- Email: [email protected]
High temperature thermodynamic investigation of the titanium-rich portion of the titanium-iridium system by knudsen cell mass spectrometry
Journal of the Less-Common Metals, 68 (1979) P31 - P38 Q Ekevier Sequoia S.A., Lausanne - Printed in the Netherlands
P31
HIGH TEMPERATURE THER~~ODYN~IC INVESTIGATION OF THE TITANIUM-RICH PORTION OF THE TITANIUM-IRIDIUM SYSTEM BY KNUDSEN CELL MASS SPECTROMETRY
M. PELINO,
S. K. GUPTA,
L. R. CORNWELL
and K. A. GINGERICH
Departmen f of Chemistry and Department of Mechanical Engineering,
Texas A and M
University, College Station, Texas 77843 (U.S.A.) (Received
March 19,1979)
Summary The vapor pressure of titanium in the titanium-rich solid Ti-Ir alloys has been determined by means of the Knudsen cell mass spectrometry in the temperature range 1480 - 1770 K for alloys with iV*i = 0.93, 0.885 and 0.796 (eutectic composition). The activities of titanium were evaluated as 0.54 and 0.32 for the NT, = 0.93 and N,i = 0.885 compositions of the fl phase, respectively, and 2.59 X lo-’ for the NT, = 0.796 eutectic composition (fi and y phases), at the average temperature of 1623 K. Using, in addition, the data for the Ir-rich portion of the Ti-Ir system (NTi = 0.5, NTi = 0.4 and N,i = 0.25) previously obtained in our laboratory by Choudary et al., the activities of Ir were evaluated for the binary system by the GibbsDuhem treatment of the tit~ium activities, and the co~esponding Gibbs energies of formation were derived. The enthalpy of formation at 298 K for Ti,Ir (y phase, N,i = 0.75) was found to be -92.0 f 14.6 kJ (g atom)-“.
1. Introduction The Engel-Brewer theory of metallic bonding [l, 21 predicts unusually high ~ermodyn~ic stabilities for the transition metal alloys between d electron-deficient transition metals (Ti, Zr, Hf etc.) and the platinum group metals which contain filled d orbit& (Ir, Pt, Pd etc.). According to this approach, an increase in the number of bonds and thus in the bond strength results from the transfer of electrons from the platinum group metal to the vacant d orbitals of the d electron-deficient metal. In the past few years, various investigations of the Group IV-platinum group metal alloys have confirmed the important role played by d-d electron interactions in determining the thermodynamic [3 - 61 and mechanical properties [ 71 of this class of alloys. Recently, Miedema et al. [S - lo] have developed an empirical model for calculating the enthalpy of formation of binary liquid or solid alloys. The enthalpy of formation is interpreted as the result of mainly two contribu-
P32
tions: a negative one due to the difference in the chemical potential of electrons which exists in the two pure metals separately (contact potential) and a second (positive) one arising from the discontinuity in electron density that occurs at the interface between dissimilar atoms when they are brought together. Inherent in this approach is a net flow of electrons from the less electronegative d electron-deficient metal to the more electronegative platinum group metal; the magnitude of the electronegativity difference contributes significantly to the stability of the alloy. While both the models invoke the concept of electron transfer between the two metals of an alloy system, they predict electron flow in opposite directions. Thus the approaches are apparently in fundamental conflict. However, from the standpoint of the molecular orbital theory of bonding this conceptual difference disappears since, in filling up the molecular orbit&, no dist~ction is made between the electrons from the two atoms. In any case, although the &gel-Brewer approach is qualitative in nature, its predictions have provided the initial stimulus for the study of the alloys of the platinum group metals with the early transition metals. The ability of Miedema’s model to estimate quantitatively the entbalpies of formation of the binary alloys has also been demonstrated. The expe~ment~ dedication of the ~ermodyn~i~ and mech~ic~ properties of these transition metal alloys is of importance from a theoretical point of view as well as for industrial applications. In order to continue the thermodynamic investigation of the Ti-Ir alloys and to correlate the thermodynamic and the mechanical properties [II] of such alloys, a high temperature ~vestigation of the T&rich portion of the Ti-Ir alloys has been carried out by Knudsen cell mass spectrometry and the results are presented here.
