Congruent Vaporization of Solid Manganese ... - ACS Publications

10586

J. Phys. Chem. B 1998, 102, 10586-10595

Congruent Vaporization of Solid Manganese Monotelluride and the Effects of Phase Transitions: A High-Temperature Mass Spectrometric Study T. S. Lakshmi Narasimhan, R. Viswanathan,* and R. Balasubramanian Materials Chemistry DiVision, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603 102, India ReceiVed: May 8, 1998; In Final Form: August 26, 1998

Vaporization studies on Mn-Te samples of initial compositions 49.6 and 54.9 at. % Te were conducted by Knudsen effusion mass spectrometry. Both these samples on continuous vaporization reached the congruently effusing compositions (CECs) ≈ 50 at. % Te. Vaporization chemistry around this composition was studied from 1194 to 1343 K to examine the effects associated with the reported phase transitions in MnTe(s) at 1228 (R T β), 1293 (β T γ), and 1323 K (γ T δ). Among these, only the R T β phase transition showed significant effects. During the phase transition, the vapor phase was relatively richer in manganese in the increasing temperature direction (i.e., as the sample was heated from T e 1203 K to T g 1238 K) and was relatively richer in tellurium in the decreasing temperature direction (i.e., as the sample was cooled from T g 1238 K to T e 1218 K). Evidence for a slight variation in the CEC with temperature was also obtained but was distinguishable from the effects associated with the R T β phase transition. From the results obtained in four series of experiments, the partial pressures of Mn(g), Te(g), and Te2(g) were deduced, and by neglecting the variations in the CECs with temperature, the enthalpy changes for the following vaporization reactions during congruent effusion were evaluated: MnTe(s) ) Mn(g) + 0.5Te2(g), ∆rH°m(298.15K) ) 463.6 ( 2.1 kJ mol-1; MnTe(s) ) Mn(g) + Te(g), ∆rH°m(298.15K) ) 592.4 ( 2.3 kJ mol-1; MnTe(s) ) Mn (g) + yTe(g) + (1 - y)/2Te2(g), ∆rH°m (298.15 K) ) 554.0 ( 4.6 kJ mol-1, ymean ≈ 0.7. These results yielded ∆fH°m(MnTe,s,298.15K) ) - 99.2 ( 6.8 kJ mol-1. An equation for the total vapor pressure during congruent effusion of MnTe(s), valid for the temperature range from 1194 to 1343 K was obtained: log(P/Pa) ) (14539 ( 273)/(T/K) + (11.159 ( 0.222).

Introduction When a congruently vaporizing condensed phase AiB(1-i) becomes unstable due to a temperature change from T1 to T2, another condensed phase, necessarily of a different stoichiometry AjB(1-j), will be generated through an incongruent vaporization reaction. Consequently, the total vapor pressure at T2 could be higher than the hypothetical value for the congruent vaporization of AiB(1-i) (at T2), while the relative atomic fractions in vapor of the components A and B will change from what were at T1. Under dynamic conditions, the vapor-phase composition and the total vapor pressure will remain invariant with time until the transformation from AiB(1-i) to AjB(1-j) is complete. Subsequently, these quantities will change again, to those corresponding to the congruent vaporization of AjB(1-j) if thermodynamically feasible, or, to those corresponding to an incongruent vaporization reaction generating a new condensed phase AkB(1-k). In the latter case, the chain of incongruent reactions will continue until the condensed phase eventually reaches a congruently vaporizing composition AlB(1-l) at T2. The sequence of events, such as those listed above, is best understood from the isothermal pressure-composition diagrams1,2 at many temperatures.3-5 If the congruently vaporizing compositions at T1 and T2 differ only very slightly, then the vapor-phase compositions during congruent vaporization at T1 or T2 will be closely similar; however, during the condensedphase transition at T2, the vapor-phase composition could be * To whom correspondence should be addressed. FAX: 91 4114 40365. E-mail: [email protected].

very different from that during congruent vaporization at T1 or T2. Thus from such anomalous changes in vapor-phase compositions, unknown phase transitions can be detected6 or better understood.7 Edwards8 had discussed in great detail the anomalous phenomena in effusion studies, while Edwards and Franzen9 discussed and presented a thermodynamic theory, explaining the occurrence of such effects in both transpiration and effusion experiments. The model developed by Edwards and Franzen implies that the nature and magnitude of the effects associated with a condensed-phase transition are chiefly governed by the following factors: i - j or i - l, the difference between the congruently vaporizing compositions at T1 and T2; Ttr - T2, the difference between the temperature of the onset of a phase transformation Ttr and T2; and (∆r1H°m - ∆r2H°m), the difference between the standard molar enthalpy changes for the congruent vaporization of the two condensed phases. With the above concepts in mind, and continuing our interest in the (manganese + tellurium) system,10 we undertook a hightemperature mass spectrometric study of solid manganese monotelluride. Our goal was to confirm the congruent vaporization behavior of MnTe(s) and to especially examine its vaporization chemistry during the three solid-state phase transitions shown in the phase diagram reported by Vassiliev et al.11 The phase transformations are R-MnTe (NiAs-type B8 hexagonal structure) T β-MnTe (ZnS, wurtzite structure) T γ-MnTe (ZnS, sphalerite structure) T δ-MnTe (NaCl structure) at 1228 ( 10, 1293 ( 10, and 1323 ( 10 K, respectively. To our knowledge, vaporization behavior of manganese telluride has been studied previously by two groups: van den

10.1021/jp982174x CCC: $15.00 © 1998 American Chemical Society Published on Web 11/25/1998

Vaporization Studies on Mn-Te Samples

J. Phys. Chem. B, Vol. 102, No. 51, 1998 10587

TABLE 1: Details for Different Series of Vaporization Experiments total no. series of runs 1 2 3 4

6 21 12 11

Knudsen cell, orificea diam alumina, 0.5 mm molybdenum, 0.4 mm molybdenum, 0.4 mm molybdenum, 0.4 mm

starting compsn, starting x(Te) mass/g 0.496 0.496 0.549 0.496

0.508 63 0.178 68 0.260 40 0.097 16

total mass lossb/g 0.035 29 0.033 14 0.101 09 0.014 58

a Knife-edged. b Deduced from the mass of the sample, measured at the conclusion of each series.

