Defect energetics and range of homogeneity of α-MnS

I Ph

m GreatBritain Chrm Sofid~1978. Vol 39.pp 339-343 PcrgamonPress Printed

DEFECT ENERGETICS AND RANGE OF HOMOGENEITY OF a-MnS HANS

RAU

Philips GmbH Forschungslaboratorium (Received

25 March

1977: accepted

Aachen, 51 Aachen, West Germany in revised form

15 July 1977)

Abstract-Sulphur pressure measurements between lo-l2 and 20atm as a function of temperature (873-1364 K) and composition were performed on a-MnS samples. From the results and literature data on optical and electrtcal properties a quantitative defect structure model is derived. In the range investigated the deviation from stoichiometry is caused by the formation of twice negatively charged manganese vacancies and, at high sulphur pressures, effectively neutral interstitial sulphur atoms (perhaps present as Si on S” sites). At low sulphur fugacities thermal generation of “holes” and “electrons” is important. These are both localized on manganese sites as Mn” and Mn’+ ions, respectively. The boundary of the homogeneity range of a-MnS towards elemental sulphur is calculated from the model.

INTRODUCTtON Simple

compounds

attracted tween

of the first row transition

some interest

band structure

because

metals

have

of the interrelations

be-

and physical

properties.

In the case of a-MnS, the stable high temperature modification with NaCl structure, the band structure has been calculated [ 1,2] and optical properties [3] have been correlated with it[4]. Electrical properties such as conductivity and Seebeck and Hall effect have been measured as a function of the sulphur fugacity[5-8l.t The deviation from stoichiometry has also been studied [5] and related to the electrical properties. From this it was concluded that a-MnS is a semiconductor containing singly and doubly charged manganese vacancies, giving rise to p-type conduction. The present study reports sulphur fugacity measurements as a function of the composition in the field between IO-‘* and more than 20 atm of sulphur pressure and temperatures between 873 and 1364K. From the results and literature data of physical properties a model of the defect structure of a-MnS is deduced. EXPERIMENTAL Starting

to 45 mg) to the solid (14.4g MnS). The method consisted of measuring the sulphur pressure as a function of the temperature for a constant over-all composition (Fig. 1). The change of the composition of the solid due to sulphur evaporation was taken into account by subtracting the amount of sulphur in the vapour phase from the total amount of sulphur present. The amount of sulphur in the vapour was computed from the vapour density (calculated with the help of the computer program given by Rau et al.[ll]) and its volume, which in turn was computed from the empty

9

mcreosing

I l

temperature

/

I

dauaosing tanlparotura I

8

i

7

materials

for the preparation of a-MnS in a sealed evacuated silica ampoule were manganese flakes (99.98%, Koch-Light Ltd., Colnbrook Bucks England) and sulphur puriss. (2 99.999%, Fluka AG, Munich). At the end of the experiments the MnS was tested for impurities by spectral analysis. Main impurities were: Si, 0.1% Mg, 0.03%. Two types of experiment (described elsewhere in detail[9, IO]) were performed: (i) Direct sulphur pressure measurements above 0.1 atm using an all-silica Bourdon gauge mounted in an autoclave[9] and performed on solids of known composition, and (ii) indirect sulphur fugacity measurements using the H2S/H2 method in a special form. In the first method, the composition of the solid was changed by addition of elemental sulphur (up

i

iI

I e 5 : i a5

L

3 800

tI / /, Sal

1GOO

1100

1200

1300

la0

TemperoturelK-

Fig. 1. Example of the direct sulphur pressure measurements for a constant overall’composition of the solid. 14.4 g MnS, 24.82 mg S excess, empty volume of the ampoule 2.63 cm’ at 298 K.

tFugacity instead of partial pressure of 5% must be taken for higher pressures when deviation from ideal behaviour occurs. 339

