- Email: [email protected]
Electrical conductivity of samarium sesquioxide
J. Phys. Chcm Sdid.\ Vol. 45. No. Printed in the U.S.A.
I l/12.
pp. 1259-1264.
0022-3697/84 $3.00 + .@I Pergamon Press Ltd.
1984
ELECTRICAL CONDUCTIVITY OF SAMARIUM SESQUIOXIDE KEU HONG KIM, Hut JUN WON and JAE Sm CHOI Department of Chemistry, Yonsei University, Seoul 120, Korea (Received 18 October 1983; accepted in revisedform 26 March 1984) Abstract-The electrical conductivity of polycrystalline samarium sesquioxide was measured in the temperature range 300-1000°C under oxygen pressures of 1O-s-1O-’ atm. The defect structure, type of semiconductor, and electrical conduction mechanism were investigated by measuring the temperature and oxygen pressure dependence of the electrical conductivity. The calculated activation energy was 1.18eV in the high temperature region and 0.39 eV in the low temperature region. The oxygen pressure dependence of the electrical conductivity is characterized by d cc P&.5 in the temperature region below 650°C and (T cc Pxi,3 in the high temperature region. SmzOJ exhibits electronic hole conduction involving two different defects, i.e., a 0: + V”, mixture and V;$ in the two temperature regions. A conduction mechanism is suggested.
INTRODUCIION The polymorphism of Sm,O, has been studied by many investigators. Sm,O, can exhibit A, B, C, X and H type structures because it is relatively thermally stable. The A, B and C type structures are classified as being hexagonal, monoclinic, and cubic, respectively, while the Hand X type structures can exist only above 2000°C. The H type structure is a hexagonal structure similar to the A type, while the structure of the X type is not known. When metallic samarium is oxidized, the oxide generally has the C type structure, which is stable below 95O’C but transforms above 950°C to the B type structure which is stable between 950 and 182O”C[ 11. A proper understanding of the polymorphic nature of Sm,03 is fundamental to any study involving this compound, particularly in view of the reaction of Smz09 at elevated temperatures. A large number of investigators, starting with Goldschmidt et al. [2], have tried to clarify the polymorphic relations. The transformation temperature of Sm,O, is not unique because it depends on the treatment procedure, purity, and the sintering temperature and Po2 of the sample, which are not the same from sample to sample. It has been reported that SmzOs is a pure electronic semiconductor[3]. Other investigators have suggested that SmzOs is a mixed ionic-electronic semiconductor[4] or a pure ionic semiconductor[5]. Thus the conduction mechanism of Sm20J is not completely understood. Noddack et a/.[31 have reported the d.c. conductivity of sintered specimens of Smr03 in air as a function of temperature in the temperature range 873 to 1573 K. They concluded that conduction in SmzOs is attributable to the electronic contribution, and that the ionic contribution is less than 0.01%. However, they could not confirm the exact conduction mechanism nor whether Smz03 was n-type or ptype. Studies similar to those of Noddack have been reported by Subba Rao et a1.[4]. They reported
that Sm,09 showed both p-type and n-type properties depending on composition and that an inflection point appeared at 500-600°C. Tare and Schmalzried[S] measured the electrical conductivity of 99.99% pure SmrOr by the solid state emf method in the temperature range 600-9OO’C under oxygen pressures of 1O-‘o-1 atm. They concluded that SmlOr is a pure ionic semiconductor. Neumin et al. [6] and Samsonov et al. [7] measured the electrical conductivity of SmzOs by the two-probe method in the temperature range 400-1200°C under various oxygen pressures and concluded that SmzOs is a pure electronic semiconductor. The main purpose of this study is to determine the defect structure, the transport process for defects, and the conduction mechanism in Smr03 (C type structure only) using the four-probe method at temperatures from 300 to 1000°C and oxygen pressures of 10-5-10-’ atm. EXPERIMENTAL SECTION Sample preparation
Sm,O, powder having a purity of 99.99% from the Johnson-Matthey Co. was heated in vaccum at 600°C for three hours to eliminate the adsorbed gases. The powder was then compressed under 49.03 MPa pressure in vacuum into a small pellet. This pellet was sintered in an electric furnace at 1000°C under atmospheric pressure for 24 hr. The sintered pellet was etched with etching solution, annealed for an additional 60 hr and then quenched to room temperature. The pellet was given a light abrasive polish on both faces in the area to serve as the interface region until voids were fully eliminated. The specimen was cut into a rectangular form, 0.5 x 1.0 x 0.15 cm3 in size, and then four equally spaced holes were drilled in a row on one surface to provide a four-probe contact. An emission spectrographic analysis of the Sm,O,
1259
1260
KEU HONG KIM et al.
