Defect structure model and transport properties of nonstoichiometric manganous sulphide

Solid State Ionics 117 (1999) 65–74

Defect structure model and transport properties of nonstoichiometric manganous sulphide a, a b S. Mrowec *, M. Danielewski , J. Gilewicz-Wolter a

University of Mining and Metallurgy, Department of Solid State Chemistry al. Mickiewicza 30, 30 -059 Cracow, Poland University of Mining and Metallurgy, Faculty of Nuclear Physics and Techniques, al. Mickiewicza 30, 30 -059 Cracow, Poland

b

Abstract Basing on electrical and nonstoichiometry data, defect structure model of Mn 16 y S sulphide has been developed. It has been shown, that depending on the temperature and sulfur activity this sulfide may be an electronic and ionic semiconductor. Self-diffusion of cations in metal-deficit Mn 12y S proceeds by simple vacancy, and in metal excess Mn 11y S by collinear interstitialcy diffusion mechanisms.  1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Self-diffusion; Manganous sulfide; Point defects; Radioactive tracer

1. Introduction Physicochemical properties of manganous sulphide have been extensively studied by different authors using various experimental techniques. In particular, nonstoichiometry [1,2] and electrical conductivity [3–6] was investigated as a function of temperature and sulfur activity over the whole homogeneity range of this compound. Further, the kinetics and mechanism of manganese sulphidation were the subject of detailed investigations [7–11] over the large temperature and sulfur pressure range. Finally, the rate of manganese evaporation into a vacuum from the surface of MnS-scale in equilibrium with the metallic phase has been studied as a function of temperature [12,13] using novel Kofstad’s method [14]. Basing on nonstoichiometry and electrical conductivity data, defect structure of Mn 16 y S has been discussed [2,13]. Sulphidation and

evaporation rate measurements, in turn, have been utilized in calculating the self-diffusion coefficients of Mn in Mn 16 y S over the phase field of this compound. It should be noted, however, that the results of these calculations have not been proved experimentally because the self-diffusion measurements in sulfides in equilibrium with sulfur vapour are much more difficult than in corresponding oxides [15]. In fact, the only sulphide in which the selfdiffusion rates of cations and anions have been studied systematically is the non-stoichiometric ferrous sulphide [16]. The aim of the present paper is an attempt to reconsider the defect structure and transport properties of Mn 16 y S and to proof experimentally the results of these calculations in studying the selfdiffusion coefficient of manganese in this sulphide using radioactive isotope of 54 Mn as a tracer. 2. Defect structure model

*Corresponding author. Tel.: 148-12-172467; fax: 148-12172493; e-mail: [email protected]

It has been shown that over the major part of the

0167-2738 / 99 / $ – see front matter  1999 Published by Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00249-5

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66

phase field, corresponding to higher sulfur activities, a-MnS, having rock-salt structure, is a metal deficit, p-type semiconductor with the predominant defects being doubly ionized cation vacancies and electron holes (Mn 12y S) [1,2]. At very low sulfur activities, on the other hand, near and at the MnuMnS phase boundary, this sulphide has been found to be a metal excess n-type semiconductor with doubly ionized interstitial cations and quasi-free electrons as predominant defects (Mn 11y S) [2,12,13]. In the intermediate part of the phase field, in turn, near and at the stoichiometric composition, the defect structure of manganous sulphide is more complex and strongly dependent on temperature. It has been shown, finally, that the anion sublattice in the discussed sulphide is virtually ordered, the concentration of anion vacancies and interstitial anions being negligibly small as compared to the degree of cation sublattice disorder [7]. As the nonstoichiometry and thereby defect concentration in manganous sulphide-even at very high temperatures ( . 1473 K)-is very low ( y , 10 22 ) their interactions may be neglected and consequently defect equilibria may be considered in terms ¨ of point defect thermodynamics [17,18], (KrogerVink [19] notation of defects is used throughout this paper):

?? KF 5 [V 99 Mn ][Mn i ]

? → V 99 1 / 2S 2 (g) ← Mn 1 2h 1 S S

(1)

Introducing this relationship into Eq. (5) yields:

→ Mn 1 2e 1 1 / 2S 2 (g) Mn Mn 1 S S ←

(2)

?? i

2

→ Mn 1 V Mn 99 Mn Mn ←

(3)

→ e2 1 h? zero9 ←

(4)

?? i

5 3.93 ? 10 210 exp

S

13.7 kJ mol 21 2 ]]]] RT

D

(7)

Ke 5 [h ? ][e 2 ] 5 4.02 ? 10 2 exp

S

281.4 kJ mol 21 2 ]]]]] RT

D

(8)

where KV , Ki , KF and Ke denote equilibrium constants of reactions Eq. (1) to Eq. (4), respectively. In thermodynamic equilibrium all defect concentrations are interrelated by the following electroneutrality condition: 2 ?? ? 2[V 99 Mn ] 1 [e ] 5 2[Mn i ] 1 [h ]

(9)

These five relationships are enough for the construction of defect diagrams of Mn 16 y S for any temperature. Before showing such selected diagrams, two limiting cases should be considered. 1. At higher sulphur pressures, when the sulphide is a metal deficit p-type semiconductor (Mn 12y S) cation vacancies and electron holes are the prevailing defects and the electroneutrality condition, Eq. (9), reduces to the following simplified form: 2[VMn ] 5 [h ? ] 4 [Mn i?? ] and [e 2 ]

(10)

1 99 g 5 ] [h ? ] f V Mn 2 5 6.99 ? 10 23 p 1S /26 exp

S

41.5kJ mol 21 2 ]]]] RT

D (11)

Applying the mass action law to these defect reactions and considering the available nonstoichiometry and electrical conductivity data the following quasi-empirical relationships have been obtained:

99 ][h ? ] 2 p S212 / 2 KV 5 [V Mn 5 4.3 ? 10 24 exp

S

124.4 kJ mol 21 2 ]]]]] RT

D

(5)

Ki 5 [Mn ??i ][e 2 ] 2 p S1 /22 5 0.146 exp

S

As can be seen, in this part of the phase field the concentration of defects increases with increasing sulphur activity and the enthalpy of defect formation is given by: D H Vf 5 124.4 kJ mol 21

At very low sulphur pressures, on the other hand, close to the dissociation pressure of the sulphide, interstitial cations and quasi-free electrons predominate (Mn 11y S) and the electroneutrality condition assumes the form: ??

21

452 kJ mol 2 ]]]] RT

D

(12)

2

?

2[Mn i ] 5 [e ] 4 [V 99 Mn ] and [h ] (6)

Introducing this condition into Eq. (6) yields:

(13)

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67

1 [Mn ??i ] 5 ] [e 2 ] 2 /6 5 2.27p 21 exp S2

S

151.0 kJ mol 21 2 ]]]]] RT

D

(14)

It follows from this relationship that in this-very narrow-part of the phase field, concentration of defects in metal excess manganous sulphide decreases with increasing sulphur activity and the enthalpy of defect formation is given by: DH if 5 452 kJ mol 21

(15)

2. In the transient pressure range, where the sulphide composition changes from metal deficit (Mn 12y S) to metal excess (Mn 11y S) the defect situations are strongly dependent on temperature because the enthalpy of Frenkel defect pair formation, Eq. (7), is considerably lower than that of intrinsic electronic disorder, Eq. (8). Consequently, at lower temperatures (T ,1000 K) intrinsic ionic disorder prevails, being independent of sulphur activity: | [V Mn | 1.97 ? 99 ] 5 [Mn ??i ] 5 10 25 exp

S

13.7 kJ mol 21 2 ]]]] 2RT

D

Fig. 2. Concentrations of ionic and electronic defects in Mn 16 y S as a function of sulfur activity for 973 K.

At higher temperatures (T .1100 K), on the other hand, intrinsic electronic defects predominate being again pressure independent:

(16) | [h ? ] 5 | 20.0 exp [e 2 ] 5

S

281.4 kJ mol 21 2 ]]]]] 2RT

D

(17)

It follows from these remarks that depending on temperature and equilibrium sulphur pressure the discussed sulphide may be an extrinsic p- or n-type semiconductor, as well as an intrinsic ionic or electronic semiconductor. All these defect situations are shown in Figs. 1 and 2.

