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On the defect structure of acceptor-doped α-Nb2O5
Journul of the Less-Common Metals, 84 (1982) 215
ON THE DEFECT
U. BALACHANDRAN
STRUCTURE
215
- 223
OF ACCEPTOR-DOPED
cr-Nb,O,
and N. G. EROR
Oregon Graduate Center, Beauerton, OR 97006 (U.S.A.) (Received September 19, 1981)
Summary The defect structure of acceptor-doped (aluminum or chromium) c1Nb,O, was investigated by measuring the oxygen partial pressure PO, (10’ lo- l8 atm) dependence of the electrical conductivity at 1000 and 1050 “C. The observed data were proportional to Po2p114for PO2< 10-l atm and were proportional to PO*+‘I4 for PO, > 10m4 atm. The absolute values of the electrical conductivity in the acceptor-doped samples were found to be lower in the n-type region compared with the values in the undoped cr-Nb,O,. The conductivity values were observed to increase with the acceptor concentration in the p-type region with a shift in the conductivity minimum towards a lower oxygen partial pressure. The effectiveness of aluminum and of chromium as acceptor impurities in or-Nb,O, was found to be nearly the same.
1. Introduction The potential use of niobium for high temperature service has focused attention on its oxides since these make up the barrier layers between the metal and the gas phase during oxidation. Nb,O, is the main oxide formed during oxidation at temperatures above 500 “C [l]. It has been shown by many investigators [2 - 63 that Nb,O, crystallizes in five different modifications. The high temperature modification, a-Nb,O,, has a monoclinic structure [3, 7, S]. The low temperature modification transforms irreversibly to a-Nb,O, at about 830 “C [3]. The nature of the non-stoichiometry in Nb,O, has been studied by a number of investigators [2, 9 - 131. Most of the studies concluded that the defect structure involves singly and doubly ionized oxygen vacancies. Recently Balachandran and Eror [13] interpreted the electrical conductivity and thermogravimetric measurements on undoped a-Nb,O, on the basis of the 0022.5088/82/0000-0000/$02.75
(0 Elsevier Sequoia/Printed
in The Netherlands
216
doubly ionized oxygen vacancies and accidental acceptor impurities present in the samples. ct-Nb,O, with added acceptor impurities, however, has not been studied in the past. The purpose of the present work was to make a detailed study of the electrical conductivity in aluminum- and chromium-doped polycrystalline CG Nb,O, at 1000 - 1050 “C while in equilibrium with the oxygen partial pressure PO, of the surrounding atmosphere. The amounts of aluminum or chromium selected were 0.003, 0.0055 and 0.008 (0.0083 for chromium) in the general formula AI,Nb, -XO, or Cr,Nb, _,O,.
2. Experimental
details
The samples employed in this investigation were prepared by a liquid mix technique [14, 151. The source materials were niobium oxalate, aluminum nitrate and chromium nitrate, all in the form of solutions. The powder samples obtained from the oxalate solutions were pressed into rectangular slabs (2.1 cm x 0.6 em x 0.05 cm) under a load of 40 000 Ibf in-’ and sintered in air at 1350 “C for 8 h. The density of the sintered slabs was 93% of the theoretical density. Electrical conductivity samples were cut from this slab using an air-brasive unit. The specimens were wrapped with four 0.03 cm platinum wires as described in the literature [16, 171. Small notches were cut in the edges of the sample to help to hold the platinum wires in place. A conventional four-probe d.c. technique was employed for all electrical conductivity measurements. The four platinum leads were insulated from one another by recrystallized high purity alumina insulators. A standard taper Pyrex joint to which capillary tubes had been sealed was mounted on top of the furnace reaction tube assembly. The platinum wires exited through the capillary tubes and were glass sealed vacuum tight into the tubes. The oxygen partial pressures surrounding the samples were controlled by flowing metered mixtures of gases past the sample. The gases were oxygen, compressed air, argon with known amounts of oxygen and CO,-CO mixtures. The error in the volumetric ratio measurements of the CO,-CO gas mixtures resulted in an error of about 1% in the Po, value reported here. The conductivity was measured as a function of PO, at 1000 and 1050 “C. The electrical conductivity was determined by measuring the voltage across the potential probes using a high impedance (greater than 10” 0) digital voltmeter (Keithley 191 digital multimeter). The current was supplied between the two outer leads by a constant-current source (Keithley 225 current source). The voltage was measured with the current in both the forward and reverse directions, and the conductivity was calculated from the average values. After each variation in the gas atmosphere surrounding the sample the conductivity was measured as it changed to the new equilibrium value. This process of change was recorded, and if the
217
conductivity no longer changed it was assumed that the state of equilibrium had been attained. This state proved to be attainable reversibly from higher or lower oxygen partial pressures. The current was varied from 10 uA to 1 mA and no significant change in conductivity was observed. Changing the ratio of the surface area to the volume by varying the size and geometry of the samples produced no detectable difference in the measured conductivity, which indicated that the measured quantity was the bulk conductivity.