as received is given in Table 1. The pellet density measured by the mercury immersion method was 7.846 g/cm3, with an average grain size of approximately 7.20 pm. The sample had 56% porosity and the average pore size was approximately 0.85 pm. Conductivity measurement procedure Details on the instruments, the vacuum system, the furnace assembly, the circuitry, a four-probe contact model, and the conductivity calculation procedure have been reported in previous publications[8lo]. The current through the sample ranged from 1 X lo-’ to I X 10-l A and the potential applied to the sample ranged between 1 X IO-* and 1 X low3 V. The oxygen partial pressures desired were established using pure oxygen or a mixture of 0.00 I% oxygen in nitrogen obtained from Matheson Gas Products. Dtflerences in the sample’s characteristics and in the ~ondit~ans of conductivity measurements Noddack er a!.[31 used 99.95% Sm,O, which was sintered at 1300°C and measured the conductivity in the temperature range 600-1200°C in air. Subba Rao et al.[4] used 99.99% Sm,O, which was sintered at 950°C under 9OOOpsi pressure. They measured the conductivity in the temperature range 600-900°C under 150 torr PO,. In this work, 99.99% SmrO, was used. The specimen was sintered at 1000°C under atmosphere pressure. The conductivities were measured in the temperature range 300-1000°C under Po2’s of 10M510-i atm. RESULTS
Temperature dependence of the electrical conductivity The observed temperature dependence of the electrical conductivity of Sm,O, is shown in Figs. 1 and 2. As shown in Fig. 1, the electrical conductivity increased with increasing oxygen partial pressure at constant temperature and decreased with decreasing temperature at constant oxygen partial pressure. The most prominent features of the temperature dependence curves are the inflections. These inflections occurred for all the ranges of oxygen partial pressure investigated. This is the first report of data on the conductivity of Smz03 to show such an inflection. This change in slope indicates that the conduction mechanism in the higher temperature region is different from that in the lower temperature region.
Table 2 shows the activation energies in the highand low-temperature regions. The average values of the activation energies in the high- and lowtemperature regions are 1.18 eV and 0.39 eV, respectively. It is suggested that 1.18 eV is a composite of energies for the formation of defects, defect ionization, and electron hole mobility at high temperature region. In the low temperature region, the activation energy, 0.39 eV, is believed to be the mi~ation energy of the electron hole which is formed in the valence band. Figure 2 provides a comparison of the temperature dependence of the electrical conductivity found in this work with those reported by Noddack et al.[3] and Rao et al.[4]. The temperature dependences of the conductivity agree with each other in the high temperature region above 65O”C, though the magnitude of the conductivity observed in this work is somewhat higher than that observed by Rao et al. [4], under the same oxygen partial pressure of 2 X 10-I atm, and somewhat lower than that of Noddack et aL[3]. Table 3 compares the activation energies observed by Noddack et al.[3], Rao et a1.[4], and in this work. The present activation energy observed for the high temperature region above 650°C agrees well with the others[3, 41. Oxygen pressure dependence of the electrical conductivity Figure 3 shows the oxygen pressure dependence of the electrical conductivity for the temperatures investigated. The conductivity increases with increasing oxygen partial pressure. This indicates that Sm,O, is p-type, characterized by c cc PgJ. As shown in Table 4, the oxygen pressure dependence of the electrical conductivity has two different values; one is a CCPb(i.’ in the temperature region below 650°C and W’ - Pgzi:”at temperatures above the other is u cc Po* 65O’C. This suggests that there are two possible defect structures for the high- and low-temperature regions. DISCUSSION
Possible defect in Srn203 at higher temperatures (- 1000”c) The dominant defect in metal oxides which exhibit p-type semi-conductor properties is the metal vacancy, and most compounds will not take oxygen interstitials because of size. In the cubic rare earth
Si
19
03
Al
13
@f9
Fe
7
rare
<3
2
earths
C6
1261
Electrical conductivity of samarium sesquioxide 1000900800700600 II I I
500 I
I
400 I
300 I
(ocf
Fb2(atm)
I _ ^ U.f)
0
I^
I
I
1.2
1.0
1.4
4
2 x 10-l
+
4 x 1o-3
-#-
5 x zo-4
+I+
2 x 1o-5
I
I
1.6
I.8
I 2.0
103,'T (K-l )
Fig. 1. Log conducti~ty
vs 10% for SmzOJ at various oxygen partial pressures.
