Determination of the atomization energies of the molecules TaO(g) and TaO2(g) by the mass-spectrometric Knudsen-cell method

J. Chem. Thermodynamics 1976,8,225-239

Determination of the atomization energies the molecules Tao(g) and Tao*(g) by the mass-spectrometric Knudsen-cell method

of

S. SMOES, J. DROWART Laboratorium voor Fysische Chemie, Vrge Universiteit B-1050 Brussels, Belgium,

Brussel,

and

C. E. MYERS Department Binghamton,

of Chemistry, State University of New York, N. Y. 13901, U.S.A.

(Received 11 September 1975) The partial pressures of the molecules TaO and TaOz above {Ta(s) + TazOs(s, I)} were determined by the mass-spectrometric Knudsen-cell method in the temperature interval 1880 to 2525 K. In addition, equilibria between Ta and gaseous Tao, TaOz, PO, TiO, AlO, and Al20 were studied. These yield the atomization energies D”(Ta0, 0) = and D”(TaOz, 0) = (350.0 & 4.5) k&i, mol-1 and the (191.5 i 3) kcal,, mol-l enthalpies of formation AHY(Ta0, 0) = (54.2 f 3) kc&, mol-I, AHY(Ta0, 298.15 K) = (53.9 LL 3) kcal,, mol-I, AHP(TaO,, 0) = -(45.4 f 4.5) kcaltn mol-I, and AH”fla02,

298.15 K) = -(46.2 + 4.5) kcal,, mol-I.

1. Introduction Differences in vapour pressures and in values for the dissociation energies of TaO and Tao, as a function of the experimental circumstances during the study(‘) of Ta + Ta,O, contained in tantalum cells were initially ascribed to the formation of a suboxide in the condensed phase. In the investigation of Ta + 0 solutions vaporizing from rhenium heaters, (2) the differences were attributed to interference from surface vaporization. The solubility and diffusivity of oxygen in tantalum are indeed pronounced, and dissolution of such oxides as Ta20s, La203, and U02 in tantalum crucibles, followed by migration of oxygen through their walls and vaporization of oxides from the entire surface of the cells has been observed.(3) The importance of tantalum in high-temperature chemistry, and its frequent use as a container for refractory oxides, justified a reinvestigation of the dissociation energies of the molecules TaO and Tao,. In addition, the interpretation of the volatilization of tantalum in the presence of oxygen at low pressures and high temperatures, studies by thermogravimetric’4) and mass-spectrometric”) methods, requires the availability of equilibrium data. Measurements, by the mass-spectrometric Knudsen-cell method, of the atomization energies of TaO and Tao, reported here were therefore performed.

226

S. SMOES, J. DROWART,

AND

C. E. MYERS

2. Experimental Various suboxides of tantalum have recently been shown to be metastablet6) and should hence not have to be taken into account in the evaluation of pressure measurements in the Ta + 0 system. Two phase diagrams”, ‘) as well as the identificationCg’ of an oxygen deficiency in TazOS, which increases with temperature above 1725 K, nevertheless suggested that Ta(s) and Ta,O,(s, 1) might interact sufficiently to cause the actual chemical potential of oxygen to differ significantly from that calculated from the tabulated values of the Gibbs free energy of formation of Ta,O,(s, l),(lO, ’ I) Therefore two types of experiments were made. The first concerned the measurement of the partial pressures of TaO and Tao, in the Ta(s) + Ta,O,(s, 1) system, for which the thermodynamic interpretation according to the equation : (l -0.4n)Ta(s)

+0.2nTa,O,(s,

1) = Tao,(g),

(n = 1, 2),

(1)

is dependent upon the data available at present for Ta,O,(s, 1). The second type of experiments pertained to the investigation of ternary or quarternary systems formed from the Ta + 0 binary system by addition of small amounts of other compounds which generate gaseous oxides by their vaporization or by interaction with Ta,O,. These multicomponent systems allow measurements whose evaluation depends upon the knowledge of the dissociation energies of the gaseous oxides of the elements added, but not of the thermodynamic data for the condensed phases (as long as Ta(s) remains at or near unit activity). The measurements for the Ta + 0 binary system were carried out with tungsten effusion cells containing as starting materials mixtures of Ta and Ta,O, containing 36 (table 4) and 47 (table 5) moles per cent of 0. Although Ta,O, itself is reduced(r) by tungsten, the thermodynamic data (lo* ‘I) show that this should not be the case for Ta(s) + Ta,O,(s, I), for which the calculated oxygen pressure is about 10-l’ atm at 2100 K.t Since systems with comparable pressures, such as U(1) + UO,(s) could be conveniently studied” 2, in tungsten cells, it was expected that the latter would be well suited, as proved to be the case. In these experiments, the pentoxide powder, mixed with metal strips, was placed in a pear-shaped thimble made from tantalum foil, 0.1 mm thick. This thimble had an opening slightly larger than the effusion orifice in front of which it was placed. The experiments with ternary or quaternary systems concerned the study of the reactions : Ta(s) + nMO(g) = Tao,(g) + nM(g), (2) Ta(s) +(n + I>AlO(g) = Tao,(g) + A120@ + (n - l)Al(g),

(3)

with n = 1 or 2 and M = P or Ti. In view of their analogy with exchange reactions, these equilibria are calIed quasi-exchange reactions. For these experiments, the following materials were used: GdP (30 mg) + Ta,O, (120 mg) + Ta (550 mg) ; A1203 (50 mg) + Ta,O, (180 mg) + Ta (1000 mg); Al,O, (30 mg) + Ti (10 mg) + Ta20, (250 mg) -+-Ta (900 mg). The mass of Ta given refers each time to that of chips and 7 Throughout

this paper atm = 101.325 kPa; eV z 1.602 x lo-la

J; calth = 4.184 J.