3. Results and discussion The measured electrical conductivities in aluminum- or chromiumdoped samples at 1000 and 1050 “C are given in Figs. 1 and 2. The results obtained in the previous investigation [13] for undoped a-Nb,O, are also shown in Figs. 1 and 2. For the acceptor-doped samples, no region in which the conductivity depended on PO,-l/6 was observed. The results show that the conductivity of the acceptor-doped samples is proportional to PO,- l/4 for PO, < 10-l atm and is proportional to Pol+ 1’4 for PO, > 10e4 atm. An increase in the acceptor concentration gives rise to higher conductivity
I
10-12
I
10-B
I
10-4
I
IO0
PO2 (ATM) Fig. 1. Electrical conductivity in acceptor-doped (aluminum or chromium) a-Nb,O, as a function of the oxygen partial pressure at 1000 “C: 0, Nb,O,; A, Al,Nb,_,O,, x = 0.003; A, Al,Nb,_,O,, x = 0.0055; n , Al,Nb,_,O,, r = 0.008; 0, Cr,Nb,-,O,, z = 0.003; V, Cr,NbZmTO,, x = 0.0055; 0, Cr,Nb,-,O,, x = 0.0083.
218
102
IO’
10-2
r+‘4 Slop.31
IO‘3 / I 10-2'
1
10-20
#
IO-'6
1
I
10-8
10-Q PO2 (ATM
1
1
10-e
IO0
f
Fig. 2. Electrical conductivity in acceptor-doped (aluminum or chromium) u-Nb,O, as a function of the oxygen partial pressure at 1050 “C. The symbols are defined in Fig. 1.
values in the p-type region and lower values in the n-type region. Thus the is n-p transition moves to lower Po, values as the acceptor concentration increased in u-Nb,O,. 3.1. Region I (PO, -c lo-? atm) The electrical conductivity in the region of P,, -c low7 atm increases with decreasing oxygen partial pressure, indicative of n-type, or metalexcess, conductivity. The log 0 versus log P,, data are linear for as many as ten decades of oxygen partial pressure for a given temperature. This extensive region of linearity affords the opportunity to determine the defect model responsible for the n-type conductivity in this region. A slope of about -l/4 is found for the log c uersus log P,, data (Table 1). The absolute values of the conductivity measured in aluminum- or chromium-doped samples are the same, indicating that aluminum and chromium are equally effective in acting as acceptor impurities in Nb,O,. A Kroger-Vink [lS] diagram is a useful representation to consider when the electrical conductivity in binary oxides with added acceptor impurities is discussed. For the purpose of illustration we shall consider Schottky-Wagner disorder to describe the non-stoichiometry of the oxide
219
TABLE
1
Po, dependence
of the electrical m for
T
0,
conductivity
tc
in I,Nb,_XO,
PO,- ‘srnat various
(I = Al or Cr) in the n-type region
x
(‘Cl
1000 1050
0.003
0.0055
0.00% (0.00%3 for Cr)
4.05 4.18
4.00 4.03
4.00 4.05
MO. Figure 3 illustrates the variation in the defect concentration as a function of the oxygen partial pressure for various atomic defects, electrons [n] and holes [p]. If we consider the left-hand side of Fig. 3 (n-type region) we recognize the familiar regions, [n] cc PO, II4 where [n] z [Vo’] and [n] x PO, I/6 where [n] z Z[Vo”], of the simplification of the electrical neutrality condition. In Fig. 4 an acceptor impurity IM that is always fully ionized, I,, ’ is added to the binary oxide MO described in Fig. 3. It should be noted that for sufficient departures from stoichiometry it may be possible for the electrical conductivity to be controlled by [n] x [V,‘] and [n] z Z[Vo”] and thereby to mask the effect of the acceptor dopant. The occurrence of an impurity-insensitive region within the experimental conditions of temperature and oxygen partial pressure depends on the amount of acceptor impurity present in the sample. In Fig. 4 there is a region with an electrical neutrality condition [J,,,‘] zz 2[Vo”] in which the electron concentration varies as PO,- “4 and the hole concentration increases as PO,+ 1/4. In this region, for certain values of PO,, the electron concentration is greater than the hole concentration and