2. Experimental The high temperature mass spectrometer used in the present investigation was a Nuclide Corporation 12 - 90 - HT single focusing magnetic deflection type instrument similar to the one previously described [12]. The electron energy used to ionize the molecular beam arising from the Knudsen cell in the source was 19 eV. The emission current and the acceleration voltage were 0.3 mA and 4500 kV, respectively. The ion currents of *‘Ti’, “‘Ag+ and 216Agb were mo nitored during the course of each experiment and were identified as parent ions by their shutter profile, isotopic distribution and ionization efficiency curves. The alloys were prepared by arc melting the required amount of high purity titanium and iridium chips and were homogenized by flipping over the resulting alloy button and remelting three or more times. The composition was calculated on the basis of the initial weights of titanium and iridium, since losses in arc melting and during the course of the preparation and vaporization were found to be negligible. The Knudsen cells used to vaporize the
P33
alloys were constructed from high purity high density graphite and were approximately 2 cm in height and 0.75 cm in diameter, with a knife-edge orifice 1 mm in diameter. A Leeds and Northrup optical pyrometer was used to determine the temperature in the Knudsen cell by sighting into a black-body hole in the bottom of the cell. The calibration of the pyrometer had previously been checked under experimental conditions at the melting point of gold. Experimentally determined window and prism corrections were applied. For the calibration of the mass spectrometer a small weighed amount (5 - 7 mg) of silver wire was added in each run to the alloy. After pumping to a vacuum of about lo-’ Torr, the temperature was raised to 1200 K and several sets of the silver monomer and dimer equilibrium ion currents were recorded as a function of temperature. The temperature was then raised to 1500 K, recording the silver intensity for several hours until its complete evaporation. The ion intensity of Ti’ was found to be constant after approximately 2 h from the change of temperature for the N,i = 0.93 and Nri = 0.885 compositions, whereas ten or more hours at constant temperature were required for the N,i = 0.796 (eutectic composition) alloy. To avoid any carbon contamination of the samples, the experimental temperature was maintained below the respective melting points of the alloys [ 13, 141 (approximately 1790 K for the Nri = 0.93 alloy, 1770 K for the Nri = 0.885 alloy and 1700 K for the N,i = 0.796 alloy). A visual examination of the sample after each run indicated that it was free from any contamination; samples of the two former alloys were shiny. Owing to the strong interaction of Ti with Ir, the intensity of the 4sTi’ peak in the Nri = 0.796 alloy was very small below the melting point. Therefore the sample was melted after nine values of the Ti’ intensity had been measured and their reproducibility had been ensured. The 48Ti’ intensities after melting and refreezing were not found to be reproducible; the values were considerably lower than those prior to melting and visible traces of carbon contamination were found on the surface of the sample. Therefore only the first nine values of the 48Ti’ intensities have been used to evaluate the Ti activity for the eutectic composition.
3. Results and discussion Table 1 shows the experimental 48Ti’ ion currents for the three solid alloys listed in the sequence of measurement. These ion currents were converted to partial pressures using the relations P,i = k,iI&T
and
kTi = kAg
‘%C’A,~A, E,,%i’Yd’h,,
P34 TABLE
1
Experimental
ioncurrents of titanium overTi--1r alloys
NTi = 0.93
NTi = 0.885
T(K)
Z(48Ti’)
1579
x lo-l2 6.390X lo-l2 1.245x lo-= 2.670x lo-l1 2.760x lo-l1 3.050x lo-l1 7.800x lo-l2 4.180x lo-l2 1.850x lo-l2 7.800x10-13 4.41ox1o-13 2.73Ox1O-12 6.600x10-12 1.350x lo-l1 2.010x lo-l1 4.220x lo-= 5.620X lo-l1 7.17ox1o-11 1.090x lo-lo 6.100x lo-l2 1.550x lo-l2 3.630x lo-l3
1614 1648 1683 1711 1691 1621 1590 1552 1516 1495 1566 1610 1646 1666 1703 1721 1734 1756 1606 1544 1484
2.930
(A)
A’Ti = 0.796
T(K)
Z(48Ti’)
1506 1551 1576 1601 1622 1648 1690 1717 1764 1701 1633 1551 1529 1500 1604 1656 1734 1670 1572 1496 1535 1479 1729
8.660x lo-l3 1.900x lo-l2 3.580x lo-l2 6,000X lo-l2 9.450x lo-l2 1.323X lo-l1 3.150x lo-l1 5.300x lo-l1 1.272x1o-1o 4.140x lo-= 1.161x lo-= 2.040X lo-l2 1.250X lo-l2 6.000x lo-l3 5.780x lo-l2 1.662X lo-= 6.930 X lo-l1 2.160x lo-l1 2.730X lo-l2 5.500x lo-l3 1.290x lo-l2 3.630X lo-l3 5.910
(A)
T(K)
I( 48Ti+) (A)
1610 1599 1582 1561 1634 1641 1659 1675 1685
3.012x10-13 2.010x10-13 1.770x lo-l3 9.300x lo-l4 5.100x lo-l3 6.450X lo-l3 1.100x lo-l2 1.500x lo-l2 1.950x10-12
x lo-”
Here the factors CI,y and IZrepresent the maximum ionization cross section, the multiplier gain and the isotopic abundance, respectively; E denotes an empirical correction factor needed to convert the experimental ion currents to correspond with those at maximum ionization cross section. The pressure calibration constant hAg was obtained by the monomerdimer technique [3,15] from the measured Ag’ and Ag3 ion currents and the known dissociation energy of the silver dimer, D,(Ag,) = 159.0 + 6.3 kJ mol-’ [16]. The following values (in atm A-’ K-l) were obtained for kAg: 1.97 f 0.2 (A’Ti = 0.93); 1.09 + 0.05 (NT1 = 0.885) and 1.77 * 0.08 (N,i = 0.796), where the error terms represent the standard deviation. The E factors were evaluated from the ionization efficiency curves and were found to be between 1.01 and 1.08 for the ions in the present investigation. The relative multiplier gain YTi/YAg was measured as 1.23 in a separate experiment. The values for CrTiand DAg were taken from Mann [17], while uAgZ was estimated by multiplying uAe by an empirical factor of 1.5 [18]. The kTi VdUes (in atm A-” K-l) found were 0.93 (NTi = 0.93), 0.52 (NTi = 0.885) and O-88 (NTi = 0.796).‘
P35
-13
1700 ,
1600 t
Fig. 1. Plots of lnP,i
T (K)
,500 ,
us. 1 /T for the titanium-rich
portion of the solid Ti-Ir alloys.