3. Transport properties

Fig. 1. Concentrations of ionic and electronic defects in Mn 16 y S as a function of sulfur activity for 1573 K.

It is well known that self-diffusion measurements in sulphides in equilibrium with sulphur vapour are much more difficult than in corresponding oxides. Consequently, only scant and fragmentary information is available concerning this important problem. In fact, the only sulphide in which the self-diffusion rates of cations and anions have been studied as a function of temperature and sulphur activity is the nonstoichiometric ferrous sulphide [16]. However,

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68

self-diffusion coefficient of cations in metal deficient sulphides can be calculated from parabolic rate constant of metal sulphidation [20,21], and in some particular cases this coefficient may also be obtained for metal excess sulphides from evaporation rate measurements [14]. Both these procedures have been utilized in calculating the self-diffusion coefficient of cations in Mn 16 y S. As the maximum deviations from stoichiometry of Mn 16 y S is very low, it can be assumed that the mobility of point defects in this sulphide is independent of their concentration. This conclusion has been confirmed recently in chemical diffusion experiments [22]. Thus, the self-diffusion coefficient of Mn in Mn 16 y S, which is the product of defect diffusion coefficient and their mobility [17,18], should depend in the same way on sulphur activity as the concentration of defects. Consequently, in agreement with Eq. (11), at higher sulphur pressures the self-diffusion coefficient of manganese in metal-deficit Mn 12y S (DMn 5 D VMn ) should be the following function of temperature and sulphur pressure: o

1/6

99 ] 5 D V p S 2 exp DMnV 5 DV [V Mn

S D E VD 2] RT

(18)

where DV denotes the defect diffusion coefficient (diffusion coefficient of cation vacancies) which is only temperature dependent, and E VD -the activation energy of Mn self-diffusion, being the sum of enthalpy of cation vacancy formation and the activation enthalpy of their migration in Mn 12y S lattice: 1 E VD 5 ] DH Vf 1 DH Vm 3 At very low sulphur pressures, in turn, near the MnuMnS phase boundary self-diffusion coefficient of manganese in metal excess Mn 11y S(DMn 5D iMn ) should be described by the following relationship: ??

o

21 / 6

DMn i 5 Di [Mn i ] 5 D i p S 2

exp

S D E iD 2] RT

(20)

where Di denotes the interstitial diffusion coefficient, and E Di is again the activation energy of Mn selfdiffusion, being the sum of enthalpy of defect (cation interstitials) formation and the activation enthalpy of their migration in Mn 11y S lattice: 1 E iD 5 ] D H fi 1 DH im 3

(21)

Self diffusion coefficient of Mn in Mn 12y S has been calculated as a function of temperature and sulphur activity from parabolic rate constants of manganese sulphidation and in agreement with Eq. (18) the following empirical relationship was obtained [13]: DMnV 5 9.81 ? 10 25 p S1 2/ 6 exp

S

121.0 kJ mol 21 2 ]]]]] RT

D (22)

Self-diffusion coefficient of Mn in metal-excess manganous sulphide (Mn 11y S) could have been calculated only as a function of temperature from evaporation rate measurements [12] carried out in equilibrium of the sulphide with manganese metal. Assuming, however, that D iMn in Mn 11y S should decrease with increasing sulphur pressure in agreement with Eq. (20), the following quasi-theoretical relationship has been obtained [13]: DMn i 5 1.72p S212 / 6 exp

S

269 kJ mol 21 2 ]]]] RT

D

(23)

The overall self-diffusion coefficient of cations in Mn 16 y S, DMn , is at any sulphur pressure equal to the sum of self-diffusion coefficients, D VMn and D iMn , due to the presence of both types of point defects: ?? DMn 5 [V 99 Mn ]D V 1 [Mn i ]D i 5 D MnV 1 D Mn i

(24)

