamon Press L:d.

1982.

.ALLOYS

Buschow

Research Laboratori-s, Eindhoven, Ihe Netherlands (Received 16 March 1982 by A.9. Miedema)

The thermal stability of a number of Ti-base and Zr-base amorphous alloys was studied by means of differential scanning calorimetry. The crystallization temperatures of these amorphous alloys and tnose reported in the literature for a variety of other amorphous alloys (actinide-base alloys an refractory metal-base alloys) were analysed in terms of the corresponding formation enthalpies. It is shown that there is no correlation between the crystallization temperatures and the formation enthalpies. On the other hand the crystallization temperatures were found to scale more or less linearly to the corresponding formation enthalpies of a hole the size of the smaller type of atom in the binary amorphous alloys.

In an earlier series of publications it was shown that the stability of amorphous A1_xBx alloys can be described in terms of a simple kinetic model where the activation energy for cyrstallization is taken to be proportional to the formation enthalpy of a hole ( AHh) the size of the smaller type of atoms (B).l** The crystallization temperatures of numerous amorphous alloys were found to obey the semi-empirical relationship Tx = C AHh, where C is a number between 7 and 8, where Tx is expressed in K and AHh is expressed in kJ/mol alloy. In alternative descriptions of the crystallization temperature (or the glass temperature T which is close to Tx) it has been proposed tf at a correlation exists between T, (or T ) and the heat of mixing or the heat of formati!!n (bH)3. As a matter of fact experimental evidence of such a correlation for several amorphous alloy systems had indeed been found. There are several aspects which would make a description of Tx in terms of AH more desirable than a description in terms of AHh. The most obvious advantage is that AH can be determined experimentally. Although the amount of experimental '.H data reported in the literature for binary systems in which the T, behaviour has been studied is still slight, there is no fundamental reason why such data cannot be obtained. It would then be possible to compare two experimental quantities, TX and AH. This advantage is absent in the description of TX in terms since the hole enthalpy in binary of r.Ii:,, alloy systems AI-~B~ is a quantity not directly open to experimental determination. In fact the values of AHh used in previous reports were values calculated by means of a minor adaptation of the expression for monovacancy energies in intermetallics given by yiedema.7 It was found recently that differences in magnetic properties between quite a variety of amorphous 3d transition metal alloys and also differences in magnetic properties between amorphous and crystalline alloys can b plained in terms of differences of
This might indicate that AX is a quantity of quite fundamental importance in the description of the physical properties of amorphous alloys. For this reason we have investigated in more detail the extent to which a correlation between TX and AH exists and whethpr this correlation is to be preferred to the semi-empirical relation TX = C mh mentioned above. The amorphous alloys studied in the present investigation were prepared by arc melting followed by melt spinning in a purified argon gas atmopshere. Representative parts of each ribbon were investigated by means of X-ray diffraction. We applied CuKrradiation in combination with an X-ray monochromator. The thermal stability of the alloys was studied by means of a differential scanning calorimeter (DSC) Du Pont 310, again using an atmosphere of purified argon gas. We used a practical heating rate of 50°C/min. The origin of the observed heat effects was studied by heating the ribbons to the various stages in the crystallization process, followed by cooling and X-ray diffraction. 'Fne crystallization temperatures (TX), defined as the temperatures corresponding to the maximum of the sharp exothermic DSC peak, have been listed in Table 1, together with crystallization temperatures obtained previously and data reported in the literature. The hole formation enthalpies Aah for amorphous alloys A1_xBx can be calculated by means of the expression AHB = 1 h

As TV

+

(l-c)(VB/':A)

5/6A$ 1v

where the effective concentrations c and l-c depend on x and VA/VB and can be regarded as a measure of the degree to which a B atom is surrounded by other 3 atoms and by A atoms, respectively. Tne quantitiesAH+ the monovacancy formation entha II pies andtiyv of the are pure elements A and B, having molar volumes VA and VB. In !?iedema's paper values of V andAH,V are listed for almost all metals so wh values can easily be calculated for any

"64?36 Zr67Fe33 zr64N136 =70Rt'30 Zr66Rh34

Ta55Rh45 m551r45 Tag Ir45 w ?e 5.2' N? Sn73Ni27 48 52 sn45C055 s"83c017

sn75"e25 Sn37Fe63

7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22

Nb55Rh45 Zr7aPt22

T120Coa0 22Coq

2

z

Tt76C024 T?24C076 Ti

Tf77c023

Nloy

-49 -59 -79 -90 -05 -67 -78 -62 -75 0 -13 -22 -10 -16

740 730 758

288 514

768 980 1133 1118 1238 *I150 293 378 290 528 -1 -2

-28 -34 -31 -28

742

-26

706 848 873 700 a63

AH(kJ/mol)

713

TX(K)

13 13

z 2 2 p.i. p.i. 10 10 10 10 11 12 12 12 12

p-i.

p.i.

p.i.

p.i. p.i.