A least-squares treatment of the In P,i uersus l/T plots shown in Fig. 1 yielded the following vapor pressure equations (ln P,i = mn/T + bN). In P,i =
In P,i =
In PTi =
-56 132 + 84 T
+ 16.39 rt 0.05
-56 175 + 108 T -68 129 + 1970 T
+ 14.67 -I 0.07
+ 20.74 + 1.21
(NTi = 0.93)
(N,
= 0.885)
(NTi = 0.796)
The heats of vaporization of titanium from the alloys AH, can be obtamed from the slopes of the respective In PTi versus l/T plots as mN R, at the mean temperature of the measurements. The partial molar enthalpy of solution of titanium Afir, is given by the difference between the heat of vaporization of titanium from the alloy and that from pure titanium at the same temperature. Thus the values Al?,, = -11.8 + 0.8 and AHTi = -12.1 + 1.0 kJ (g atom)-’ were obtained for the N,i = 0.93 and NTi = 0.885 compositions, respectively. Here the error limits correspond to three times the standard deviation. A similar evaluation of Agri for the eutectic composition (Nri = 0.796) would be of little significance since the composition of the coexisting phases changes with temperature.
P36
The activities of titanium lated through the expression
in the Ti-Ir alloys studied here were calcu-
where m, = -54 713 and b. = 16.13 are the constants of the pressure equation for pure titanium obtained from Hultgren et al. 1191. The activities were evaluated at 1623 K, the average temperature of the present measurements, and have been listed in Table 2. Also shown in Table 2 are the activities at 1623 K of titanium in the iridium-rich portion of the Ti-Ir alloys extrapolated from the activity data at 2000 K obtained previously in this laboratory by Chouda.ry et al. [13], neglecting any dependence of the enthalpy of formation and entropy of mixing on temperature in the 2000 1623 K range.
TABLE Activitiesa
2 and Gibbs energies
of formation
of Ti-Ir
alloys at 1623 K -
NTi
aTi
air
AGM (kcal (g atom)-‘)
0.93 0.885 0.796b
0.54 0.32 2.59 X 1O-2
1.96 x 1o-5 2.01 x 1o-5 3.54 x 1o-5
-4.3 -7.2 -
0.5 0.4b 0.25
1.93 x 1o-4 5.96 X 1O-5 3.09 x 1o-5
8.84 X 1O-5 8.80 x 1O-4 2.65 x lo-’
-28.8
f 2
-17.2
+ 1.8
fr 0.3 ?r 0.6
%andard state: solid Ti and solid Ir. bTwo-phase alloy (0.88 > NTi > 0.75 and 0.43 > NTi > 0.28) [13, 141.
The activities of iridium in the Ti-Ir alloy system were evaluated by a graphical integration of the Gibbs-Duhem equation [ 201 over the entire range of composition. The derived activity values, together with the respective Gibbs energies of formation, are listed in Table 2. Using the same procedure, the activities of titanium and iridium were also evaluated for the Nri = 0.6 (S phase) and NTi = 0.75 (TisIr, y phase) compositions. For the 6 phase the activity values obtained are ari = 1.9 X 10e3 and al, = 6.8 X 10u6; these yield a value of -102.5 -+ 8.4 kJ (g atom)-’ for the Gibbs energy of formation AG”. The corresponding values for the y phase are: ari = 3.1 X 10e2, err = 5.1 X lop5 and AGM = -68.6 f 8.4 kJ (g atom)-‘. Similar evaluations for the other compositions were not carried out because of the presence of two coexisting phases. The variation of AGM with Nri at 1623 K is shown in Fig. 2. In order to derive the enthalpy of formation of Ti31r, the excess entropy of formation of Ti,Ir was estimated through the empirical relationship of Kubaschewski and Slough [ 3,211
P37
T=l623
-3o-
%
K
-25-
4 9 -2oMC ,2
/
-15-
/' -10 -
I' /'
_5-
I
i'
I' Of 0.0
1 .I
I .2
.3
.4
5
.6
7
.8
.9
I
NT,
Fig. 2. Variation of the Gibbs energy composition (at.% Ti).
