On the defect structure and diffusion kinetics in transition metal sulphides and oxides

Reactivity of Solids, 5 (1988) 241-268 Elsevier Science Publishers B.V., Amsterdam

241 - Printed

in The Netherlands

ON THE DEFECT STRUCTURE AND DIFFUSION KINETICS IN TRANSITION METAL SULPHIDES AND OXIDES

STANISLAW

MROWEC

Institute of Materials Science, Academy of Mining and Metallurgy, 30-059 Krakbw (Poland) (Received

January

21st, 1987; accepted

January

al. Mickiewicza

30,

14th, 1988)

ABSTRACT Defect and transport properties of transition metal sulphides are discussed showing similarities and differences between them and the oxide systems. Metal sulphides show the same type of predominant defects as metal oxides, the concentration of defects in the majority of sulphides being much higher than in the corresponding oxides. Defect mobility in sulphides is generally higher than in the corresponding oxides but these differences do not exceed one order of magnitude. Thus, much higher diffusivities in the majority of sulphides are due mainly to the higher concentration of defects.

INTRODUCTION

Atomic disorder and transport phenomena in solids have remained for many years the corner-stone of solid state chemistry and have important implications in materials science. The reactivity of solids and their principal physical and chemical properties depend even more on the kind and concentration, as well as on the mobility of defects than on the nature of the solids themselves [l-3]. Nonstoichiometry, for instance, in all inorganic compounds is inherently related to atomic disorder. Point defects are responsible for lattice diffusion which determines or strongly influences a number of important properties and processes in solids, such as mass transport, solid state reactions, sintering, many precipitation reactions, high temperature creep, gas-metal reactions, phase transformations etc. Electronic defects, in turn, which are strictly related to, and often determined by ionic disorder, are responsible for semiconductivity, thermoelectric, electrooptical and many other important properties of solids. This is the reason why defect structures and diffusion processes in solids are being extensively studied. In this field of research transition metal oxides and sulphides focus particular attention because of their importance from both a fundamental and practical point of view. 0168-7336/88/$03.50

0 1988 Elsevier Science Publishers

B.V.

242

The aim of the present paper is an attempt to show the similarities and differences between defect and transport properties of both groups of these materials.

GENERAL

REMARKS

First of all it should be noted that defect structure and transport properties of metal sulphides are still less known than those of oxides. This results mainly from much greater experimental difficulties in studying high temperature reactions in sulphur-containing atmospheres [4]. Sulphur is, namely, not gaseous under normal conditions and its vapour is extremely aggressive at elevated temperatures. Consequently, the standard thermogravimetric equipment commonly used in studying the deviations from stoichiometry and diffusion processes in metal sulphides is not applicable under these conditions. The only device enabling such measurements to be made is a spiral thermobalance. In the case of the H,/H,S gas mixture the situation is simpler than in sulphur vapour, since there is no danger of sulphur condensation on cool parts of the apparatus. A diagram of this type of equipment is shown in Fig. 1. However, in this atmosphere only rather low sulphur pressures can be obtained, not exceeding 10P3 atm and there is still a possibility of hydrogen dissolution in the sulphide which may influence defect equilibria [5]. Thus measurements in pure sulphur vapour are necessary. In this case the problem is much more complicated because all parts of

WINCH AND FORKS FOR POSITIONING SPECIMENS

CATHETOMETER BYPASS

WITH

FOR ADJUSTING

CAUSTIC

SO

SPECIMEN

Fig. 1. Thermobalance for studying the kinetics from stoichiometry in metal sulphides in H,-H,S

of metal-sulphur mixtures [S].

reactions

deviations

243

31 5 D E’

Fig. 2. Microthermobalance for studying defect equilibria in sulphides and the kinetics of metal sulphidation in sulphur vapour. 1, mercury manometer, 2, thermoelement, 3, quartz rod showing deflections of membrane, 4, thermal insulation, 5, quartz membrane manometer, 6, regulating thermoelements, 7 and 12, thermoelements controlling temperature of furnaces, 8, sample, 9, clamps fixing reaction tube, 10 and 11, suspension of spiral, 13, quartz spiral, 14, vacuum valve, 15, scale for reading elongation of spiral, 17, additional heating element for sulphur, 18, screen of heating element, 19, sulphur, 20, Pyrex glass-quartz joints, K,-K,, vacuum taps, A, furnace thermostating spiral, B, reaction furnace, C, sulphur-heating furnace, D, furnace thermostating sulphur vapour leads [6].

the apparatus, including the balance chamber, should be maintained at a temperature higher than that of the liquid sulphur acting as its vapour source [6]. Such an apparatus is shown in Fig. 2. It makes possible the measurement of the deviations from stoichiometry and the reequilibration kinetics (chemical diffusion) of metal sulphides with very high accuracy, of the order of 10P6 g at sulphur pressures ranging between 1 and 10e4 atm.