Ref.

690 633 808

Tt@$, Tf37i063

41 42 43

43

658 604

" 73" ," 6523527

438,

57

545 555 553 560 593

613 613

453 443 473 483 563 569 590 645 619

TX(K)

" 80C020 " 6oC040 lJ aoFe20 " 60~~40

' aON: %9?31 " 60~~40

m60Fe40 Gd76Pd24 Tb50Fe50

P'65N135 La69Nf 31 Pr60N140 Gd82Rh18

La?@>22

Alloy

34 35 36 37 38

32 33

23 24 25 26 27 28 29 30 31

NO.

p.i. 2 1 1 14 14 p.i. p.i. p.i. 15 15

-57 -25 -32 -34

-16 -31

1s 15 15 15 15 15 p.i. p.i. p.i.

-12 -24 -6 -11 -4 +1 -2 -10 -44 -3

-90

Ref.

aH(kJ/mol)

temperatures (TX) for several amorphous alloys and formation enthalpies (AH) calculated by means of Miedema's model for the corresponding (hypothetical) inter-metallic compounds.'7 The hH values are given in units of kJ per mol of alloy.

1. Crystallization

2

1

NO.

Table

vo?. $3, No. 3

STABILITY OF MORPHOUS ALLOYS

combination

Al_xBx.7 21 general quite a satisfactory correlation was found between Tx and Ash. A SCOT;of T, versus h:ih was presented for the conbinations B=3d metal and A=Hf, Tn, ?sb,Sn, Y, _Prin Ref. 1. A similar plot for various combinations Zr-3d and for alloys of La, Eu and Cd with a variety of 3d and non-3d elements was shown in Ref. 2 and for various alloys based on Cu in Ref. 16.In all these cases one could speak of a more or less linear relationship expressed as Tx = CAHh with C between 7 and 8. In Fig. 1 we have produced a similar plot using the presently obtained data on Til_xCo, Tb,_xFex Th&QD, HfS7V43 together with literature data of alloys based on U,and on refractory metals. The large amount of additional data

AH,lkJ/moll

Fig. 1. Dependence of the crystallization temperature Tx in various amorphous alloys Al-xBx on the formation enthalpy of a hole the size of the smaller type of atom (B). reported in the meantime for Sn-3d alloys was also included in this plot.The broken line represents the relationship Txq.5 &Ih. The plot shown in Fig. 1 is different from the three plots presented earlier in that it extends to much higher Tx and AHh values. In the range arOunddHh=15C kJ/mole there are some deviations from the linear relationship mentioned above but, in general, the correlation between Tx and AHh is still quite convincing. (The possibility of having small deviations from this linear behaviour was discussed in Ref. 2). In order to investigate the relationship between Tx and AH, the same Tx values were used in a plot of Tx and AH shown in Fig. 2. Since experimental data on AH (heat of compound formation in the solid state) are available only in a few cases we used AH values calculated by means of Miedema's model.17 These values are included in Table 1. The use of Miedema's model has the advantage that the AH values can be tailored to match the concentrations of the corresponding amorphous alloys. To m&e the Tx versus AH plot sufficiently accessible to data inspection without

Ii3

loss of generality, only some of the Tx values available were used: it can be seen from the plot in Fig. 2 that the Til_xC% data cluster is situated around Tx =800,aHa27. Since a similar clustering also occurs for the series based on Sn and U we have included in Table 1 and Fig. 2 only the Tx and AH values pertaining to the two outermost 3d atom concentrations. Included in Table 1 and Fig. 2 are furthermore a few representative alloys of Zr and rare earth elements with 3d, 4d or 5d metals (the satisfactory behaviour of these alloys with respect to the relation Tx=C hHh was shown earlier). It will be clear from the results shown in Fig. 2 that there is riocorrelation between the crystallization temperature and the heat of compound formation. (The same results is obtained if one uses the heat of mixing instead of the heat of formation). The present results do not refute the possibility that Tx may occasionally be found to show a samilar trend to .AH in series such as Zr7B3 (or A7Co3) where B (or A) is varied over relatavel few and not too different elements.5,6"However, when extended over a sufficiently high number of amorphous alloys varying widely in the concentration and nature of the components, the correlation between Tx and AH is seen to break down completely. Predictions of the thermal stability of amorphous alloys based on formation enthalpies can therefore be expected to lead to the wrong result. As an alternative way of expressing the above findings one could say that there is little correlation between the formation enthalpy and the energy associated with the migration of the (smaller sized) atoms B in the crystallization process of the amorphous alloy Al_xBx. In this connection it is interesting to compare the concentration dependence of the hole enthalpy AHh and the formation enthalpy AH in a given binary system. With increasing concentration of the A metal (having a larger atomic volume and usually a lower surface energy) formation of a hole the size of the smaller B atom becomes increasingly more favourable than formation of a monovacancy in the pure B metal. This means that AHh increases continuously with x while AH first increases with x and then decreases, the maximum being located at slightly higher x values than the equiatomic composition.l7 It would therefore be expected that a possible correlation between AHh and AH would be confined to relatively low x values. It is in this very region that the few cases of a correlation between Tx and AH were reported to exist.5,6 Finally it should be noted that there is another, more subtle way in which the formation enthalpy may exert its influence on Tx.3 In the statisticalmechanical model of Adam and Gibbs18 the average cooperative transition probability is determined by the exponential exp(AE/TS,) where, apart from the activation energy AE in the numerator, there is the configurational entropy SC in the denominator. In the derivation of the relation Tx=C hHh this configurational entropy was assumed to be temperature-independent and the same for all amor-