AS:,,
=
of formation
of Ti-Ir
alloys as a function
of the
AGEmU 0.78(7’,,
+ T,,)
- Texpt
where T,, and T,, are the boiling points. At 1623 K, AS”,,, (TisIr) is calculated as -10.5 + 3.3 J mol-’ KP1 yielding the corresponding value, ASM = -14.6 + 3.3 J molll K-l. Assuming AC, to be equal to zero, in accordance with Neumann and Kopp’s rule [ 221 which has been found valid for a large number of reactions and especially for alloy phases, the enthalpy of formation of TiaIr at 298 K, AHr.sa8, is calculated to be -92.0 + 14.6 kJ (g atom)) ‘. This value is in fair agreement with the value of AHr,zas = -54.4 kJ (g atom))’ calculated on the basis of Miedema’s cellular model using eqn. (8) of ref. 8 and various parameters listed therein. The large negative values of the Gibbs energies of formation of the titanium-iridium alloys and their variation with composition are consistent with the corresponding results obtained previously for titanium-platinum group alloys [5,6, 23,241.
Acknowledgments The authors are grateful for financial support for this work from the National Science Foundation under grants DMR 73-02625 and CHE 7808711. This work was performed at the Mechanics and Materials Center of the Texas A and M University Experimental Engineering Station. References 1 N. Engel, Powder Metall. Bull., 2 L. Brewer, Science, 161 (1968)
7 (1954) 115.
8.
P38 3 U. V. Choudary, K. A, Gingerich and L. R. Cornwell, J. Less-Common Met., 50 (1976) 201. 4 L. Brewer and P. R. Wengert, Metals. Trans., 4 (1973) 83. 5 P. J. Meschter and W. L. Worrel, Metall. Trans., 7A (1976) 299. 6 U. V. Choudary, K. A. Gingerich and L. R. Cornwell, Metall. Trans., 8A (1977) 1487. 7 E. W. Collings and H. L. Gegel, in E. W. Collings and H. L. Gegel (eds.), Physics of Solid Solution Strengthening, Plenum Press, New York, 1975, p. 147. 8 A. R. Miedema, J. Less-Common Met., 46 (1976) 67. 9 A. R. Miedema, F. R. de Boer and R. Boom, Caiphad, 1 (1977) 341. 10 A. R. Miedema, Philips Tech. Reu., 36 (1976) 8. 11 V. Kandarpa, L. R. Cornwell and K. A. Gingerich, Proc. 2nd Znt. Conf Mechanical Behauior of Materials, Boston, 1976, pp. 1737 - 40. 12 K. A. Gingerich, J. Chem. Phys., 49 (1968) 14. 13 V. N. Eremenko and T. D. Shtepa, Zzu. Acad. Nauk SSSR, Met., 203 (1970) 197. 14 V. Kandarpa, L. R. Cornwell and K. A. Gingerich, Microsc. Sci., 5 (1977) 384. 15 R. T. Grimley, in J. L. Margrave (ed.), Characterization of High Temperature Vapors, Wiley-Interscience, New York, 1967, pp. 195 - 243. 16 K. A. Gingerich, J. Cryst. Growth, 9 (1971) 31. 17 J. B. Mann, in K. Ogata and T. Hayakawa (eds.), Recent Developments in Mass Spectrometry, University of Tokyo Press, 1970, pp. 814 - 19. 18 J. Drowart and P. Goldfinger,Angew. Chem. Znt. Ed. Engl., 6 (1967) 581. 19 R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley and D. D. Wagman, Selected Values of Thermodynamic Properties of the Elements, Am. Sot. Metals, Metals Park, Ohio, 1973. 20 R. A. Swalin, Thermodynamics of the Solids, 2nd edn, Wiley-Interscience, New York, 1972, pp. 134 - 135. 21 P. Kubaschewski and W. Slough, Prog. Mater. Sci., 14 (1963) 3. 22 P. Kubaschewski and E. L. L. Evans, Metallurgical Thermochemistry, Pergamon Press, New York, 1958, p. 185. 23 R. M. German and G. R. St. Piere, Metalt. Trans., 3 (1972) 2819. 24 P. J. Meschter, Ph.D. Thesis, University of Pennsylvania, Philadelphia, 1974.