ATOMIZATION

ENERGIES OF Tao(g) AND TaOa

227

of foils shaped as described above, which were again placed in tungsten Knudsen cells. In all experiments, the tungsten cells had 3 mm thick walls and circular knifeedged effusion orifices 0.8 to 1 mm in diameter. The Knudsen-cell assembly, heated by electron bombardment, as well as the mass spectrometer and the experimental procedure have been described.(12> 13) For the present measurements, ionizing electron intensities of 30 J.LA were used at energies 12 and 4.5 eV above the thresholds for ionization of the individual species in the first and second type of experiments respectively. In order to avoid frequent resettings of the ionizing electron energies, which differ for each species of interest here, the measurements were in practice made with 20 and 12.5 eV electrons respectively. The intensities at the energies selected for the evaluation of the results, were then calculated by comparison with intensities interpolated on ionization efficiency curves established at regular time intervals between the thresholds for ionization and 25 eV. Approximate ionization potentials were determined by the vanishing current method, the energy scale being calibrated against the known ionization potentials of the Ag, Al, P, or Ti atoms. They are for: AlO, 9.9; A120, 8.0; PO, 9.1; Tao, 7.5; Tao,, 8.5; and TiO, 6.8 eV, with an accuracy of f0.5 eV. The ions formed from the molecules present in the effusing vapours were identified by their masses, isotopic distribution where applicable, ionization potentials, and intensity profiles. The latter were monitored continuously in order to verify in particular the absence of vaporization from the surface of the Knudsen cell surrounding the effusion orifice. The pressure calibrations were based on the complete vaporization of known masses of silver (1 to 2 mg) in each experiment. The relative cross sections o,,, at the maximum of the ionization efficiency curves, used to derive the pressures of the atomic species, were taken from the literature.(14) For the molecules AlO, TiO, Tao, and Tao,, the ratio cr(MO)/o(M) = a(MO,)/a(MO) = 0.7, qualitatively justified elsewhere,(l 5, is taken by analogy with the experimental values for several oxides (YO, La0,f13’ CeO,(‘“) UO and U02). (12117) For PO, the ratio a(PO)/c(P) = 1.2, is used by comparison with a(NO)/a(N) as discussed earlier.‘15’ In keeping with the above hypotheses c(Al,O) = 0.75a(A12), with a(A1,) = 1.75a(Al) by analogy with other diatomic molecules,(’ 3, is adopted. Relative efficiencies y of the secondary electron multiplier were read from its calibration curve and corrected, where necessary, for molecular effects.(l*) The incidence of the estimated uncertainties in these parameters on the reaction enthalpies is detailed in the footnotes of table 3. 3. Thermodynamic

functions and auxiliary

data

The numerical values of the thermodynamic functions (G”(T)-W(O))/2 and WV) - ff”fO)) re 4 uired for the evaluation of the measurements were taken from the literature sources cited: Al(g);(19’ A1,0(g);(19) P(g);(19) PO(g);(19) Ta(s);(20) Ti(g);‘19’ Ta205(s, I);“” TiO(g).(‘“) The thermodynamic functions for Tao(g) and Tao,(g), based in reference 10 on superseded spectroscopic results, were recalculated with the usual statistical-

228

S. SMOES, J. DROWART, TABLE State

TaO’21. 21)

T./cm-l

‘%!s

=&,z

A10’a4’

zJz+

TaOz (2a)

2B

2&,2 ah.

0 3505

0

1. Molecular w&m-l 1030.81 1028.69 979.23 728.50 728.50

C. E. MYERS

parameters w,x,/cm - 1 3.59 3.51 6.97 4.15 4.15

B&m-

1

0.40358 0.40288 0.64136 0.53740 0.53740

a&m-l 0.00187 0.00182 0.00580 -

971, 410,

912 structure CzV,.(23) same interatomic distance as in Tao; valence angle of 110” estimated by analogy with other triatomic molecules ; bending frequency estimated by valence-bond approximation.

mechanical formulae with the thermodynamic functions for the low-lying excited A2ni (G”(T) - W’(O))/~ and (H”(T)

TABLE

0

5218 5346

AND

molecular constants(21-23) summarized in table 1. The AlO were likewise recalculated to take into account state. (24) The numerical values of the functions -H”(O)} are summarized in table 2.

