Thermodynamic properties of silicides V. Fluorine-combustion calorimetric determination of the standard molar enthalpy of formation at the temperature 298.15 K of trimolybdenum monosilicide Mo3Si, and a critical assessment of its thermodynamic properties

WE-014 J. Chem. Thermodynamics 1996, 28, 29–42

Thermodynamic properties of silicides V. Fluorine-combustion calorimetric determination of the standard molar enthalpy of formation at the temperature 298.15 K of trimolybdenum monosilicide Mo3 Si, and a critical assessment of its thermodynamic properties Iwona Tomaszkiewicz, Chemical Kinetics and Thermodynamics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 , U.S.A., and Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland

G. A. Hope, Griffith University, Nathan, Queensland 4111 , Australia

Charles M. Beck II, Analytical Chemistry Research Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 , U.S.A.

and P. A. G. O’Hare a Chemical Kinetics and Thermodynamics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 , U.S.A.

(Received 3 July 1995; in final form 30 July 1995) The massic (formerly called specific) energies of combustion in fluorine of two different specimens of trimolybdenum monosilicide have been measured in a bomb calorimeter and the standard molar enthalpy of formation Df H°m(Mo3 Si,cr,298.15 K) determined to be −(125.225.8) kJ·mol−1. A critical evaluation of the thermodynamic properties of Mo3 Si is also presented, and recommended values for the standard molar enthalpy increments, standard molar heat capacities, standard molar enthalpies of formation, and standard molar Gibbs free energies of formation have been tabulated to T=2300 K. 7 1996 Academic Press Limited

a

Author to whom correspondence should be addressed.

0021–9614/96/010029+14 $12.00/0

7 1996 Academic Press Limited

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I. Tomaszkiewicz et al.

1. Introduction Silicides of Group 6 of the Periodic Table have become very important in several modern technologies because, in no small measure, of their resistance to oxidation, brought about by the formation of a strongly adhering protective surface layer of SiO2 . In order precisely to understand and predict their behavior, for example in engineering applications at high temperatures,(1) trustworthy values of chemical thermodynamic properties of those materials are essential. Such quantities are, on the whole, sparse and quite uncertain, as recent reviews(2,3) make clear. Those drawbacks arise, in part, from the refractory nature of most metal silicides, and the concomitant difficulty of reacting them with, for example, O2(g) or mineral acids in combustion or solution calorimeters, to yield the standard molar enthalpy of formation Df H°m . Measurements of what are often very low partial pressures of Si(g) in equilibrium with silicides in Knudsen effusion experiments even at high temperatures, are also difficult and may be vitiated by the reactivity of Si(g) toward crucibles and cell materials. Such problems tend to render suspect derived values of the molar Gibbs free energy of formation Df G°m . Accordingly, we and others continue to address these deficiencies, and several recent thermodynamic investigations have dealt with most of the known silicides of molybdenum and tungsten: MoSi2 ,(4,5) Mo5 Si3 ,(6) WSi2 ,(7,8) and W5 Si3 .(9,10) Nevertheless, values of many of the fundamental thermodynamic properties of Mo3 Si and Mo5 Si3 are still not known with certainty. Work in our laboratory on the determination of Df H°m(Mo5 Si3 ) is nearly at an end, and we hope to report the results soon.(6) The study of Mo3 Si to be described here continues our recent fluorine-bomb combustion determinations of the standard massic (formerly called specific) energies of combustion and, thence, the Df H°m s of MoSi2 ,(4) WSi2 ,(8) and W5 Si3 .(10) We are aware from experience(4,8,10) that silicides of Mo and W can be made to react quantitatively with F2(g) in the calorimetric bomb when tungsten is used as an auxiliary substance to drive the fluorination to completion. We anticipated that, with a similar arrangement, the combustion reaction would proceed according to: Mo3 Si(cr)+11F2(g)=3MoF6(g)+SiF4(g).

(1)

2. Experimental A major part of the experimental work to be reported here involved two sequential efforts: the first, to synthesize pure single-phase silicide with targeted mole ratio n(Mo)/n(Si)=3; and the second, to characterize that product accurately by chemical analysis. An early preparation, otherwise satisfactory, contained more Si than required for stoichiometric Mo3 Si, and X-ray powder diffraction examination revealed a nontrivial amount of a second phase, identified as Mo5 Si3(11) and estimated to be present at the 0.1 mass fraction level. Nevertheless, we proceeded with calorimetric measurements on this specimen because it seemed at the time that a superior material could probably not be synthesized by solid–solid reaction in the arc furnace.