P31
HIGH TEMPERATURE THER~~ODYN~IC INVESTIGATION OF THE TITANIUM-RICH PORTION OF THE TITANIUM-IRIDIUM SYSTEM BY KNUDSEN CELL MASS SPECTROMETRY
M. PELINO,
S. K. GUPTA,
L. R. CORNWELL
and K. A. GINGERICH
Departmen f of Chemistry and Department of Mechanical Engineering,
Texas A and M
University, College Station, Texas 77843 (U.S.A.) (Received
March 19,1979)
Summary The vapor pressure of titanium in the titanium-rich solid Ti-Ir alloys has been determined by means of the Knudsen cell mass spectrometry in the temperature range 1480 - 1770 K for alloys with iV*i = 0.93, 0.885 and 0.796 (eutectic composition). The activities of titanium were evaluated as 0.54 and 0.32 for the NT, = 0.93 and N,i = 0.885 compositions of the fl phase, respectively, and 2.59 X lo-’ for the NT, = 0.796 eutectic composition (fi and y phases), at the average temperature of 1623 K. Using, in addition, the data for the Ir-rich portion of the Ti-Ir system (NTi = 0.5, NTi = 0.4 and N,i = 0.25) previously obtained in our laboratory by Choudary et al., the activities of Ir were evaluated for the binary system by the GibbsDuhem treatment of the tit~ium activities, and the co~esponding Gibbs energies of formation were derived. The enthalpy of formation at 298 K for Ti,Ir (y phase, N,i = 0.75) was found to be -92.0 f 14.6 kJ (g atom)-“.
1. Introduction The Engel-Brewer theory of metallic bonding [l, 21 predicts unusually high ~ermodyn~ic stabilities for the transition metal alloys between d electron-deficient transition metals (Ti, Zr, Hf etc.) and the platinum group metals which contain filled d orbit& (Ir, Pt, Pd etc.). According to this approach, an increase in the number of bonds and thus in the bond strength results from the transfer of electrons from the platinum group metal to the vacant d orbitals of the d electron-deficient metal. In the past few years, various investigations of the Group IV-platinum group metal alloys have confirmed the important role played by d-d electron interactions in determining the thermodynamic [3 - 61 and mechanical properties [ 71 of this class of alloys. Recently, Miedema et al. [S - lo] have developed an empirical model for calculating the enthalpy of formation of binary liquid or solid alloys. The enthalpy of formation is interpreted as the result of mainly two contribu-
P32
tions: a negative one due to the difference in the chemical potential of electrons which exists in the two pure metals separately (contact potential) and a second (positive) one arising from the discontinuity in electron density that occurs at the interface between dissimilar atoms when they are brought together. Inherent in this approach is a net flow of electrons from the less electronegative d electron-deficient metal to the more electronegative platinum group metal; the magnitude of the electronegativity difference contributes significantly to the stability of the alloy. While both the models invoke the concept of electron transfer between the two metals of an alloy system, they predict electron flow in opposite directions. Thus the approaches are apparently in fundamental conflict. However, from the standpoint of the molecular orbital theory of bonding this conceptual difference disappears since, in filling up the molecular orbit&, no dist~ction is made between the electrons from the two atoms. In any case, although the &gel-Brewer approach is qualitative in nature, its predictions have provided the initial stimulus for the study of the alloys of the platinum group metals with the early transition metals. The ability of Miedema’s model to estimate quantitatively the entbalpies of formation of the binary alloys has also been demonstrated. The expe~ment~ dedication of the ~ermodyn~i~ and mech~ic~ properties of these transition metal alloys is of importance from a theoretical point of view as well as for industrial applications. In order to continue the thermodynamic investigation of the Ti-Ir alloys and to correlate the thermodynamic and the mechanical properties [II] of such alloys, a high temperature ~vestigation of the T&rich portion of the Ti-Ir alloys has been carried out by Knudsen cell mass spectrometry and the results are presented here.