2. Thermodynamic functions - {G”(T) z H”(O))/Tcal,, K-l mol-l (first row for each substance) and {H’(T) - H”(0))/Tcal,r, K-l mol-1 (second row for each substance) (cab,, = 4.184 J) riK

298.15

Al(g) 1.653

AlOk) 2.099

4B(d 2.777

J%z> 1.481

PO(g) 2.245

TaW 1,347

Tao(g) 2.094

TaO&) 2.616

TaZO& I>

5.495

TW 1.802

TiCW 2.290

1800'

2000

2200

2400

2600

43.22 9.15 58.92 15.53 72.44 22.55 42.95 8.95 59.75 14.92 15.30 11.30 64.33 15.41 76.74 22.13 68.59 69.74 47.22 9.73 62.88 15.53

43.76 10.14 59.84 17.62 73.76 25.30 43.47 9.96 60.62 16.69 15.97 12.77 65.24 17.35 78.04 24.87 72.73 79.60 47.79 10.88 63.79 17.35

44.24

44.68

11.14

12.13

45.08 13.13 62.21 24.13 77.12 33.59 44.78 13.07 62.83 22.00 17.68 17.49 67.55 23.19 81.34 33.14 86.51 148.49 49.24 14.64 66.08 22.87

60.69 19.76 74.97 28.06 43.94 10.98 61.42 18.45 16.58 14.29 66.07 19.29 79.23 27.63 76.95 126.09 48.31 12.08 64.62 19.19

61.48 21.94 76.09 30.82 44.38 12.01 62.15 20.23 17.15 15.86 66.84 21.24 80.33 30.38

81.94 137.29 48.79 13.33 65.38 21.02

ATOMIZATION

ENERGIES

OF Tao(g)

AND

Ta02(g)

229

The standard enthalpies of formation and the dissociation energies used in the evaluation of the data are D”(Al0, 0) = (121.5* 1) kcal,, mol-1,(25) AH,“(Ta, g, 0) = (186.750.6) kcal,, mo1-1,(20) D”(Al,O, 0) = (247.253.0) kcal,, mol-l,(‘g’ w AH,“(Ta,O,, 0) = -(486.3f0.4) kcal,, mol-l,(‘oy rl) D”(Ti0, 0) = (157.8+2) kcal,, mol-1,(27’ D”(P0, 0) = (141.7+2) kcal,, mol-1.(15) In view of the low limiting mole fraction x of oxygen in 01Ta, which varies between 1825 and 2155 K from 0.051 to 0.057 according to logIo(102x) = l-08-699.4 K/T,@’ and decreases at higher temperatures, approximately as logIo(102x) = - 1.35 + 4600 K/T (deduced from figure 2 in reference 8), it was assumed that the Ta activity remains unity.

4. Results Ta + TaaOs SYSTEM The partial pressures of the molecules TaO and Tao, are presented in figure 1 in the usual logp against T-l fashion. The variation of logp can be represented by straight lines intersecting at (2115&15) K, the monotectic temperature in the system

I

I 4.0

I 4.5

I 5.0 lo4 K/T

FIGURE 1. Variation with reciprocal temperature of the TaO and TaOz pressures in the Ta(s) + TazO,(s, 1) system and comparison with literature data. V, table 4; & table 5; 0, reference 1; D, reference 5; 0, reference 28. Open symbols refer to Tao, closed ones to TaOz. 16

230

S. SMOES,

.I. DROWART,

AND

C. E. MYERS

[(2153 + 30) K in reference S]. Least-squares equations are given in table 3 for the individual experiments. With points from the separate experiments given equal weight, the partial pressures are represented by the linear least-squares equations: log,,(p(TaO)/atm) = -(32970f385) K/T+(8.44&0.19), (1900 to 2115 K), (4) = -(30030$200) K/Z-+(7.06&0.09), (2115 to 2527 K), (5) log,,{p(TaO,)/atm) = -(320OOf300) K/T+(8.74f0.15), (1880 to 2115 K), (6) = -(28270f230) K/T+(6.99+0.10), (2115 to 2527 K). (7) TABLE

T,IK

7-6

A/K a

1902 1942 2115 2115

2115 2115 2512 2527

-335101510 -321001510 -287701180 -30570&180

1880 1911 2115 2115

2115 2115 2512 2527

2043

2466

2043

2466

2092

2507

2092

2507

1960

2411

1960

2411

3. Reaction enthalpies and atomization energies (Cal,, = 4.184 J; atm = 101.315 kPa) B”

AH”{ T = O)/kcal,, mol - 1 D,,(T-+O, III)/kcal,, mol- Ib second law third law Tao, TaO