1

thermocoupl)

sutphur

Fig. 3. Microthermobalance mixtures.

for studying

trap

the kinetics of metal-sulphur

reactions

[7] in He-S,

Sulphur pressure in the reaction chamber is directly measured with a special quartz membrane manometer. Recently, a new version of this microthermobalance, shown schematically in Fig. 3, has been developed [7], enabling the measurements to be made with the same accuracy but over a much wider pressure range, down to 10e9 atm. The main difference consists in mixing sulphur vapour with helium, the flow rate of which together with the temperature of the liquid sulphur determine the partial pressure of its vapour in this gas mixture of which the total pressure is 1 atm. The partial pressure of sulphur vapour in the reaction chamber is measured in this case by means of a special semiconducting probe of manganous sulphide doped with vanadium. An additional serious difficulty in this area of research results from the fact that metal sulphides are much more numerous than the corresponding

245

T,K 1273 I

1173 I

0 L._?ho:,~undorv ‘-.-.-.-._._,_

1073

973

Cr2S31tr!/C*S3

@h,

-32 -

I

7

I

I

8

9

10

1oc -i- t(K1)

Fig. 4. Equilibrium

sulphur

and oxygen pressures

in Cr-S

and Cr-0

systems

[62,64].

oxides. For instance, in the chromium-oxygen system there is only one thermodynamically stable oxide at elevated temperatures (Cr,O,) in analogy to the nickel-oxygen system (NiO). In contrast to this in the Cr-S and Ni-S systems there are many stable sulphides as shown in Figs. 4 and 5. It follows

TABLE

1

Free enthalpies

of sulphide

and oxide formation

Sulphide

- AG,z

FeS NiS cos Cr2 S, MnS MoS, TiS TiS,

21.9 15.4 17.0 34.9 46.5 18.5 44.0 31.3

K

at 1123 K (kcal/g

atom S or 0)

Oxide

- AGIl

Fe0 NiO coo Cr203 MnO MOO, TiO TiO,

45.0 32.0 37.5 66.5 77.5 47.0 98.5 88.5

K

246 TABLE 2 Melting

points of some sulphides

and oxides and metal-sulphide

eutectics

[4]

Sulphide

Melting point (K)

Oxide

Melting point (K)

TiS

2313 2353 2333 Q

TiO

2023 2490 1963 2353 3323 3113 2683 _

La& Cea S, NbS, ThS,

La ,03 Cez03 NbO, ThO,

2198

2123 1873 1823 3

“0,

MOO, MnO Fe0 cu,o coo

A’*% ‘n*S, NiS Ni,S, Ins

1431 1803 1468 1403 1373 1373 1326 1083 1061 965

Mn-MnS cu-cu,s Fe- FeS co-co,s, Ni-Ni 3 S 2

1513 1343 1258 1153 918 I

“S, Y,S, crs Cr, S, MoS, MnS FeS cu,s cos

y203 _

NiO _

2607 2200 2058 1697 1515 2083 2319 2273 2230 _

In0

1325

Cr203

A’ 203 In203

Metal-sulphide

eutectics

from these plots that all sulphides in both systems are less thermodynamically stable than the oxides. This is a general rule [9], the free energy of formation of the majority of metal sulphides being approximately one half of those for oxides (Table 1). Also, metal sulphides melt at lower temperatures than the corresponding oxides with the metal-sulphide eutectics of most common metals having particularly low melting points (Table 2).

TABLE 3 Maximum

deviations

from stoichiometry

of some metal sulphides

and oxides

Sulphide

Formula

Oxide

Formula

Fe 1-t S Ni I-1’ S

Fee.ssS Ni 0.91 S

Fe, -,,O Ni, -YO

Fe,asO Ni 0.9994 0

co

coo.9930

s

COO.84S

co,

Cr ? t,

S3

Cr2.,,S3

Cr 2+y .O 3

nonstoichiometry

Cll?

,.s

cu,.x,s

CU2_),0

cu

lb,

,,o

I .998 0

at 1273 K [4]

small

T.K 773 I

1273ll73lo73973 073 11 I I I

1

’

’

0

’

10

’

’

12

’

673 I

’

1L

’

‘$,K-‘1

Fig. 5. Equilibrium

sulphur

and oxygen pressures

in Ni-S

and Ni-0

systems

[63.64].