type C structure like nonstoichiometric Sm,O,, however, deviation from the stoichiometric composition can be achieved by the introduction of excess oxygen
at interstitial oxygen positions. The radius of the anion is similar to that of the cation in Sm,O, (O*- = 124pm, Sm3+ = 109.8pm). Sm203 has the I
I
8o0°C
I
700°c
600°C
-
Noddack et al. 3)
e
'Ihiswork Subba Rae et al.4)
------
-6
I 0.8
I
I
0.9
1.0
I 1.1
103/T (K -I)
Fig. 2. Comparison of log conductivity vs l/T for SmzOS at various oxygen partial pressures.
1262
KEU
HONGKIM et al.
Table 2. Activation energies for the conductivity of Sm,O, under various oxygen pressures Activation PO2
(atno
Imw
Energy
Temperature
(ev)
High
Region
Temperature Region
-1 2 x 10
0.38
1.17
4 x 10-3
0.39
1.17
5 x 10-4
0.39
1.18
2 x 10-5
0.40
1.20
same structure as YzO, at the temperatures investigated. Bratton[ 1l] reported that the principal defects in lOmol% ZrOo2-Y203 are oxygen interstitials. It was also suggested that oxygen interstitials exist in undoped Y,03. According to the metal vacancy model, the formation of an effectively negative doubly charged metal vacancy, Vb, can be expressed as follows, 30, &
600 + 4V; + 8/i
(1)
where 0, is a lattice oxygen and h’ represents an effective positive singly charged electron hole. If the doubly ionized metal vacancies proceed to fully ionized metal vacancies in this sesquioxide, the following equilibrium exists, 4V& E& 4Vj + 4/i
(2)
where VL is an effective negative triply charged metal vacancy. In the presence of a metal vacancy, if the two equilibria are achieved, one can write the sum of the two reactions: 30, &
60, + 4V” + 12h’.
K3 = K, - K2 = [V”14P”Po:.
In eqns (4) and (5), P is the concentration of the effective positive singly charged electron holes. If the conservation of metal vacancies can be written as [VL] = [VL] + [VL], where VG is the total metal vacancy, then for [Vi] = 0, with charge being conserved and assuming that the electrical neutrality condition is [Vk] = %P in equilibrium (3), the equilibrium constant K3 is (f)4P’6 P$. If K1 and Kz are known, if one solves for P as a function of Po2 at constant temperature, the result is P = (34-K,) “I6 Px6. If the electrical conductivity is proportional to the hole concentration in the high temperature region above 650°C (i.e. the mobility is not PO, dependent), it is obvious from this that the oxygen pressure dependence of the electrical conductivity is a cc P = K’Pg6. This theoretical exponent of $ based on the disorder reaction (3) is consistent with the experimental value of &-& found for temperatures above 65O’C. Possible defects ( - 65OT)
(3)
If the concentration of defects is low, and the interactions among defects are negligible, the three equilibrium constants are: K, = [V”,]4p8Pz,
(4)
K2 = [V;]4P-+[V$,-4,
(5)
in Sm,O,
at
lower
This
1.16
et FL.~'
Subba
Rae
1.28
temperatures
At temperatures below 650°C the oxygen pressure dependence of the conductivity (u a Pgz.‘) is different from that at temperatures above 650°C. As shown in Table 2, the activation energy observed in the high temperature region is larger than that observed in the low temperature region. This indicates that the defect structure in Sm,O, in the low temperature region is different from that in the high temperature region and the conduction mechanism is also different in the two temperature regions. The remaining dominant defect in Sm,O, @-type) is the oxygen interstitial. The oxygen interstitial is formed by the following disorder reactions,
Table 3. Observed activation energies (ev) for the d.c. conductivity of Sm,O,
Noddack
(6)
et a1.4)
High
Temp.
1.18
work LOW
Temp.