0.6Ta(s) + 0.2TaZOs(s, 1) = Tao(g) c d 8.7110.25 d 159.5 e 155.8*2.0 c* “187.312.1 c.’ 8.Ol~tO.25 153.1 155.8+2.0 187.342.1 65110.08 146.3 156.1121 186.9h2.2 7.2930.08 154.6 156.152.1 186.952.2 0.2Ta(s) + 0.4Tas0,(s, 1) = TaOa c -3214O&490 8.81~tO.24 156.6 157.952.0 341.2&2.3 ‘* ’ 341.152.3 -31810~310 86410.15 155.0 158.Ok2.0 149.7 340.8f2.4 -269001190 6.39~tO.08 158.412.1 158.7 340.8h2.4 -28850f190 7.2410.09 158.4h2.1 Ta(s) + TiO(g) = Tao(g) + Ti(g) -32730&140 6.95rtO.07 151.3k2.0 = 152.8+2.0” 191.6+2.8 f Ta(s) + 2TiO(g) = TaOz(g) + 2Ti(g) -33160+260 6.5510.12 151.412.8 151.91-2.2 350.4*4.6 ’ Ta(s) + 2AlO(g) = Tao(g) + AlzOk) 191.0&3.4 3010&270 0.15rtO.12 -9.6h1.9 --8X&1.9 Ta(s) + 3410(g) = Tao,(g) + Al(g) + Al,O(s) 35O.Ort4.2 11080~410 -0.53&0.18 -47.3*3.8 -46.Oh2.1 Ta(s) + PO(g) = Tao(g) + P(g) 191.812.9 -29910f450 7.0310.20 139.3rt4.4 136.542.1 Ta(s) + 2PO(g) = TaOZ + 2P(g) 125.8h4.5 120.4h2.4 349.7f4.7 -281801480 6.90f0.21

a log,,K” = A/T -I- B; A and B are obtained by least-squares treatment of the results. b Dissociation or atomization energy obtained from AH’(T = 0, III). c Non-stoichiometry in solid Ta205 and interaction between liquid TazOs and a Ta are neglected in these reactions. d The uncertainty cited equals the standard deviation. e The uncertainties in AEF’(T, II) result from twice the standard deviation in A (column 3), the uncertainty in the temperature (ho.5 per cent) and in {H”(T) - H”(O)}. f The uncertainties are exclusive of those in {G”(T) - H”(O)}/T for TaO and Tao, and take into account, for AH’(7’ = 0, III), twice the standard deviation from the mean, the uncertainty in the temperature, the uncertainty in the product of the cross sections (It50 per cent), and for D&T = 0, III), the uncertainty in AHr”(Ta, T = 0), AGF(Ta205, T = 0) and the dissociation or atomization energy of TiO, AlO, AlzO, and PO.

ATOMIZATION

ENERGIES

OF Tao(g)

231

AND Tao,(g)

Within experimental uncertainty, these equations reproduce the partial pressures of Tao and of Tao, in the Ta + M + 0 or Ta + Gd f P + 0 systems, which were also determined by the silver calibration method. The third-law treatment of the pressures according to the formal reactions (1 - 0.4n)Ta(s) + 02nTa,O,(s, 1) = Tao,(g) (n = 1 or 2) yields AH,“(TaO, 0) = (156.0f2.0) kcal,, mol-‘, AH,“(TaO,, 0) = (158.1+2.0) kcal,, mol-‘, TABLE

4. Partial pressures and enthalpies of vaporization a of TaO and TaOz in the system Ta(s) + TazOs(s, 1) (atm = 101.325 kPa; c& = 4.184 J)

loa&/atm) TaO 2001 1939 2040 2079 2102 2155 2031 2073

1949 1908 1902 1979 2007 2015 2063 2115 1914 1880 2150 2207

2139 2347 2199 2370 2420 2243 2443 2321 2512 2492 2301 2288 2255 2220 2162

-8.035 -8.610 -7.767 -7.485 -7.199 -6.852 -7.719 -7.446 -8.418 -8.813 -8.941 -8.216 -8.011 -7.946 -7.504 -7.091

-6.528 -6.950 -5.767 -6.578 -5.644 -5.384 -6.332 -5.243 -5.883 -4.955 -5.032 -6.005 -6.072 -6.257 -6.420 -6.762

TaOa -7.231 -7.779 -7.003

- 6.725 - 6.407 -6.101 -7.012 -6.688 -7.600 -7.993 -8.081 -7.463 -7.252 -7.179 -6.752 -6.302 -7.948 -8.303 -6.156 -5.802 -6.193 -5.085 - 5.860 -4.968 -4.734 -5.618 -4.591 -5.194 -4.317 -4.403 -5.310 -5.366 -5.533 -5.732 -5.995

Average and standard deviation:

AH:( T = 0)/k&, Tao

mol - 1 TaOz

155.82

157.74

156.28 156.24 156.43 155.34 155.57 155.69 155.63

158.01 158.50 158.70 157.28 157.79 157.93

157.92 157.18

155.34

155.46 156.55

157.50 157.80 158.21 158.38 158.30 157.81 157.13 157.58 157.99 158.00 158.11 157.65 158.77

155.77 156.60

158.20 158.78

156.69

158.96 158.38 158 61 158.46 159.15 159.09 158.55 158.39 158.21 158.18 157.19

155.65 156.29 155.81 156.05 156.05 155.45

155.19

155.79

156.08 156.45 156.22 157.10 156.86 156.29 156.19 156.06 155.52 155.16 (156.0

zt 0.5)

(158.1

f

a These enthalpies refer to equation (7), uncorrected for interaction between Ta and TazOs.