The following important point of general character is, that the sulphides of common metals show generally much higher deviations from stoichiometry than oxides [4]. There are, however, some exceptions as can be seen in Table 3. Namely, in the case of FeS and Fe0 maximum nonstoichiometry is practically the same, but wtistite (ferrous oxide) shows an exceptionally large homogeneity range for oxides. On the other hand, manganous sulphide shows a smaller homogeneity range than MnO, but MnS shows an exceptionally small nonstoichiometry for sulphides. We will come back to this interesting problem later.

DEFECT

STRUCTURE

AND NONSTOICHIOMETRY

As far as the defect structure of sulphides is concerned, most work has been done on ferrous sulphide. This sulphide shows large deviations from stoichiometry towards metal deficit, the predominant defects being cation vacancies. The dependence of nonstoichiometry on sulphur vapour pressure

248

Fig. 6. The dependence of nonstoichiometry

in Fe, _,L,Son sulphur pressure IlOj.

is not a simple power function as in the case of noninteracting defects (cf. Fig. 7). In addition, defect concentration decreases with increasing temperature, as in ferrous oxide [13] (wiistite), which is unusual for a simple defect structure. It has been shown [14] that this atypical character of the dependence of nonstoichiometry on sulphur pressure and temperature results from strong repulsive interactions between doubly-ionized cation vacancies. From this theory it follows, namely, that the logarithm of the square root of the sulphur pressure divided by the nonstoichiometry should be a linear function of the product of y and (2 - JJ) which is in agreement with experimental data (Fig. 6). The energy of interaction between cation vacancies calculated from the slope of these lines is in agreement with theoretical values evaluated from the Libowitz [14] model. From the comparison of the dependence of nonstoichiometry in Fe,_,S and Fe, _),O on sulphur and oxygen pressure (Fig. 7), it follows that in both cases these effects are analogous and the values of nonstoichiometry are comparable. These great similarities do not imply, however, the existence of a completely analogous defect structure. In both compounds the predominant defects are indeed doubly-ionized cation vacancies, but in ferrous oxide there is a relatively high concentration of interstitial cations, which, together with cation vacancies, form extended defects [3,13] as can be seen in Fig. 8. In ferrous sulphide, on the other hand, interstitial cations have not been found and as a consequence, there are no three-dimensional defect clusters in this material. An analogous defect situation exists in Ni, _$ (Fig. 9) and Co, _,S (Fig. 10). In both these cases the unusual dependence of nonstoichiometry on sulphur pressure and temperature can be explained by the Libowitz model. From the comparison of the dependence of nonstoichiometry in Ni, _ S and Ni , _ ,,O as well as in Co, _,S and Co, _,O on sulphur and oxygen pressure it folio& clearly that - in contrast to Fe, _S and Fe, _],O - defect concentrations in nickel and cobalt sulphides are orders of magnitude higher than in the corresponding oxides. In addition, the nonstoichiometry in both these

249

10-a -20

-18

-16

-1L

-12

-10

-6

-6

-L

-2

0

log PS2 1 PO* I, am

Fig. 7. The dependence of nonstoichiometry pressures, respectively [10,12,15].

in Fe, _, S and Fe, _ ,.O on sulphur

and oxygen

oxides increases with increasing temperature and is a simple power function of oxygen pressure. Such a dependence suggests that the interaction of cation vacancies in Ni, _ ,.O and Co, _ ,.O is negligible which is conceivable if one considers the very ldw concentraiion of defects in these oxides.

(a)

(b)

4 1 CLUSTER

6 2 CLUSTER

8: 3 CLUSTER

12 4 16 5 CLUSTER

Fig. 8. Clustering

of defects

in ferrous oxide [16].

CLUSTER

250

i:;.

.

0

-36. .

[email protected])

-MI@.

MREiMROWECl19731 1rnK /

1173K

. ./.

,

-10.

4. -8

-6 -4 -2 0 ~~Fs2.1~~2 lotml

Fig. 9. The dependence of nonstoichiometry pressures, respectively [ 17,191.

in Ni,_,S

and Ni,_,O

on sulphur

and oxygen

As far as the six chromium sulphides are concerned, the defect structure in only two of them has been explained so far. These are Cr,S, and Cr,S,. The first one is a metal excess n-type semi~nductor, predo~nant defects being interstitial cations (Cr *+&). Consequently, nonstoichiometry of this sulphide decreases with increasing sulphur pressure as shown in Fig. 11. The nonstoichiometry in chromium oxide, Cr,O,, has not been determined to date due to its very low values. Kofstad and Lillerud [23] and Atkinson and Taylor [24] have shown that at low oxygen pressures predominant defects in this oxide, like in the sulphide, are interstitial cations, and at higher pressures cation vacancies predominate. At any pressure, however, the defect

Fig. 10. The dependence

pressures.

respectively

of nonstoichiometry [1X,20].

in Co, _$j and Co, _,O on sulphur

and oxygen

251

1

2

3

4

5

log PS2.