0.39
Electrical conductivity of samarium sesquioxide
1263
-2 ' 2 x 10-5
' 5 x 10-4
I 2 x 10-l
' 4 x 10-3
PO2
(etm)
6OO'C 500°C 400°C
-81
I
I
-5
-4
I -3
1 -2
I -1
,
Log Po2 (atm)
Fig. 3. Log conductivity vs log PO, for Sm203 at various temperatures.
(7) o;z$o:l+r;
(8)
where 0: and 0; are effective negative singly and doubly charged oxygen interstitials, respectively. If the disorder reaction (7) proceeds to (8), the following equilibrium can exist for Sm,O, in the low temperature region. ;o, The
equilibrium
&+*A.
constant
(9) can
be
written
as
K = [W]pP&“*’ and assuming [w] is equal to ;P as
an electrical neutrality
condition in equilibrium
K = iP3Po$“2). If the electrical conductivity is proportional to the hole concentration in the low temperature region, the oxygen pressure dependence of the conductivity is u cc P = (2K)“‘P$. This theoretically predicted exponent of d based on the disorder reaction (9) is not consistent with the experimental value of &, If equilibrium (7) exists in Smz03 in the low temperature region, the theoretically predicted dependence is u cc Pb’,“.Therefore, equilibrium (7) can not be predominant in Sm203. One must consider alternative defects which might be involved in Sm,Oj in the low temperature region, i.e. a possible mixture of VG and 0: defects. If V” and 0; exist in Sm203, it is reasonable to write the sum of the two equilibria (3) and (9)
(9), 20&30,+0;+2V;+8h.
Table 4. l/n values obtained from the equation log Q = I/n log PO, + constant for Sm203 Temperature (“C,
l/n
The above equilibrium follows:
constant
(10) can be written as
K’ = [o;][V$]zP* PZ. 300
l/5.5
400
l/5.5
500
y5.5
600
l/5.5
700
l/5.3
800
l/5.3
900
l/5.2
1000
l/5.2
(11)
Because P is equal to 2[q + 3[V;;] and [O;] _N[&I in the defect mixture in equilibrium (IO), S[V$!,] = P and K’ is (5)’ P”P$. If the electrical conductivity is proportional to the hole concentration, the conductivity dependence on oxygen partial pressure is u a P = (5’K’)““P$’
’.
This value of fi which was evaluated
based on the disorder reaction (10) is consistent with the experimental value of & shown in Table 4. It is reasonable to suggest that the possible defect in Sm,03 at low
1264
temperatures and 0;.
KEXJHONG KIM et al.
below
650°C
is a mixture
of V”
Acknowledgement-We are grateful to the Ministry of Education of Korea for financial support and to Dr. Young Hwan Kang and Prof. Ki Hyun Yoon for helpful discussions. We also thank Mr. Jong Ho Jun for his assistance with the paper and Dr. Ki Hyun Yoon at the Department of Ceramic Engineering, Yonsei University for the measurements of pellet density, grain size, porosity, and pore size of the sample. REFERENCES 1. Boulesteix C., Pardo B., Caro P. F. and Gasgnier M., Acta Crystallogr. Sect. B. 216 (1971). 2. Goldschmidt V. M., Ulrich F. and Barth T., Skrfrifter Norska Videnskaps-Akad. Oslo, I. Mat. Naturv KI 1, 117 (1925).
3. Noddack W. and Walch H., Z. Elektrochem. 63, 269 (1959). 4. Subba Rao, G. V., Ramdas S., Mehrotra P. N. and Ramachandr Rao C. N., J. Solid. St. Chem. 2, 377 (1970). 5. Tare V. B. and Schmalzried H., Z. Physik. Chem. N. F., 43, 30 (1964). 6. Neumin A. D., Balakireva V. B. and Palguev S. F., Dokl. Akad. Nauk SSSR 209, 1150 (1973). 7. Samsonov G. V., Gilman I. Y. and Andreeva A. F., Izv. Akad. Nauk SSSR Neorg. Mater. 10, 1645 (1974). 8. Choi J. S., Lee H. Y. and Kim K. H., J. Phys. Chem. 77, 2430 (1973). 9. Choi J. S. and Kim K. H., J. Phys. Chem. 80, 666 (1976). 10. Choi J. S., Kang Y. H. and Kim K. H., J. Phys. Chem. 81, 2208 (1977). 11. Bratton R. J., J. Am. Ceram. Sot. 52, 213 (1969).
