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On the defect structure of chromium sulphide
J. Phys.
Chem. Solids
Pergamon Press 1966. Vol. 27, pp. 1027-1030.
ON THE DEFECT STRUCTURE
Printed in Great Britain.
OF CHROMIUM
SULPHIDE S. MROWEC Department
of Inorganic
Chemistry, (Received
and
M. ZASTAWNIK
School of Mining and Metallurgy, 28 September
Cracow, Poland
1965)
Abstract-The kinetics and mechanism of the solid state reaction in the chromium-ulphur and chromium-nickel-sulphur systems have been investigated in the temperature range 600-750°C. It has been found that sulphurization of pure chromium yields homogeneous scale of chromium sulphide, whereas sulphurization of the chromium-nickel alloys produces the scale composed of the solid solution of NiS in C&s. Growth of the reaction product in the both systems proceeds exclusively due to the outward diffusion of the metal, the rate of formation of the solid solution being lower than that of pure chromium sulphide. It is concluded that chromium sulphide exhibits defects in the cation sublattice in form of cation vacancies and electron holes. THE
defect structure of sulphides is not so well understood as that of oxides. It results first of all from the greater experimental difficulties encountered in studies of the type of defects in sulphides than in oxides. The measurements of the electric conductivity for instance, cannot be employed in the case of sulphides to determination of the defect structure, as the concentration of the electronic defects, being often very high, cannot be described in terms of Boltzmann statistics.(l) In addition several sulphides are intrinsic semiconductors. The present paper gives results of studies on kinetics and mechanism of sulphurization of chromium and chromium-nickel alloys which allow one to draw some conclusions regarding the type of defects in CrsSs lattice. EXPERIMENTAL PROCEDURE Experiments were carried out in sulphur vapour at atmospheric pressure in the temperature range 600-750°C using the apparatus described in detail in the previous papers.(ss) The kinetic measurements were made using the continuous gravimetric method which consisted in following the weight gain of the sample during the sulphurization. The experiments were performed on the two-phase alloys containing 18 and 37 at.% nickel and on pure chromium (99.99% Cr). The alloys were
prepared in the vacuum induction furnace. The samples used had the form of flat plates (2 x 1.5 x O-1 cm) and were cut out directly from the casts. In order to remove the stresses and to obtain the homogenous structure, the samples were annealed at 750°C in atmosphere of pure helium for 100 hr. The surface of the specimens was polished with emery paper (including No. 4/O) and then washed with water, methanol and acetone. The kinetic measurements showed that formation of the reaction product on the surface of pure chromium, as well as on the surface of its alloys with nickel, obeys the parabolic rate law: = K,“t+C Am
denotes the ( ) surface a&a of the metallic where
weight gain
per
unit
sample, Kp”-parabolic rate constant, t-sulphurization time, C-constant, which values, different from nought, reflect the deviation from the parabolic run at the beginning of the process, when the system does not reach the stationary state. The parabolic rate constants of the sulphurization process of chromium-nickel alloys, calculated graphically are given in Table 1. Figure 1 represents the relationship between the sulphurization rate of chromium and chromiumnickel alloys and temperature. l(327
1028
S.
MROWEC
and
M.
ZASTAWNIK
Table 1. Parabolic rate constants k” (g2 cm-4 m&z-l) of the solid state reaction in the chromium-sulphur and chromium-nickel-sulphur systems Nickel content at. y0
600
650
700
0.0
8.3 x 10-7
le.5 x 10-e
2.4 x 1O-6
3.6 x10-6
18.0
5.2 x 10-g
1 .o x 10-7
2.1 x 10-7
3.8 x 10-7
37.0
7.6 x 10-E
1.2 x 10-T
1.7 x 10-T
2.8 x 10-7
Temperature
“C 750
-.-
‘cTs I 1
I I.0
0.9
+X103 I 900
I 750
I
I
700
I
I
I.1
I.2
OK-1
650
I
600
I
550
OC FIG. 1. Dependence of sulphurization rate on temperature. x -pure chromium. O-chromium-nickel alloy containing 18 at. o/0 Ni. ~-chromium-nickel alloy containing 37 at.% Ni.