Fig. 11. The dependence temperatures [21,22].

6

7

Pa

of nonstoichiometry

in Cr 2+,.S3 on sulphur

pressure

at several

concentration in chromium oxide is many orders of magnitude smaller than in chromium sulphide. The character of deviations from stoichiometry in the second chromium indicates that this compound can exist with both metal sulphide, Cr&, excess or metal deficit (Cr,,,S, - Cr,.,S,). Smeltzer [25] has shown that the absolute value of nonstoichiometry in this sulphide decreases initially with increasing sulphur pressure and subsequently it increases, as can be seen in Fig. 12. This implies that at lower pressures interstitial cations are the predominant defects and at higher pressures, cation vacancies predominate. Another sulphide which deserves attention is manganous sulphide being the only stable compound in the manganese-sulphur system above 473 K. It has been shown [26-291 that over the major part of the phase field this sulphide is a metal deficit p-type semiconductor (Mn, _ ,.S) while close to the Mn/MnS phase boundary it is a metal excess n-type semiconductor (Mn, +.),S) as shown in Figs. 13 and 14. It means, that over almost the whole homogeneity range predominant defects in manganous sulphide are doublyionized cation vacancies and electron holes (Mn, _,.S) and only in the

-9 logPI521,atm

Fig. 12. The dependence

of nonstoichiometry

in Cr 3 * .,S, on sulphur

pressure

at 973 K [25].

252

1 Fig. 13. The dependence temperatures [29].

IO

of nonstoichiometry

in Mn 1*,,S on sulphur pressure at several

narrow range of very low sulphur pressures do doubly-ionized interstitial cations and quasi-free electrons predominate, (Mn, +S). In the intermediate part of the phase field, near and at the stoichiomet~c composition, the defect structure is strongly dependent on temperature. At lower temperatures (< 1173 K), intrinsic ionic defects of the Frenkel-type predominate, and at higher temperatures ( > 1173 K) intrinsic electronic disorder prevails. This is illustrated by the diagrams presented in Figs. 15 and 16. Such a simple defect structure which is rather unusual in the case of transition

l Rasneur.Oherbomez (19811 A LeBrusq n Fuektetai~1~011111K

Fig. 14. The dependence of electrical conductivity of Mn, _+ )’S on sulphur pressures at several ten~peratufes 126-281.

253

10-k.

873 K

f ”

10-7.

>+l.[h'l

:z

2

1. \

/'

10-8.

/'

'\ '1 \

/'

.\

1'

10-g. /'

/'

‘\

‘\

+

STOICHIOMETRIC COMF'OSITlON

lC+1o-2o

10-15

Fig. 15. Concentrations pressure at 873 K [29].

lo-10

10‘10

‘\

‘\

k ,!Q1-psy

\

10-s

1

of ionic and electronic

lo-5

1

\._ , 105

defects

in Mn, f ,,S as a function

of sulphur

defects

in Mn, * ,S as a function

of sulphur

105

PS2.b

Fig. 16. Concentrations of ionic and electronic pressure at 1573 K [29].

254

1673

ll.73

1273

I

I

I

1073 I--+%

Le BRUSQ

103 T

DELMAIRE

>K

Fig. 17. The dependence of nonstoichiometry of Mn,_,.S and Mn, -,,O on temperature several sulphur and oxygen pressures, respectively [27,33-351.

for

metal sulphides, results from the fact that deviations from stoichiometry and consequently defect concentration in the sulphide discussed are very low. Manganous oxide, on the other hand, shows a much larger homogeneity range (Table 3) and consequently defect concentration, than the corresponding sulphide, predominant defects being also cation vacancies and electron holes (Mn,_,O) [30-321. The main difference consists in the presence of interstitial cations which ~ as in the case of wtistite - form together with cation vacancies three-dimensional defect clusters (extended defects). Consequently, the nonstoichiometry of Mn, __!O, in contrast to Mn, _,,S, decreases with increasing temperature, as shown m Fig. 17. There is not much more information concerning nonstoichiometry and defect structure of other sulphides. It should be noted that defect structure in refractory metal sulphides is completely unknown, which is mainly due to the very low, and consequently difficult to measure, deviations from stoichiometry. Rau [36] has shown for instance, that the nonstoichiometry of molybdenum sulphide at about 1000°C is smaller than 8 X 10e5 mol of