I l/12.
pp. 1259-1264.
0022-3697/84 $3.00 + .@I Pergamon Press Ltd.
1984
ELECTRICAL CONDUCTIVITY OF SAMARIUM SESQUIOXIDE KEU HONG KIM, Hut JUN WON and JAE Sm CHOI Department of Chemistry, Yonsei University, Seoul 120, Korea (Received 18 October 1983; accepted in revisedform 26 March 1984) Abstract-The electrical conductivity of polycrystalline samarium sesquioxide was measured in the temperature range 300-1000°C under oxygen pressures of 1O-s-1O-’ atm. The defect structure, type of semiconductor, and electrical conduction mechanism were investigated by measuring the temperature and oxygen pressure dependence of the electrical conductivity. The calculated activation energy was 1.18eV in the high temperature region and 0.39 eV in the low temperature region. The oxygen pressure dependence of the electrical conductivity is characterized by d cc P&.5 in the temperature region below 650°C and (T cc Pxi,3 in the high temperature region. SmzOJ exhibits electronic hole conduction involving two different defects, i.e., a 0: + V”, mixture and V;$ in the two temperature regions. A conduction mechanism is suggested.
INTRODUCIION The polymorphism of Sm,O, has been studied by many investigators. Sm,O, can exhibit A, B, C, X and H type structures because it is relatively thermally stable. The A, B and C type structures are classified as being hexagonal, monoclinic, and cubic, respectively, while the Hand X type structures can exist only above 2000°C. The H type structure is a hexagonal structure similar to the A type, while the structure of the X type is not known. When metallic samarium is oxidized, the oxide generally has the C type structure, which is stable below 95O’C but transforms above 950°C to the B type structure which is stable between 950 and 182O”C[ 11. A proper understanding of the polymorphic nature of Sm,03 is fundamental to any study involving this compound, particularly in view of the reaction of Smz09 at elevated temperatures. A large number of investigators, starting with Goldschmidt et al. [2], have tried to clarify the polymorphic relations. The transformation temperature of Sm,O, is not unique because it depends on the treatment procedure, purity, and the sintering temperature and Po2 of the sample, which are not the same from sample to sample. It has been reported that SmzOs is a pure electronic semiconductor[3]. Other investigators have suggested that SmzOs is a mixed ionic-electronic semiconductor[4] or a pure ionic semiconductor[5]. Thus the conduction mechanism of Sm20J is not completely understood. Noddack et a/.[31 have reported the d.c. conductivity of sintered specimens of Smr03 in air as a function of temperature in the temperature range 873 to 1573 K. They concluded that conduction in SmzOs is attributable to the electronic contribution, and that the ionic contribution is less than 0.01%. However, they could not confirm the exact conduction mechanism nor whether Smz03 was n-type or ptype. Studies similar to those of Noddack have been reported by Subba Rao et a1.[4]. They reported
that Sm,09 showed both p-type and n-type properties depending on composition and that an inflection point appeared at 500-600°C. Tare and Schmalzried[S] measured the electrical conductivity of 99.99% pure SmrOr by the solid state emf method in the temperature range 600-9OO’C under oxygen pressures of 1O-‘o-1 atm. They concluded that SmlOr is a pure ionic semiconductor. Neumin et al. [6] and Samsonov et al. [7] measured the electrical conductivity of SmzOs by the two-probe method in the temperature range 400-1200°C under various oxygen pressures and concluded that SmzOs is a pure electronic semiconductor. The main purpose of this study is to determine the defect structure, the transport process for defects, and the conduction mechanism in Smr03 (C type structure only) using the four-probe method at temperatures from 300 to 1000°C and oxygen pressures of 10-5-10-’ atm. EXPERIMENTAL SECTION Sample preparation
Sm,O, powder having a purity of 99.99% from the Johnson-Matthey Co. was heated in vaccum at 600°C for three hours to eliminate the adsorbed gases. The powder was then compressed under 49.03 MPa pressure in vacuum into a small pellet. This pellet was sintered in an electric furnace at 1000°C under atmospheric pressure for 24 hr. The sintered pellet was etched with etching solution, annealed for an additional 60 hr and then quenched to room temperature. The pellet was given a light abrasive polish on both faces in the area to serve as the interface region until voids were fully eliminated. The specimen was cut into a rectangular form, 0.5 x 1.0 x 0.15 cm3 in size, and then four equally spaced holes were drilled in a row on one surface to provide a four-probe contact. An emission spectrographic analysis of the Sm,O,
1259
1260
KEU HONG KIM et al.