0.5)

232

S. SMOES,

J. DROWART,

AND

C. E. MYERS

without trend with temperature (tables 4 and 5). By insertion cycles, D”(Ta0, 0) = (187.1f2.1) kcal,, mol-‘, Dzt(Ta02, 0) = (341.Ok2.3) kcal,, mol-‘, are calculated therefrom. TABLE

5. Partial

pressures

and enthalpies of vaporization” of TaO system Ta(s) + TazOe,(s, 1) (atm = 101.325 kPa; calth = 4.184 J)

bhddatm)

T/K

TaO

2062 1992 1943 1988 2029 2042 1952 2067 2053 2054

-7.569 -8.101 -8.490 -8.126 -7.846 -7.726 -8.473 -7.568 -7.612 -7.558 -7.955

1946 1911 1970 1930 1936 2108 2082 2070 2102 2150 2112 2143 2137 2205 2246 2296 2237 2340 2181 2374 2274 2341 2447 2187 2485 2527 2270 2206 2400 2394

-7.225 -7.396 -7.222 -6.894 -7.189 -6.978 -7.027 -6.543 -6.312 -6.050 -6.371 -5.784 -6.779 -5.606 -6.157 -5.742 -5.209 -6.687 -5.032 -4.795 -6.167 -6.575 -5.422 -5.467 Average

a These

enthalpies

refer

to equation

in the appropriate

and TaOz

AH,“(T = 0)/k&,

in the

mol-l

TaOz

Tao

TaOz

-6.790 -7.321 -7.759 -7.379 -7.075 -6.969 -7.625 - 6.727 -6.837 -6.808 -7.185 -7.689 -8.012 -7.511 -7.836 -7.824 -6.457 -6.631 -6.710 -6.462 -6.141 - 6.427 -6.224 -6.291 -5.802 -5.605 -5.340 -5.655 -5.101 -6.049 -4.926 -5.448 -5.068 -4.560 -5.948 -4.395 -4.182 -5.454 -5.862 -4.757 -4.795

156.00 155.75 155.53 155.68 156.17 156.01 156.07 156.35 155.74 155.31 155.24

158.10 157.89 158.14 158.13 158.37 158.33 157.63 157.86 157.89 157.69 157.47 157.75 157.90 157.97 157.83 158.18 158.17 158.02 157.92 157.81 157.86 158.14 158.21 158.48 157.99 158.42 158.58 158.41 158.54 158.95 158.55 158.44 158.25 158.48 158.32 158.63 158.37 158.27 158.65 158.12 158.21

and standard (7), uncorrected

156.01 155.80 155.56 155.65 155.93 156.00 156.07 155.81 156.06 156.45 156.10 156.31 156.59 156.42 156.21 155.92 156.30 156.07 156.46 156.09 156.07 156.20 155.94 156.08 deviation:

(156.0

for interaction

f 0.3) between

(158.2 Ta and TaaOs.

rrt 0.3)

ATOMIZATION

QUASI-EXCHANGE

ENERGIES

OF Tao(g)

AND TaOz(g)

233

REACTIONS

The variation with reciprocal temperature of the equilibrium constants of the quasiexchange reactions between Tao(g) and Tao,(g) on the one hand and AlO( Al,O(g), PO(g), and TiO(g) on the other hand, is shown in figures 2 and 3. The corresponding equations are summarized in table 3, together with the third-law values of the reaction enthalpies. The virtually identical atomization energies derived I

‘g

-5

\

I

0 ‘0

-7 f T k 0 8 -8

-9

-10

I

4.5

5.0

lo4 K/T FIGURE 2. Variation with reciprocal temperature of the equilibrium constants of the quasiexchangereactions: 0, Ta(s) + ZPO(g) = Tao,(g) + 2P(g); 0, Ta(s) + PO(g) = Tao(g) + P(g); A, TabI + TiO(g) = Tao(g) + Ti(g); A, Ta(s) + 2TiO(g) = Taos(g) + 2Ti(g).

S. SMOES,

234

J. DROWART,

AND C. E. MYERS

I

I

5.0 -

4

4.5

-

4.0

-

,,A

l )’

,//.

Y

1.0 -

2

2.0

-

I

I

4.0

4.5

: 5.0

IO’ K/ 7FIGURE 3. Variation with reciprocal temperature of the equilibrium exchange reactions: 0, Ta(s) + 3AlO(g) = TaOz(g) + Al(g) + ALO(

constants of the quasi0, Ta(s) + 2AlO(g)

= Tao(g) + AWW. therefrom yield the average values: D”(Ta0, 0) = (191.5rfi3.0) kcal, mol-‘, Dzt(TaO,, 0) = (35O.Ok4.5) kcal,,, mol-‘. The quasi-exchange reaction : 2TaO(g) = Ta(s) +TaOAg), (8) does not yield results independent of the previous ones. It affords however a cross check between the various experiments and, as for the other exchange reactions, a comparison between the second- and third-law results over the entire temperature interval covered in this study. It is therefore presented in table 6 for each experiment separately and in figure 4 for the various experiments together. 5. Discussion Ta + Taz05 SYSTEM

The comparison of the present results is made graphically in figure 1 with those of mass-spectrometric pressure determinations in tantalum cell@ and of thermogravimetric Langmuir measurements for tantalum covered with Ta205.(‘*) The latter results were interpreted in terms of mass spectrometric studies,@) under Langmuir conditions, of the rate of vaporization of tantalum in the presence of moIecular

ATOMIZATION TABLE

System Ta +TazOs Ta+TazOs Ta+TaaOS+Ti Ta+Taz05+GdP Ta+Taz05+A120s

ENERGIES

OF TaO(g) AND Tao,(g)