[nleIVdl1
InI=
21V~l
I
)
[nl
= IPI
I
I I
IPI
I
-
Z[V;‘l
IIPI-iv,‘1 1
I
)
LOG PO2Fig. 3. Concentration with Schottky-Wagner
of defects as a function disorder.
of the oxygen partial pressure for the oxide MO
I
I
I LOG PO)-
Fig. 4. Concentration fully ionized acceptor
of defects as a function of the oxygen pressure for the oxide MO with a impurity I,’ and Schottky-Wagner disorder.
hence the conductivity is n type and proportional to P& 1’4.As the oxygen partial pressure increases, the hole concentration becomes greater than the electron concentration above a certain value of PO, and the material becomes p type with a conductivity proportional to Po2+114. When the PO, value is increased further, the hole concentration becomes equal to the acceptor concentration, which is constant, and hence the electrical conductivity is independent of PO,, with the charge neutrality condition [&,‘I z [p] as shown in Fig. 4. The observation of Po,-independent conductivity with a charge neutrality equation [&,‘I z [p] depends on the amount of acceptor impurity added to the oxide and the PO, values used in the investigation. It should be pointed out here that only a single-level acceptor impurity was considered when Fig. 4 was drawn. If the acceptor impurities are doubly charged (as in the present study), then the charge neutrality condition in the intermediate region in Fig. 4 should read [Vo’ j z [IM”]. The observed slope of - l/4 (see Table 1) in this region must therefore be due to added acceptor impurities. The condition of charge neutrality is [Vo' j N”&“I
= constant
(1)
where IM” is a doubly charged acceptor impurity, and in the present case it will represent Al3 + or Cr3 + on an Nb’ + site, i.e. Al,,” or CrNb”. The concentration of oxygen vacancies is fixed by the amount of acceptor added as shown by Alz03 (or Cr,O,)
Nbzo5b2AlNb” (or 2Cr,,“) + 30, + 2Vo”
(2)
221
We should also consider the removal of an oxygen atom from the normal lattice site into the gas phase leaving a doubly ionized oxygen vacancy and two electrons available for conduction, as given by
0 o~402fVo”+2e The equilibrium
constant
K, z [V,‘j[n]2P02”‘2
for reaction = exp --$$ C
(3) is
1
where [n] z e’. It is assumed that the defects exist in a dilute solution and do not interact. The Gibbs standard free-energy change for reaction (3) is represented by AG,. Expressing the free-energy change in terms of the enthalpy change AH, and the entropy change AS, and substituting the charge neutrality condition eqn. (1) into eqn. (4), the electrical conductivity becomes
(5) where e is the electronic charge and p is the mobiIity of the electrons. If we assume that the mobility is independent of the change in the concentration of oxygen vacancies, a plot of log D versus log PO, should result in a straight line with a slope of -l/4. The data in Table 1 are in excellent agreement with the predicted dependence of the conductivity on Po,-114. The added acceptor impurities decrease the concentration of electrons available for conduction and therefore the measured conductivity is lower than that observed in the undoped sample for the same oxygen pressure in the n-type region (see Figs. 1 and 2). 3.2. Region II (PC,, > l0-4atrn) The electrical conductivity in the region of PO, > 10m4 atm increases with increasing oxygen partial pressure, indicative of p-type, or oxygenexcess, conductivity. A slope of about + l/4 is found for the log (r uersus log Po, data (see Table 2) in the p-type region. The region of linearity in this region of P,, increases in width with acceptor concentration. It is seen from Fig. 4 that in the region with the neutrality condition
TABLE 2 Po, dependence T
PC)
loo0 1050
of the electrical
conductivity
in I,Nb, _,O, (I z Al or Cr) in the p-type region
m for (T, cc Po, + lim at uarious x ..