255

T,K

0 SULFIDES ,._l,._,1,

~S~2-MRDWECetal Cal-yS 3-RAU (1976)

11980)

L-RAUll9751 5-MIKAt.4ldal (19721 1 -Lo BRUSQDELMAIRE c I197L 1

ps2=eo2

hl-yS

10’2atm

MoS2 ----

I

6-k

BRUSD.DEh&RE

6 -RAu II9761 tZbLEE.FtAPPl198L) OXIDES

yJ~~tz+6y

NII-~O ‘3~2.~0 MITI.~O

13. MITOFF(l961) IL-TRETYAKOV RAPP1196 i IS-OSBURN,V&J (19701 16.MRDWEC tlal (197Ll 17.HED,TANNHAUSERIlP~

103.K T

Fig. 18. Collective plot of the dependence of nonstoichiometry oxides on temperature [15,17,18,22,27,29,33-35,65-721.

in several metal sulphides and

sulphur per mol of the sulphide. Defect concentration in refractory metal sulphides is then supposed to be very low. To summarize this short discussion of defect properties, in Fig. 18 a comparison of maximum nonstoichiometry of some sulphides and oxides is presented. It follows from this comparison that sulphides of important common metals show deviations from stoichiometry many times higher and thereby significantly higher defect concentration than corresponding oxides. The only exception is manganous sulphide with the nonstoichiometry lower

256

than in the oxide. On the other hand, the unusually high nonstoichiometry of wiistite is comparable with that of ferrous sulphide. Finally, refractory metal sulphides show probably very small deviations from stoichiometry, and thereby defect concentrations, of the order of that in nickel oxide.

TRANSPORT

PROPERTIES

At high temperatures, matter transport in metal sulphides, as in oxides, proceeds mainly through point defects (volume diffusion). The kinetics of this process are thus dependent on defect concentration and their mobility, the measure of which is the diffusion coefficient of defects, Dd, related to the self-diffusion coefficient of atoms, D,, and defect concentration, cd, by the following relationship [l-3]:

When the defect concentration is significantly lower than that of atoms, ca, in a given sublattice, as is usually in the case with metal oxides, eq. 1 simplifies to: D, z D,N, E DdJJ

(2)

where Nd denotes the mole fraction of predominant defects, being practically equal to the deviation from stoichiometry y. This simplification does not, however, hold for metal sulphides because of the generally high concentration of defects. In this case a better approximation is given by Mott’s and Gurney’s equation [38]:

DaEDdL

(3)

1-Y

The chemical diffusion coefficient, 6, in turn, being a measure of defect mobility in non-equilibrium conditions, is related to the self-diffusion coefficient by [4]: D = 1/2Da$

C. d In p(X,) d In cd

(4

where X denotes oxidant. When the defect concentration is low enough, so that they do not interact, the derivative, d In p(X,)/d In cd, remains constant and eq. 4 assumes the following simplified form [l-4]: Da

=

where defect

Nd

WPID p denotes

concentration

effective charge of defects. In metal sulphides, however, is generally so high that their interactions cannot be

251

excluded, and In cd is no longer a linear function of In p(X,) (Figs. 7, 9, 10). In these cases general eq. 4 should be used. The diffusion coefficient of defects, Dd, being the direct measure of defect mobility in the absence of a concentration gradient, cannot be determined experimentally, like the self-diffusion coefficient describing the mobility of atoms under the same conditions. These two coefficients can, however, be calculated from directly measurable chemical and tracer diffusion coefficients. The relationship between Dd and b is [4]:

’ = 1/2Dd

d ln P(&) d

or in the absence

Dd=1+

b ]p]

ln

c

d

of interaction

between

defects:

(7)

On the other hand, the self-diffusion coefficient of atoms, D,, can be calculated from the tracer diffusion coefficient, D,, if only the diffusion mechanism and thereby correlation factor, f, are known [l-3]: Da=

3 f

(8)