235

6. Equilibrium constant and reaction enthalpy for the equilibrium: 2TaO(g) = Ta(s) + Tao&) (atm = 101.325 kPa; calth = 4.184 I)

T,/K

WK

1902 1943 2043 1960 2092

2512 2527 2466 2411 2507

lokhWa~-l) (32550&270) (32430+220) (32290f120) (3164Of280)

AH"(T = O)/kcaL mol-l second law

-152.5A3.0 -151.942.5 K/T-7.35&0.06 -151.3kl.8 K/T-7.16&0.13 -148.3f3.0 (-153.8) a Average : -151,6&2.5

K/T-7.4510.13 K/T-7.40&0.10

third law -153.8&2.2 -153.8x!c2.1 -153.7+2.0 -152.7zt2.1 (-154.6) n -153.7&2.1

n These second- and third-law reaction enthalpies were obtained by combining the enthalpy differences associated with the reactions: Ta(s) + AlO = Tao(g) -t Also(g) and Ta(s) + 3AlO(g) = TaOa + Al(g) + AlaO( given in table 3 and the atomization energies of AlO and AlaO(

r-

8-

1

I

I

4.0

4.5

5.0 lo4 K/T

FIGURE 4. Variation with reciprocal temperature of the equilibrium constant of the reaction 2TaO(g) = Ta(s) + Tao,(g); 0, 0, system (Ta + TaaOs), tables 4 and 5 respectively; v, system (Ta -t- Ta,O, + Ti); A, system (Ta -I- TazOs + GdP); ---, kinetic data, reference 5.

236

S. SMOES, J. DROWART,

AND

C. E. MYERS

oxygen, under circumstances where the combined rates of formation of gaseous TaO and Tao, are lower than the rate of absorption of oxygen. The net uptake of oxygen then evidently leads to saturation of c1Ta and formation of the two phase system Ta + Ta,O,. The TaO and Tao, fluxes measured under these conditions were recalculated with the relative ionization cross sections of Ta, Tao, and Tao, used here. For the thermogravimetric measurements, (“) the rates of vaporization, expressed in terms of equivalent pressures pL were taken proportional to the relative fluxes in the mass-spectrometric experiments. (5) Taking into account the uncertainties in temperatures resulting from emissivity corrections, figure 1 shows that the Langmuir studies yield pressures close to those measured here under Knudsen conditions, so that the vaporization coefficients of TaO and Tao, are close to unity. Consequently, the ratio pL(TaO,)/&TaO) measuredc5’ under Langmuir conditions over a wide interval of temperatures and pressures, and thus oxygen concentrations in a Ta, also correspond quite closely to the equilibrium constant of reaction (8). At the higher temperatures, the ratio p,(TaO,)/pi(TaO) is higher than the equilibrium constant p(Ta0,)/p2(TaO) and suggests that the rates of formation of Tao(g) and Tao,(g) grow lower than the thermodynamically allowed ones, this effect being more pronounced for Tao,(g) than for Tao(g). The measurements with tantalum Knudsen cells(‘) are high, in particular for Tao(g), as a result of interference of surface vaporization with effusion, as discussed in detail in reference 2. The atomization energies of TaO and Tao, calculated from reaction (1) do not agree with those derived from the quasi-exchange reactions. In fact the disagreement for D;*(TaO,, 0) is double that for D”(Ta0, 0). This strongly suggests that the evaluation of the oxygen activity is involved in the discordance in that either the standard Gibbs free energy of formation of Ta,O, is incorrect or that the phase diagram, in the temperature region of interest, is such that reaction (1) is an inappropriate approximation. The standard Gibbs free energy of formation of stoichiometric TazO, can hardly be suspected to be incorrect because several determinations(rr) of the standard enthalpy of formation mutually agree and because electromotive force measurements,cz9) confirm the tabulated AG,” values(lO) in the interval 1073 to 1473 K. The alternate interpretation, adopted here, is that interaction between Ta and liquid Ta,O, is pronounced. This implies that the third-law treatment of reaction (1) gives upper bounds for the enthalpies of vaporization and formation of Tao(g) and TaOz(g) and lower bounds for their dissociation energies. According to the phase diagram,“’ a Ta coexists at 1823 K with liquid II and solid Taz05, the mole fraction of 0 in the eutectic being 0.71. At the monotectic temperature, c1Ta coexists with liquid I and liquid II, with a mole fraction of 0 for the former of 0.43. If, at least formally, the liquids could be treated as solutions of TazO, and Ta, the entropies of mixing alone would yield insufficient corrections, although these are of the appropriate sign. For such solutions, the application of cycles used to estimate(30’ enthalpies of mixing of alloys from the composition and temperature along the liquidus would give, in the regular-solution approximation, values of the interaction energies of the magnitude required to bring the results deduced from reactions (1) and (2) or (3) into agreement, AG(Ta,05) E 20 kcal,, mol- ‘). The extrapolation in the interval