-__
0.003
0.0055
0.008 (0.0083 for Cr)
4.00 3.92
3.94 3.85
4.00 3.80
.-.-_
222
[&,‘I x 2[Vo”] there is a region where [p] > [n]. The conductivity will be controlled by the holes, where [p] a PO,II4 . For the amounts of acceptor used in this investigation, the hole concentration becomes greater than the electron concentration for P o22 10d4 atm. The p-type conductivity is due to the incorporation of oxygen atoms into the impurity-related oxygen vacancies and the reaction is [Vo’ j +40,
& 0, + 2h’
where [p] s h’. The charge neutrality
(6) condition
in this region will still be
(eqn. (I)) [IV,“]
e [IM”] = constant
The chemical gives
mass action expression
0 cc Po2+1’4
for eqn. (6) combined
with eqn. (1) (7)
as observed, as long as only a minor fraction of the impurity-related [Vo”] is filled. The onset of the p-type conductivity depends on the amount of acceptor impurity added to the sample. With increase in the acceptor concentration, the impurity-related oxygen vacancy concentration increases. This means that a larger number of oxygen atoms can be incorporated into these vacancies, leading to an increased concentration of holes. This gives rise to the observed increase in the conductivity values with added acceptor impurities in the p-type region.
4. Conclusions The electrical conductivity of aluminum- or chromium-doped cr-Nb,O, was found to be proportional to PO, _ ‘I4for PO, < 10-l atm and proportional to Po2+1/4for PO, > 10m4 atm. For the entire oxygen partial pressure range used in this investigation, the defect chemistry of a-Nb,O, is dominated by the added acceptor impurities and their related oxygen vacancies (eqn. (1)). The absolute value of the electrical conductivity in the acceptor-doped samples is less than that of the undoped sample in the n-type region. The p-type conductivity results from a stoichiometric excess of oxygen which occupies the impurity-related oxygen vacancies (eqn. (6)). A stoichiometric excess of oxygen is achieved even when not all of the available oxygen sites are occupied. As the concentration of aluminum or chromium is increased, there is an appreciable increase in the value of the measured conductivity in the p-type region and a shift in the minimum of the conductivity towards lower oxygen partial pressure. For equal concentrations of aluminum or chromium the conductivity values were observed to be the same which indicated that aluminum and chromium are equally effective as acceptor impurities in cl-Nb,O,.