Boomgaard12 using sublimation experiments and Wiedemeier and Sadeek13 using the mass-loss Knudsen effusion method. Wiedemeier and Sadeek assumed a constant congruently effusing composition (CEC) of x(Te) ) 0.5 in their calculation of vapor pressures, based on the fact that the residues in their preliminary congruency-test runs at 1373 and 1523 K were essentially stoichiometric. van den Boomgaard,12 however, drew separate congruently vaporizing composition (CVC) curves for the solid and liquid phases, the curve for the solid bending to the Te-rich side and terminating at T ) 1480 K, and the curve for the liquid starting at T ) 1460 K and bending to the Mn-rich side. Such CVC curves will influence the vaporization behavior during a temperature change, but these effects can be distinguished from those due to phase transitions by a careful mass spectrometric investigation. We conducted many vaporization experiments on solid MnTe and obtained results indicative of both a monotonically varying CEC and a discontinuous change in the CEC to the Te-rich side, the latter associated with the R T β phase transition in MnTe. The discontinuities in the CECs due to the β T γ or due to the γ T δ transitions were not readily recognizable, but we infer that the CEC of the γ phase is Mn-rich in comparison to that of the β phase and that the CEC of the δ phase is Terich in comparison to that of the γ phase. We discuss in this paper the salient results of the experiments and the methodology employed by us to deduce the above information. We also present thermodynamic properties for the vaporization of solid MnTe at its nominal congruently effusing composition of 50 at. % Te. Experimental Section The vaporization experiments were conducted with a VG micromass MM 30 BK Knudsen-cell mass spectrometer. The instrument has been described previously.14-16 Two samples of compositions 49.6 and 54.9 at. % Te were prepared by direct reaction of elements (Leico Industries, Inc., U.S.A., purity: 99.999 mass % for Te and 99.9 mass % for Mn) in evacuated and sealed quartz tubes. The preparation involved heating at T ) 680 K for ∼ 10 days, at T ) 900 K for 11 (sample 1) and 7 days (sample 2), and at T ) 690 K once again for 14 days (sample 2). Both samples were characterized by X-ray diffraction. The pattern for sample 2 corresponded to the two-phase field (MnTe + MnTe2), while that for sample 1 showed the presence of the MnTe phase and some faint lines due to the MnTe2 phase. Four series of vaporization experiments were conducted, one in alumina and the other three in molybdenum Knudsen cells. Table 1 lists for each series the experimental details of the Knudsen cell and the sample employed and the number of runs conducted. Except one run of series 3 where the measurements were carried out at T as high as 1343 K, all runs were restricted to T < 1278 K. The residue from each series remained tightly stuck to the bottom of the crucible.

In each series, the initial experiments were aimed at reaching the congruently effusing composition as quickly as possible. A freshly loaded sample was first heated at T < 700 K and later at different higher temperatures up to T < 1208 K, ensuring that the total vapor pressure was less than ≈10 Pa. The ion intensities of 256Te2+ and 130Te+ were measured all along, so also was 55Mn+ once the latter became measurable at T ≈ 1050 K. It usually took about 6 min for accumulating a set comprising I(256Te2+), I(130Te+), and I(55Mn+), measured in that sequence. The first run in a series was designated when such sets gave for the first time a definite indication of congruent effusion. Thereafter, any subsequent measurements which involved heating the sample from room temperature were considered as a separate run. From every set of intensities of Te2+, Te+, and Mn+, the ion intensity ratios I(Mn+)/I(Te+) and I(Te2+)/I(Te+) were first calculated and subsequently R′c, an apparent ratio of the atomic fraction of Mn to that of Te in the condensed phase assuming congruent effusion of Te2(g), Te(g), and Mn(g). Calculation of R′cs with this assumption rendered it possible to deduce the actual congruently effusing composition of the condensed phase (CEC) as well as to infer when and whether the condensed phase was Mn-rich or Te-rich compared to the CEC. Denoting the formula of the congruently effusing condensed phase as Mn(1-x)Tex, R′c was calculated for each set from

R′c ) (1 - x)/x ) {p(Mn) M(Mn)-1/2}/{p(Te) M(Te)-1/2 + 2p(Te2) M(Te2)-1/2} ) C{I(Mn )/I(Te )}/{1 + DI(Te2+)/ +

+

I(Te+)} (1) where

C ) {M(Te)/M(Mn)}1/2{σ(Te)/σ(Mn)}{γ(Te+)/γ(Mn+)} × {n(Te+)/n(Mn+)} (2) D ) 21/2{σ(Te)/σ(Te2)}{γ(Te+)/γ (Te2+)}{n(Te+)/ n (Te2+)} (3) In the above equations, p, M, and σ refer to the partial pressure, molar mass, and ionization cross-section of the neutral gaseous species given in parentheses; γ and n refer to the relative gain of the detector and the relative isotopic abundance of the ion given in parentheses. Table 2 gives the values of σ, γ, and n used by us. σ for Mn(g) and Te(g) were taken from Mann’s tables18 and that for Te2(g) was taken as 1.44 σ(Te). γ for Mn+ and Te+ were taken from Pottie et al.,19 while γ for Te2+ was assumed to be the same as that for Te+. The validity of these γ values was ascertained by comparing the ratios of γ(Te+)/γ(Mn+) and γ(Te2+)/γ (Mn+) with those deduced from the ratios of I+(secondary electron multiplier)/I+(Faraday cup) measured for each ion on three occasions during this study. From the intensity ratios I(Mn+)/I(Te+) and I(Te2+)/I(Te+), Rv, the ratio of atomic fraction of manganese to that of tellurium in the equilibrium vapor phase was also calculated for each set from the relation

Rv ) p(Mn)/{p(Te) + 2p(Te2)} ) C{M(Te)/M(Mn)}-1/2{I(Mn+)/I(Te+)}/ {1 + 21/2DI(Te2+)/I(Te+)} (4) where C is given by eq 2 and D is given by eq 3.

10588 J. Phys. Chem. B, Vol. 102, No. 51, 1998

Lakshmi Narasimhan et al.

TABLE 2: Properties Pertinent to Ionization of the Neutral Speciesa and Measurement of Ion Intensitiesb species Mn(g) Te(g) Te2(g)

series 1 σ (at 12.0 V)


3.882 2.320 3.341


3.921 2.385 3.434

for all series


4.152 2.773 3.993

3.959 2.450 3.528

ion 55

Mn

+

130Te+

256Te + 2

γc

n

0.926 0.756 0.756

1 0.338 0.229

a σ ) relative ionization cross-section at the electron energy used in different series. b γ ) relative secondary electron multiplier gain for the ion monitored; n ) the relative isotopic abundance of the most abundant ion that was chosen for measurements. c Values for Mn+ and Te+ taken from Pottie et al.19 and γ(Te2+) taken to be same as γ (Te+).