The X-ray analysis showed that the sulphurization product of the alloys is built of the same phase as the product on pure chromium, namely from C&s. Chemical analysis however showed, that the reaction product of both alloys contained about 1 per cent of nickel. These facts suggest that the scale formed on the alloys was the solid solution of nickel sulphide in chromium sulphide. The marker experiments were carried out in order to elucidate the contribution of the particular reagents in the process of material transport through the scale.
Small pieces of platinum wire 1 mm long and 0.05 in. dia. were placed on the surface of the specimens. The specimens were then sulphurized in the horizontal position. After the reaction, the specimens mounted in plastic resin were cut vertically to the marked surface and the cross sections were prepared. Location of the markers in the scale was determined microscopically. It has been found that in both cases: on the pure chromium as well as on two alloys containing 18 and 37 at.% nickel, the platinum markers were observed at the scale/metal interface. That indicates that formation
ON
THE
DEFECT
STRUCTURE
of the layer of the reaction product on chromium and on chromium-nickel alloys investigated in the present paper, occurs due to the outward diffusion of metal, the diffusion coefficient of cations being much greater than that of anions (Dcation 3 Danion). At the same time the possibility of the inward diffusion of the oxidizer is practically excluded.
CONCLUSIONS
From the experimental data discussed above it follows that the diffusion of chromium into the phase of the reaction product is the rate determining step of reaction on pure chromium as well as on its alloys with nickel. The reaction mechanism in both Cr-S and Cr-Ni-S systems is then the same. This conclusion is confirmed by practically the same values of the activation energy of the sulphurization of pure chromium and Cr-Ni alloys (Fig. 1 and Table 2). Table 2. Activation energies of the sulphurization process of pure chromium and chromium-nickel alloys Nickel concentration at. o/0
Temperature range “C
Activation energy kcal
0.0 18.0 37.0
600-750 600-700 600-750
18.3 20.7 17.2
Assuming that the diffusion in the scale takes place according to the Wagner’s theor+) in the form of ions and electrons through the lattice defects of the reaction product, it follows that the chromium sulphide shows point defects mainly in the cation sublattice, although the existence of defects of this type in the anion sublattice is thermodynamically possible. These types of defects may be due to the presence of cation vacancies and equivalent number of electron holes, or to the presence of interstitial cations and equal number of quasi-free electrons. The formation of these two types of defects in the chromium sulphide lattice, mentioned above, may be represented schematically by
OF
CHROMIUM
1029
SULPHIDE
equations : QSs Z? 2CrotTg + 60
+
Crkh
(2)
+ 332
(3)
and CrsSs
e
2Cro*** + 68
where Cro... and CrU,, denote interstitial, trivalent chromium ion and cation vacancy in the chromium sulphide lattice respectively. Symbols 0 and @ denote quasi-free electron in the lattice and electron hole. The lower sulphurization rate in comparison with pure chromium shows, that the ion defect concentration in the scale formed on the alloys is lower than in the scale formed on pure chromium. In order to explain the different rate of sulphurization observed for pure chromium and chromiumnickel alloys one must consider the influence of nickel as a doping agent on the concentration of the two types of defects in the CrsSs lattice presented schematically by equations (2) and (3). The incorporation of bivalent nickel ions into the CrsSs lattice of the defect structure presented by equation (2) can be presented schematically by the equation : @) 2NiS+$Ss
*
2Nie(cr,+2@+CraSs
(4)
or by equation: 3NiS+Crm,,*
z
3Niw(cr,+CrsSs
(5)
where Nia#ccrj denotes bivalent nickel ion replacing trivalent chromium ion on the negative charge in respect to the lattice. The incorporation of nickel ions into the CrsSs lattice of the defect structure presented schematically by equation (3) may be written: 2NiS+20+
%$z
2Niw(cr,+CrsSs
(6)
or 3NiS
e
3 Nie(c,,+Cro***
+ Crass (7)
From the considerations presented above it follows that the process of incorporation of the bivalent nickel ions into the CrsSs lattice of the
1030
S.