Thermochemistry of Mo3 Si

31

Subsequent efforts at Griffith University led to the production of much more satisfactory Mo3Si, a single-phase material analytically acceptable in every way. In the present paper, therefore, we shall be reporting measurements on two samples of quite different composition that, as it turned out, yielded harmonious values for the massic energy of combustion of pure Mo3 Si. Specimens of Mo3 Si were synthesized by melting Mo and Si together in an arc furnace under an atmosphere of high-purity Ar. Molybdenum foil (Aldrich, catalog no. 35,721-9, mass fraction of Mo: 0.999), cut into 1-cm2 pieces to facilitate handling, was first cleaned by immersion in NH3(aq) (analytical grade, BDH Chemicals), rinsed with deionized H2O, and then heated to incandescence at a pressure less than 10−6 Pa to remove any remaining surface oxides. High-purity Si (Koch-Light, catalog no. 92210, mass fraction of Si: 0.99999) was used as received. Stoichiometric amounts of Mo and Si, sufficient to give a charge of approximately 15 g, rested on the hearth of the arc furnace, while high-purity Ar (Commonwealth Industrial Gasses, mass fraction of Ar: 0.99997) flowed through the reactor for 30 min before the start of the synthesis. The reactor and technique did not differ from those described previously for the preparation of W5 Si3 ,(10) except that a molybdenum electrode generated the arc. The synthesis comprised four melting steps. After each one, the product was inverted when it had solidified and cooled, its mass being monitored as the synthesis progressed. This procedure yielded a uniform shiny button of metallic appearance, which, afterwards, was ground in a tungsten carbide Retsch Spectromill, and the X-ray diffraction pattern of the powder computer-matched with standards contained in the JCPDS-ICDD file. As mentioned, the analytical chemistry results for Si content of the first preparation (designated sample A) as well as the X-ray diffraction pattern showed clear evidence for the presence of Mo5 Si3 . A second specimen (sample B), synthesized some time later after completion of calorimetric measurements on sample A, was shown by analysis and X-ray diffraction(12) to be pure Mo3 Si. The following technique was devised for assays of Si. Accurately-weighed 180 mg specimens in quartz boats were oxidized in a muffle furnace by slowly raising the temperature from 673 K to 1323 K over a period of 5 d. This procedure accomplished two objectives: It converted the starting material to a mixture of SiO2 and molybdenum oxides with an overall composition probably close to MoO3 ; and, at temperatures above 1973 K, it caused the ‘‘MoO3 ’’ to volatilize, thus effecting separation of the silicon and molybdenum oxides. The temperature was raised very slowly to prevent ejection of either the starting material or SiO2 from the boat by MoO3 as it sublimed. Although, predominantly, just SiO2 remained, X-ray analyses revealed small but significant masses (11 mg from a total mass of 150 mg) of MoO3 that had not volatilized. Therefore, the residue in the boat was transferred to a platinum crucible, HF(aq) was added to convert the SiO2 to SiF4(g), and the mass of the remaining molybdenum oxide determined by difference. That having been allowed for, we arrived at the mass of SiO2 formed during the initial oxidation of the starting material and, therefore, of Si contained in the starting material. Analyses for C, H, O, and N (LECO, St. Joseph, MI) were also performed, with standard reference materials run in parallel. Insufficient quantities of sample

32

I. Tomaszkiewicz et al.

TABLE 1. Analytical results (mass fraction) for calorimetric samples; for designation of samples, see text

Sample A Sample B a

C

H

O

N

Si

Mo a

35·10−6 81·10−6

27·10−6

142·10−6 731·10−6

52·10−6 35·10−6

0.0965 0.0887

0.9033 0.9104

Mo content determined by difference.

A remained to determine H, and it was assumed to be present to a trivial extent. No analyses for trace metals were performed because the starting Mo and Si contained negligible quantities of such contaminants. The Mo content was taken as the difference between unity and the sum of the mass fractions of C, H, O, N, and Si. Detailed results of the analyses are given in table 1. As with all new measurements by fluorine-bomb calorimetry, a satisfactory combustion technique had to be devised. It turned out that the arrangement used previously(10) in our investigation of W5 Si3 also succeeded with Mo3 Si. Accordingly, crushed Mo3 Si that had passed through a sieve of mesh area 0.02 mm2 was weighed on a tungsten saucer that, in turn, rested on an 125-g prefluorinated cylindrical nickel crucible with small holes bored just above its base to enhance circulation of fluorine as the combustion progressed. Masses of Mo3Si chosen for the experiments were such that, as depicted in equation (1), and on the basis of the vapor pressure of the hexafluoride at T1298 K,(13) only MoF6(g) formed. Sprinkled on the surface of the silicide, a small weighed quantity of rhombohedral sulfur served as a fuse. The crucible rested on the cap of the inner compartment of our two-chamber reaction vessel.(14) High-purity F2(g), prepared by distillation and passed through a column of NaF (to remove HF),(15) was transferred to the outer compartment until the pressure reached 1 MPa at T1293 K; thus, in a typical experiment, n(F2 )10.1 mol. The two chambers were then connected, removed from the glovebox (circulating atmosphere of N2 , mass fractions 1·10−6 and 5·10−6 of O2 and H2O) in which most of the preceding operations took place, and positioned in the calorimeter, after the N2 had been pumped away. An acceptable forerating period having been established, the isolation valve was opened remotely, F2(g) expanded into the inner chamber, the sulfur fuse ignited spontaneously, and combustion of the W and Mo3 Si ensued. When satisfactory afterperiod temperatures had been recorded, the vessel was removed from the calorimeter, and the gaseous combustion products analyzed by F.t.i.r. No peaks appeared apart from those due to SiF4 and MoF6 (from the Mo3 Si), SF6 (from the fuse), and WF6 (from the W). The crucible contained no solid residues. Thus, the combustion proceeded according to reaction (1).