Thus, using Eq. (24) and considering quasi-empirical Eq. (22) and Eq. (23) a diagram of DMn vs equilibrium sulphur pressure has been constructed for several temperatures, Fig. 3. From the comparison of this diagram with those of defect structure of Mn 16 y S it follows clearly that the lowest diffusion rate of cations in the discussed sulphide is a result of the minimum concentration of point defects. This fact may be considered as an indirect proof of the correct way of the calculations. However, DMn -values have not been determined experimentally and the dependence of this coefficient on sulphur activity is purely theoretical. In particular, the dependence of DMn on pS2 in low pressure region, where interstitial cations and quasi-free electrons predominate, results only from theoretical assumption and not from calculated values DMn in Mn 11y S, because DMn in this pressure range has been calculated from Mnevaporation kinetics for one (lowest) sulphur pres-

S. Mrowec et al. / Solid State Ionics 117 (1999) 65 – 74

Fig. 3. Calculated dependence of manganese self-diffusion coefficient in manganous sulphide upon equilibrium sulfur pressure for several temperatures.

sure only, equal to the dissociation pressure of the sulphide [12,13]. Thus, not only the absolute values of manganese self-diffusion coefficients in Mn 16 y S but also its dependence on sulphur activity should be proved experimentally. That was one of the main targets of the present paper.

4. Tracer diffusion measurements The starting material (a-MnS) has been obtained by sulphidation of spectrally pure manganese (Johnson & Matthey Ltd) in an apparatus described elsewhere [23]. Rectangular manganese samples of dimensions 2.031.530.3 cm have been sulphidized completely at 1273 K in pure sulfur vapour at 10 2 Pa. Under these conditions a compact, coarse-grained a-MnS scales have been formed, with grain-size ranging from 400 up to 1800 mm. This material has been powdered and cold-pressed to get compact pellets of 2.0 cm in diameter and 0.2 cm thick. They were then annealed at 1273 K during 48 h in sulfur vapour atmosphere at 5?10 3 Pa in order to obtain dense, coarse-grained samples. The average grainsize of such well sintered, polycrystalline samples, with the density of 3.79 g cm 23 , was about 170 mm.

69

Subsequently, the samples were polished to get the surface flatness within 61 mm. Finally, all the samples were preannealed at the same temperature and sulfur pressure at which the following diffusion experiment was to be carried out. This was done in order to establish the required defect concentration throughout the sample from the very beginning of subsequent diffusional annealing. As the source of the radioactive manganese isotope, 54 Mn, a carrier free solution of 54 MnCl 2 in ethyl alcohol, was used. This isotope emits g-radiation with an energy of 0.83 MeV. The surface of the MnS-samples, prepared in the described way, have been coated with 54 MnCl 2 solution and dried under infra-red radiation. The obtained activity of the sample was about 0.4 MBq which corresponded to about 1 ng cm 22 of 54 Mn isotope. Such a mass per unit surface area fulfilled the conditions of thin layer geometry. The diffusion experiments were performed by annealing the samples within evacuated and sealed quartz ampules at several temperatures (1073–1373) K and sulfur pressures (10 211 –10 4 ) Pa, Fig. 4. Experimental procedure has been described elsewhere [24]. The source of the sulfur vapour in low pressure experiments constituted FeS 2 –FeS mixture, and in high pressure annealing it was liquid sulfur. After diffusional annealing the ampules were rapidly cooled and sample edges were cut to eliminate the possibility of additional radioactivity, originating from the sides of the specimen. The 54 Mn penetration curves were obtained by the serial-sectioning technique. The samples were mounted in a polyacryline resin together with three steel spheres having a well-known diameter (0.4988 cm) as illustrated in Fig. 5 [25]. The thin layers of the sulphide were then removed from the specimen surface by step-wise abrasion. The steel spheres were ground together with the specimen. To calculate the thickness of the removed sulphide layer the diame-

Fig. 4. Schematic drawing of the quartz ampule containing the sulfur and the specimen.