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1823 to 2100 K of the activity co&cient of atomic oxygen in saturated a Ta, which can be computed t31) from AG,“(Ta,O,, T) in the interval 1500 to 1823 K, where cxTa coexists with Ta,O,(s), leads on the other hand to negligible corrections to reaction (1). It is therefore suggested that in the temperature interval 1500 to 1823 K, CITa in fact coexists with substoichioaetric Ta,O,-,fs) with a standard Gibbs free energy of formation appreciably more negative than that of Ta,O,(s). In keeping with the above argument, the differences in the second-law enthalpies of vaporization of Tao(g) and Tao,(g) below and above 2115 K, corresponding for Ta,OS to (50 & 10) kcal, mol-‘, depend not only on the variation with temperature of the enthalpies of formation of Ta,O,(s, 1), TaO(g), and Tao,(g), but further on the variation of the composition of the liquids with temperature and on the variation of the partial molar enthalpy of solution with composition and temperature. Therefore these differences are not directly related to the enthalpy of fusion of Ta205, estimated to be 36 kcaJ, mol- I. For the same reasons, the reduction, neglecting the partial molar enthalpies of sdution, of the second-law AH’(T) values to T = 0 also yields upper limits for AH,“(T = 0) according to reaction (1). With respect to Ta,O,(s) near stoichiometry, the dissociation energies of TaO and Tao, retained below imply that the main vaporization reaction is Ta,O,(s) = 2TaO,(g) -!-$0,(g). Qualitative confirmation that the oxygen decomposition pressure is then cIose to the partial pressure of TaOz results from the observation@) that in a tungsten effusion cell, at a temperature which is not specified, but which may be assumed to be in the vicinity of 2100 K, the partial pressures of both WO, and WO, are comparable to those of Tao,. Since the standard Gibbs free energies of formationog) of WO,(g) and WO,(g) are such as to require that p(W0,) w p(W0,) E ~$0,) at this temperature, the observation that p(WOJ w p(W03) E p(Ta0,) implies that ~(0,) z p(Ta0,). QUASI-EXCHANGE REACTIONS AND ATOMIZATION TAO(g) AND ‘MM3

ENERGIES OF

The results of the quasi-exchange reactions depend, for reaction (2), on the absolute pressures of Tao or Tao, and on the ratios p(MO)b(M) or I(MO)/l(M), whereas for reaction (3) only relative pressures or intensities are required. In both types of quasi-exchange reactions, the Ta activity influences the result to the same extent as in reaction (l), since the partial pressures of TaO and of Tao, are the same in the Ta + 0 binary as in the Ta + M + 0 or Ta + Gd + P + 0 multicomponent systems. The systematic differences in D”(Ta0, 0) and D”(TaO,, 0) determined in the binary and in the multicomponent systems can therefore not be attributed to a pronounced lowering, in the latter systems, of the tantalum activity, that would, at constant oxygen activity, lead to D”(O) values that are too low. The dissociation energies of the molecules PO and AI0 are on the other hand obtained both from spectroscopic and thermochemical data as discussed in references 17 and 25 respectively. Dzt(Al,O, 0) has been determined on several occasions by mass-spectrometric and by gravimetric measurements. (a61 Recalculated with the same thermodynamic functions and auxiliary data, these methods yield values in mutual agreement. Since the dissociation energies D”(Al0, 0),(25a) and D”(Ti0, 0),(27a) the consistency of

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which was further studied as part of the present experiments, and D”(P0, 0)(15) have been determined with the equipment used here, instrumental factors involved in the determination of D”(Ta0, 0) and D”(TaO,, 0) by reactions (2) and (3) cancel out. The only factors which do not are the ratios ay(TaO)/oy(Ag) and oy(TaO,)/ oy(Ag) which are however the same for the evaluation of the quasi-exchange reactions (2) and (3) and for the calculation of the vaporization enthalpies in the binary Ta + 0 system according to reaction (1). Possible systematic errors in the partial pressures of TaO and Tao, would therefore be the same in both types of determinations and would hence shift all results by the same amount, without removing the observed discordances in D”(Ta0, 0) and Dit(TaO,, 0) and without causing that for &(TaO,, 0) to be double the discordance for D”(Ta0, 0). For these various reasons, and because of the likelihood that Taz05(s), like several other oxides, is substoichiometric in contact with the metal at high temperatures, as argued in the preceding section, preference is given to the atomization energies of Tao and Tao, deduced from the quasi-exchange reactions. For reaction (8), the agreement between the second- and third-law treatments shows that (G”(T) - H”(O)}/T for Tao,, calculated from partly estimated molecular parameters, is correct within the accuracy resulting mainly from the need to estimate relative ionization cross sections, and less so, of neglecting the contribution of eIectronically excited states in Tao(g) and of assuming that the activity of tantalum in the binary Ta + 0 and in the multicomponent systems investigated here remains essentially unity. In conclusion, the values for the atomization energies of TaO and Tao, retained are : D”(Ta0, T = 0) = (191.5 + 3.0) kcal, mol-‘, Dit(TaO,, T = 0) = (350.0f4.5) kcaJh mol-‘, with uncertainties resulting primarily from those in the estimated ratio of the cross sections of these molecules and of the silver atom and to a lesser extent from the uncertainties in their thermodynamic functions and in the auxiliary thermochemical data. The corresponding standard enthalpies of formation are AH,“(TaO, 0) = (54.2+ 3) kcal,, mol -l, AH;(TaO, 298.15 K) = (53.9+3) kcal, mol-‘, A\HfO(Ta02, 0) kcal,hmol-l. = -(45.4+4.5) kcalthmolY1, and AH,“(Ta02, 298.15 K) = -(46.2f4.5) The authors thank Messrs W. Van Campenhout and G. Verhelle for assistance with the preliminary measurements and their evaluation. They acknowledge support from the Fund for Collective Fundamental Research, Belgium. REFERENCES 1. 2. 3. 4. 5. 6. 7.