3. Results Tables 2 and 3 contain the essential numerical information for the combustion of the samples of Mo3 Si. A detailed explanation of the symbols used there may be found

33

Thermochemistry of Mo3 Si

TABLE 2. Massic energy of combustion of Mo3 Si(cr) (sample A) in fluorine; T=298.15 K, p°=101.325 kPa

m/g m(W)/g m(S)/g Duc /K DU(blank)/J DU(gas)/J DU(cont)/J DU(W)/J DU(S)/J o(calor)(−Duc ) a J Dcu/(J·g−1 )

1

2

4

5

6

0.33665 0.70759 0.00053 0.95605 −0.5 0.9 −13.3 6633.4 20.1

0.16114 0.71513 0.00140 0.71410 −0.5 0.8 −9.9 6704.1 53.1

0.23228 0.72553 0.00142 0.82248 −0.5 0.8 −11.4 6801.6 53.9

0.18273 0.68735 0.00227 0.72842 −0.5 0.8 −10.1 6443.7 86.2

0.21032 0.69684 0.00292 0.77543 −0.5 0.8 −10.7 6532.7 110.8

−13289.2

−9926.1

−11432.6

−10125.1

−10778.6

−19729

−19710

−19749

−19725 −19753 Dc u=−(1973328) J·g−1 b Impurity correction=(267214) J·g−1 c Dc u°=−(19466221) J·g−1 d

a The energy equivalent of the calorimetric system o(calor)=(13900.120.7) J·K−1 was determined by combustion in O2(g) of standard reference material benzoic acid (NIST-SRM-39i). b Uncertainty is the standard deviation of the mean of the individual values of Dc u. c Uncertainty corresponds to twice the standard deviation of the mean. d Calculation of uncertainty is outlined in the text.

in an earlier publication.(16) For the conversion of apparent mass to mass, the density of Mo3 Si was taken to be 8700 kg·m−3 .(12) Contributions to the overall energy of the combustion reaction from the conversion of sulfur and of tungsten TABLE 3. Massic energy of combustion of Mo3 Si(cr) (sample B) in fluorine; T=298.15 K, p°=101.325 kPa

m/g m(W)/g m(S)/g Duc /K DU(blank)/J DU(gas)/J DU(cont)/J DU(W)/J DU(S)/J o(calor)(−Duc ) a J Dc u/(J·g−1 )

8

9

10

11

0.24691 0.69247 0.00315 0.82080 2.5 0.8 −11.4 6491.7 119.6

0.28392 0.73725 0.00076 0.89574 2.5 0.8 −12.5 6911.5 28.8

0.20802 0.72124 0.00273 0.78455 1.4 0.8 −10.9 6761.4 103.6

0.28465 0.72466 0.00348 0.89517 1.4 0.8 −12.4 6793.5 132.1

−11409.2

−12450.9

−10905.3

−19465 −19441 −19464 Dc u=−(19447211) J·g−1 b Impurity correction=−(025) J·g−1 c Dc u°=−(19447224) J·g−1 d

−12443.0 −19419

a The energy equivalent of the calorimetric system o(calor)=(13900.120.7) J·K−1 was determined by combustion in O2(g) of standard reference material benzoic acid (NIST-SRM-39i). b Uncertainty is the standard deviation of the mean of the individual values of Dc u. c Uncertainty corresponds to twice the standard deviation of the mean. d Calculation of uncertainty is outlined in the text.

34

I. Tomaszkiewicz et al. TABLE 4. Thermochemical corrections for impurities in samples

Sample

Impurity

Assumed form

Concentration

Reaction products

mass fraction A B A B A B A

C

MoC

O

SiO2

N

Si3 N4

Mo5 Si3

Mo5 Si3

0.0007 0.0003 0.0014 0.0003 0.00009 0.00013 0.1171

Dc u (impurity) a

Correction

J·g−1

J·g−1

MoF6(g), CF4(g)

−22193

SiF4(g), O2(g)

−11732

3SiF4(g), 2N2(g)

−29235

5MoF6(g), 3SiF4(g)