340

HANS RAG

volume

in the gauge at room temperature and the thermal expansion of the solid. This was estimated according to the Griineisen law, i.e. the molar volume of a-MnS was assumed to be 7% more at the melting point of about l800K than at OK. Thus the composition of the solid could be calculated as a function of the sulphur fugacity (again calculated by the computer program of Rau el a/.[lI]). For the indirect sulphur pressure measurements 80.9 g MnS were treated with about 25 cm3 of hydrogen at pressures up to I atm. During this treatment at temperatures between 873 and 1364 K, which was continued until equilibrium was reached, the hydrogen took up sulphur from the solid, thus forming a H2S/H2 mixture. This was subsequently analysed by tensivolumetric measurements (for more details see [9]). From the results the sulphur fugacity in equilibrium with the solid using, the known formation equilibrium of H$[12] and, moreover, the change of the composition of the solid, since all sulphur found as H2S in the vapour came from the solid, could be calculated. When such treatments with hydrogen were repeated several times on the same solid at the same or another temperature, a set of composition-fugacity data for several temperatures was derived. When the H2S content of the gas phase became too small (below 0.01~01%) the composition of the solid was changed by addition of a known amount of H,S. After that, the reduction by small steps was continued. This second series finally overlapped with the first series within close limits (about 0.5% of the total composition change) thus showing that these data were all correct. The appearance of metallic manganese could not be observed during these experiments. This would occur at very low H2S concentrations which could not be analysed with the apparatus available. The HzSIH2 measurements briefly described here give accurate data of the composition changes of the solid, not of the composition itself. Thus in principle the compositions are dependent on the value of a common addition constant. This was calculated from the defect model presented in the following section. Since the direct sulphur pressure determinations were performed on the same solid (after having ended the indirect measurements) the same shifting constant also applies to the direct measurements. The results of the measurements are presented in Fig. 2 where they are compared with values calculated from the defect model.

DEFECT

MODEL

FOR n-MnS

The defect model for a-M& should be in agreement with all the known properties of this compound. Therefore it seems convenient first to summarize the features and the defect models already proposed. a-MnS is a p-type semiconductor[5-8]. Two different exponents for the sulphur fugacity dependence of the conductivity (T have been reported: acrf(S~)“~.~[6] and uaf (Sz) 1’6.*4[8].On the basis of the first of these results it was concluded that there are singly and doubly charged

atomic per cent sulphur

-

Fig. 2. Boundary of the homogeneity range of a-MnS towards elemental sulphur as calculated from the eqns (5)-(13). The boundary towards elemental manganese cannot be given. but iI is very near to the composition MnS or a composition richer in manganese.

manganese vacancies present[5]. This assumption is in conflict with the results presented here. If this were true, one would expect more singly charged vacancies to be present at low temperatures and more doubly charged vacancies at high temperatures, i.e. the exponent should become smaller with increasing temperature. The opposite is the case. From the analysis of the conductivity Fueki et al.[8] concluded that the conduction takes place by hopping of 3d holes. Accordingly these holes are formed by the reaction with H,S (or SJ by HzS + 2 Mn” = HZ + Vd. t 2Mn3’ + Ss.

(I)

This mechanism is in agreement with optical observations and band structure calculations. According to Chou and Fan[4] the strong absorption starting at about 2.8 eV (at 298 K) is not due to electrons excited from the valence band to the conduction band (this energy is about 5 eV) but due to the excitation of electrons from the relatively sharp 3d-levels located at the Mn2+ ions, either to the conduction band, where they can move freely, or to localized states on other Mn*’ ions, thus forming Mn I+ ions: Mn’* + hv = Mn3’ t n

(2)

2Mn2++hv=Mn3++Mn”. It seems quite reasonable that the second possibility (eqn 3) takes place [4] in the similar compound MnO, although a final conclusion was not drawn for MnS. The defect model of a-MnS can be expected to be somewhat similar to that of MnO, which has the same structure and shows similar optical behaviour. It is known that the conductivity of MnO is p-type at high oxygen pressures (with a ~(0~)“~ dependence) and ntype at low oxygen pressures (with a ~(0~)~“’ dependence)[13]. In the intermediate range, where both “holes” and “electrons” are present (in localized states as concluded from optical investigations, see above) the

341

Defect energetics and range of homogeneity of a-MnS

oxygen pressure dependence of the deviation from stoichiometry S is expected to change from a value of Sap(Oz)“” (when “electrons” can be neglected) to Sap(02)“* (when the concentrations of “holes” and “electrons” are approximately equal and much higher than the deviation from stoichiometry 6). One would also expect this change of the pressure dependence (at a given deviation from stoichiometry) to be strongly dependent on temperature, because the thermal generation of “holes” and “electrons” (similar to the reaction 3) is related to the photon energy of strong absorption. This picture apparently holds well for MnO, and it will be shown now that it is also in agreement with the experimental results of ol-MnS, although only p-type cocduction was observed for this compound up to now[5-81. n-Type behaviour could perhaps be reached at very low sulphur fugacities, not investigated here. The defect model for a-MnS is therefore formulated in the following way. (1) Sulphur from the vapour phase reacts with the solid forming doubly charged manganese vacancies and two “holes”, e.g. Mn” ions: l/2 Sz + 2 Mn” = 2 Mr?’ + V&t Ss.

log(C,) = S, + HJT.

(5)

(2) Thermal energy generates “holes” and “electrons”: 2Mn” = Mn3++ Mn’+, C2 = [Mn”].[Mn”] log (Cz) = Sz t Hz/T.