and
MROWEC
defect structure presented by equation (2) results in the decrease in concentration of the cation vacancies and simultaneous increase in the electron holes concentration. On the other hand, in the case of the defect structure described by equation (3) this process leads to the increase in concentration of the interstitial cations and simultaneous decrease in concentration of quasi-free electrons. As the kinetic measurements showed, the rate of formation of chromium sulphide doped with nickel is lower than that of pure chromium sulphide. As the sulphurization rate is expected to be proportional to the defect concentration in the layer of the reaction product, it follows that the defect structure of CrsSs is of the type described by equation (2). It may be supposed, that chromium sulphide is a metal deficit p-type semiconductor and has cation vacancies. The proposed model of defect structure of chromium sulphide is presented in Fig. 2. DEREK?et d.(7) had established that the chromium oxide, which shows the 2
S2-
S2-
S’-
S?__
S2-
crs+ S’__
0 s2Cr3 + S2-
Cr3+ s2Cra+ S2-
Cr3+ S?-
Cr3+ SZ-
&a, S2-
Cr3+ S?-
0 S?-
Cr6+ S”_
Cr3+ S2-
FIG. 2. Defect structure of chromium
sulphide.
M.
ZASTAWNIK
analogous type of defects in the lattice, had electron holes which were represented at high temperatures by hexavalent chromium ions Cr+s. Bearing in mind the numerous analogies between CrsSs and CrsOa one can assume the analogous valency of chromium, representing the electron holes, in the lattice of chromium sulphide. In order to check the above given conclusions regarding the model of formation of the defects in the CraSs lattice, some experiments on selfdiffusion of chromium and sulphur in pure and doped chromium sulphide with application of the radioactive indicators are being carried at present.
REFERENCES 1. HAUFFE K., Oxidation oon Metallen wad Legierungen, p. 310. Berlin, Springer (1956). 2. MROWEC S. and WERBER T., Chemia Analit. 7, 605 (1962). 3. CZER~KI L., MROWEC S. and WERBER T., J. Electrothem. Socl 109,273 (1962). 4. WAGNER C.. 2. Phvs. Chem. 21. 25 (19331. 5. WAGNER C. ; Diffson and High. Tem$era&e Oxidation of Metals, p. 153. Atom Movements, Cleveland (1951). 6. HAUFFE K., Reaction in und an festen Stoffen, p. 128. Berlin, Springer (1955). 7. DEREK J., HABER J., PODG~RECKAA. and BURZYK J. J. Catal. 2, 161 (1963).
Chem. Solids
Pergamon Press 1966. Vol. 27, pp. 1027-1030.
ON THE DEFECT STRUCTURE
Printed in Great Britain.
OF CHROMIUM
SULPHIDE S. MROWEC Department
of Inorganic
Chemistry, (Received
and
M. ZASTAWNIK
School of Mining and Metallurgy, 28 September
Cracow, Poland
1965)
Abstract-The kinetics and mechanism of the solid state reaction in the chromium-ulphur and chromium-nickel-sulphur systems have been investigated in the temperature range 600-750°C. It has been found that sulphurization of pure chromium yields homogeneous scale of chromium sulphide, whereas sulphurization of the chromium-nickel alloys produces the scale composed of the solid solution of NiS in C&s. Growth of the reaction product in the both systems proceeds exclusively due to the outward diffusion of the metal, the rate of formation of the solid solution being lower than that of pure chromium sulphide. It is concluded that chromium sulphide exhibits defects in the cation sublattice in form of cation vacancies and electron holes. THE
defect structure of sulphides is not so well understood as that of oxides. It results first of all from the greater experimental difficulties encountered in studies of the type of defects in sulphides than in oxides. The measurements of the electric conductivity for instance, cannot be employed in the case of sulphides to determination of the defect structure, as the concentration of the electronic defects, being often very high, cannot be described in terms of Boltzmann statistics.(l) In addition several sulphides are intrinsic semiconductors. The present paper gives results of studies on kinetics and mechanism of sulphurization of chromium and chromium-nickel alloys which allow one to draw some conclusions regarding the type of defects in CrsSs lattice. EXPERIMENTAL PROCEDURE Experiments were carried out in sulphur vapour at atmospheric pressure in the temperature range 600-750°C using the apparatus described in detail in the previous papers.(ss) The kinetic measurements were made using the continuous gravimetric method which consisted in following the weight gain of the sample during the sulphurization. The experiments were performed on the two-phase alloys containing 18 and 37 at.% nickel and on pure chromium (99.99% Cr). The alloys were
prepared in the vacuum induction furnace. The samples used had the form of flat plates (2 x 1.5 x O-1 cm) and were cut out directly from the casts. In order to remove the stresses and to obtain the homogenous structure, the samples were annealed at 750°C in atmosphere of pure helium for 100 hr. The surface of the specimens was polished with emery paper (including No. 4/O) and then washed with water, methanol and acetone. The kinetic measurements showed that formation of the reaction product on the surface of pure chromium, as well as on the surface of its alloys with nickel, obeys the parabolic rate law: = K,“t+C Am
denotes the ( ) surface a&a of the metallic where
weight gain
per
unit
sample, Kp”-parabolic rate constant, t-sulphurization time, C-constant, which values, different from nought, reflect the deviation from the parabolic run at the beginning of the process, when the system does not reach the stationary state. The parabolic rate constants of the sulphurization process of chromium-nickel alloys, calculated graphically are given in Table 1. Figure 1 represents the relationship between the sulphurization rate of chromium and chromiumnickel alloys and temperature. l(327
1028
S.