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70

As the concentration of the radioactive tracer is directly proportional to its specific activity,

U

≠I C 5 const ?] , ≠x t tracer diffusion coefficient may easily be calculated from the slope of such straight lines, Eq. (26), using the following relationship [27]: 1 DT 5 2 ] 4t Fig. 5. The sample mounting unit, where: 1-specimen; 2-abrasive disk; 3-steel spheres; 4-resin and 5-metal tube.

ters of the cross-section of the spheres were measured with the accuracy of 61 mm. The residual activity of a specimen was counted in a constant geometry following the removal of each section. The NaJ(Tl) crystal scintillation counter was used. The statistical error was less then 1%. The counting rates were corrected for background and counter dead time. In order to avoid the influence of probable instability of the apparatus the counts were standardized to the counting rate of 54 Mn standard source. The durations of diffusional annealing have been chosen in such a way that the thickness of the samples was always greater than the penetration depth of the tracer. This allows to consider the discussed system in terms of the approximation to semi-infinite solid. Thus, the solution of Fick’s second law gives the following simple equation [26]: C0 C 5 ]]] ]] exp 2œp DT t

S

x2 2 ]] 4DT t

D

≠x 2 ]]] ≠I ≠ ln ] ≠x

1

S

D2

,

(27)

t

where I is the counting rate. Figs. 5 and 6 illustrate some of the obtained penetration depth profiles for the diffusion of 54 Mn tracer in Mn 16 y S [25,28]. As can be seen, at all temperatures and sulfur pressures straight lines have been obtained enabling the selfdiffusion coefficients of manganese in metal excess and metal deficit manganous sulphide to be calculated from Eq. (27) Fig. 7. The results of these calculations are summarized in Table 1 and plotted as a function of temperature and sulfur pressure in Figs. 8 and 9. It follows clearly from these plots that in agreement with the defect model of Mn 16 y S the mechanism of Mn self-diffusion at very low sulfur

(25)

where C is the concentration of the tracer at a distance x from the sample surface; C0 -its concentration on the surface before diffusional annealing, and t-time of the annealing and DT the tracer diffusion coefficient. From the Eq. (25) one obtains the linear relationship between ln C and x 2 : C0 x2 ]] ln C 5 ln ]]] 2 , ]] 2œp DT t 4DT t

(26)

which is convenient for graphical interpretation.

Fig. 6. Penetration depth profile of 54 Mn tracer atoms in Mn 11y S after 936 h annealing in equilibrium with sulfur vapours.

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71

Fig. 7. Penetration depth profile of Mn tracer atoms in Mn 12y S after 8 h annealing in equilibrium with sulfur vapours.

Fig. 8. Pressure dependence of 54 Mn tracer diffusion coefficient in Mn 16 y S (double logarithmic plot).

pressures is different from that observed in a high pressure region. At low pressures, namely, the rate of self-diffusion decreases with increasing sulfur pressure, as predicted for metal excess Mn 11y S sulphide,

Eq. (20) and Eq. (23), and at higher pressures it increases, what is again in agreement with the defect structure model for metal deficit Mn 12y S, Eq. (18) and. In addition, the activation energy of Mn selfdiffusion in Mn 11y S is much higher than that in

54

Table 1 Diffusion coefficients of Mn in Mn 16 y S T (K)

pS2 (Pa)

DT (cm 2 s 21 )

DMn 5DT /f (cm 2 s 21 )

1253 1273 1123 1172 1210

10 211

(3.660.25)?10 210 (5.760.20)?10 210 (1.4260.06)?10 211 (5.560.20)?10 211 (1.1560.09)?10 210

f50.6666 (5.460.40)?10 210 (8.660.30)?10 210 (2.1360.09)?10 211 (8.260.30)?10 211 (1.760.10)?10 210

10 210

1073 1173 1273 1253 1323 1373

4.3?10 3

1273 1273 1253 1273

6.2?10 2 53 10

(2.2660.05)?10 210 (1.1960.05)?10 29 (7.560.05)?10 210 (2.760.10)?10 29 (2.2360.08)?10 29 (4.6160.08)?10 29 (7.5560.05)?10 29 (7.9760.05)?10 29 (1.8060.06)?10 29 (1.2160.05)?10 29 (1.160.10)?10 29 (8.760.60)?10 210