2. Experimental The high temperature mass spectrometer used in the present investigation was a Nuclide Corporation 12 - 90 - HT single focusing magnetic deflection type instrument similar to the one previously described [12]. The electron energy used to ionize the molecular beam arising from the Knudsen cell in the source was 19 eV. The emission current and the acceleration voltage were 0.3 mA and 4500 kV, respectively. The ion currents of *‘Ti’, “‘Ag+ and 216Agb were mo nitored during the course of each experiment and were identified as parent ions by their shutter profile, isotopic distribution and ionization efficiency curves. The alloys were prepared by arc melting the required amount of high purity titanium and iridium chips and were homogenized by flipping over the resulting alloy button and remelting three or more times. The composition was calculated on the basis of the initial weights of titanium and iridium, since losses in arc melting and during the course of the preparation and vaporization were found to be negligible. The Knudsen cells used to vaporize the
P33
alloys were constructed from high purity high density graphite and were approximately 2 cm in height and 0.75 cm in diameter, with a knife-edge orifice 1 mm in diameter. A Leeds and Northrup optical pyrometer was used to determine the temperature in the Knudsen cell by sighting into a black-body hole in the bottom of the cell. The calibration of the pyrometer had previously been checked under experimental conditions at the melting point of gold. Experimentally determined window and prism corrections were applied. For the calibration of the mass spectrometer a small weighed amount (5 - 7 mg) of silver wire was added in each run to the alloy. After pumping to a vacuum of about lo-’ Torr, the temperature was raised to 1200 K and several sets of the silver monomer and dimer equilibrium ion currents were recorded as a function of temperature. The temperature was then raised to 1500 K, recording the silver intensity for several hours until its complete evaporation. The ion intensity of Ti’ was found to be constant after approximately 2 h from the change of temperature for the N,i = 0.93 and Nri = 0.885 compositions, whereas ten or more hours at constant temperature were required for the N,i = 0.796 (eutectic composition) alloy. To avoid any carbon contamination of the samples, the experimental temperature was maintained below the respective melting points of the alloys [ 13, 141 (approximately 1790 K for the Nri = 0.93 alloy, 1770 K for the Nri = 0.885 alloy and 1700 K for the N,i = 0.796 alloy). A visual examination of the sample after each run indicated that it was free from any contamination; samples of the two former alloys were shiny. Owing to the strong interaction of Ti with Ir, the intensity of the 4sTi’ peak in the Nri = 0.796 alloy was very small below the melting point. Therefore the sample was melted after nine values of the Ti’ intensity had been measured and their reproducibility had been ensured. The 48Ti’ intensities after melting and refreezing were not found to be reproducible; the values were considerably lower than those prior to melting and visible traces of carbon contamination were found on the surface of the sample. Therefore only the first nine values of the 48Ti’ intensities have been used to evaluate the Ti activity for the eutectic composition.
3. Results and discussion Table 1 shows the experimental 48Ti’ ion currents for the three solid alloys listed in the sequence of measurement. These ion currents were converted to partial pressures using the relations P,i = k,iI&T
and
kTi = kAg
‘%C’A,~A, E,,%i’Yd’h,,
P34 TABLE
1
Experimental
ioncurrents of titanium overTi--1r alloys
NTi = 0.93
NTi = 0.885
T(K)
Z(48Ti’)
1579
x lo-l2 6.390X lo-l2 1.245x lo-= 2.670x lo-l1 2.760x lo-l1 3.050x lo-l1 7.800x lo-l2 4.180x lo-l2 1.850x lo-l2 7.800x10-13 4.41ox1o-13 2.73Ox1O-12 6.600x10-12 1.350x lo-l1 2.010x lo-l1 4.220x lo-= 5.620X lo-l1 7.17ox1o-11 1.090x lo-lo 6.100x lo-l2 1.550x lo-l2 3.630x lo-l3
1614 1648 1683 1711 1691 1621 1590 1552 1516 1495 1566 1610 1646 1666 1703 1721 1734 1756 1606 1544 1484
2.930
(A)
A’Ti = 0.796
T(K)
Z(48Ti’)
1506 1551 1576 1601 1622 1648 1690 1717 1764 1701 1633 1551 1529 1500 1604 1656 1734 1670 1572 1496 1535 1479 1729
8.660x lo-l3 1.900x lo-l2 3.580x lo-l2 6,000X lo-l2 9.450x lo-l2 1.323X lo-l1 3.150x lo-l1 5.300x lo-l1 1.272x1o-1o 4.140x lo-= 1.161x lo-= 2.040X lo-l2 1.250X lo-l2 6.000x lo-l3 5.780x lo-l2 1.662X lo-= 6.930 X lo-l1 2.160x lo-l1 2.730X lo-l2 5.500x lo-l3 1.290x lo-l2 3.630X lo-l3 5.910
(A)
T(K)
I( 48Ti+) (A)
1610 1599 1582 1561 1634 1641 1659 1675 1685
3.012x10-13 2.010x10-13 1.770x lo-l3 9.300x lo-l4 5.100x lo-l3 6.450X lo-l3 1.100x lo-l2 1.500x lo-l2 1.950x10-12
x lo-”
Here the factors CI,y and IZrepresent the maximum ionization cross section, the multiplier gain and the isotopic abundance, respectively; E denotes an empirical correction factor needed to convert the experimental ion currents to correspond with those at maximum ionization cross section. The pressure calibration constant hAg was obtained by the monomerdimer technique [3,15] from the measured Ag’ and Ag3 ion currents and the known dissociation energy of the silver dimer, D,(Ag,) = 159.0 + 6.3 kJ mol-’ [16]. The following values (in atm A-’ K-l) were obtained for kAg: 1.97 f 0.2 (A’Ti = 0.93); 1.09 + 0.05 (NT1 = 0.885) and 1.77 * 0.08 (N,i = 0.796), where the error terms represent the standard deviation. The E factors were evaluated from the ionization efficiency curves and were found to be between 1.01 and 1.08 for the ions in the present investigation. The relative multiplier gain YTi/YAg was measured as 1.23 in a separate experiment. The values for CrTiand DAg were taken from Mann [17], while uAgZ was estimated by multiplying uAe by an empirical factor of 1.5 [18]. The kTi VdUes (in atm A-” K-l) found were 0.93 (NTi = 0.93), 0.52 (NTi = 0.885) and O-88 (NTi = 0.796).‘
P35
-13
1700 ,
1600 t
Fig. 1. Plots of lnP,i
T (K)
,500 ,
us. 1 /T for the titanium-rich
portion of the solid Ti-Ir alloys.