−21791

2.1 0.9 −10.6 −2.1 0.9 1.3 274.5

a Calculated on the basis of values of Df H°m(298.15 K): MoC, −10.0 kJ·mol−1;(39) MoF6(g), −1557.7 kJ·mol−1;(21) CF4(g), −933.2 kJ·mol−1;(34) SiO2 , −910.9 kJ·mol−1;(34) SiF4(g), −1615.8 kJ·mol−1;(22) Si3 N4 , −787.8 kJ·mol−1;(34) and Mo5 Si3 , −328.0 kJ·mol−1.(6)

to their hexafluorides come from the massic energies of fluorination, −37956 J·g−1(17) and −9386 J·g−1 ,(18) respectively. The quantity DU(blank)(17) was determined in separate experiments. How the impurities were assumed to be combined in the samples and reacted with F2(g) is outlined in table 4, as are the corresponding individual thermochemical corrections. Recall that sample B contained Mo5 Si3 . Its concentration was arrived at as follows. First, the content of Si determined gravimetrically (essentially by oxidation in air; see table 1) had to be adjusted to allow for conversion, during the analysis, of the nitride impurity to 3SiO2 and 2N2(g), and also for the SiO2 (the presumed form of the oxygen impurity), which would have behaved as an inert contaminant. Our final calculation showed the (molybdenum+silicon) portion of sample B to be composed of mass fractions 0.1171 of Mo5 Si3 and 0.8807 of Mo3 Si. This conclusion is in accord with the previously mentioned X-ray diffraction measurements, which were consistent with the presence of an estimated mass fraction 0.1 of Mo5 Si3 . Impurity corrections for samples A and B, the sums of the appropriate quantities in the column on the far right of table 4, are shown in tables 2 and 3. Uncertainties attached to the values of the standard massic energies of combustion Dc u°, given in tables 2 and 3 as twice the standard deviation of the mean, take into account the scatter of the individual values of Dc u, and uncertainties accrued from: the five quantities denoted by DU; o(calor)(−Duc ); and the impurity corrections. Our results for Dc u°(Mo3 Si): −(19447224) J·g−1 and −(19466221) J·g−1 , agree satisfactorily. A mean value, −(19456216) J·g−1 , obtained by weighting those results inversely as the squares of the uncertainties,(19) is chosen for the massic energy of combustion according to reaction (1). Taking the molar mass of Mo3 Si as 315.91 g·mol−1 ,(20) we calculate the molar quantities for reaction (1): DcU°m=−(6146.3425.05) kJ·mol−1; Dn gRT=−17.35 kJ·mol−1; and, thus, Dc H°m = −(6163.725.1) kJ·mol−1 . The latter result, combined with 3·Df H°m(MoF6 ,g) = 3· −(1557.720.9) kJ·mol−1(21) and Df H°m(SiF4 ,g) = −(1615.820.5) kJ·mol−1(22)

Thermochemistry of Mo3 Si

35

yields: Df H°m(Mo3 Si,cr,298.15 K)=−(125.225.8) kJ·mol−1 . Here, the uncertainties in the Df H°m s and Dc H°m were combined in quadrature. The formation reaction is: 3Mo(cr)+Si(cr)=Mo3 Si(cr),

(2)

at T=298.15 K and p°=101.325 kPa.

4. Discussion Thermodynamic studies of Mo3 Si reported in the literature fall conveniently into two categories: those that deal with the molar heat capacity C°p,m(T ) and molar enthalpy increments DTT' H°m , where T '=298.15 K;(23–27) and those that deal with the standard molar Gibbs free energies of formation Df G°m .(28–30) Thermochemical and thermophysical information on the molybdenum silicides has been summarized and evaluated in reviews.(1,2,31,32) In the following discussion, uncertainties correspond to twice the standard deviation of the mean.

HEAT CAPACITY AND ENTHALPY INCREMENTS OF Mo3 Si

In 1957, King and Christensen(23) reported values of the low-temperature heat capacity and high-temperature enthalpy increments of Mo3 Si. Over a period of approximately two years in the early 1970s, Bondarenko et al.(24–27) authored four papers that dealt with the high-temperature thermodynamic properties of Mo3 Si. No other similar investigations have been described in the literature. King and Christensen’s measurements of the heat capacity by low-temperature adiabatic calorimetry were performed on a sample whose composition was assumed to be Mo3 Si0.925O0.075 because of the presence of mass fraction 15·10−3 of oxygen impurity. The lowest experimental temperature was 53.67 K, which necessitated an extrapolation of the C°p,m(T ) against T curve to T 4 0 by means of a Debye–Einstein treatment. King and Christensen corrected C°p,m(T ) for the impurity, and calculated the standard molar entropy DT0 S°m (T=298.15 K) to be (106.320.8) J·K−1·mol−1 . These authors also reported results at individual temperatures for the enthalpy increment DTT' H°m {T '=298.15 K; 400E(T/K)E1450.7 K} from drop-calorimetry: DTT' H°m /(J·mol−1 )=91.96·(T/K)+9.58·10−3·(T/K)2+4.18·105·(T/K)−1−29673. (3) The first differential of equation (3) gives: C°p,m /(J·K−1·mol−1 )=91.96+1.916·10−2·(T/K)−4.18·105·(T/K)−2 .