MROWEC
and
M.
ZASTAWNIK
Table 1. Parabolic rate constants k” (g2 cm-4 m&z-l) of the solid state reaction in the chromium-sulphur and chromium-nickel-sulphur systems Nickel content at. y0
600
650
700
0.0
8.3 x 10-7
le.5 x 10-e
2.4 x 1O-6
3.6 x10-6
18.0
5.2 x 10-g
1 .o x 10-7
2.1 x 10-7
3.8 x 10-7
37.0
7.6 x 10-E
1.2 x 10-T
1.7 x 10-T
2.8 x 10-7
Temperature
“C 750
-.-
‘cTs I 1
I I.0
0.9
+X103 I 900
I 750
I
I
700
I
I
I.1
I.2
OK-1
650
I
600
I
550
OC FIG. 1. Dependence of sulphurization rate on temperature. x -pure chromium. O-chromium-nickel alloy containing 18 at. o/0 Ni. ~-chromium-nickel alloy containing 37 at.% Ni.
The X-ray analysis showed that the sulphurization product of the alloys is built of the same phase as the product on pure chromium, namely from C&s. Chemical analysis however showed, that the reaction product of both alloys contained about 1 per cent of nickel. These facts suggest that the scale formed on the alloys was the solid solution of nickel sulphide in chromium sulphide. The marker experiments were carried out in order to elucidate the contribution of the particular reagents in the process of material transport through the scale.
Small pieces of platinum wire 1 mm long and 0.05 in. dia. were placed on the surface of the specimens. The specimens were then sulphurized in the horizontal position. After the reaction, the specimens mounted in plastic resin were cut vertically to the marked surface and the cross sections were prepared. Location of the markers in the scale was determined microscopically. It has been found that in both cases: on the pure chromium as well as on two alloys containing 18 and 37 at.% nickel, the platinum markers were observed at the scale/metal interface. That indicates that formation
ON
THE
DEFECT
STRUCTURE
of the layer of the reaction product on chromium and on chromium-nickel alloys investigated in the present paper, occurs due to the outward diffusion of metal, the diffusion coefficient of cations being much greater than that of anions (Dcation 3 Danion). At the same time the possibility of the inward diffusion of the oxidizer is practically excluded.