A least-squares treatment of the In P,i uersus l/T plots shown in Fig. 1 yielded the following vapor pressure equations (ln P,i = mn/T + bN). In P,i =
In P,i =
In PTi =
-56 132 + 84 T
+ 16.39 rt 0.05
-56 175 + 108 T -68 129 + 1970 T
+ 14.67 -I 0.07
+ 20.74 + 1.21
(NTi = 0.93)
(N,
= 0.885)
(NTi = 0.796)
The heats of vaporization of titanium from the alloys AH, can be obtamed from the slopes of the respective In PTi versus l/T plots as mN R, at the mean temperature of the measurements. The partial molar enthalpy of solution of titanium Afir, is given by the difference between the heat of vaporization of titanium from the alloy and that from pure titanium at the same temperature. Thus the values Al?,, = -11.8 + 0.8 and AHTi = -12.1 + 1.0 kJ (g atom)-’ were obtained for the N,i = 0.93 and NTi = 0.885 compositions, respectively. Here the error limits correspond to three times the standard deviation. A similar evaluation of Agri for the eutectic composition (Nri = 0.796) would be of little significance since the composition of the coexisting phases changes with temperature.
P36
The activities of titanium lated through the expression
in the Ti-Ir alloys studied here were calcu-
where m, = -54 713 and b. = 16.13 are the constants of the pressure equation for pure titanium obtained from Hultgren et al. 1191. The activities were evaluated at 1623 K, the average temperature of the present measurements, and have been listed in Table 2. Also shown in Table 2 are the activities at 1623 K of titanium in the iridium-rich portion of the Ti-Ir alloys extrapolated from the activity data at 2000 K obtained previously in this laboratory by Chouda.ry et al. [13], neglecting any dependence of the enthalpy of formation and entropy of mixing on temperature in the 2000 1623 K range.
TABLE Activitiesa
2 and Gibbs energies
of formation
of Ti-Ir
alloys at 1623 K -
NTi
aTi
air
AGM (kcal (g atom)-‘)
0.93 0.885 0.796b
0.54 0.32 2.59 X 1O-2
1.96 x 1o-5 2.01 x 1o-5 3.54 x 1o-5
-4.3 -7.2 -
0.5 0.4b 0.25
1.93 x 1o-4 5.96 X 1O-5 3.09 x 1o-5
8.84 X 1O-5 8.80 x 1O-4 2.65 x lo-’
-28.8
f 2
-17.2
+ 1.8
fr 0.3 ?r 0.6
%andard state: solid Ti and solid Ir. bTwo-phase alloy (0.88 > NTi > 0.75 and 0.43 > NTi > 0.28) [13, 141.
The activities of iridium in the Ti-Ir alloy system were evaluated by a graphical integration of the Gibbs-Duhem equation [ 201 over the entire range of composition. The derived activity values, together with the respective Gibbs energies of formation, are listed in Table 2. Using the same procedure, the activities of titanium and iridium were also evaluated for the Nri = 0.6 (S phase) and NTi = 0.75 (TisIr, y phase) compositions. For the 6 phase the activity values obtained are ari = 1.9 X 10e3 and al, = 6.8 X 10u6; these yield a value of -102.5 -+ 8.4 kJ (g atom)-’ for the Gibbs energy of formation AG”. The corresponding values for the y phase are: ari = 3.1 X 10e2, err = 5.1 X lop5 and AGM = -68.6 f 8.4 kJ (g atom)-‘. Similar evaluations for the other compositions were not carried out because of the presence of two coexisting phases. The variation of AGM with Nri at 1623 K is shown in Fig. 2. In order to derive the enthalpy of formation of Ti31r, the excess entropy of formation of Ti,Ir was estimated through the empirical relationship of Kubaschewski and Slough [ 3,211
P37
T=l623
-3o-
%
K
-25-
4 9 -2oMC ,2
/
-15-
/' -10 -
I' /'
_5-
I
i'
I' Of 0.0
1 .I
I .2
.3
.4
5
.6
7
.8
.9
I
NT,
Fig. 2. Variation of the Gibbs energy composition (at.% Ti).