(4)

When calculated from equation (4), the C°p,m s of Mo3 Si merge smoothly with those from the low-temperature adiabatic calorimetry.

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I. Tomaszkiewicz et al.

In 1971, Bondarenko et al.(25) reported, at round temperatures only, DTT' H°m of several silicides of molybdenum and tungsten determined by drop calorimetry from T=1200 K to T=2200 K. (The English translation of this work(26) appeared about two years later.) For Mo3 Si, they gave the expression: DTT' H°m /(J·mol−1 )=37.037·10−3·(T/K)2−5.215·(T/K)−18.951·106·(T/K)−1+61828, (5) which, by differentiation, yields: C°p,m /(J·K−1·mol−1 )=−5.215+74.074·10−3·(T/K)+18.951·106·(T/K)−2 .

(6)

Elsewhere, Bondarenko et al.(24) described high-temperature adiabatic calorimetric measurements of C°p,m(T ) between T=400 K and T=1200 K, with the result: C°p,m /(J·K−1·mol−1 )=98.32+2.096·10−2·(T/K)−1.598·106·(T/K)−2 .

(7)

(Although both papers(24,25) appeared in the literature within approximately a year of each other, no mention is made in one to the other.) These determinations of DTT' H°m and C°p,m(T ) overlap. At the common temperature 1200 K, according to equation (6), C°p,m = 96.8 J·K−1·mol−1 and (dC°p,m /dT ) = 52·10−3 J·K−2·mol−1; according to equation (7), C°p,m=122.4 J·K−1·mol−1 and (dC°p,m /dT )=23·10−3 J·K−2·mol−1 . There is a difference of approximately 25 per cent between these C°p,m s, and the slopes of the curves of C°p,m against T are in disagreement. By contrast, C°p,m(1200 K)=114.7 J·K−1·mol−1 from King and Christensen is midway between the Bondarenko et al. results, with (dC°p,m /dT )=20·10−3 J·K−2·mol−1 . We note in passing that Callanan et al.(7) were unable to reconcile Bondarenko et al’s. values for DTT' H°m of WSi2 at temperatures between 1173 K and 2113 K with their own low-temperature adiabatic calorimetric results or with the high-temperature enthalpy increments reported by Mezaki et al.(33) When Chart(31) published his review of the thermodynamic properties of transition-metal silicides in 1972, only King and Christensen’s study and the drop-calorimetric work of Bondarenko et al. had been described in the literature. Chart combined the enthalpy increments from those investigations (presumably, the values at round temperatures from Bondarenko et al. and the experimental results from King and Christensen, although he does not state precisely how that was done) to obtain the expression: C°p,m(Mo3 Si)/(J·K−1·mol−1 )=85.84+2.268·10−2·(T/K)+3.207·104·(T/K)−2 .

(8)

By integrating equation (8) and evaluating the constant of integration, one obtains: DTT' H°m(Mo3 Si)/(J·mol−1 )=85.84·(T/K)+ 1.134·10−2·(T/K)2−3.207·104·(T/K)−1−26494.

(9)

In table 5, we compare the experimental results for DTT' H°m with those calculated from equation (9), and list also the derived C°p,m s. In the region of overlap

37

Thermochemistry of Mo3 Si

TABLE 5. Comparison of experimental (expt) and calculated (calc) molar enthalpy increments DTT' H°m and molar heat capacities C°p,m of Mo3 Si (p°=101.325 kPa, T '=298.15 K)

T/K 298.15 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200

e

expt a

DTT' H°m /(kJ·mol−1 ) expt b

calc c

93.11 103.06 113.58 124.71 136.45 148.85 161.91 175.65 190.07 205.19 221.00

9.54 19.3 29.1 39.2 49.4 59.9 70.6 81.7 92.9 104.3 115.8 127.7 139.9 152.1 164.7 177.6 190.5 203.7 217.2

expt d 93.0

9.71 19.54 29.66 40.08 50.71 61.42 72.17 83.14 94.47 106.15 118.16 130.50

C°p,m /(J·K−1·mol−1 ) calc e

calc f

93.05 95.06 97.40 99.60 101.8 104.1 106.3 108.6 110.8 113.1 115.3 117.7 119.8

92.97 97.01 99.87 102.3 104.5 106.6 108.7 110.7 112.7 114.7 116.6 118.6 120.5

a Reference 23. b Reference 25. c Reference 31. d From low-temperature adiabatic calorimetry.(23) Reference 31. f Derived from the values of DTT' H°m reported by King and Christensen.(23)

(1200E(T/K)E1500), the DTT' H°m s are in agreement to within 5·10−2·DTT' H°m . Chart’s selected values lie inside the likely uncertainty limits of the experimental DTT' H°m s and C°p,m(T )s, and we accept his evaluation. It is not possible to reconcile the adiabatic calorimetric results for C°p,m from Bondarenko et al.(24) with the selected values, as the differences lie well outside the probable uncertainties of both sets. Values of C°p,m(T ) and DTT' H°m calculated from equations (8) and (9) are combined with our result for Df H°m(Mo3 Si,cr,298.15 K) to obtain the thermodynamic functions of Mo3 Si shown in table 6. As part of the underpinnings of the table, we used the thermodynamic functions of Mo(cr) and Si(cr) recommended by Gurvich et al.(34)