TABLE 3: Thermal Functions Used in the Present Study T/K

Te2(g)

a

Te(g)

a

Mn(g)

b

MnTe(s)

Φ°m ) {-(G°T - H°298.15)/T}/(J mol-1 K-1) 298.15 258.8 182.6 173.7 1100 281.4 194.6 185.7 1200 284.1 195.9 187.0 1300 286.6 197.2 188.3 1400 289.0 198.4 189.5 1100 1200 1300 1400 a

(H°T - H°298.15)/(kJ mol-1) 33.1 16.8 16.7 37.5 18.9 18.7 41.9 21.1 20.8 46.4 23.3 22.9

c

93.7 127.6 131.3 135.0 138.4

Results

47.2 53.2 59.2 65.2

From ref 21. b From ref 24. c From ref 23.

The values of R′c, x, and Rv were calculated for every set of intensities to serve as indicators of the changes in the vaporization behavior at a constant temperature as well as when a temperature change was made in the increasing and decreasing directions. From the ion intensities measured during congruent effusion, the partial pressures of the gaseous species Mn(g), Te(g), and Te2(g) were computed by using the following relation:

p(i)/Pa ) k(Te){σ(Te)/σ(i)}{γ(Te+)/γ(i+)}{n(Te+)/ n(i+)}I(i+)T (5) where k(Te) is the pressure calibration constant for Te(g). A mean value of k(Te) was obtained from those calculated at different temperatures according to the following relation:

ln k(Te) ) -{∆disH°m(Te2,g,298.15K)/(RT)} + {[2Φm°(Te,g) - Φm°(Te2,g)]/R} - ln {21/2D-1T[I(Te+)]2/ [101325I(Te2+)]} (6) where ln denotes natural logarithm, R refers to the gas constant, ∆disH°m(Te2,g,298.15K) refers to the dissociation enthalpy of Te2(g) (257.6 ( 4.1 kJ mol-1 at 298.15 K),20 Φm° refers to the Gibbs free energy function, and D is given by eq 3. The values of Φm°s were taken from Gronvold et al.21 and given in Table 3. From the partial pressures, the following equilibria were evaluated by second- and third-law methods.22

MnTe(s) ) Mn(g) + yTe(g) + 0.5(1 - y)Te2(g)

(7)

MnTe(s) ) Mn(g) + 0.5Te2(g)

(8)

MnTe(s) ) Mn(g) + Te(g)

(9)

y in eq 7 is the degree of dissociation of gaseous dimeric tellurium and calculated from the ratio I(Te2+)/I(Te+):

y ) p(Te)/{p(Te) + 2p(Te2)} ) {1 + 21/2DI(Te2+)/ I(Te+)}-1 (10) where D is given by eq 3.

The necessary auxiliary thermal functions employed are listed in Table 3 and were taken from Mills23 for MnTe(s), and from JANAF24 for Mn(g).

Upon heating a freshly loaded sample, the I(Te2+) at T < 750 K over both samples yielded p(Te2) which corresponded to (MnTe + MnTe2),17 and the I(Te+)/I(Te2+) was as low as ≈0.04. As the temperature was increased to 750 K e T e 800 K, the sample entered into the MnTe single-phase region from the (MnTe + MnTe2) two-phase region. Further increase in temperatures to 1194 K e T e 1208 K in steps ranging from 50 to 100 K resulted in a continuous increase of I(Te+)/I(Te2+) and I(Mn+)/I(Te+) ratios. Finally both of these ratios reached a value of ≈5 and remained invariant with time. The ionization efficiency curves for the ions Te+, Te2+, and Mn+ showed that they were generated by the simple ionization of their neutral precursors Te(g), Te2(g), and Mn(g), respectively. The invariant intensity ratios yielded R′c ≈ 1 and x ≈ 0.5 on application of eq 1, y ≈ 0.7 on application of eq 10, and Rv ≈ 0.6 on application of eq 4. These values were ascribed to the congruent effusion of R-MnTe(s). Results given henceforth are those obtained on samples having exhibited congruent effusion behavior, at least once, previously. Tables 1S, 2S, and 3S (Supporting Information) give results from some selected runs in series 1, 2, and 3, respectively. These tables essentially show how the ion intensities, Rc′s, Rvs, and the total vapor pressures varied with time when the congruently effusing sample was heated or cooled across T ) 1228 K, the temperature of the R T β phase transition.11 In brief, the general features of the results fell into three types: type 1, representing the results during the heating cycle which involved the phase transformation of R-MnTe(s) to β-MnTe(s); type 2, representing the results during the cooling cycle which involved the phase transformation of β to R; and type 3, representing the results during the cooling cycle which did not involve any phase transformation. Figure 1 shows an example of how the ion intensities varied with time in each type: Figure 1a (type 1), Figure 1b (type 2), and Figure 1c (type 3). Figure 2 shows the variation in terms of Rvs, the Mn-to-Te atomic fraction ratios in vapor. The expanded insets in Figure 2 are from around the region involving the phase transformation of β to R. Figure 3 shows the results of a run conducted to examine the effects of temperature changes as small as 5 K (from 1198 to 1278 K) on the vapor compositions. Figure 4 contains the results of the same run but exclusively those from the last five sets of data at each temperature where the condensed-phase compositions corresponded to invariant CECs. Figures 5 and 6 show results from different runs in series 3 in which the phase transitions in MnTe(s) were effected between preselected temperatures, once in increasing and once in decreasing temperature directions. Figure 5 serves to show the vaporization behavior during and after phase transitions at 1243



Figure 1. Measurements of ion intensities of Mn+, Te+, and Te2+ with time in run 6 (beginning on Jan 7, 1997) of series 2: (a) congruent effusion at T ) 1218 K before T was increased to 1238 K; (b) congruent effusion at 1238 K before T was decreased to 1218 K; (c) congruent effusion at 1218 K before T was decreased to 1198 K.

Figure 2. Mn-to-Te atomic fraction ratios in vapor with time at different temperatures in run 6 of series 2. The insets focus on the results pertinent to the changes in T from 1238 to 1218 K and from 1258 to 1198 K.

(R to β) and 1203 K (β to R). Figure 6 shows the results of the only run which covered all three solid-state phase transitions: Ttr,R-β ) 1228 ( 10 K, Ttr,β-γ ) 1293 ( 10 K, and Ttr,γ-δ ) 1323 ( 10 K.11 The insets in Figures 5 and 6 show a 200 min long stable value of Rv ) 0.48 at 1203 K. Table 4 gives the mean values of p(Mn), p(Te), and p(Te2) from the final few sets at different temperatures where unambiguous proof for congruent effusion was obtained. These results were from different runs of all series, including those which did not involve phase transitions in solid MnTe. Table 4 also lists the values of R′c, y, and the third-law ∆rH°m(298.15K) values for reactions 7-9. The mean third-law

enthalpy for each reaction is also given in Table 4. The uncertainties are the standard deviations. The equilibrium constants which yielded the third-law values listed in Table 4 were least-squares-fitted, and the following relations were obtained:

log K7° ) -(28403 ( 757)/(T/K) + (11.802 ( 0.615) (11) log K8° ) -(22295 ( 488)/(T/K) + (8.752 ( 0.396) (12) log K9° ) -(28865 ( 515)/(T/K) + (11.440 ( 0.418) (13) Together with the necessary auxiliary thermal functions, these



Figure 3. Mn-to-Te atomic fraction ratios in vapor with time at different temperatures in run 14 (beginning on Jan 20, 1997) of series 2. The inset focuses on the results pertinent to the change in T from 1243 to 1208 K.