The self-diffusion coefficient can also be calculated from the parabolic rate constant of metal oxidation (or sulphidation) if the mechanism of scale growth is known [l-4,39]. Thus, transport properties of metal oxides and sulphides can be described by means of self- and chemical diffusion coefficients. It should be noted, however, that in contrast to oxides, transport properties of metal sulphides are less well known. In a few cases only, self- and chemical diffusion coefficients have been determined as a function of temperature and sulphur vapour pressure. However, in order to obtain a more complete picture, fragmentary diffusion data and the results of sulphidation kinetics have also been utilized in order to calculate or at least estimate the order of magnitude of diffusion coefficients. Also in this field of research ferrous sulphide and ferrous oxide have been most extensively studied. It has been shown [37,40] that in agreement with the defect model of Fe, _YS, the self-diffusion coefficient of sulphur in this material is by many orders of magnitude smaller than that of iron. The values of the self-diffusion coefficient for iron in polycrystalline material and in single crystals are in good agreement [11,40-441. This shows clearly that diffusion of iron in ferrous sulphide proceeds practically only through point defects. It has been shown [45,46] also that the chemical diffusion coefficient is practically independent of composition over the whole homogeneity range of Fer_$, as shown in Fig. 19. It does not mean, however,

258

LlOL

008

012

016

020

Fig. 19. The dependence of the chemical diffusion at several temperatures [11,40,41,43,45,46].

coefficient

in Fe, _ YS on nonstoichiometry

that the mobility of defects in ferrous sulphide is independent of their concentration. Recalculation of the chemical diffusion coefficient into the defect diffusion coefficient, being the direct measure of defect mobility, shows, namely, that it decreases with the increase of nonstoichiometry (Fig. 20). This is conceivable if one considers that due to the side blocking effect [47,48] the jump frequency of cation vacancies decreases with the increase in their concentration. Analogous results have been obtained concerning selfand chemical diffusion rates in ferrous oxide [49], although the diffusion mechanism in this oxide is more complicated due to the formation of three-dimensional defect clusteres. The temperature dependence of self- and chemical ‘diffusion coefficients in Fe, _,S and Fe, _ ,O are compared in Fig.

10-7

‘\

“.A

10-e . .

-5

Fig. 20. The dependence several temperatures [4].

of defect

diffusion

coefficient

in Fe,_,,S

on nonstoichiometry

at

259

1373 k

1273

1173

’

’

’

1073 I

973 I

873 I

j

FepyS,FepyO

A-CONCIIT

et ai (i97L)

P, T

K

Fig. 21. The dependence of self- and chemical diffusion coefficients in Fe,_, ,S and Fe,_,0 on temperature [11,40,50,51].

21 in order to show the great similarities in transport properties for the oxide and sulphide of the same metal. The self-diffusion coefficient of manganese in manganous sulphide has been calculated from the sulphidation kinetics [52] as well as from the diffusional evaporation of manganese from the surface of MnS scale [53] by means of a novel method developed by Kofstad [54]. The results of these calculations are shown in Fig. 22 in a double logarithmic plot. As could be predicted from the defect model, the self-diffusion coefficient of manganese over practically the whole phase field of MnS increases with sulphur pressure with a gradient of l/6, suggesting a simple vacancy diffusion mechanism. Only in the very narrow part of the phase field, near the Mn/MnS phase boundary, does diffusion of manganese in Mn,+,S occur by an interstitialcy mechanism. Kofstad [55] has shown that an analogous situation exists in the case of MnO as shown in Fig. 23. Figure 24, in turn, shows the comparison of self-diffusion coefficients of manganese in MnS and MnO as a function of temperature, in order to demonstrate the exceptional case of practically the same diffusion rates and activation energies of this process in the oxide and sulphide of the same metal. It should be noted, however, that despite these great analogies, the diffusion

10-n

Jr-y13m-9

10-S

lo-1

103

ps2J+3

Fig. 22. The dependence of self-diffusion pressure at several temperatures [53].

coefficient

of manganese

in Mn,*,S

on sulphur

mechanism of manganese in manganous oxide is much more complicated than in MnS because of the interaction and clustering of defects. There is not much more information concerning transport properties of other sulphides. Chemical diffusion coefficients have recently been measured in chromium [57] and cobalt [58] sulphides. In the remaining sulphides only a rough estimation of self- and chemical diffusion rates can be made using sulphidation kinetic data and deviations from stoichiometry.

10.6 v) 1o'7

12OO’C

MnO

1100 d

,@?*LL 10-30

OXYGUt~OCC~lKT’, or0

Fig. 23. The dependence of self-diffusion pressure at several temperatures [55].

coefficient

of manganese

in Mn, + _ YO on oxygen

261

Fig. 24. Comparison of self-diffusion coefficients in Mn, _,S and Mn, _,,O /53,56].