as received is given in Table 1. The pellet density measured by the mercury immersion method was 7.846 g/cm3, with an average grain size of approximately 7.20 pm. The sample had 56% porosity and the average pore size was approximately 0.85 pm. Conductivity measurement procedure Details on the instruments, the vacuum system, the furnace assembly, the circuitry, a four-probe contact model, and the conductivity calculation procedure have been reported in previous publications[8lo]. The current through the sample ranged from 1 X lo-’ to I X 10-l A and the potential applied to the sample ranged between 1 X IO-* and 1 X low3 V. The oxygen partial pressures desired were established using pure oxygen or a mixture of 0.00 I% oxygen in nitrogen obtained from Matheson Gas Products. Dtflerences in the sample’s characteristics and in the ~ondit~ans of conductivity measurements Noddack er a!.[31 used 99.95% Sm,O, which was sintered at 1300°C and measured the conductivity in the temperature range 600-1200°C in air. Subba Rao et al.[4] used 99.99% Sm,O, which was sintered at 950°C under 9OOOpsi pressure. They measured the conductivity in the temperature range 600-900°C under 150 torr PO,. In this work, 99.99% SmrO, was used. The specimen was sintered at 1000°C under atmosphere pressure. The conductivities were measured in the temperature range 300-1000°C under Po2’s of 10M510-i atm. RESULTS
Temperature dependence of the electrical conductivity The observed temperature dependence of the electrical conductivity of Sm,O, is shown in Figs. 1 and 2. As shown in Fig. 1, the electrical conductivity increased with increasing oxygen partial pressure at constant temperature and decreased with decreasing temperature at constant oxygen partial pressure. The most prominent features of the temperature dependence curves are the inflections. These inflections occurred for all the ranges of oxygen partial pressure investigated. This is the first report of data on the conductivity of Smz03 to show such an inflection. This change in slope indicates that the conduction mechanism in the higher temperature region is different from that in the lower temperature region.
Table 2 shows the activation energies in the highand low-temperature regions. The average values of the activation energies in the high- and lowtemperature regions are 1.18 eV and 0.39 eV, respectively. It is suggested that 1.18 eV is a composite of energies for the formation of defects, defect ionization, and electron hole mobility at high temperature region. In the low temperature region, the activation energy, 0.39 eV, is believed to be the mi~ation energy of the electron hole which is formed in the valence band. Figure 2 provides a comparison of the temperature dependence of the electrical conductivity found in this work with those reported by Noddack et al.[3] and Rao et al.[4]. The temperature dependences of the conductivity agree with each other in the high temperature region above 65O”C, though the magnitude of the conductivity observed in this work is somewhat higher than that observed by Rao et al. [4], under the same oxygen partial pressure of 2 X 10-I atm, and somewhat lower than that of Noddack et aL[3]. Table 3 compares the activation energies observed by Noddack et al.[3], Rao et a1.[4], and in this work. The present activation energy observed for the high temperature region above 650°C agrees well with the others[3, 41. Oxygen pressure dependence of the electrical conductivity Figure 3 shows the oxygen pressure dependence of the electrical conductivity for the temperatures investigated. The conductivity increases with increasing oxygen partial pressure. This indicates that Sm,O, is p-type, characterized by c cc PgJ. As shown in Table 4, the oxygen pressure dependence of the electrical conductivity has two different values; one is a CCPb(i.’ in the temperature region below 650°C and W’ - Pgzi:”at temperatures above the other is u cc Po* 65O’C. This suggests that there are two possible defect structures for the high- and low-temperature regions. DISCUSSION
Possible defect in Srn203 at higher temperatures (- 1000”c) The dominant defect in metal oxides which exhibit p-type semi-conductor properties is the metal vacancy, and most compounds will not take oxygen interstitials because of size. In the cubic rare earth
Si
19
03
Al
13
@f9
Fe
7
rare
<3
2
earths
C6
1261
Electrical conductivity of samarium sesquioxide 1000900800700600 II I I
500 I
I
400 I
300 I
(ocf
Fb2(atm)
I _ ^ U.f)
0
I^
I
I
1.2
1.0
1.4
4
2 x 10-l
+
4 x 1o-3
-#-
5 x zo-4
+I+
2 x 1o-5
I
I
1.6
I.8
I 2.0
103,'T (K-l )
Fig. 1. Log conducti~ty
vs 10% for SmzOJ at various oxygen partial pressures.