223
Acknowledgment The authors carrying
thank
the Gas Research
Institute
for financial
support
in
out this research.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
P. Kofstad and H. Kjollesdal, Trans. Am. Inst. Min. Metall. Pet. Eng., 221 (1961) 285. G. Brauer, 2. Anorg. AlZg. Chem., 248 (1941) 1. F. Holtzberg, A. Reisman, M. Berry and M. Berkenblit, J. Am. Chem. Sot., 79 (1957) 2039. H. J. Goldschmidt, J. Inst. Met., 87 (1959) 235. M. W. Shafer and R. Roy, 2. Kristallogr., 110 (1958) 241. R. A. Zvinchuk, J. Crystallogr. Acad. Sci. U.S.S.R., 3 (1960) 750. L. K. Frevel and H. N. Rinn, Anal. Chem., 27 (1955) 1329. B. M. Gatehouse and A. D. Wadsley, Acta CrystaZZogr., 17 (1964) 1545. E. H. Greener, D. H. Whitmore and M. E. Fine, J. Chem. Phys., 34 (1961) 1017. P. Kofstad and P. B. Anderson, J. Phys. Chem. Solids, 21 (1961) 280. P. Kofstad, J. Phys. Chem. Solids, 23 (1962) 1571. W. K. Chen and R. A. Swalin, J. Phys. Chem. Solids, 27 (1966) 57. U. Balachandran and N. G. Eror, J. Mater. Sci., 17 (1982) in the press. M. Pechini, U.S. Patent 3,330,697, July 11, 1967. N. G. Eror and U. Balachandran, J. Solid State Chem., 40 (1) (1981) 85. S. P. Mitoff, J. Chem. Phys., 35 (1961) 882. J. B. Price and J. B. Wagner, 2. Phys. Chem., 49 (1966) 257. F. A. Kroger and H. J. Vink, Solid State Phys., 3 (1956) 307.
ON THE DEFECT
U. BALACHANDRAN
STRUCTURE
215
- 223
OF ACCEPTOR-DOPED
cr-Nb,O,
and N. G. EROR
Oregon Graduate Center, Beauerton, OR 97006 (U.S.A.) (Received September 19, 1981)
Summary The defect structure of acceptor-doped (aluminum or chromium) c1Nb,O, was investigated by measuring the oxygen partial pressure PO, (10’ lo- l8 atm) dependence of the electrical conductivity at 1000 and 1050 “C. The observed data were proportional to Po2p114for PO2< 10-l atm and were proportional to PO*+‘I4 for PO, > 10m4 atm. The absolute values of the electrical conductivity in the acceptor-doped samples were found to be lower in the n-type region compared with the values in the undoped cr-Nb,O,. The conductivity values were observed to increase with the acceptor concentration in the p-type region with a shift in the conductivity minimum towards a lower oxygen partial pressure. The effectiveness of aluminum and of chromium as acceptor impurities in or-Nb,O, was found to be nearly the same.
1. Introduction The potential use of niobium for high temperature service has focused attention on its oxides since these make up the barrier layers between the metal and the gas phase during oxidation. Nb,O, is the main oxide formed during oxidation at temperatures above 500 “C [l]. It has been shown by many investigators [2 - 63 that Nb,O, crystallizes in five different modifications. The high temperature modification, a-Nb,O,, has a monoclinic structure [3, 7, S]. The low temperature modification transforms irreversibly to a-Nb,O, at about 830 “C [3]. The nature of the non-stoichiometry in Nb,O, has been studied by a number of investigators [2, 9 - 131. Most of the studies concluded that the defect structure involves singly and doubly ionized oxygen vacancies. Recently Balachandran and Eror [13] interpreted the electrical conductivity and thermogravimetric measurements on undoped a-Nb,O, on the basis of the 0022.5088/82/0000-0000/$02.75
(0 Elsevier Sequoia/Printed
in The Netherlands
216
doubly ionized oxygen vacancies and accidental acceptor impurities present in the samples. ct-Nb,O, with added acceptor impurities, however, has not been studied in the past. The purpose of the present work was to make a detailed study of the electrical conductivity in aluminum- and chromium-doped polycrystalline CG Nb,O, at 1000 - 1050 “C while in equilibrium with the oxygen partial pressure PO, of the surrounding atmosphere. The amounts of aluminum or chromium selected were 0.003, 0.0055 and 0.008 (0.0083 for chromium) in the general formula AI,Nb, -XO, or Cr,Nb, _,O,.