(6)

The enthalpy parameter HZ is related to the strong absorption edge of a-MnS H(abs) (2.8 eV at 298 K[4]). At the temperatures of investigations (around 1300K) this energy will be lower. The temperature dependence of this edge is only known at low temperatures[4]. Assuming a linear dependence with a temperature coefficient remaining the same as at low temperatures, the absorption edge can be estimated to be H(abs) = 67200- 8.79 x T cal

(7)

H(abs)/2.303 R = 14700-- 1.92x T. (3) At very high sulphur fugacities (pressures) a third defect reaction must be taken into account: l/2 sz = s,,

2 [VL.] + [Mn”] = [Mn”] s = [V&,1+ [S,].

(9) (10)

The experimental data (composition of the solid as a function of temperature and sulphur fugacity) were fitted to the set of eqns (5t(lO) by a least squares computer program. Five energetic parameters (S,, SZ, S3, H,, H,) were varied and also the composition shifting parameter (the uncertainty of the composition, which is a constant to be added to all the composition values). The absorption edge energy (eqn 7) divided by the gas constant R was taken for the enthalphy value HZ. Thus the following set of mass action constants is able to describe the system log,, (C,) = - 3.363-6500/T

(11)

log,, (Cz) = 0.684-(14700/T - 1.92)

(12)

log,, (C,) = - 2.473-2076/T.

(13)

(4)

This equation is equivalent to eqn (1). Taking [S,] and [Mr?‘] as constant (brackets mean site fractions) Cr = [Mn”l’~[V~,l/f(S,)“*,

In addition to the eqns (5), (6) and (8) the neutrality condition and the deviation from stoichiometry S have to be formulated:

c, = [Sil/f(S,)“‘,

(8) log (C,) = S, + HJT. Neutral sulphur interstitials Si might be present in the form of S; groups on S” sites. This seems reasonable since at low temperatures MnS2 (pyrite type) as well as MnS exists in the Mn-S diagram.

In Fig. 3 deviations from the stoichiometry thus calculated are compared with experimental results. Other interesting defect concentrations are also given. Equations (5t(13) enable the boundary of the homogeneity range at high sulphur pressures to be calculated, provided the sulphur fugacity at this boundary is known. A measurement of the limiting sulphur pressures with the direct (autoclave) method on a solid of about 52 atomic per cent sulphur content showed complete agreement with the sulphur saturation pressures[l4] up to at least 1227K. Consequently, the sulphur fugacity in saturated sulphur vapour limits the sulphur activity in solid (YMnS. The sulphur fugacity in saturated sulphur vapours was introduced into the eqns (5)-(13) resulting in the composition boundary shown in Fig. 2. Above 1313K this boundary is not defined, because above this temperature a-MnS can be in equilibrium with supercritical sulphur, the fugacity of which can be varied within wide limits. The boundary of the homogeneity range towards elemental manganese cannot be given here. Although the limiting sulphur fugacities are known here (from thermodynamic investigations[l4] it is not clear whether the defect model described can be extrapolated to such low fugacities without new defects arising. On the contrary, one might expect that, as in the case of MnO, interstitial manganese atoms become majority atomic defects at very low sulphur fugacities. About the concentration of these interstitial manganese atoms, e.g. of the order of magnitude of the Frenkel-constant

Cd = [Mn?‘]~[V&J, nothing can be said at the moment,

(14)

342

HANS RAU

-10

-3

-3

-

-8

-6

-4

-2

0

-10

-8

-6

-4

-2

0

1189K

c

973K

873K

Fig. 3. Experimental values (crosses) compared with calculated (eqns 5-13) dewations from the stoichiometry 6 (solid lines). Other defect concentrations are also given. Abscisses: log,,, of the S2 fugacity. Ordinates: log,,, of the mole fractions of the defects or 6. Error limits of the indirect measurements (log,,, ( /(S2))c -21 are about ~0.3 logarithmic units at ordinate values of - 6 and go down to + 0.02 at ordinate values of - 4 and higher. Direct measurements (rest of the points) have error limits of about ? 0.02 on the ordinate axis at all temperatures except 873 K. where they are higher.