STANDARD MOLAR GIBBS FREE ENERGY OF FORMATION OF Mo3 Si

There has been no direct determination of Df H°m(Mo3 Si,cr,298.15 K). However, high-temperature studies of reactions of Mo3 Si have been described in the literature, from which Df G°m(T ) can be deduced and, thence, values of Df H°m(298.15 K) estimated, albeit with large uncertainties.

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I. Tomaszkiewicz et al.

TABLE

6.

Molar

thermodynamic functions of Mo3 Si(cr), R=8.31451 J·K−1·mol−1 a

T K

C°p,m (T ) R

DT0 S°m R

F°m b R

0 298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00 1100.00 1200.00 1300.00 1400.00 1500.00 1600.00 1700.00 1800.00 1900.00 2000.00 2100.00 2200.00 2300.00

0.000 11.195 11.199 11.448 11.709 11.976 12.245 12.515 12.786 13.058 13.330 13.602 13.874 14.146 14.418 14.691 14.963 15.235 15.508 15.780 16.053 16.325 16.598

0.000 12.785 12.854 16.109 18.692 20.850 22.717 24.369 25.859 27.220 28.478 29.649 30.749 31.787 32.772 33.711 34.610 35.473 36.304 37.106 37.883 38.636 39.368

a 12.785 12.785 13.227 14.071 15.025 15.994 16.939 17.849 18.719 19.550 20.343 21.102 21.828 22.525 23.195 23.840 24.463 25.064 25.646 26.211 26.758 27.291

DTT' H°m 103·R·K −2.045 0.000 0.021 1.153 2.311 3.495 4.706 5.944 7.209 8.501 9.821 11.167 12.541 13.942 15.370 16.826 18.308 19.818 21.355 22.920 24.511 26.130 27.777

with

p°=101.325 kPa

and

Df H°m (T ) 103·R·K

Df G°m (T ) 103·R·K

−15.06 −15.06 −15.06 −15.07 −15.12 −15.17 −15.22 −15.27 −15.31 −15.34 −15.37 −15.39 −15.42 −15.45 −15.45 −15.52 −21.60 −21.63 −21.67 −21.72 −21.78 −21.86 −21.96

−15.06 −15.12 −15.12 −15.14 −15.16 −15.16 −15.15 −15.14 −15.12 −15.10 −15.07 −15.04 −15.01 −14.98 −14.95 −14.91 −14.83 −14.44 −14.03 −13.63 −13.23 −12.82 −12.40

a Thermodynamic functions are estimated to be uncertain by 23·10−2·X, where X denotes C°p,m (T ), DT0 S°m , F°m , or DTT' H°m ; Df H°m (T )/103·R·K and Df G°m (T )/103·R·K are both uncertain by 20.7. Note that DTT' H°m (T 4 0) is an estimate as are, therefore, Df H°m (T ) and Df G°m (T ) at T 4 0. b F°m=(DT0 S°m−DTT' H°m /T ).

Searcy and Tharp(28) carried out the first such investigation. They determined the equilibrium pressure p(Si) for the dissociation: Mo3 Si(cr)=3Mo(cr)+Si(g),

(10)

by mass-loss Knudsen effusion from molybdenum and tungsten cells. Thirty-five measurements of p(Si) were reported over the temperature range 2015 K to 2288 K, with 11 effusion orifices of different area. We have reevaluated these results by means of a third-law procedure in conjunction with the thermodynamic properties of Mo(cr) and Si(g) selected by Gurvich et al.(34) and those of Mo3 Si given in table 6. This analysis reveals a large drift with T of Dr H°m(298.15 K) for reaction (10), equivalent to an unlikely error of 43 J·K−1·mol−1 in Dr S°m (10). If this worrisome shortcoming is ignored, Dr H°m(298.15 K) is calculated to be (558219) kJ·mol−1 . (Searcy and Tharp explicitly assigned an uncertainty of 25 kJ·mol−1 to this quantity, but apparently used approximately 211 kJ·mol−1 in their final computation; our analysis is consistent with an even larger uncertainty of 219 kJ·mol−1 .) We combine

Thermochemistry of Mo3 Si

39

Dr H°m(298.15 K) with Dsub H°m(Si,cr,298.15 K) = (45028) kJ·mol−1(34) to derive Df H°m(Mo3 Si,cr,298.15 K)=−(108221) kJ·mol−1 . In order to circumvent the experimental difficulty of measuring p(Si)s in reaction (10) that are small even at temperatures as high as 2000 K, and the additional problem of the combination of Si(g) with crucible materials to form other refractory silicides, Chart(29) adopted a different approach. He measured p(SiO) for the reaction: Mo3 Si(s)+SiO2(cr,a-quartz)=3Mo(s)+2SiO(g),

(11)

by the mass-loss, Knudsen-effusion technique, which led to the following result for reaction (11) at T =1500 K: DrG°m /(J·mol−1 )=−332.37·(T/K)+804263.