Figure 4. Mn-to-Te atomic fraction ratios in condensed phase (Rc′) and in vapor (Rv) during “congruent effusion” at different temperatures in run 14 of series 2.

relations yielded the second-law enthalpies at 298.15 K as 560.6 ( 14.4 kJ mol-1 (for reaction 7 and with y ) 0.7), 443.7 ( 9.3 kJ mol-1 (reaction 8), and 569.4 ( 9.9 kJ mol-1 (reaction 9). The uncertainties are the standard deviations deduced from those in the second-law slopes. A linear least-squares-fit of total vapor pressures, P, was done which yielded the equation:

log(P/Pa) ) - (14539 ( 273)/(T/K) + (11.159 ( 0.222) (14) We also deduced the enthalpy of formation of MnTe(s) at 298.15 K from the mean third-law enthalpies for reactions 7-9: -(99.5 ( 6.2) kJ mol-1 (from reaction 7 and y ) 0.70), -(98.7 ( 4.8) kJ mol-1 (from reaction 8), and -(99.6 ( 4.8) kJ mol-1 (from reaction 9). The values of enthalpy of formation at 298.15 K of Mn(g) (283.3 ( 4.2 kJ mol-1),24 of Te2(g) (163.2 ( 0.5 kJ mol-1),21 and of Te(g) (209.5 ( 0.7 kJ mol-1)21 were employed for this purpose. Discussion We termed R′c as “apparent congruently effusing composition” because except during congruent effusion its value would never represent the true Mn-to-Te ratio in the condensed phase.

For a convenient discussion of the results, we will henceforth denote the properties corresponding to congruently effusing compositions with a subscript CEC. The R′c,CEC values (given in Table 4) at different temperatures, obtained in various runs, were all close to 1, apparently in agreement with the experimental verification of Wiedemeier and Sadeek13 that stoichiometric MnTe vaporizes congruently. On the other hand, an examination of how following a temperature change from T1 to T2, the R′c and Rv values first moved away from and later moved back to R′c,CEC, and Rv,CEC values indicated a small but a definite variation of the CECs with temperature. With reference to R′c,CEC (≈1) and Rv,CEC, (≈0.6), the R′c and Rv values were for varying durations relatively higher when T2 > T1 and lower when T2 < T1. The initial increase in Rv and eventual return to Rv,CEC for every increase in T, even as small as 5 K, are evident from Figure 3. Consistent observations of a similar nature in a number of runs led us to infer that the CEC of solid manganese monotelluride changes with temperature toward higher tellurium content, up to at least 1268 K. We believe that the magnitude of this change must be very small because it was not obvious solely from the R′c,CEC values at different temperatures. Also the uncertainties associated with our R′c,CEC computations (( 0.05) would not permit a meaningful estimation of changes in the CECs smaller than 0.5 at. % Te. It is truly remarkable that van den Boomgaard12 identified the shift in the CVCs with temperature to tellurium-rich compositions on the basis of relatively simple sublimation experiments. We have insufficient information from the present study to refute or confirm his inference that the CVC shift is stronger between 1323 and 1453 K than between room temperature and 1323 K. A close examination of the vaporphase Mn-to-Te ratios shown in Figure 6 led us to believe that the CEC at 1343 K might be only very slightly Te-rich relative to the CEC at 1305 K. By applying Gibbs phase rule, we could distinguish the changes in Rvs due to condensed-phase transitions in solid manganese monotelluride from those due to a monotonic variation in the CECs with temperature. Results shown in Figure 2 demonstrate this aspect in the case of two temperature



Figure 5. Mn-to-Te atomic fraction ratios in vapor with time in run 5 (beginning on Apr 2, 1997) of series 3. The inset focuses on the results pertinent to the change in T from 1243 to 1203 K.

Figure 6. Mn-to-Te atomic fraction ratios in vapor with time in run 6 (beginning on Apr 7, 1997) of series 3. The inset focuses on the results pertinent to the change in T from 1268 to 1203 K.

changes of equal magnitude, first from 1238 to 1218 K and subsequently from 1218 to 1198 K. Each temperature change triggered an immediate decrease in Rv from Rv,CEC (≈0.6); however, in the latter case (1218 to 1198 K), the recovery to stable Rv,CEC values (≈0.6 again) started immediately through a monotonic increase in Rv, whereas in the former case (1238 to 1218 K), the Rv remained stable at a low value of ≈0.5 for about 80 min before increasing monotonically to a stable value of ≈0.6. In both cases, the initial decrease in Rv due to a 20 K decrease in temperature indicated a Te-enrichment in the vapor, and the monotonic increase in Rv to stable Rv,CEC indicated adjustment of the condensed phase at the new temperature to the CEC that is relatively Mn-rich. The 80 min stability period

corresponding to the low Rv (≈0.5) in the case of the former was taken to indicate the period during which a condensedphase transition was taking place. Among the three phase transitions reported to occur in solid Mn-Te,11 we focused our attention mainly on the R T β phase transition at 1228 ( 10 K. The three-phase equilibrium involving the transformation of high-temperature phase β to lowtemperature phase R was consistently discernible whenever the temperature was decreased from T1 > 1228 K to T2 < 1208 K, provided congruent effusion was ensured at T1 . While the Rv,CEC at T1 and Rv,CEC at T2 themselves were barely distinguishable, the difference between the Rv during phase transformation at T2 (three-phase equilibrium) and the Rv,CECs at T1 or T2 was