As far as refractory metal sulphides are concerned it should be stressed that marker experiments have shown [59,60] that the compact sulphide scale on molybdenum and tungsten grows due to the inward diffusion of sulphur. Consequently, estimated values of self-diffusion coefficients in MoS, and WS, refer to sulphur diffusion. Nevertheless, it clearly follows from these data that the diffusion rate of sulphur or metal in refractory metal sulphides is very low. Figure 25 shows the results of calculated and estimated diffusion coefficients in these sulphides with the analogous data concerning certain refractory metal oxides. It follows from this plot that the rates of self-diffusion in oxides and sulphides under discussion, in contrast to the majority of other oxides and sulphides, are analogous, although the activation energy of diffusion in oxides is significantly higher. Figure 26 shows the collective plot of some measured, calculated and estimated values of self-diffusion coefficients in metal sulphides and oxides. It is clearly seen that the diffusion rates in sulphides of common metals are many orders of magnitude higher than those in refractory metals, manganous sulphide being in an intermediate position. The self-diffusion rate in several sulphides is of the same order of magnitude as in the corresponding oxides. These are, namely, MnS and MnO and FeS and FeO. The rate of self-diffusion in a number of other sulphides is orders of magnitude higher than in the corresponding oxides.

262 TK ,0-9

I’\ u.73

:

1373 ’

\I 1!73 \

1273 1

\\Nb205

\ 9’

/

973 I

1073 1 WS2 ZrO2

?f’us’o”

J

sJ’fides (I-GER~ACH,HAMELit970)‘

t.4oS2

(2.GERLACH,HAMEL

NbS2

(3.KOVALCHENKO

11970!

TaS2

(L-KOVALCHENKOeto:.

KOFSTAO

\\ \

6\

\

0-dhffusmn

\\

‘\ 7\

\,yPo*‘o \’

Latm

etai. 119711

-

l197Li

-

11972)-

\ -1 lO\

\ 10-13.

L 07

‘\

,

oa

‘\8

I 10

09 !+,

3

-

1 11

K-1

Fig. 25. Comparison of self-diffusion coefficients refractory metals [59,61,73].

in some metal sulphides and oxides of

A question then arises, what is the main reason for the fact that the diffusion rate in metal sulphides is generally much higher than that in oxides. As the self-diffusion coefficient is a product of defect mobility and their concentration, the deviations from stoichiometry and chemical diffusion coefficients should be compared in both groups of these materials. Such a comparison concerning nonstoichiometry in oxides and sulphides has already been made (Fig. 18). In Fig. 27 chemical diffusion coefficients in some metal sulphides and oxides are compared. It follows from this plot that the rate of this process and consequently, the mobility of defects in metal oxides and sulphides do not differ significantly. In fact, the rate of chemical diffusion is generally higher in metal sulphides, but the differences do not exceed one order of magnitude. This means that in the majority of cases, the significantly higher rate of self diffusion in metal sulphides results mainly

263

l773lml373

1m

573

m

m3

m

CrbyS3

+S

SULFIMS

: $% I 3 r4mdEcadIl

n

'

Q5 06 07

08 II9 IO

Fig. 26. Comparison of self-diffusion [11,40,41,53,57,60,74-791.

11 1.2 13 1X 15 7.K 103 -1

coefficients

in some

metal

16

17

sulphides

I

18 1.9 '

and

oxides

from higher defect concentration and not from greater defect mobility. There are, however, some exceptions. For instance, defect concentration in manganous sulphide is lower than in the oxide (Fig. 18), but their mobility is higher. Due to this compensation effect, the self diffusion rates in Mn,_,S and Mn,_,O are comparable (Fig. 24). Ferrous sulphide and oxide, in turn, exhibit comparable deviations from stoichiometry, but the chemical diffusion coefficient in the oxide is lower. As a consequence, the self diffusion rate in Fe,_,S is correspondingly higher than in the oxide (Fig. 21). It is

264

1573 1373

c E

11731073 973

m

MeS,MeO

lo-&:

-I

O~LEVIN.WAGNER (196% m-LANDLER,KOHAREK 119661 A.CAMPBELL I19691 &LAUBE,WAGNER 119731 O-RICKER,WEoPNER097~1 O-MROWEC et01 (1961) PRiCE,WACiNER 09661

,fj”b] KOEL,GELLINGS 9. I 10. 1 It : 12

COI-~D

_I

OXIDES

1 2 3 I S I 6 7

%I-YO

873

(1972)

MROWEC ef al. (19731 WIMMER etol .ll975l SOSSA,PETDT-ERVAS DOMl~G~S.~DRlG~Z

11962) &oIJlQ621-

10-5:

10+,

10-7:

\

E I

1o-8

dfj

0.7

Fig. 27. Comparison of chemical [10,11,19,20,50,53,57,74,80-971.