(12)

Earlier, Kubaschewski and Chart(30) reported for: Si(s)+SiO2(cr,a-quartz)=2SiO(g), DrG°m /(J·mol−1 )=−329.62·(T/K)+683619.

(13) (14)

From the combination of reactions (11) and (13), and equations (12) and (14), we obtain: DrG°m /(J·mol−1 )=2.75·(T/K)−120644,

(15)

for the formation of Mo3 Si(cr) according to reaction (2). Thus, from equation (15), we deduce Df G°m(Mo3 Si,1500 K)=−116.5 kJ·mol−1 and Df H°m(Mo3 Si,1500 K) = −120.6 kJ·mol−1. On the basis of a third-law calculation, and employing those sources of auxiliary thermodynamic functions of Mo(cr), Si(cr), and Mo3 Si quoted earlier in the present paper, we derive Df H°m(Mo3 Si,298.15 K)=−117.4 kJ·mol−1. A second-law calculation yields Df H°m(Mo3 Si,298.15 K)=−124.1 kJ·mol−1 . Chart(31) assigned an uncertainty of 211.7 kJ·mol−1 , which we retain, to Df H°m derived from his own work. Ohmori et al.(35) determined Df G°m(T ) of Mo3 Si from measurements of the e.m.f.s E of two solid-state electrochemical cells. The overall reactions in the cells were given: Mo3 Si+(2/3)Cr2O3=3Mo+(4/3)Cr+SiO2 ,

(17)

Mo3 Si+(8/3)Fe+(2/3)B2O3=3Mo+(4/3)Fe2 B+SiO2 .

(18)

The corresponding molar Gibbs free energies are calculated from: Df G°m(Mo3 Si)=Df G°m(SiO2 )−(2/3)·Df G°m(Cr2O3 )−DrG°m(17),

(19)

Df G°m(Mo3 Si)=Df G°m(SiO2 )+(4/3)·Df G°m(Fe2 B)−(2/3)·Df G°m(B2O3 )−DrG°m(18). (20)

40

I. Tomaszkiewicz et al.

The Faraday constant F=96.485 kJ·V−1·mol−1 , DrG°m(17)=−4·F·E(17), E(17)= −0.009 V, DrG°m(18)=−4·F·E(18), and E(18)=−0.032 V. All the Df G°m s in equations (19) and (20), with the exception of Df G°m(Fe2 B), are available in modern critically evaluated tables.(34) The missing quantity is derived from the following electrochemical-cell reactions studied by Ohmori and Moriyama:(36) (4/3)Fe2 B+O2(g)=(2/3)B2O3+(8/3)Fe, Df G°m(Fe2 B)=(1/2)·Df G°m(B2O3 )−(3/4)·RT·ln{p(O2 )/p°}−DrG°m(21);

(21) (22)

(4/3)Fe2 B+(2/3)Cr2O3=(2/3)B2O3+(8/3)Fe+(4/3)Cr,

(23)

Df G°m(Fe2 B)=(1/2)·Df G°m(B2O3 )−(1/2)·Df G°m(Cr2O3 )−DrG°m(23),

(24)

where DrG°m(21)=−4·F·E(21), E(21)=1.376 V, DrG°m(23)=−4·F·E(23), E(23)= 0.019 V, p(O2 )=21.28 kPa, and p°=101.325 kPa. We take T=1200 K as a representative intermediate temperature for these measurements. Equations (22) and (24), in combination with values of −(977.721.9) kJ·mol−1(34) and −(826.328.4) kJ·mol−1(34) for Df G°m(1200 K) of B2O3 and Cr2O3 , respectively, yield the results: −(78.921.2) kJ·mol−1 and −(70.224.5) kJ·mol−1 for Df G°m(Fe2 B,1200 K). These quantities do not agree within the combined uncertainties; we use the average, −(7525) kJ·mol−1 , as we proceed with the evaluation of equation (20). Ohmori and Moriyama stated that Df G°m(Fe2 B,T ) was the same whether calculated from equations (22) or (24): thus, at T = 1200 K, Df G°m(Fe2 B) = −(77.321.2) kJ·mol−1 . As we have just shown, the overlap can be satisfactory only if the uncertainties are larger than Ohmori and Moriyama estimate. Their relation for Df G°m(T ) against T implies Df H°m(Fe2 B,1200 K)1−101.3 kJ·mol−1 . That value is inconsistent with what appears to be a reliable calorimetric determination of Df H°m(Fe2 B,298.15 K)=−(67.8728.05) kJ·mol−1 by Sato and Kleppa,(37) and a less precise result: −(67221) kJ·mol−1 from Gorelkin et al.(38) We have also noticed discrepancies between Ohmori’s values(40) of Df G°m(T ), at T=1200 K, for example, of other borides determined by the e.m.f. technique and those recommended by Gurvich et al.(34): 7 kJ·mol−1 for Mo2 B; 4 kJ·mol−1 for MoB; 14 kJ·mol−1 for WB; and 20 kJ·mol−1 for W2 B. Ohmori and Moriyama also performed preliminary measurements to check the performance of their apparatus. On the basis of their results, a value of Df G°m(Cr2O3 ,1200 K)=−(807.321.6) kJ·mol−1 can be calculated which is seriously at variance with the value of −(826.328.4) kJ·mol−1 recommended by Gurvich et al.(34) Returning to equations (19) and (20), we note that Ohmori et al. presented evidence to support their assumption that the SiO2 formed in the electrochemical cells was vitreous. They were also satisfied that no extraneous reactions had occurred in the cells during the measurements. Accordingly, we combine the values for Df G°m(1200 K)/(kJ·mol−1 ): −(692.021.2),(34) −(826.328.4),(34) −(7525), and −(977.721.7),(34) for SiO2(vit), Cr2O3 , Fe2 B, and B2O3 , respectively, with the experimental results, to calculate Df G°m(Mo3 Si,1200 K) = −(14526) kJ·mol−1 from equation (19), and Df G°m(Mo3Si, 1200 K) = −(15327) kJ·mol−1 from