TABLE 4: Results from Series 1 to 4, Exclusively for Congruent Effusion of MnTe(s) third-law ∆rH°m(298.15K)/(kJ mol-1) T (K)

p(Mn)/Pa

p(Te)/Pa

p(Te2)/Pa

reaction 7

reaction 8

reaction 9

R′c

y

464.0 469.6 464.7 467.7 469.0

593.4 599.1 592.6 596.5 597.4

0.99 0.99 1.05 0.91 0.95

0.71 0.72 0.73 0.71 0.74

1194 1265 1242 1265 1265

3.7 × 10-2 1.4 × 10-1 1.2 × 10-1 1.5 × 10-1 1.5 × 10-1

4.3 × 10-2 1.7 × 10-1 1.4 × 10-1 2.0 × 10-1 1.9 × 10-1

9.1 × 10-3 3.3 × 10-2 2.5 × 10-2 4.0 × 10-2 3.4 × 10-2

Series 1 555.2 562.9 558.6 559.7 563.9

1258 1238 1258 1238 1218 1218 1198 1218 1238 1218 1198 1258 1198 1278 1278 1278 1218 1228 1228 1218 1218 1218 1228 1198 1203 1208 1213 1218 1223 1228 1233 1238 1243 1248 1253 1258 1263 1268 1273 1278 1243 1208 1213 1208 1198 1198 1203 1203 1203

2.0 × 10-1 1.3 × 10-1 2.1 × 10-1 1.3 × 10-1 7.7 × 10-2 7.8 × 10-2 4.8 × 10-2 7.4 × 10-2 1.1 × 10-1 7.0 × 10-2 4.2 × 10-2 1.6 × 10-1 4.5 × 10-2 2.7 × 10-1 2.6 × 10-1 2.5 × 10-1 6.7 × 10-2 8.6 × 10-2 8.4 × 10-2 7.2 × 10-2 6.8 × 10-2 6.4 × 10-2 8.3 × 10-2 4.3 × 10-2 4.8 × 10-2 5.5 × 10-2 5.9 × 10-2 7.2 × 10-2 8.4 × 10-2 8.2 × 10-2 9.2 × 10-2 1.0 × 10-1 1.1 × 10-1 1.2 × 10-1 1.4 × 10-1 1.5 × 10-1 1.7 × 10-1 1.9 × 10-1 2.1 × 10-1 2.2 × 10-1 1.0 × 10-1 5.1 × 10-2 5.6 × 10-2 5.0 × 10-2 3.9 × 10-2 4.0 × 10-2 4.4 × 10-2 4.0 × 10-2 4.3 × 10-2

2.2 × 10-1 1.5 × 10-1 2.3 × 10-1 1.5 × 10-1 9.2 × 10-2 8.5 × 10-2 5.6 × 10-2 8.0 × 10-2 1.3 × 10-1 8.0 × 10-2 5.0 × 10-2 1.8 × 10-1 5.1 × 10-2 2.8 × 10-1 2.8 × 10-1 2.7 × 10-1 7.5 × 10-2 9.3 × 10-2 9.3 × 10-2 7.8 × 10-2 7.5 × 10-2 7.4 × 10-2 9.1 × 10-2 5.0 × 10-2 5.5 × 10-2 6.1 × 10-2 6.7 × 10-2 7.7 × 10-2 8.8 × 10-2 9.3 × 10-2 1.0 × 10-1 1.1 × 10-1 1.3 × 10-1 1.4 × 10-1 1.6 × 10-1 1.7 × 10-1 1.9 × 10-1 2.1 × 10-1 2.4 × 10-1 2.6 × 10-1 1.2 × 10-1 5.8 × 10-2 6.4 × 10-2 5.6 × 10-2 4.6 × 10-2 4.4 × 10-2 5.0 × 10-2 5.0 × 10-2 4.9 × 10-2

5.7 × 10-2 3.8 × 10-2 5.7 × 10-2 3.7 × 10-2 2.2 × 10-2 1.9 × 10-2 1.3 × 10-2 1.7 × 10-2 2.7 × 10-2 1.6 × 10-2 9.9 × 10-3 4.0 × 10-2 9.2 × 10-3 6.1 × 10-2 6.1 × 10-2 5.9 × 10-2 1.5 × 10-2 1.8 × 10-2 1.9 × 10-2 1.5 × 10-2 1.4 × 10-2 1.4 × 10-2 1.7 × 10-2 9.2 × 10-3 1.0 × 10-2 1.1 × 10-2 1.2 × 10-2 1.5 × 10-2 1.7 × 10-2 1.8 × 10-2 2.1 × 10-2 2.3 × 10-2 2.6 × 10-2 2.8 × 10-2 3.1 × 10-2 3.5 × 10-2 3.9 × 10-2 4.5 × 10-2 5.0 × 10-2 5.6 × 10-2 2.4 × 10-2 1.1 × 10-2 1.2 × 10-2 1.1 × 10-2 8.3 × 10-3 7.6 × 10-3 8.7 × 10-3 8.9 × 10-3 8.4 × 10-3

Series 2 545.0 544.4 545.8 546.1 548.7 551.4 550.0 552.9 553.1 554.9 556.0 554.4 557.5 554.0 554.1 554.7 557.5 558.1 556.8 556.5 557.5 559.3 558.3 557.6 558.0 557.9 559.2 556.9 555.7 557.6 557.0 557.6 557.6 558.1 557.8 558.1 557.5 557.0 556.9 556.8 558.7 559.3 559.5 559.4 559.9 561.5 561.2 561.7 562.0

460.4 459.9 460.1 460.1 461.0 461.7 461.1 462.6 463.4 463.4 463.6 464.6 463.3 464.1 464.6 464.9 464.5 464.7 464.6 463.6 464.4 465.2 465.0 463.8 464.1 464.0 464.8 463.7 463.1 464.9 464.9 465.4 465.4 465.9 466.0 466.1 466.0 466.0 466.2 466.6 466.5 465.1 465.4 465.4 465.3 465.5 465.6 466.5 466.1

589.5 589.1 588.7 588.8 589.8 590.4 590.1 591.6 592.3 592.2 592.4 593.6 591.7 592.8 593.5 594.0 593.3 593.3 593.5 592.2 593.2 593.8 593.8 592.3 592.7 592.5 593.3 592.3 591.7 593.7 593.7 594.4 594.3 594.8 595.0 595.0 595.0 595.1 595.2 595.9 595.7 593.9 594.2 594.4 594.1 594.2 594.4 595.4 594.9

1.05 1.00 1.05 1.01 0.96 1.07 0.99 1.09 1.03 1.04 1.00 1.05 1.08 1.11 1.06 1.09 1.06 1.11 1.07 1.10 1.09 1.05 1.10 1.05 1.05 1.09 1.07 1.12 1.15 1.05 1.06 1.05 1.04 1.02 1.03 1.04 1.04 1.04 1.03 1.01 1.03 1.07 1.05 1.06 1.04 1.10 1.09 0.97 1.08

0.66 0.65 0.67 0.67 0.68 0.70 0.69 0.70 0.70 0.71 0.72 0.70 0.73 0.70 0.69 0.70 0.72 0.73 0.72 0.72 0.72 0.73 0.72 0.73 0.73 0.73 0.74 0.73 0.72 0.72 0.72 0.71 0.72 0.72 0.71 0.71 0.71 0.71 0.70 0.70 0.71 0.73 0.73 0.73 0.73 0.75 0.74 0.74 0.75