I

0.8

diffusion

23. SMELTZER e+ 01. 119791 12‘ MROWEC eloI. 119801 25 -‘4ROWEC etol.119851 , 4 26 coicuioted lrom y and ON, “Li”.rS / 1x3: ‘4 3zy52:y 27 STOKtOSA,STRINGER 119771 c;2.,5328 vROWEC eta~.119851 N”,_~s 29 DA?IIELEWSKI ,MROWEC 119651 Fer-yS

7 kIy:

I

0.9

coefficients

I

10

,

111

in some metal sulphides

_

L

1.2

and oxides

interesting to note that the activation energies of chemical diffusion in metal sulphides and oxides are comparable, whereas the activation energy of self-diffusion in metal oxides is much higher than in the corresponding sulphides. This is generally due to the higher enthalpy of defect formation in oxides than in sulphides. It should be noted that the diffusion mechanism in metal sulphides is as a rule more complicated than in oxides, which follows mainly from the higher concentration of defects and their mutual interac-

265

tions. The classical exception is manganous sulphide in which diffusion proceeds either by a simple vacancy (Mn,_,S) or interstitialcy (Mn,+,S) mechanism due to the low concentrations of defects. Perhaps an analogous situation exists in the case of refractory metal sulphides, where very low defect concentrations should be expected.

CONCLUSIONS

Summing up this short discussion, concerning defect and transport properties of transition metal sulphides and oxides, the following conclusions may be formulated. The thermodynamic stability and melting points of metal sulphides are considerably lower than those of oxides. Only rare-earth and refractory metal sulphides, showing high thermodynamic stability, melt at temperatures exceeding 2000 K. The lower thermodynamic stability of the sulphides, together with the different character of the chemical bonds are the main reasons for much higher deviations from stoichiometry, and consequently defect concentrations, in these materials. In this respect refractory metal sulphides, characterized by very low deviations from stoichiometry, are the only known exceptions. The second important conclusion of general character is, that metal sulphides show predominant defects of the same type as metal oxides. In the majority of cases these are cation vacancies or interstitial cations, in other (refractory metal sulphides and oxides), anionic defects. It should be mentioned, however, that the latter conclusion is based only on the sulphidation mechanism of tungsten and molybdenum. Due to the high concentration of defects, their structure in metal sulphides is generally much more complicated than in oxides. This is reflected in some cases in negative values of the enthalpy of defect formation (Fe,_,S, co l_YS, Ni,_,S, Cu,_,S) and in a complicated dependence of deviations from stoichiometry on equilibrium sulphur pressure. These phenomena can be explained by strong repulsive interactions between defects (cation vacancies). The analogous effect of temperature and oxygen pressure on defect calculation in highly defected oxides (Fe,_,0 and Mn, _YO) is due to other reasons i.e., formation of extended defects. Defect structure in refractory metal sulphides has not been explained so far, due mainly to their very low concentrations. A comparison of chemical diffusion coefficients in metal sulphides and oxides shows that defect mobility in sulphides is higher than in oxides, but the differences do not exceed one order of magnitude. On the other hand, the self-diffusion rate in some sulphides is of the same order of magnitude as in oxides, and in others it differs by many orders of magnitude. This is due

266

to the fact that the self-diffusion coefficient appears to be a product of defect concentration and their mobility, the measure of which is the chemical diffusion coefficient. As a consequence, if the differences between defect concentrations are much greater than those between their mobilities, the defect concentration is responsible for the higher rate of self-diffusion in sulphides. This applies for instance, to Ni,_,O and Ni,_,,S as well as to Co, _,O and Co,_,S. The cation vacancy concentration in both these sulphides is, namely, several orders of magnitude higher than that in oxides and consequently, the self-diffusion in Co, __S and Nil-S is much faster than in the corresponding oxides. For the same reasons the self-diffusion rate of chromium in Cr2+,S, is higher by several orders of magnitude than in Cr,+,,O,. On the other hand, in the case of Fe,_,,S and Fe,_,.0 defect concentrations are comparable, but their mobility in Fe,_,S is higher than in Fe, _“O. Due to this the self-diffusion of iron in ferrous sulphide is correspondingly faster than in the oxide. In manganous sulphide and oxide, respectively a compensation effect is observed. Defect mobility in Mn,_,S is, namely, higher than in Mn,_,O, but defect concentration in Mn, _YS is lower. As a consequence, the sell-diffusion rate of manganese in Mn,_,S is comparable with that in Mn,_,O. As far as refractory metal sulphides are concerned, data on defect concentrations and their mobilities are not available. It is known, however, that defect concentrations in these sulphides are very low. It can then be assumed that this fact accounts for the extremely low diffusion rates in these materials.

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