2. Experimental
details
The samples employed in this investigation were prepared by a liquid mix technique [14, 151. The source materials were niobium oxalate, aluminum nitrate and chromium nitrate, all in the form of solutions. The powder samples obtained from the oxalate solutions were pressed into rectangular slabs (2.1 cm x 0.6 em x 0.05 cm) under a load of 40 000 Ibf in-’ and sintered in air at 1350 “C for 8 h. The density of the sintered slabs was 93% of the theoretical density. Electrical conductivity samples were cut from this slab using an air-brasive unit. The specimens were wrapped with four 0.03 cm platinum wires as described in the literature [16, 171. Small notches were cut in the edges of the sample to help to hold the platinum wires in place. A conventional four-probe d.c. technique was employed for all electrical conductivity measurements. The four platinum leads were insulated from one another by recrystallized high purity alumina insulators. A standard taper Pyrex joint to which capillary tubes had been sealed was mounted on top of the furnace reaction tube assembly. The platinum wires exited through the capillary tubes and were glass sealed vacuum tight into the tubes. The oxygen partial pressures surrounding the samples were controlled by flowing metered mixtures of gases past the sample. The gases were oxygen, compressed air, argon with known amounts of oxygen and CO,-CO mixtures. The error in the volumetric ratio measurements of the CO,-CO gas mixtures resulted in an error of about 1% in the Po, value reported here. The conductivity was measured as a function of PO, at 1000 and 1050 “C. The electrical conductivity was determined by measuring the voltage across the potential probes using a high impedance (greater than 10” 0) digital voltmeter (Keithley 191 digital multimeter). The current was supplied between the two outer leads by a constant-current source (Keithley 225 current source). The voltage was measured with the current in both the forward and reverse directions, and the conductivity was calculated from the average values. After each variation in the gas atmosphere surrounding the sample the conductivity was measured as it changed to the new equilibrium value. This process of change was recorded, and if the
217
conductivity no longer changed it was assumed that the state of equilibrium had been attained. This state proved to be attainable reversibly from higher or lower oxygen partial pressures. The current was varied from 10 uA to 1 mA and no significant change in conductivity was observed. Changing the ratio of the surface area to the volume by varying the size and geometry of the samples produced no detectable difference in the measured conductivity, which indicated that the measured quantity was the bulk conductivity.
3. Results and discussion The measured electrical conductivities in aluminum- or chromiumdoped samples at 1000 and 1050 “C are given in Figs. 1 and 2. The results obtained in the previous investigation [13] for undoped a-Nb,O, are also shown in Figs. 1 and 2. For the acceptor-doped samples, no region in which the conductivity depended on PO,-l/6 was observed. The results show that the conductivity of the acceptor-doped samples is proportional to PO,- l/4 for PO, < 10-l atm and is proportional to Pol+ 1’4 for PO, > 10e4 atm. An increase in the acceptor concentration gives rise to higher conductivity
I
10-12
I
10-B
I
10-4
I
IO0
PO2 (ATM) Fig. 1. Electrical conductivity in acceptor-doped (aluminum or chromium) a-Nb,O, as a function of the oxygen partial pressure at 1000 “C: 0, Nb,O,; A, Al,Nb,_,O,, x = 0.003; A, Al,Nb,_,O,, x = 0.0055; n , Al,Nb,_,O,, r = 0.008; 0, Cr,Nb,-,O,, z = 0.003; V, Cr,NbZmTO,, x = 0.0055; 0, Cr,Nb,-,O,, x = 0.0083.
218
102
IO’
10-2
r+‘4 Slop.31
IO‘3 / I 10-2'
1
10-20
#
IO-'6
1
I
10-8
10-Q PO2 (ATM
1
1
10-e
IO0
f
Fig. 2. Electrical conductivity in acceptor-doped (aluminum or chromium) u-Nb,O, as a function of the oxygen partial pressure at 1050 “C. The symbols are defined in Fig. 1.