DMn (cm 2 s 21 ) (calculated) f50.970 (3.760.26)?10 210 (5.960.20)?10 210 (1.4660.06)?10 211 (5.760.20)?10 211 (1.1960.09)?10 210

f50.78158 (2.8960.07)?10 210 (1.5260.06)?10 29 (9.660.07)?10 210 (3.560.20)?10 29 (2.8560.10)?10 29 (5.9060.10)?10 29 (9.6660.06)?10 29 (1.0260.06)?10 28 (2.3060.08)?10 29 (1.5560.07)?10 29 (1.460.20)?10 29 (1.1160.08)?10 29

7.42?10 210 1.10?10 29 5.28?10 211 1.10?10 210 2.20?10 210 5.03?10 210 1.60?10 29 4.24?10 29 3.53?10 29 6.53?10 29 9.74?10 29 3.07?10 29 2.04?10 29 1.70?10 29 1.54?10 29

S. Mrowec et al. / Solid State Ionics 117 (1999) 65 – 74

72

ments, i.e., tracer diffusion coefficients, DT , must be recalculated into ‘real’ self-diffusion coefficients, DMn , by taking into account correlation effect [29– 31]. These two diffusion coefficients are interrelated by the correlation factor: DMn 5 DT /f

Fig. 9. Temperature dependence of the 54 Mn tracer diffusion coefficient in Mn 16 y S for two different sulfur pressures.

Mn 12y S, being in excellent agreement with the value calculated from evaporation kinetic measurements, Table 2. This energy in a high pressure region (Mn 12y S) is also in qualitative agreement with that calculated from manganese sulphidation kinetics, Table 2. Finally, the pressure dependence of the self-diffusion coefficient in metal-excess and metaldeficit manganous sulphide determined experimentally is in good agreement with that calculated from evaporation and sulphidation kinetics, Eq. (22) and Eq. (23). The question then arises, whether not only temperature and pressure dependence of self-diffusion rate but also absolute values of manganese selfdiffusion coefficient calculated from kinetic experiments are in agreement with those determined experimentally. In order to make such a comparison diffusion coefficients obtained from tracer experi-

(28)

where f denotes the correlation factor, which values depend on mechanisms of diffusion and crystal structure of a given solid. In the case under discussion the different correlation factors should be applied for vacancy and interstitialcy mechanisms of diffusion (a simple interstitial mechanism of diffusion consisting in successive jumps of interstitial cations from one interstitial position to another should a priori be excluded because of purely geometrical reasons [18]). In the first case of a vacancy mechanism, consisting of Mn 12 ions jumping from the lattice sites into neighbouring cation vacancies, the correlation factor for face centred cubic lattice of a-MnS assumes the value: f 50.7815 [32,33]. In the case of interstitialcy diffusion, the situation is more complex, because at least two different mechanisms of this process are possible. In both of them the elementary act of diffusion consists in displacement of a lattice atom by its interstitial neighbour into interstitial position. However, this process may take place in two ways. The displacing and displaced atoms can move along the straight line (collinear interstitialcy) and the correlation factor for the discussed crystal structure assumes the value f 50.6666 [32,33]. If, on the other hand, the displaced atom moves to the interstitial position at an angle to the direction of displacing atom (non-collinear interstitialcy) the correlation factor f 50.970 [34]. Using these three correlation factors and Eq. (28) tracer diffusion coefficients of 54 Mn in Mn 16 y S have been recalculated into self-diffusion coefficients of

Table 2 Activation energies of Mn self diffusion in nonstoichiometric manganous sulfide (Mn 16 y S) Temperature range (K) 1073–1373 1073–1273

PS2 (Pa) 3

4.3?10 1?10 210

Sulfide composition

ED (kJ mol 21 ) experimental

calculated

Mn 12y S Mn 11y S

142 260

121 269

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73

diffusion. In order to support this conclusion autoradiographs of surfaces normal to the diffusion direction have been taken from several samples with different penetration depths. If grain-boundary diffusion would prevail the network of grain-boundaries would be visible on the autoradiographs taken on highly sensitive films. The autoradiographs showed uniform blackening of the film, clearly indicating that in agreement with the above conclusion, grainboundary diffusion of cations in Mn 16 y S can be neglected. In fact, this conclusion follows also from the character of 54 Mn-tracer distribution in a-MnS samples after diffusional annealing. Fisher [36] showed, namely, that when diffusion along grainboundaries predominates, the logarithm of tracer concentration C is a linear function of x and not of x 2 , as it has been found in our experiments (Figs. 6 and 7). Fig. 10. The calculated and measured values of manganese selfdiffusion coefficient in a -MnS at 1253 K.