DISCU!WON

The defect model presented here is in reasonable agreement with all experimental investigations on aMnS. A certain discrepancy remains with respect to the electrical conductivity measured by Le Brusq et al. [5-71. From the defect model (compare Fig. 2) a sulphur fugacity dependence very similar to that found by Fueki et al. [8] would be expected, whereas Le Brusq found a somewhat steeper fugacity dependence. It cannot be said which of the two conflicting conductivity measurements is correct, but that of Fueki et a/.[81 agrees with the model given here. The concentration of the Mn’+ ions (or “electrons”) given in Fig. 3 are certainly not very accurate. The temperature dependence of the thermal generation of “holes” (Mn”) and “electrons” (Mn”) (eqn 6) was estimated from the low temperature optical absorption edge and its temperature dependence near room temperature. A somewhat different temperature dependence of the enthalpy parameter Hz would result in somewhat different concentrations of “electrons” espe-

cially at low temperatures, since the mass action constant CZ is mainly determined by the results at the highest temperatures. A change of the temperature dependence of Hz would result in a respective change of Sz (the first term in eqn (12)) to allow the mass action constant Cz to remain nearly the same at the highest temperatures. The mass action constant C, is very well defined (about t 1%) but CT is less safe (about t 20%), due to experimental uncertainties reflected in greater deviations of the calculated from the measured values at the highest sulphur fugacities. However, since the interstitial sulphur atoms are only of minor importance, this uncertainty does not influence very much the boundary of the homogeneity range presented in Fig. 2. This might be safe to within 24%. The parameter S2 (first term in eqn (12), the third term comes from the temperature dependence of the absorption edge) is related to the entropy of reaction (6). Written in a somewhat different way (with defect numbers instead of site fractions) this equation can be

Defect energetics and range of homogeneity of a-MnS formulated as

(Mr?‘)(Mn”)

= N(Mr?‘)N(Mn”) exp (- AH/RT)

(15)

where AH is the absorption edge energy (eqn 7) and N(Mn”) and N(Mn”) are (in the first approximation) equal to the number of sites over which Mn3+ and Mn’+ ions could be randomly distributed. If the “electrons” were not localized, N(Mn”) should be replaced by the density of states in the conduction band N,, which can be calculated from quantum mechanics to be (16) where rnt is the effective mass of electrons moving in the conduction band. From eqn (12) it follows that the pre-exponential in eqn (IS) is N(Mn3’)(N(Mn”) = 1Oo.684 = 4.83

(17)

expressed in mole fractions. For a cm3 of a-MnS (molar volume 21.47cm3) and expressed in numbers of atoms this gives N(Mn”)(N(Mn”)

= 3.80 x 104’cmm6.

(18)

The number of sites over which the Mr?’ ions can be distributed is the number of Mr?+ ions per cm3 (= 2.81 x lo**). Thus N(Mn”) is to a first approximation N(Mn”) = 1.35x 10z3cme3.

(19)

This value agrees well with the assumption that the number of sites over which the Mn’+ ions can be dis-

343

tributed is again the number of Mn” ions per cm3 (= 2.81 x lO**),while it is much higher than the density of states in the conduction band for an effective electron mass not too far from the free electron mass (=2.53x 1Ol9 for mb = m, at 300 K). The remaining difference between the number of Mn*’ ions squared and the product N(Mn3’).N(Mn”) might be due to a change of the lattice vibrational frequencies around the atomic defects (vibrational entropy). Thus it is much more probable that, as in MnO, the “electrons” are localized on manganese sites instead of moving nearly free in the conduction band. This agrees well with the analysis of the optical properties presented by Chou and Fan[4].

I. Bartling 1. Q., Thesis. University of California. Riverside, Calif. (1%9).2. Wilson T. M.. fnr. 1. Qunnlum Chem. Symp. 3,757 (1969). 3. Huffman D. R. and Wild R. L., Phvs. Reo. 156.989 (1967). 4. Chou H-H. and Fan H. Y., Phys. kev. BlO, 901 (1974). 5. Le Brusq H. and Delmaire J. P., C.R. Acad. Sci. Ser. C. 272, 1034(1971). 6. Le Brusq H., Delmaire J. P. and Marion F., C.R. Acad. Sci. Ser. C. 273, 139(1971). 7. Le Brusq H. and Delmaire J. P., Rev. Inf. Hautes Temp. Rejracr. 11, 193(1974). 8. Fueki K., Oguri Y. and Makaibo T., Denki Kagaku 38, 758 (1970). 9. Rau H.. 1. Phys. Chem. Solids 35, 1415(1974).

IO. Rau H.. Kutty T. R. N. and Guedes de Carvalho J. R. F., 1. Chem. Thermodynamics 5 291 (1973).

11. Rau H., Kutty T. R. N. and Quedes de Carvalho J. R. F., J. Chem.

Thermodynamics

5.833

(1973).

12. Preuner G. and Schupp W., Z. Phys. C/tern. 68, 157 (1910). 13. Le Brusq H. and Delmaire J. P., Rev. Int. Haufes Temp. Refract 10. 15 (1973). 14. Kubaschweski 0.. Evans E. LI. and Alcock C. B.. Metal/wgical Thermochemistry, 4th Edn. Pergamon Press, Oxford (1967).