AS:,,
=
of formation
of Ti-Ir
alloys as a function
of the
AGEmU 0.78(7’,,
+ T,,)
- Texpt
where T,, and T,, are the boiling points. At 1623 K, AS”,,, (TisIr) is calculated as -10.5 + 3.3 J mol-’ KP1 yielding the corresponding value, ASM = -14.6 + 3.3 J molll K-l. Assuming AC, to be equal to zero, in accordance with Neumann and Kopp’s rule [ 221 which has been found valid for a large number of reactions and especially for alloy phases, the enthalpy of formation of TiaIr at 298 K, AHr.sa8, is calculated to be -92.0 + 14.6 kJ (g atom)) ‘. This value is in fair agreement with the value of AHr,zas = -54.4 kJ (g atom))’ calculated on the basis of Miedema’s cellular model using eqn. (8) of ref. 8 and various parameters listed therein. The large negative values of the Gibbs energies of formation of the titanium-iridium alloys and their variation with composition are consistent with the corresponding results obtained previously for titanium-platinum group alloys [5,6, 23,241.
Acknowledgments The authors are grateful for financial support for this work from the National Science Foundation under grants DMR 73-02625 and CHE 7808711. This work was performed at the Mechanics and Materials Center of the Texas A and M University Experimental Engineering Station. References 1 N. Engel, Powder Metall. Bull., 2 L. Brewer, Science, 161 (1968)
7 (1954) 115.
8.
P38 3 U. V. Choudary, K. A, Gingerich and L. R. Cornwell, J. Less-Common Met., 50 (1976) 201. 4 L. Brewer and P. R. Wengert, Metals. Trans., 4 (1973) 83. 5 P. J. Meschter and W. L. Worrel, Metall. Trans., 7A (1976) 299. 6 U. V. Choudary, K. A. Gingerich and L. R. Cornwell, Metall. Trans., 8A (1977) 1487. 7 E. W. Collings and H. L. Gegel, in E. W. Collings and H. L. Gegel (eds.), Physics of Solid Solution Strengthening, Plenum Press, New York, 1975, p. 147. 8 A. R. Miedema, J. Less-Common Met., 46 (1976) 67. 9 A. R. Miedema, F. R. de Boer and R. Boom, Caiphad, 1 (1977) 341. 10 A. R. Miedema, Philips Tech. Reu., 36 (1976) 8. 11 V. Kandarpa, L. R. Cornwell and K. A. Gingerich, Proc. 2nd Znt. Conf Mechanical Behauior of Materials, Boston, 1976, pp. 1737 - 40. 12 K. A. Gingerich, J. Chem. Phys., 49 (1968) 14. 13 V. N. Eremenko and T. D. Shtepa, Zzu. Acad. Nauk SSSR, Met., 203 (1970) 197. 14 V. Kandarpa, L. R. Cornwell and K. A. Gingerich, Microsc. Sci., 5 (1977) 384. 15 R. T. Grimley, in J. L. Margrave (ed.), Characterization of High Temperature Vapors, Wiley-Interscience, New York, 1967, pp. 195 - 243. 16 K. A. Gingerich, J. Cryst. Growth, 9 (1971) 31. 17 J. B. Mann, in K. Ogata and T. Hayakawa (eds.), Recent Developments in Mass Spectrometry, University of Tokyo Press, 1970, pp. 814 - 19. 18 J. Drowart and P. Goldfinger,Angew. Chem. Znt. Ed. Engl., 6 (1967) 581. 19 R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley and D. D. Wagman, Selected Values of Thermodynamic Properties of the Elements, Am. Sot. Metals, Metals Park, Ohio, 1973. 20 R. A. Swalin, Thermodynamics of the Solids, 2nd edn, Wiley-Interscience, New York, 1972, pp. 134 - 135. 21 P. Kubaschewski and W. Slough, Prog. Mater. Sci., 14 (1963) 3. 22 P. Kubaschewski and E. L. L. Evans, Metallurgical Thermochemistry, Pergamon Press, New York, 1958, p. 185. 23 R. M. German and G. R. St. Piere, Metalt. Trans., 3 (1972) 2819. 24 P. J. Meschter, Ph.D. Thesis, University of Pennsylvania, Philadelphia, 1974.