1240 1203 1203 1240 1240 1203 1243 1278 1243 1203 1203 1268 1305 1343

1.4 × 10-1 5.4 × 10-2 6.1 × 10-2 1.3 × 10-1 1.4 × 10-1 6.1 × 10-2 1.4 × 10-1 2.8 × 10-1 1.4 × 10-1 5.8 × 10-2 6.0 × 10-2 2.2 × 10-1 4.8 × 10-1 9.0 × 10-1

1.6 × 10-1 6.3 × 10-2 6.8 × 10-2 1.5 × 10-1 1.5 × 10-1 6.8 × 10-2 1.5 × 10-1 3.1 × 10-1 1.5 × 10-1 6.6 × 10-2 6.7 × 10-2 2.6 × 10-1 5.3 × 10-1 1.0

4.0 × 10-2 1.4 × 10-2 1.6 × 10-2 3.6 × 10-2 3.6 × 10-2 1.6 × 10-2 3.7 × 10-2 7.8 × 10-2 3.4 × 10-2 1.4 × 10-2 1.5 × 10-2 6.4 × 10-2 1.3 × 10-1 2.6 × 10-1

Series 3 544.7 551.5 547.5 546.9 547.5 546.8 548.0 548.1 550.1 550.0 548.8 548.4 548.8 550.3

459.7 461.5 459.4 460.7 460.6 459.4 461.4 462.3 461.8 460.4 459.9 462.5 463.1 465.3

588.5 590.1 588.0 589.8 589.4 588.1 590.5 591.4 590.6 588.9 588.4 591.5 592.0 594.4

1.00 1.00 1.03 1.04 1.04 1.02 1.04 1.03 1.05 1.03 1.03 0.96 1.01 0.99

0.66 0.70 0.69 0.67 0.68 0.68 0.67 0.67 0.69 0.70 0.69 0.67 0.66 0.66



TABLE 4 (Continued) third-law ∆rH°m(298.15K)/(kJ mol-1) T (K)

p(Mn)/Pa

p(Te)/Pa

p(Te2)/Pa

reaction 7

1305 1268 1203

4.8 × 10-1 2.3 × 10-1 5.6 × 10-2

5.4 × 10-1 2.6 × 10-1 6.2 × 10-2

1.4 × 10-1 6.3 × 10-2 1.3 × 10-2

548.7 548.7 551.1

1203 1208 1213 1213 1218 1223 1228 1233 1238 1243 1253 1258 1263 1258 1203 1208 1208 1258 1208 1218 1218 1223 1203 1203 1203 1243

5.5 × 10-2 6.1 × 10-2 6.2 × 10-2 7.0 × 10-2 7.9 × 10-2 8.6 × 10-2 9.2 × 10-2 1.0 × 10-1 1.1 × 10-1 1.2 × 10-1 1.5 × 10-1 1.7 × 10-1 1.9 × 10-1 1.7 × 10-1 4.9 × 10-2 5.5 × 10-2 5.6 × 10-2 1.7 × 10-1 5.7 × 10-2 7.1 × 10-2 7.0 × 10-2 8.0 × 10-2 4.9 × 10-2 3.4 × 10-2 4.6 × 10-2 1.1 × 10-1

6.5 × 10-2 6.9 × 10-2 7.7 × 10-2 8.3 × 10-2 9.2 × 10-2 9.8 × 10-2 1.1 × 10-1 1.2 × 10-1 1.3 × 10-1 1.4 × 10-1 1.8 × 10-1 2.0 × 10-1 2.2 × 10-1 2.0 × 10-1 5.9 × 10-2 6.5 × 10-2 6.7 × 10-2 2.0 × 10-1 6.9 × 10-2 8.1 × 10-2 8.0 × 10-2 9.1 × 10-2 5.9 × 10-2 4.0 × 10-2 5.5 × 10-2 1.3 × 10-1

1.4 × 10-2 1.5 × 10-2 1.8 × 10-2 1.9 × 10-2 2.0 × 10-2 2.1 × 10-2 2.5 × 10-2 2.7 × 10-2 3.0 × 10-2 3.3 × 10-2 4.2 × 10-2 4.6 × 10-2 5.1 × 10-2 4.7 × 10-2 1.2 × 10-2 1.3 × 10-2 1.5 × 10-2 4.6 × 10-2 1.4 × 10-2 1.7 × 10-2 1.7 × 10-2 1.9 × 10-2 1.2 × 10-2 8.4 × 10-3 1.2 × 10-2 2.9 × 10-2

mean

reaction 8

reaction 9

R′c

y

Series 3 462.9 462.3 461.1

591.6 591.2 589.8

1.01 0.99 1.07

0.67 0.67 0.70

551.4 551.2 550.9 549.5 550.4 551.4 550.7 551.0 551.4 551.0 550.9 551.4 551.5 551.1 554.2 554.8 552.1 551.3 554.0 554.0 553.6 553.2 553.9 560.4 553.8 554.1

461.2 461.5 462.4 460.9 461.1 461.8 462.2 462.5 462.8 463.2 463.4 463.6 463.5 463.2 463.0 463.2 462.5 463.3 462.5 463.2 463.2 463.0 463.0 468.4 463.7 465.4

589.6 590.3 591.4 589.4 589.6 590.4 590.9 591.4 591.7 592.5 592.6 592.7 592.4 592.0 591.8 591.8 591.5 592.3 591.0 592.0 592.2 591.9 591.8 599.3 593.1 595.2

1.00 1.03 0.94 0.97 1.00 1.03 0.96 0.98 1.00 1.01 0.96 0.98 0.98 0.99 0.98 1.00 0.99 1.00 0.99 1.03 1.02 1.03 0.98 1.00 0.96 0.96

0.70 0.70 0.69 0.69 0.70 0.70 0.69 0.69 0.69 0.68 0.68 0.68 0.68 0.68 0.71 0.71 0.70 0.68 0.71 0.70 0.70 0.70 0.71 0.70 0.70 0.68