CONCLUSIONS
From the experimental data discussed above it follows that the diffusion of chromium into the phase of the reaction product is the rate determining step of reaction on pure chromium as well as on its alloys with nickel. The reaction mechanism in both Cr-S and Cr-Ni-S systems is then the same. This conclusion is confirmed by practically the same values of the activation energy of the sulphurization of pure chromium and Cr-Ni alloys (Fig. 1 and Table 2). Table 2. Activation energies of the sulphurization process of pure chromium and chromium-nickel alloys Nickel concentration at. o/0
Temperature range “C
Activation energy kcal
0.0 18.0 37.0
600-750 600-700 600-750
18.3 20.7 17.2
Assuming that the diffusion in the scale takes place according to the Wagner’s theor+) in the form of ions and electrons through the lattice defects of the reaction product, it follows that the chromium sulphide shows point defects mainly in the cation sublattice, although the existence of defects of this type in the anion sublattice is thermodynamically possible. These types of defects may be due to the presence of cation vacancies and equivalent number of electron holes, or to the presence of interstitial cations and equal number of quasi-free electrons. The formation of these two types of defects in the chromium sulphide lattice, mentioned above, may be represented schematically by
OF
CHROMIUM
1029
SULPHIDE
equations : QSs Z? 2CrotTg + 60
+
Crkh
(2)
+ 332
(3)
and CrsSs
e
2Cro*** + 68
where Cro... and CrU,, denote interstitial, trivalent chromium ion and cation vacancy in the chromium sulphide lattice respectively. Symbols 0 and @ denote quasi-free electron in the lattice and electron hole. The lower sulphurization rate in comparison with pure chromium shows, that the ion defect concentration in the scale formed on the alloys is lower than in the scale formed on pure chromium. In order to explain the different rate of sulphurization observed for pure chromium and chromiumnickel alloys one must consider the influence of nickel as a doping agent on the concentration of the two types of defects in the CrsSs lattice presented schematically by equations (2) and (3). The incorporation of bivalent nickel ions into the CrsSs lattice of the defect structure presented by equation (2) can be presented schematically by the equation : @) 2NiS+$Ss
*
2Nie(cr,+2@+CraSs
(4)
or by equation: 3NiS+Crm,,*
z
3Niw(cr,+CrsSs
(5)
where Nia#ccrj denotes bivalent nickel ion replacing trivalent chromium ion on the negative charge in respect to the lattice. The incorporation of nickel ions into the CrsSs lattice of the defect structure presented schematically by equation (3) may be written: 2NiS+20+
%$z
2Niw(cr,+CrsSs
(6)
or 3NiS
e
3 Nie(c,,+Cro***
+ Crass (7)
From the considerations presented above it follows that the process of incorporation of the bivalent nickel ions into the CrsSs lattice of the
1030
S.
and
MROWEC
defect structure presented by equation (2) results in the decrease in concentration of the cation vacancies and simultaneous increase in the electron holes concentration. On the other hand, in the case of the defect structure described by equation (3) this process leads to the increase in concentration of the interstitial cations and simultaneous decrease in concentration of quasi-free electrons. As the kinetic measurements showed, the rate of formation of chromium sulphide doped with nickel is lower than that of pure chromium sulphide. As the sulphurization rate is expected to be proportional to the defect concentration in the layer of the reaction product, it follows that the defect structure of CrsSs is of the type described by equation (2). It may be supposed, that chromium sulphide is a metal deficit p-type semiconductor and has cation vacancies. The proposed model of defect structure of chromium sulphide is presented in Fig. 2. DEREK?et d.(7) had established that the chromium oxide, which shows the 2
S2-
S2-
S’-
S?__
S2-
crs+ S’__
0 s2Cr3 + S2-
Cr3+ s2Cra+ S2-
Cr3+ S?-
Cr3+ SZ-
&a, S2-
Cr3+ S?-
0 S?-
Cr6+ S”_
Cr3+ S2-
FIG. 2. Defect structure of chromium
sulphide.
M.
ZASTAWNIK
analogous type of defects in the lattice, had electron holes which were represented at high temperatures by hexavalent chromium ions Cr+s. Bearing in mind the numerous analogies between CrsSs and CrsOa one can assume the analogous valency of chromium, representing the electron holes, in the lattice of chromium sulphide. In order to check the above given conclusions regarding the model of formation of the defects in the CraSs lattice, some experiments on selfdiffusion of chromium and sulphur in pure and doped chromium sulphide with application of the radioactive indicators are being carried at present.
REFERENCES 1. HAUFFE K., Oxidation oon Metallen wad Legierungen, p. 310. Berlin, Springer (1956). 2. MROWEC S. and WERBER T., Chemia Analit. 7, 605 (1962). 3. CZER~KI L., MROWEC S. and WERBER T., J. Electrothem. Socl 109,273 (1962). 4. WAGNER C.. 2. Phvs. Chem. 21. 25 (19331. 5. WAGNER C. ; Diffson and High. Tem$era&e Oxidation of Metals, p. 153. Atom Movements, Cleveland (1951). 6. HAUFFE K., Reaction in und an festen Stoffen, p. 128. Berlin, Springer (1955). 7. DEREK J., HABER J., PODG~RECKAA. and BURZYK J. J. Catal. 2, 161 (1963).