41

Thermochemistry of Mo3 Si

equation (20). The weighted mean is −(14825) kJ·mol−1 . This result differs greatly from −(101.720.8) kJ·mol−1 at T=1200 K implied by the Df G°m(Mo3 Si,T ) against T relation given in the paper of Ohmori et al. The 150 kJ·mol−1 discrepancy arises, largely, from our use of the most up-to-date Df G°m s for the compounds involved in the electrochemical cell reactions. Standard molar entropies of Mo(cr),(34) Si(cr),(34) and Mo3 Si (table 6) lead to Df S°m(Mo3 Si, 1200 K) = −2.46 J·K−1·mol−1 and, therefore, −1 Df H°m(Mo3 Si,1200 K)=−(14526) kJ·mol . That leads, by way of the enthalpy increments at T=1200 K for Mo,(34) Si,(34) and Mo3 Si (table 6) to Df H°m(Mo3 Si,298.15 K) = −(14826) kJ·mol−1 . Note that our calculated Df S°m(Mo3 Si) is in disagreement with Ohmori et al.’s value of 12.1 J·K−1·mol−1 . Interestingly, when we combine Df H°m(Fe2 B,298.15 K) from Sato and Kleppa with the estimate by Kubaschewski et al.(41) of DT0 S°m and C°p,m(T ), we obtain Df G°m(Fe2 B,1200 K)=−56 kJ·mol−1 . That value, inserted into equation (20), leads to Df G°m(Mo3 Si,1200 K)1−128 kJ·mol−1 , in good agreement with −125 kJ·mol−1 recommended in table 6. This may be no more than a coincidence, implying as it does the existence of systematic errors in some of the measurements, but not in others. Our value for Df H°m(Mo3 Si,cr,298.15 K), −(125.225.8) kJ·mol−1 , agrees with, but is less uncertain, than those recalculated from Searcy and Tharp: −(108221) kJ·mol−1 , and from Chart: −(117212) kJ·mol−1 (third law) and −(124212) kJ·mol−1 (second law). These determinations all differ markedly from the reworked results of Ohmori et al. Referring to the disagreement of their own findings with those of Ohmori et al., Sato and Kleppa(37) commented: ‘‘It is well known that the emf method frequently fails to yield reliable enthalpy and entropy data.’’ In the course of this paper, we have alluded to the very low partial pressure p(Si,g) in equilibrium with decomposing Mo3 Si, reaction (10), and the concomitant experimental difficulties associated with its measurement even at high temperatures. This is made clear in table 7, where we have used the thermodynamic properties of Mo3 Si, Mo, and Si(g) recommended in the present paper to calculate p(Si,g) as a function of T. The p(Si)s are estimated to be uncertain by roughly 0.5·p(Si,g). TABLE

7.

Partial

pressure

p(Si) as a function of Mo3 Si(cr)=3Mo(cr)+Si(g) a

temperature

for

the

T/K

p(Si)/Pa

T/K

p(Si)/Pa

298.15 500 1000 1500

8·10−89 4·10−48 5·10−18 5·10−8

2000 2100 2200 2300

4.8·10−3 2.5·10−2 0.11 0.42

a

reaction:

Sources of thermodynamic quantities used in the calculations are given in the text.

We are grateful to Dr M. W. Chase, Jr., and Ms Dorothy Blakeslee for access to the JANAF computer codes. We have benefited from correspondence with Dr M. S. Chandrasekharaiah.

42

I. Tomaszkiewicz et al.

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