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THERMODYNAMIC EVALUATION OF THE Cu-Ti SYSTEM IN VIEW OF SOLID STATE
AMORPHIZATION REACTIONS
L. Battezzati, M. Baricco, G. Riontino, I. Soletta
To cite this version:
L. Battezzati, M. Baricco, G. Riontino, I. Soletta. THERMODYNAMIC EVALUATION OF THE Cu-
Ti SYSTEM IN VIEW OF SOLID STATE AMORPHIZATION REACTIONS. Journal de Physique
Colloques, 1990, 51 (C4), pp.C4-79-C4-85. �10.1051/jphyscol:1990409�. �jpa-00230769�
THERMODYNAMIC EVALUATION OF THE Cu-Ti SYSTEM IN VIEW OF SOLID STATE AMORPHIZATION REACTIONS
L. BATTEZZATI*
,
M. BARICCO*~ * " " ",
G. RIONTINO" * " * and I. SOLETTA* * * '~ipartimento di Chimica Inorganics, Chimica Fisica e Chimica dei Materiali, Universitd d i Torino, Italy" " ~ s t i t u t o Elettrotecnico Nazionale Galileo Perraris, Torino, Italy
*.* Dipartimento di Chimica, Universitd di Sassari, Italy
* e t *
INPM, Unita' di Ricerca d i Torino, Italy
Resumk -La description thermodynamique du sist6me Cu-Ti est reconsideree, c a r l e s c a l c u l s he l a l i t t g r a t u r e , bien q u e d o n n a n t u n e bonne representation du diagramme de phase, ne prevoient pas la possibilit6 de l'amorphisation. Une nouvelle courbe d'knergie libre pour la phase liquide est prohos6e, prenent en compte un excks de chaleur spkcifique de melange.
Cette dernikre quantit6 a 6t6 obtenue pour quelques compositions de la difference entre la chaleur de fusion et la chaleur de cristallisation de rubans amorphes. On montre que la stabilit6 de la phase liquide cro'lt lorsque la temperature decroit. Les courbes T et To pour Cu-Ti sont calcul6es, et 1' intervalle d'amorphisation discut86.
Abstract
-
The thermodynamic description of the Cu-Ti system is revised as current evaluations of it, while giving a reasonable fit to the phase diagram, do not predict the possibility of amorphization. A new free energy curve for the liquid phase is derived accounting for an excess specific heat of mixing. This latter quantity has been obtained for a few compositions from the difference between the heat of fusion and the heat of crystallization of melt spun ribbons. An increase in stability of the liquid phase on decreasing temperature is shown. Tg and To curves for Cu- Ti are calculated and the glass forming range is discussed.1
-
INTRODUCTIONCu-Ti has been one of the first metal-metal systems to show good glass forming tendency by liquid quenching /l/. Recently, it has been found that amorphization is possible in Cu-Ti either by reacting the pure solid elements /2/ or by grinding two intermetallic compounds / 3 / . The amorphizing range is wide and covers also compositions of intermetallic compounds. The Cu-Ti phase diagram displays steep liquidus curves in the terminal regions and a number of relatively low melting compounds in its central part; here the liquid field e x t e n d s to l o w temperature w i t h a s h a l l o w l i q u i d u s curve. A s the intermetallics melt within a narrow range between 1281 K and 1153 K, it may be inferred that they are of similar and limited stability
.
This condition should certainly favour solid state amorphization.In spite of the vast evidence reported for vitrification in Cu-Ti, current evaluations of its thermodynamic properties, while giving a reasonable fit to the phase diagram, do not predict the possibility of amorphization by any technique, as the free energy of the liquid, extrapolated to the undercooled regime, never falls below that of competing solid solutions / 4 / . This implies that the locus of equal free energy between the liquid and solid solutions (To curves) stands well above the glass transition temperature. Under these circumstances, glassy alloys would never be produced, because a homogeneous close-packed phase would form at all compositions.
On the other hand, the ability of amorphizing in the solid state indicates an enhanced stability of the liquid phase with respect to extended solid solutions.
We reconsider here the thermodynamics of the Cu-Ti system with attention to the description of the free energy of the liquid phase. Experimental data are reported on the heat of fusion and crystallization of some alloys and T curves are calculated in order to make a comparison with the experiment&?
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990409
COLLOQUE DE PHYSIQUE
glass forming range.
2
-
EXPERIMENTALCu BTi34, Cu60Ti40, C U ~ ~ TigOCu10 alloys hkve been prepared by arc T ~ ~ ~ , mefting the pure elemen S omogeneity was ensured by remelting the alloy buttons several times. Pieces of crushed alloys were melted and spun onto a copper wheel under helium to produce amorphous ribbons. Amorphization was almost complete in all cases as checked by x-ray diffraction.
Few milligrams of ribbon were used to determine the heat of crystallization of the amorphous alloy by DSc at .5 K/s heating rate. Fast heating (5 K/s) revealed the occurrence of a glass transition in Cu QTi and Cug6Tig4. The heat of fusion of the alloys was measured with a %iga% DTA apparatus by comparison of melting and solidification peaks with those of pure A1 and Cu.