554.0 ( 4.6

463.6 ( 2.1

592.4 ( 2.3

1.03 ( 0.04

0.70 ( 0.02

Series 4

unambiguously large. Figure 5 shows that the Mn-to-Te ratio in the vapor phase during phase transformation at 1203 K was ≈0.48, whereas the value during congruent effusion at 1243 or 1203 K is between 0.62 and 0.65. Evidence for similar effects was shown in Figure 2 (between 1238 and 1218 K and between 1258 and 1198 K), in Figure 3 (between 1243 and 1208 K), and in Figure 6 (between 1268 and 1203 K). In conformity with the theory of Edwards and Franzen,9 the difference between the Rv during the two-phase equilibrium (CEC of β + vapor) and the Rv during the three-phase equilibrium (β + R + vapor) increased as the difference between T1 and T2 increased. Figure 1b of this work may be compared with Figure 1 of Roberts and Searcy,6 to examine the features associated with condensed-phase transformations (in decreasing temperature direction) in MnTe(s) and Ga2S3(s), respectively. In the case of MnTe(s), the CEC of the low-temperature phase is Mn-rich relative to that of the high-temperature phase, and in the case of Ga2S3(s), the CEC of the low-temperature phase is S-rich relative to that of the high-temperature phase. Qualitatively, the features for Te2+ and Te+ were similar to that for Ga2S+; and the features for Mn+ were similar to those for S2+. The striking difference, however, was that Roberts and Searcy6 observed a 50% increase in the intensity of Ga2S+ at 1203 K (during phase transition) over that at 1230 K (during congruent effusion), whereas we never obtained tellurium intensities that were higher at lower temperatures than at higher temperatures. Another difference was the sharp increases in the p(Ga2S)/p(S2) ratios during the phase transition in the Ga2S3 system: a factor of 6 (ref 6; 1203 K) to 11 (ref 7; 1180 K). Converting these pressure ratios to Ga-to-S atomic fraction ratios in vapor reveal that during phase transformation in Ga2S3(s), the latter would

only be a factor of 2 higher than that during congruent effusion. As shown above, an increase of similar magnitude (in the Teto-Mn atomic fraction ratio) was observed in the present study also. We surmise that it is because of the existence of gallium in vapor as Ga2S(g) instead of as Ga(g) that the partial pressure of Ga2S(g) had to increase anomalously during phase transition (to lose gallium and reach the CEC that is S-rich). In the case of MnTe(s), because of the existence of tellurium in vapor as Te(g) and Te2(g), the tellurium partial pressures did not have to increase a lot (to lose tellurium and reach the CEC that is Mn-rich). The three-phase equilibrium involving the phase transition from the R-phase to the β-phase (T2 > T1) could not be identified with certainty. The possible reasons are as follows: the smaller width of the (R + β) two-phase region and the higher rate of vaporization at T2 than at T1. Even in the study of Ga2S3 5 and Ga2Se3 25 by Edwards and co-workers, the three-phase equilibria during the phase transitions were convincingly identified only in the decreasing temperature direction. In the increasing temperature direction, the total vapor pressures shown in refs 5 and 25 were never invariant for long enough to be associated to the three-phase equilibria. As mentioned already, only one run was conducted to probe the vaporization behavior associated with the β T γ and γ T δ transitions reported11 to occur at 1293 ( 10 K and 1323 ( 10 K, respectively. Because of a rather small temperature range of stability for the γ-phase, interpretation of the results associated with the β T γ and γ T δ transitions would be subject to larger errors than that associated with the R T β transition. If the stable Rv values shown in Figure 6 at 1268, 1305, and 1343 K were taken to correspond to the CECs of the β, γ, and δ modifications of solid MnTe, then it could be inferred that the

10594 J. Phys. Chem. B, Vol. 102, No. 51, 1998 CEC of the γ-phase is slightly Mn-rich relative to the CEC of the β-phase and that the CEC of the δ-phase is slightly Te-rich relative to the CEC of the γ-phase. We realize, however, that the CEC values deducible from the R′c,CEC values were not precise enough to support the above interpretation quantitatively. For instance, the CECs of the four phases deduced from the R′c,CEC values listed in Table 4 are 49.2 ( 1.1 at. % Te (RMnTe, 1194-1223 K, mean of 48 data); 49.5 ( 1.1 at. % Te (β-MnTe, 1228-1278 K, mean of 46 data); 49.7 ( 0.1 at. % Te (γ-MnTe, 1305 K, mean of 2 data); 50.3 at. % Te (δ-MnTe, 1343 K, 1 datum). In the temperature range of the present study, the above CEC values are within the homogeneity range of solid MnTe and far outside the range of existence of the liquid phase.11 Thus, whether or not the samples melted at some time during our experiments is not clear. It might be that adhesion of the sample to the crucible was caused by diffusional effects. In a separate preliminary experiment, we observed that a freshly loaded sample (49.6 at. % Te) after being heated to 1204 K yielded a residue that could be easily removed from the crucible by gentle tappings, whereas the same aliquot after being heated at 1242 K left a residue that remained tightly stuck to the bottom and could not be taken out. A little of the latter residue was scratched out for X-ray diffraction analysis, which showed only the lines due to the MnTe phase. Tables 1S-3S show that, unlike in Rvs, there was no significant difference between the vapor pressures during β-to-R transformation and the vapor pressures during congruent effusion of R-MnTe. Obviously, a condensed-phase transformation did not produce noticeable effect on the total vapor pressures in the Mn-Te system unlike in Ga-S5 or Ga-Se25 systems. In the latter systems, the vapor pressures during the transformation of the high-temperature phase into the low-temperature phase were by a factor of 2-3 times higher than the vapor pressures during congruent effusion of the low-temperature phase. We deduced only a single P-T relation (eq 14) instead of a separate relation each for the congruent effusion of R-, β-, γ-, and δ-phases of MnTe(s), based on the following facts: insignificant differences in the CECs and in the degree of dissociation of Te2(g), small temperature ranges of measurements for each phase, and no noticeable trend in third-law values for reactions 7-9 (see Table 4). The total vapor pressure as computed from eq 14 at T ) 1250 K is 0.34 Pa. At this temperature, the total vapor pressure measured by Wiedemeier and Sadeek13 and calculated by van den Boomgaard12 both is 0.17 Pa, a factor of 2 smaller. The discrepancy between our value and van den Boomgaard’s value is not real because the latter was deduced by assuming eq 8 as the congruent vaporization reaction, i.e., by taking the mole fractions of Mn(g) and Te2(g) as 2/3 and 1/3, respectively. Our recalculation using the same equilibrium constant, but with the mole fractions of Mn(g) (0.4132), Te(g) (0.4832), and Te2(g) (0.1036), yields a total pressure value of 0.34 Pa, in excellent agreement with our value. The mole fractions given in the parentheses were deduced for reaction 7 with ymean ) 0.7. A factor of 2 disagreement between our value and Wiedemeier and Sadeek’s value is hard to explain, especially when our pressure calibration was based on a value of dissociation enthalpy of Te2(g) which is nearly the same as that used by Wiedemeier and Sadeek. One fact which is apparent is that much of the data in the present study were from 1194 to 1280 K, whereas those in Wiedemeier and Sadeek’s study were from 1300 and 1435 K. That the relatively higher vapor pressures in the present study were not caused by large errors in the factors