5. Conclusions cations in this sulphide. The results of these calculations have been plotted as a function of temperature and sulfur activity in Fig. 10 on the background of data obtained from sulphidation [35] and evaporation kinetics [12]. As can be seen, over the whole phase field of Mn 16 y S the calculated values of DMn in this sulphide are in agreement with those determined experimentally. It should be stressed however, that DMn values obtained from tracer diffusion data by assuming the collinear interstitialcy mechanism ( f 5 0.6666) are in better agreement with calculated DMn coefficients than those obtained for non-collinear diffusion mechanism ( f 50.970). These results strongly suggest that the self-diffusion of cations in metal excess manganous sulfide proceeds by collinear interstitialcy mechanism. The satisfactory agreement between calculated and experimentally determined DMn values and the fact that the pressure dependence of the self-diffusion rate in both, metal-excess and metal-deficit manganous sulphide agrees very well with the defect model of this sulphide strongly suggests that at high temperatures (T .1000 K) grain-boundary diffusion does not play an important role in the overall matter transport in this polycrystalline material. Consequently, self-diffusion coefficients of cations reported in the present work describe volume (lattice)

The results described in the present paper allow the following conclusions to be formulated. 1. Depending on temperature and sulphur activity the nonstoichiometric manganous sulphide, Mn 16 y S, may be an extrinsic or intrinsic electronic semiconductor, as well as an intrinsic ionic conductor. In the major part of the phase field, corresponding to higher sulphur activities, this sulphide is a metaldeficit p-type semiconductor (Mn 12y S) with doubly ionized cation vacancies and electron holes as the predominant defects. Near the Mn / MnS phase boundary, on the other hand, doubly ionized interstitial cations and quasi-free electrons constitute the prevailing defects and the sulphide is a metal-excess n-type semiconductor (Mn 11y S). In the transient range of sulphur activities, where the sulphide composition changes from metal deficit (Mn 12y S) to metal excess (Mn 11y S) the sulphide becomes intrinsic ionic semiconductor at lower temperatures (,1000 K) and intrinsic electronic semiconductor at higher temperatures (.1000 K). 2. Self-diffusion of cations in Mn 16 y S at temperatures exceeding 900 K proceeds mainly through point defects, i.e., by volume diffusion. In agreement with the defect model, at very low sulphur activities, when interstitial cations and quasi-free electrons

74

S. Mrowec et al. / Solid State Ionics 117 (1999) 65 – 74

predominate (Mn 11y S) self-diffusion of cations proceeds by collinear interstitialcy mechanism, consisting in pushing the cations from their normal lattice sites into neighbouring interstitial positions (both, the displacing and displaced ions moving along a straight line). At higher sulphur activities, when cation vacancies and electron holes constitute the predominant disorder (Mn 12y S) the self diffusion of cations proceeds by simple vacancy mechanism, consisting in Mn 21 ions jumping from the lattice sites into neighbouring cation vacancies. 3. The satisfactory agreement between experimentally determined self-diffusion coefficients of Mn in Mn 11y S and those calculated from sulphidation and evaporation kinetics clearly indicates that both these methods can successfully be utilized in studying the transport properties of transition metal sulphides and oxides. The first of these two methods, called FuekiWagner method, consisting in calculating the DMe values from parabolic rate constants of metal sulphidation or oxidation, has already been proved experimentally on Fe–Fe 12y S–S 2 and Co–Co 12y O–O 2 systems. However, this method cannot be used at very low oxidant pressures, close to the dissociation pressure of the compound forming the scale. Such a possibility offers Kofstad’s method, consisting in determining the metal evaporation rate into vacuum from the surface of the scale in equilibrium with the metallic phase. Excellent agreement of DMn values calculated from manganese evaporation kinetics with those determined experimentally constitutes the first verification of this novel fascinating method, clearly indicating that it can successfully be used in studying the transport properties of metal sulphides and oxides in equilibrium with the metallic phase.

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