values in the p-type region and lower values in the n-type region. Thus the is n-p transition moves to lower Po, values as the acceptor concentration increased in u-Nb,O,. 3.1. Region I (PO, -c lo-? atm) The electrical conductivity in the region of P,, -c low7 atm increases with decreasing oxygen partial pressure, indicative of n-type, or metalexcess, conductivity. The log 0 versus log P,, data are linear for as many as ten decades of oxygen partial pressure for a given temperature. This extensive region of linearity affords the opportunity to determine the defect model responsible for the n-type conductivity in this region. A slope of about -l/4 is found for the log c uersus log P,, data (Table 1). The absolute values of the conductivity measured in aluminum- or chromium-doped samples are the same, indicating that aluminum and chromium are equally effective in acting as acceptor impurities in Nb,O,. A Kroger-Vink [lS] diagram is a useful representation to consider when the electrical conductivity in binary oxides with added acceptor impurities is discussed. For the purpose of illustration we shall consider Schottky-Wagner disorder to describe the non-stoichiometry of the oxide
219
TABLE
1
Po, dependence
of the electrical m for
T
0,
conductivity
tc
in I,Nb,_XO,
PO,- ‘srnat various
(I = Al or Cr) in the n-type region
x
(‘Cl
1000 1050
0.003
0.0055
0.00% (0.00%3 for Cr)
4.05 4.18
4.00 4.03
4.00 4.05
MO. Figure 3 illustrates the variation in the defect concentration as a function of the oxygen partial pressure for various atomic defects, electrons [n] and holes [p]. If we consider the left-hand side of Fig. 3 (n-type region) we recognize the familiar regions, [n] cc PO, II4 where [n] z [Vo’] and [n] x PO, I/6 where [n] z Z[Vo”], of the simplification of the electrical neutrality condition. In Fig. 4 an acceptor impurity IM that is always fully ionized, I,, ’ is added to the binary oxide MO described in Fig. 3. It should be noted that for sufficient departures from stoichiometry it may be possible for the electrical conductivity to be controlled by [n] x [V,‘] and [n] z Z[Vo”] and thereby to mask the effect of the acceptor dopant. The occurrence of an impurity-insensitive region within the experimental conditions of temperature and oxygen partial pressure depends on the amount of acceptor impurity present in the sample. In Fig. 4 there is a region with an electrical neutrality condition [J,,,‘] zz 2[Vo”] in which the electron concentration varies as PO,- “4 and the hole concentration increases as PO,+ 1/4. In this region, for certain values of PO,, the electron concentration is greater than the hole concentration and
[nleIVdl1
InI=
21V~l
I
)
[nl
= IPI
I
I I
IPI
I
-
Z[V;‘l
IIPI-iv,‘1 1
I
)
LOG PO2Fig. 3. Concentration with Schottky-Wagner
of defects as a function disorder.
of the oxygen partial pressure for the oxide MO
I
I
I LOG PO)-
Fig. 4. Concentration fully ionized acceptor
of defects as a function of the oxygen pressure for the oxide MO with a impurity I,’ and Schottky-Wagner disorder.
hence the conductivity is n type and proportional to P& 1’4.As the oxygen partial pressure increases, the hole concentration becomes greater than the electron concentration above a certain value of PO, and the material becomes p type with a conductivity proportional to Po2+114. When the PO, value is increased further, the hole concentration becomes equal to the acceptor concentration, which is constant, and hence the electrical conductivity is independent of PO,, with the charge neutrality condition [&,‘I z [p] as shown in Fig. 4. The observation of Po,-independent conductivity with a charge neutrality equation [&,‘I z [p] depends on the amount of acceptor impurity added to the oxide and the PO, values used in the investigation. It should be pointed out here that only a single-level acceptor impurity was considered when Fig. 4 was drawn. If the acceptor impurities are doubly charged (as in the present study), then the charge neutrality condition in the intermediate region in Fig. 4 should read [Vo’ j z [IM”]. The observed slope of - l/4 (see Table 1) in this region must therefore be due to added acceptor impurities. The condition of charge neutrality is [Vo' j N”&“I
= constant
(1)
where IM” is a doubly charged acceptor impurity, and in the present case it will represent Al3 + or Cr3 + on an Nb’ + site, i.e. Al,,” or CrNb”. The concentration of oxygen vacancies is fixed by the amount of acceptor added as shown by Alz03 (or Cr,O,)
Nbzo5b2AlNb” (or 2Cr,,“) + 30, + 2Vo”
(2)
221