ST.ABILITY OF .XfORPHOCS ALLOYS

Vol. 43, No. 3

.16 .LO

5

9L3

L

l*.3

.L' l*30 37 .32 1:6 .33 39 29*

.

a28

g35 l27 .*25 g26 . 2L 18 190 .,7

22.j;36;L.20

21.

l9

l8

7

l23

50 -AH (kJ/moll

Fig. 2. Plot of experimental crystallization temperatures Tx in various amorphous alloys versus the corresponding heats of compound formation in the solid state. The numbering corresponds to the data listed in table 1.

phous alloys,l as is usually done.'9 This may be a reasonable assumption if the atomic arrangement in all amorphous alloys were indeed the same as for instance in a dense random packing of atoms. The experimental observation of the presence of compositional short-range ordering in some amorphous alloys 20 and the contentiona, that the degree of this latter ordering is determined by AH may re-

quire a slight re-evaluation of the data in this sense. Investigations relating SC to AH are currently being carried out. Acknowledgement. The author wishes to express his gratitude to Chr. Janot for making available to him numerical values of the crystallization temperatures found in amorphous alloys of Sn and 3d metals.

References 1. BUSCHOW K.H.J. and BEEKXXNS N.M., Solid State Comm. 2, 233 (1980). 2h3 (1981); J. Physique 5, ~8-559 (1980). 2. BLJSCHOW K.H.J., J. Less-Common Met. 3, TAKAYAMA S., J. Mat. Sci. 2, 164 (1976): :: CKEV H.S., Acta Met. 2, 1505 (1974). LAPKA R., RGSEL F., OELHAFEN P. and GUNTHERODT E.J., 5. KUB!_ER J.,BENNEMANN_K.H., Phys.;Rev. (B) 23 5176 (198‘1). 6. BUSCHOW K.H.J. Gd'BEE'KMmS X.X., Phys. Stat. Sol. (a) $, 193 (1980). _.. 7. MIEDEMA A.R., 2. Metallkde. 70;' 345 (1979). , 1177 (‘i981) 3. BLJSCHOW K.H.J. and van ENCEN P.G., blat. Res. Bull. & 9. VAN DER KRAAN A.M. and BUSCHOW K.H.J. , Phys. Rev. (B) (1982). 10. DAVIS S., FISCHER M., GIESSEN B.C. and POLK D.E. in "Rapidly Quenched .LIetals" Vol. 2 p. 425, Chameleon Press, London (1978) 9. Cantor Ed. 11. WANG R., MERZ M.D., BRI>tHALL J.M. and DAHLGREN S.D., in "Rapidly Quenched Metals" Vol. 1. p. 420, Chameleon Press, London (1975) a. Cantor Ed. C8-47'7 (1980). 12. MARCHAL G., GENY,J.F., Ph. Mangin and JANOT Chr., J. Physique 3, 13. ELARCHAL G., TEIRLINCK D., MAXGIN Ph., JANOT Chr. and HUBSCH J., J. Physique 41, m-662 (1980). 14. BUSCHOW K.H.J.,

ALGRA H.A. and HENSKENS R.A., J. Appl. Phys. 51 561 (1980). B.C. and ELLIOT R.O. in "Rapidly Quenched Metals" Vol. 1 p. 406 Chsmeleon Press, London (1978) B. Cantor Ed. Acta Met (to be published). BUSCHOW K.H.J. 1 (1980). MIEDEMA A-R., di CHXTEL P.F. and DE BOER F.R. , Physica m, ADA&l G. and GIBBS J.H., J. Chem. Phys. a, 373 (1958). DAVIES H.A., Phys. Chem. Glasses '7, 159 (1976). SAKATP, M., COWLAM N. and DAVIES H.A.,_J. Phys. F. 11, L157 (1981).

15. GIESSEN 16. 17. 18. 19. 20.