The accuracy of the results is lower than that obtained with standard techniques, however the deviations were mantained within a band of 10%.
3 - RESULTS
The experiments devised in this work aim at determining the specific heat difference between liquid and solid phases, A ~ p l - s from
where AHf is the heat of fusion at the melting point, Tf, and AH, is the heat of crystallization of the amorphous alloy. Tx is the .temperature of the maximum of the DSc peak. If the amorphous p ase is considered as an highly undercooled liquid, an average value for ACp - S is calculated between Tf and T
.
The heat of fusion was determined for the C U ~ eutectic (13.1 kJ/mol), ~ T ~ ~ ~ tEe congruent CuTi (15.8 kJ/mol) and the Cu3Ti (13.3 kJ/mol) and Ti2Cu (13.2 kJ/mol) compounds which decompose peritecticafiy at a few degrees below the liquidus. The heats of crystallization are 6.5, 4.6, 6.5 and 7.2 kJ/mol respectively. They pertain to alloys completely amorphous under x-ray diffraction apart from C U ~ where a small crystalline fraction was ~ T ~ ~ ~ detected, In this case the heat of crystallization is slightly underestimated.The onset crystallization temperatures correspond to those reported in /l/.
From eq. (l), the average specific heat has been obtained as given in Fig. 1.
Fig. 1
-
Average specific heat difference between liquid and solid phases for some Cu-Ti alloys. Dashed line: parabolic fit to the data.calculated in the next section. If the reference state in Fig, 1 is changed from the specific heat of solid elements to that of liquid elements, the excess specific heat of mixing, ACp, is obtained. For the purpose of extending the calculation to all compositions, the points. have been fitted by a parabola, with the awareness that it overestimates the quantity for very dilute solutions.
The mixing effect on ACp is remarkable at intermediate concentration a s expected for a system undergoing ordering. The chosen trend is symmetrical with respect to composition within the experimental error. However a skewness towards higher Cu content, in accordance to that of the Cowley short range order parameter /6/, may be possible. In fact, it can be caused simply by a slight change in the properties of the reference pure elements which carry a strong uncertainty, as discussed below.
4
-
DETAILS OF THE CALCULATIONThe free energy of the solution phases is written as
where GA and GB are the lattice sf bilities of the pure elements taken from Kaufmann /7/ and Saunders /8/, AGid is the ideal free energy of mixing and A G an excess term. ~ ~
As we are going to describe the free energy of the liquid in undercooling regime, the reference state of pure Cu is calculated at every temperature accounting for the difference between a constant specific heat for the liquid and that of crystal phases /g/. The Kauzmann temperature of vanishing entropy,TK, often considered as an ideal glass transition temperature, is 257 K for Cu and the average
AcP1-'
is 4.7 (Fig. l ).
The assessment of the reference state for pure Ti in undercooling regime is more difficult. A recent collection of data /10/ reports a value of 8
+
3J/mol K for A C ~ at the melting point and a constant specific heat for the ~ - ~ liquid. Therefore, the extrapolation of the entropy to low temperatures leads to T K = 0 . 6 2 T w h e r e a s e x t r a p o l a t i o n o f t h e actual glas: t r a n s i t i o n temperature in %;nary systems to zero Ti concentration gives Tp
-
0.3 T Ill/.So, the specific heat of liquid undercooled Ti appears overestlmated. If TK is taken at 0.25Tf for Ti as for other pure metals /12/, an effective speclfic heat difference between liquid and DTi of 5.4 J/mol K is derived. The specific heat of aTi was taken from /10/ and extrapolated to its melting point; the specific heat of fcc Ti was considered equal to that of aTi. The free energy of the solid solutions was taken as in / 8 / .
The choice of the Ti reference state has direct consequence on the mixing properties in the liquid state. In fact, the known values depend on the heat of mixing of solid Ti with liquid C u at 1373 K /13/. With the present hypothesis on liquid Ti, the enthalpy of fusion at 1373 turns out to be 11.5 kJm01 instead of 6.94 kJ/mol. The enthalpy of mixing, AHmil, becomes somewhat more negative and may be approximated by means of a regu ar solution model with an interaction parameter of -26800 kJ/mol instead of -16300. Combining with AGmix data from /14/, the entropy of mixing, AS,,, is obtained f h x a maximum value of 3,7 J/mol R at X = 0.6. It is definiiely lower than the ideal entropy of mixing, thus indic?&ing a tendency to ordering in the liquid state. It is expected that the degree of order will increase o n decreasing temperature /6/ and, as a consequence, that the thermodynamic properties will be temperature dependent /14/. This finds confirmation in the existence of an excess ACp as shown in Fig. 1 which is used to calculate AGex at every temperature. It is of primary importance for the glass-forming ability of a system, because the liquid i s stabilized on undercooling.