I&ram, M. G.; Chupka, W. A.; Berkowitz, J. J. Chem. Phys. 1957,27, 569. Krikorian, 0. H.; Carpenter, J. H. .7. Phys. Chem. 1965, 69,4399. Ackermann, R. J.; Thorn, R. J. Prog. Cerum. Sci. 1961,1, 39. Fromrn, E.; Jehn, H. Z, Mefdk. 1967, 58, 61. De Greve, F.; Drowart, J. Rev. ATB Metallurg. 1966, 6, 115. Niebuhr, J. J. Less Comm. Metals 1966, 10, 312. Dubrovskaya, L. B.; Shveikin, G. P.; Geld, P. V. Zh. Neorg. Khim. 1964, 9, 1182; Russ. J. Znorg. Chem. 1964, 9, 647.

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8. Jehn, H,; Olzi, E. J. Less Comm. Metals 1972, 27, 297. 9. Kofstad, P. J. Electrochem. Sot. 1962, 109, 776; Kudrak, D. R.; Sienko, M. J. Znorg. Chem. 1967, 6, 880; Stroud, J. E.; Tripp, W. C.; Winner, J. M. J. Amer. Ceram. Sot. 1974, 57, 172. 10. Schick, H. L., editor. Thermodynamic Properties of Certain Refractory Compounds. Academic Press, Inc.: New York. 1966. 11. Kubaschewski, O., editor. Tantalum, Special Issue No. 3, Atomic Energy Review. I.A.E.A.: Vienna, 1972. ; Pattoret, A. ; Drowart, J. ; 12. Drowart, J. ; Pattoret, A. ; Smoes, S. Proc. Brit. Ceram. Sot. 1967,8,67 Smoes, S. Bull. Sot. Fr. Ceram. 1967, 77, 75. 13. Drowart, J.; Goldfinger, P. Angew. Chem., Intern. Ed. Engl. 1967, 6, 581. 14. Mann, J. B. In Recent Developments in Mass Spectrometry. Ogata, K.; Hayakawa, T., editors. Tokyo Univ. Press: Tokyo. 1970, p. 814. 15. Drowart, J.; Myers, C. E.; Szwarc, R.; Uy, 0. M. Faraday Trans. II 1972, 68, 1749. 16. Ackermann, R. J.; Rauh, E. G. J. Chem. Y%ermodynamics 1971, 3, 609. 17. Blackburn, P. E.; Danielson, P. M. J. Chem. Phys. 1972, 56, 6156. 18. Stanton, H. E.; Inghram, M. G.; Chupka, W. A. Rev. Sci. Znstr. 1956, 27, 109. 19. JANAF Thermochemical Tables, PB 168 370-O to 3, Clearinghouse for Federal Scientific and Technical Information, Washington, D.C. 1965-1971. 20. Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K.; Wagman, D. D. Selected Values of the il7lermodynamic Properties of the Elements. American Society for Metals: Metals Park, Ohio 44073. 1973. 21. Presmawarup, D.; Barrow, R. F. Nature 1957, 180, 602. 22. Weltner, W., Jr.; McLeod, D., Jr. J. Chem. Phys. 1965, 42, 882. 23. Kaufman, M. ; Muenter, J.; Klemperer, W. J. Chem. Phys. 1967, 47, 3365. 24. McDonald, J. K.; Innes, K. K. J. Mol. Spectrosc. 1969, 32, 501. 25. Drowart, 3. Faraday Symposia of the Chemical Society 1973, 8, 165 and references cited there; Dadigian, P. J.; Crnse, H. W. ; Zare, R. N. J. Chem. Phys. 1975, 62, 1824. 26. Thompsen, K. R. High Temp. Sci. 1973, 5, 62 and references cited there; unpublished results, this laboratory. 27. Drowart, J.; Coppens, P.; Smoes, S. J. Chem. Phys. 1969, 50, 1040; Hampson, P. J.; Gilles, P. W. J. Chem. Phys. 1971, 55, 3712. 28. Kofstad, P. J. Less Comm. Metals 1964, 7, 241. 29. Matsushita, Y.; Goto, K. In Thermodynamics. I.A.E.A. : Vienna. 1966, p. 111; Worrell, W. L. Ibid., p. 131; Ignatowics, S.; Davies, M. W. J. Less Comm. Meta&- 1968, 15, 100; Bardi, G. B. 2. Naturforsch. 1970, 25a, 1515. 30. Kubaschewski, 0. In Thermodynamics of Nuclear Materials. I.A.E.A.: Vienna. 1962, p. 219. 31. Swalin, R. A. Thermodynamics of Solids, 2nd edition. John Wiley and Sons: New York. 1972, pp. 168-173.