type C structure like nonstoichiometric Sm,O,, however, deviation from the stoichiometric composition can be achieved by the introduction of excess oxygen
at interstitial oxygen positions. The radius of the anion is similar to that of the cation in Sm,O, (O*- = 124pm, Sm3+ = 109.8pm). Sm203 has the I
I
8o0°C
I
700°c
600°C
-
Noddack et al. 3)
e
'Ihiswork Subba Rae et al.4)
------
-6
I 0.8
I
I
0.9
1.0
I 1.1
103/T (K -I)
Fig. 2. Comparison of log conductivity vs l/T for SmzOS at various oxygen partial pressures.
1262
KEU
HONGKIM et al.
Table 2. Activation energies for the conductivity of Sm,O, under various oxygen pressures Activation PO2
(atno
Imw
Energy
Temperature
(ev)
High
Region
Temperature Region
-1 2 x 10
0.38
1.17
4 x 10-3
0.39
1.17
5 x 10-4
0.39
1.18
2 x 10-5
0.40
1.20
same structure as YzO, at the temperatures investigated. Bratton[ 1l] reported that the principal defects in lOmol% ZrOo2-Y203 are oxygen interstitials. It was also suggested that oxygen interstitials exist in undoped Y,03. According to the metal vacancy model, the formation of an effectively negative doubly charged metal vacancy, Vb, can be expressed as follows, 30, &
600 + 4V; + 8/i
(1)
where 0, is a lattice oxygen and h’ represents an effective positive singly charged electron hole. If the doubly ionized metal vacancies proceed to fully ionized metal vacancies in this sesquioxide, the following equilibrium exists, 4V& E& 4Vj + 4/i
(2)
where VL is an effective negative triply charged metal vacancy. In the presence of a metal vacancy, if the two equilibria are achieved, one can write the sum of the two reactions: 30, &
60, + 4V” + 12h’.
K3 = K, - K2 = [V”14P”Po:.
In eqns (4) and (5), P is the concentration of the effective positive singly charged electron holes. If the conservation of metal vacancies can be written as [VL] = [VL] + [VL], where VG is the total metal vacancy, then for [Vi] = 0, with charge being conserved and assuming that the electrical neutrality condition is [Vk] = %P in equilibrium (3), the equilibrium constant K3 is (f)4P’6 P$. If K1 and Kz are known, if one solves for P as a function of Po2 at constant temperature, the result is P = (34-K,) “I6 Px6. If the electrical conductivity is proportional to the hole concentration in the high temperature region above 650°C (i.e. the mobility is not PO, dependent), it is obvious from this that the oxygen pressure dependence of the electrical conductivity is a cc P = K’Pg6. This theoretical exponent of $ based on the disorder reaction (3) is consistent with the experimental value of &-& found for temperatures above 65O’C. Possible defects ( - 65OT)
(3)
If the concentration of defects is low, and the interactions among defects are negligible, the three equilibrium constants are: K, = [V”,]4p8Pz,
(4)
K2 = [V;]4P-+[V$,-4,
(5)
in Sm,O,
at
lower
This
1.16
et FL.~'
Subba
Rae
1.28
temperatures
At temperatures below 650°C the oxygen pressure dependence of the conductivity (u a Pgz.‘) is different from that at temperatures above 650°C. As shown in Table 2, the activation energy observed in the high temperature region is larger than that observed in the low temperature region. This indicates that the defect structure in Sm,O, in the low temperature region is different from that in the high temperature region and the conduction mechanism is also different in the two temperature regions. The remaining dominant defect in Sm,O, @-type) is the oxygen interstitial. The oxygen interstitial is formed by the following disorder reactions,
Table 3. Observed activation energies (ev) for the d.c. conductivity of Sm,O,
Noddack
(6)
et a1.4)
High
Temp.
1.18
work LOW
Temp.