We should also consider the removal of an oxygen atom from the normal lattice site into the gas phase leaving a doubly ionized oxygen vacancy and two electrons available for conduction, as given by
0 o~402fVo”+2e The equilibrium
constant
K, z [V,‘j[n]2P02”‘2
for reaction = exp --$$ C
(3) is
1
where [n] z e’. It is assumed that the defects exist in a dilute solution and do not interact. The Gibbs standard free-energy change for reaction (3) is represented by AG,. Expressing the free-energy change in terms of the enthalpy change AH, and the entropy change AS, and substituting the charge neutrality condition eqn. (1) into eqn. (4), the electrical conductivity becomes
(5) where e is the electronic charge and p is the mobiIity of the electrons. If we assume that the mobility is independent of the change in the concentration of oxygen vacancies, a plot of log D versus log PO, should result in a straight line with a slope of -l/4. The data in Table 1 are in excellent agreement with the predicted dependence of the conductivity on Po,-114. The added acceptor impurities decrease the concentration of electrons available for conduction and therefore the measured conductivity is lower than that observed in the undoped sample for the same oxygen pressure in the n-type region (see Figs. 1 and 2). 3.2. Region II (PC,, > l0-4atrn) The electrical conductivity in the region of PO, > 10m4 atm increases with increasing oxygen partial pressure, indicative of p-type, or oxygenexcess, conductivity. A slope of about + l/4 is found for the log (r uersus log Po, data (see Table 2) in the p-type region. The region of linearity in this region of P,, increases in width with acceptor concentration. It is seen from Fig. 4 that in the region with the neutrality condition
TABLE 2 Po, dependence T
PC)
loo0 1050
of the electrical
conductivity
in I,Nb, _,O, (I z Al or Cr) in the p-type region
m for (T, cc Po, + lim at uarious x ..
-__
0.003
0.0055
0.008 (0.0083 for Cr)
4.00 3.92
3.94 3.85
4.00 3.80
.-.-_
222
[&,‘I x 2[Vo”] there is a region where [p] > [n]. The conductivity will be controlled by the holes, where [p] a PO,II4 . For the amounts of acceptor used in this investigation, the hole concentration becomes greater than the electron concentration for P o22 10d4 atm. The p-type conductivity is due to the incorporation of oxygen atoms into the impurity-related oxygen vacancies and the reaction is [Vo’ j +40,
& 0, + 2h’
where [p] s h’. The charge neutrality
(6) condition
in this region will still be
(eqn. (I)) [IV,“]
e [IM”] = constant
The chemical gives
mass action expression
0 cc Po2+1’4
for eqn. (6) combined
with eqn. (1) (7)
as observed, as long as only a minor fraction of the impurity-related [Vo”] is filled. The onset of the p-type conductivity depends on the amount of acceptor impurity added to the sample. With increase in the acceptor concentration, the impurity-related oxygen vacancy concentration increases. This means that a larger number of oxygen atoms can be incorporated into these vacancies, leading to an increased concentration of holes. This gives rise to the observed increase in the conductivity values with added acceptor impurities in the p-type region.
4. Conclusions The electrical conductivity of aluminum- or chromium-doped cr-Nb,O, was found to be proportional to PO, _ ‘I4for PO, < 10-l atm and proportional to Po2+1/4for PO, > 10m4 atm. For the entire oxygen partial pressure range used in this investigation, the defect chemistry of a-Nb,O, is dominated by the added acceptor impurities and their related oxygen vacancies (eqn. (1)). The absolute value of the electrical conductivity in the acceptor-doped samples is less than that of the undoped sample in the n-type region. The p-type conductivity results from a stoichiometric excess of oxygen which occupies the impurity-related oxygen vacancies (eqn. (6)). A stoichiometric excess of oxygen is achieved even when not all of the available oxygen sites are occupied. As the concentration of aluminum or chromium is increased, there is an appreciable increase in the value of the measured conductivity in the p-type region and a shift in the minimum of the conductivity towards lower oxygen partial pressure. For equal concentrations of aluminum or chromium the conductivity values were observed to be the same which indicated that aluminum and chromium are equally effective as acceptor impurities in cl-Nb,O,.
223
Acknowledgment The authors carrying
thank
the Gas Research
Institute
for financial
support
in
out this research.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
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