Lakshmi Narasimhan et al. such as σ and γ was ascertained by calculating the mole fractions x(i) from the relation

x(i) ) I(i+)[σ(i) γ(i+) n(i+)]-1/

∑{I(i+)[σ(i) γ(i+) n(i+)]-1}

(15)

where i ) Mn(g), Te(g), and Te2(g). The values were in accord with those deducible for congruent effusion of stoichiometric MnTe (reaction 7 and y ) 0.7). Although there is fair agreement between the second- and the third-law enthalpy values for reactions 7-9, we recommend the mean third-law enthalpies because the latter will be relatively less affected than the second-law values when the results from different runs in different series were pooled together for evaluation. Furthermore, variations in the CECs with temperature of the MnTe phase (however small they might be) may not affect the third-law values. Reaction 7 does not have a unique balancing number for y, the value of which will be different for a congruent effusion (0.700) and for a congruent vaporization reaction (0.767). Thus, expressing a chemical change by means of reaction 7 may be misleading. On the other hand, expressing chemical changes in terms of the two simultaneous vaporization reactions 8 and 9 that occur (during congruent effusion or congruent vaporization) are more correct, and so are the corresponding equilibrium constants. Therefore, we recommend the mean value of enthalpy of formation of MnTe(s), -(99.2 ( 6.8 kJ mol-1), deduced from the enthalpies of these two reactions. This value is about 5 kJ mol-1 less and 12 kJ mol-1 greater than the calorimetric values obtained by Fabre26 and Morazova and Stolyarova,27 respectively. Acknowledgment. We thank Dr. G. Periaswami, Head, Materials Chemistry Division, for his encouragement during this study. We also thank the X-ray group for their help in the characterization of the samples and the electronics group for the maintenance of the mass spectrometer. Supporting Information Available: Tables 1S-3S, list the ion intensites, Mn-to-Te atomic fraction ratios in the condensed phase and in the vapor phase, the degree of dissociation of Te2(g), and the total vapor pressures as a fuction of time at different temperatures (6 pages). See any current masthead page for ordering information. References and Notes (1) Gilles, P. W. In Application of Fundamental Thermodynamics to Metallurgical Processes (Proceedings of the first conference on the thermodynamic properties of materials); Fitterer, G. R., Ed.; Gordon & Breach Science Publishers: New York, 1967; p 281. (2) Gilles, P. W. In The Characterization of High-Temperature Vapors; Margrave, J. L., Ed.; John Wiley & Sons: New York, 1967; Chapter 2. (3) Cater, E. D.; Mueller, B. H.; Fries, J. A. In Characterization of High-Temperature Vapors and Gases; Hastie, J. W., Ed.; NBS Special Publication 561; National Bureau of Standards: Washington, D.C.; 1979; p 237. (4) Myers, C. E.; Kematick, R. J. J. Electrochem. Soc. 1987, 134, 720. (5) Edwards, J. G.; Uram, R. S. J. Phys. Chem. 1992, 96, 8561. (6) Roberts, J. A., Jr.; Searcy, A. W. Science 1977, 196, 525. (7) Edwards, J. G.; Mukdeeprom-Burckel, P.; Hilpert, K.; Kath, D. Thermochim. Acta 1997, 297, 177. (8) Edwards, J. G. High Temp. Sci. 1991, 32, 37. (9) Edwards, J. G.; Franzen, H. F. J. Phys. Chem. 1995, 99, 4779. (10) Sai Baba, M.; Lakshmi Narasimhan, T. S.; Balasubramanian, R.; Mathews, C. K. J. Nucl. Mater. 1993, 201, 147. (11) Vassiliev, V.; Bykov, M.; Gambino, M.; Bros, J. P. Z. Metallkd. 1993, 84, 461. (12) van den Boomgaard, J. Philips Res. Rep. 1969, 24, 284. (13) Wiedemeier, H.; Sadeek, H. High Temp. Sci. 1970, 2, 252.

Vaporization Studies on Mn-Te Samples (14) Viswanathan, R.; Darwin Albert Raj, D.; Lakshmi Narasimhan, T. S.; Balasubramanian, R.; Mathews, C. K. J. Chem. Thermodyn. 1993, 25, 533. (15) Sai Baba, M.; Viswanathan, R.; Mathews, C. K. Rapid Commun. Mass Spectrom. 1996, 10, 691. (16) Lakshmi Narasimhan, T. S.; Balasubramanian, R.; Nalini, S.; Sai Baba, M. J. Nucl. Mater. 1997, 247, 28. (17) Lakshmi Narasimhan, T. S.; Viswanathan, R.; Sai Baba, M.; Balasubramanian, R. Manuscript in preparation. (18) Mann, J. B. Recent Developments in Mass spectrometry. In Proceedings of the International Conference on Mass Spectrometry; Ogata, K., Hayakawa, T., Eds.; University of Tokyo Press: Tokyo, Japan, 1970; p 814. (19) Pottie, R. F.; Cocke. D. L.; Gingerich. K. A. Int. J. Mass Spectrom. Ion Phys. 1973, 11, 41. (20) Viswanathan, R.; Sai Baba, M.; Darwin Albert Raj, D.; Balasubramanian, R.; Lakshmi Narasimhan, T. S.; Mathews. C. K. Spectrochim. Acta 1994, 3, 243.

J. Phys. Chem. B, Vol. 102, No. 51, 1998 10595 (21) Gronvold, F.; Drowart, J.; Westrum, E. F., Jr. The Chemical Thermodynamics of Actinide Elements and Compounds. Part 4. The Actinide Chalcogenides (Excluding Oxides); International Atomic Energy Agency: Vienna, 1984. (22) Drowart, J. Mass Spectrometry. In Proceedings of the International School of Mass Spectrometry; Marsel, J., Ed.; Stefan Institute: Lubljana, 1971; p 187. (23) Mills, K. C. Thermodynamic Data for Inorganic Sulphides, Selenides and Tellurides; Butterworth: London, 1974. (24) Chase M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed. J. Phys. Chem. Ref. Data 1985, 14. Suppl. No. 1. (25) Viswanathan, R.; Edwards, J. G. J. Phys. Chem. B 1998, 102, 2419. (26) Fabre, A. Ann. Chim. Phys. 1887, 10, 472 (as given in ref 11). (27) Morozova, M. P.; Stolyarova, T. A. Vestn. Leningrad UniV. Ser. Fiz. i. khim. 1964, 19, 150.

Congruent Vaporization of Solid Manganese ... - ACS Publications

Recommend Documents