0.39
Electrical conductivity of samarium sesquioxide
1263
-2 ' 2 x 10-5
' 5 x 10-4
I 2 x 10-l
' 4 x 10-3
PO2
(etm)
6OO'C 500°C 400°C
-81
I
I
-5
-4
I -3
1 -2
I -1
,
Log Po2 (atm)
Fig. 3. Log conductivity vs log PO, for Sm203 at various temperatures.
(7) o;z$o:l+r;
(8)
where 0: and 0; are effective negative singly and doubly charged oxygen interstitials, respectively. If the disorder reaction (7) proceeds to (8), the following equilibrium can exist for Sm,O, in the low temperature region. ;o, The
equilibrium
&+*A.
constant
(9) can
be
written
as
K = [W]pP&“*’ and assuming [w] is equal to ;P as
an electrical neutrality
condition in equilibrium
K = iP3Po$“2). If the electrical conductivity is proportional to the hole concentration in the low temperature region, the oxygen pressure dependence of the conductivity is u cc P = (2K)“‘P$. This theoretically predicted exponent of d based on the disorder reaction (9) is not consistent with the experimental value of &, If equilibrium (7) exists in Smz03 in the low temperature region, the theoretically predicted dependence is u cc Pb’,“.Therefore, equilibrium (7) can not be predominant in Sm203. One must consider alternative defects which might be involved in Sm,Oj in the low temperature region, i.e. a possible mixture of VG and 0: defects. If V” and 0; exist in Sm203, it is reasonable to write the sum of the two equilibria (3) and (9)
(9), 20&30,+0;+2V;+8h.
Table 4. l/n values obtained from the equation log Q = I/n log PO, + constant for Sm203 Temperature (“C,
l/n
The above equilibrium follows:
constant
(10) can be written as
K’ = [o;][V$]zP* PZ. 300
l/5.5
400
l/5.5
500
y5.5
600
l/5.5
700
l/5.3
800
l/5.3
900
l/5.2
1000
l/5.2
(11)
Because P is equal to 2[q + 3[V;;] and [O;] _N[&I in the defect mixture in equilibrium (IO), S[V$!,] = P and K’ is (5)’ P”P$. If the electrical conductivity is proportional to the hole concentration, the conductivity dependence on oxygen partial pressure is u a P = (5’K’)““P$’
’.
This value of fi which was evaluated
based on the disorder reaction (10) is consistent with the experimental value of & shown in Table 4. It is reasonable to suggest that the possible defect in Sm,03 at low
1264
temperatures and 0;.
KEXJHONG KIM et al.
below
650°C
is a mixture
of V”
Acknowledgement-We are grateful to the Ministry of Education of Korea for financial support and to Dr. Young Hwan Kang and Prof. Ki Hyun Yoon for helpful discussions. We also thank Mr. Jong Ho Jun for his assistance with the paper and Dr. Ki Hyun Yoon at the Department of Ceramic Engineering, Yonsei University for the measurements of pellet density, grain size, porosity, and pore size of the sample. REFERENCES 1. Boulesteix C., Pardo B., Caro P. F. and Gasgnier M., Acta Crystallogr. Sect. B. 216 (1971). 2. Goldschmidt V. M., Ulrich F. and Barth T., Skrfrifter Norska Videnskaps-Akad. Oslo, I. Mat. Naturv KI 1, 117 (1925).
3. Noddack W. and Walch H., Z. Elektrochem. 63, 269 (1959). 4. Subba Rao, G. V., Ramdas S., Mehrotra P. N. and Ramachandr Rao C. N., J. Solid. St. Chem. 2, 377 (1970). 5. Tare V. B. and Schmalzried H., Z. Physik. Chem. N. F., 43, 30 (1964). 6. Neumin A. D., Balakireva V. B. and Palguev S. F., Dokl. Akad. Nauk SSSR 209, 1150 (1973). 7. Samsonov G. V., Gilman I. Y. and Andreeva A. F., Izv. Akad. Nauk SSSR Neorg. Mater. 10, 1645 (1974). 8. Choi J. S., Lee H. Y. and Kim K. H., J. Phys. Chem. 77, 2430 (1973). 9. Choi J. S. and Kim K. H., J. Phys. Chem. 80, 666 (1976). 10. Choi J. S., Kang Y. H. and Kim K. H., J. Phys. Chem. 81, 2208 (1977). 11. Bratton R. J., J. Am. Ceram. Sot. 52, 213 (1969).