Finally, the glass transition temperature is reached and an amorphous solid is formed having approximately the same specific heat as the crystal phases. At Tg, the difference in free energy between liquid and equilibrium phases will be smaller than expected in the absence of a substantial ACp and the liquid phase may be even more stable than other crystal phases as the solid solutions. In this case, solid state reactions of the pure elements below T may produce an amorphous solid if the equilibrium intermetallics show a slog
COLLOQUE DE PHYSIQUE
kinetics of formation /15/.
Tg is reported at 676 for Cu66 7Ti33 /l/. We have found a manifest Tg for C U ~ at 681 ~ T K ~and for cu6g'~i it 683 ~ ~ K. The isoentropic temperature should occur at a somewhat lower tzmperature. At TK for every composition an entropy balance is established /11,16/
The entropy of fusion of the alloy, AS
,
is zero at T g ; the entropy of formation of the crystal phases, ASfor, fand that of mixing in the liquid, ASpix, may be expressed either by experimental data or by suitable models. Theen ropy of fusion of a pure element is ,"
With this position, eq.(3) is solved for T at each composition. Current literature evaluations /8/ and estimates of %he present work point to values of ASf
,
for Cu-Ti compounds from 0.5 to -3.35 J/mol K. An average value of -1 J/mol2
was adopted. ASmi, for all compositions was calculated at TK from the values at 1373 K and the ACp function of Fig. 1. Calculated T s are shown in Big. 2, curve a. The isoentropic temperature for Cu60Tig0 is 5%0 K. The trend of TK is also reported in Fig. 2 , curve b, which would occur if the entropy of mixing did not change with temperature.Fig. 2
-
Trend for ideal glass transition temperature in the Cu-Ti system.Curve a and b are described in the text.
5
-
RESULTS OF THE CALCULATIONThe free energy for solution phases at 300 K is shown in Fig. 3. The curve for the liquid stands below that of solid solutions in a wide composition range.
The common tangent construction gives an amorphizing range from 51 to 72 at%
Cu. Partial amorphization can occur between the To points at 28 and 83 at% Cu.
The limit for complete vitrification on the Cu rich side reproduces quite well the ball milling results of Cocco et al. /17/, whereas the To limit seems to correspond to the range reported in /2/. The agreement is less satisfactory on the Ti rich side where complete amorphization has been reported up to 60 % Ti.
In this composition range our calculation is very much affected by the choice of the properties of pure Ti: an error of 1 J/mol K in the definition of the specific heat of liquid Ti would modify AGmix at 300 K for TigpCu10 of 1 kJ/mol. Correspondingly, the glass forming range would be changed o more than
Fig. 3
-
Free energy curves for amorphous and solid solution phases in Cu-Ti at 300 K.10%. In Cu-Ti,
AHmiXN:iZ;nly
moderately negative if compared with other glass- forming systems as,
Ni-Ti, A1-Ti and usual uncertainties acquire more relevance.However, our calculation predicts a substantial glass-forming range with respect to previous ones / 4 / . This is partially due to the revision of the properties of Ti, but more relevant is the use of the experimental excess specific heat of mixing. Among the previous calculations only the Saunders model expressed a temperature dependence for the liquid free energy /8/, The excess heat capacity which accounts for it is yet too low in comparison with
a) this work, iperbolic b) this work, linear
C ) calculated f mm R e f l
Fig. 4 -Specific heat difference between liquid and solid phases for Cu Ti
.
6 0 40
C4-84 COLLOQUE DE PHYSIQUE
that de ived from our data, as shown in Fig. 4 for Two expressions for *C f-s ave been considered: linear and hyperbolic (FI.~. 4, curves a and b), an8 *C '-S has been posed equal to ASf at Tf. The results do not depend appeciablypon the form of the function used.
The application of the present approach to the A1-Ti system showed a range for vitrification by ball milling in agreement with experiments /18/.
To curves for Cu-Ti are shown in Fig. 5. Although our calculation is based only on data obtained at medium and low temperature, the Ti rich branch is still reasonably reproduced. Below the liquidus, the curves bend steeply because of the effect of the liquid free energy, which is increasingly negative. At the glass transition a wide composition field is not crossed by To curves, so partitionless solidification of the liquid into solid solutions may be avoided by rapid quench.
2000 l I I I
v.-. bcc hcp
f cc
-
-
TgFig. 5
-
To curves for the Cu-Ti system.This result is at .variance with that of Massalski and Woychik who used a To curve lying above
Tg
and attributed glass formation in Cu-Ti to the depressi,on of the nucleation temperature by quenching /19/. Although this'may be of great i m p o r t a n c e i n e x p l a i n i n g t h e k i n e t i c h i n d r a n c e to the f o r m a t i o n of intermetallics, it would not account for solid state amorphization. On the other hand, it is interesting to observe that our To curve for fcc solutions crosses those for hcp and bcc around 30 at% Ti, indicating that the fcc phase would compete with glass formation by melt quenching. This agrees with the experimental results obtained in laser melted Cu-Ti alloys /IS/.ACKNOWLEDGMENTS
Work performed under ENEA contracts 3405 (L.B., G.R. ) , 14943 (M.B. ) and 3965 ( 1 . S . ) .
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