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Measuring oxygen diffusivity and solubility in solid silver with a gas-tight electrochemical cell
Volume 9. number
MATERIALS
9
May 1990
LETTERS
MEASURING OXYGEN DIFFUSIVITY AND SOLUBILITY WITH A GAS-TIGHT ELECTROCHEMICAL CELL Jong-Hee
IN SOLID SILVER
PARK
Materials and Components Technology Division, Argonne National Laboratory, Argonne, IL 60439. USA Received
20 February
1990
The diffusivity and solubility of oxygen in solid silver were determined in the temperature range 740-9 15°C by means of a gastight yttria-stabilized zirconia electrochemical cell. The diffusivity of oxygen, Do, in solid silver can be represented by Do = 3.2 x 10W3e-0~5”cV’*T cm*/s, where k is the Boltzmann constant, and T the absolute temperature, and the solubility of oxygen, Co, at 1 atm O2 is given by Co = 1.2~ 10W3e-0.40cV/k’ mol O/cm3 Ag. Results are compared with earlier data obtained by various techniques.
1. Introduction The diffusion and solubility of oxygen in solid and liquid metals is relevant to several problems. For example, it is frequently necessary to remove oxygen from Cu, Ag, Au, Na, and Li to improve specific properties of these materials such as conductivity and corrosivity. Another example is the use of these metals in electrodes for solid-state electrochemical oxygen cells, where a reaction involving oxygen species, oxide ions, and electrons occurs. Transport of oxygen to the electrolyte interface is related to electrode kinetics. Recently, attention has focused on a silver-doped or composite superconducting ceramic oxide, YBa2Cu307, because silver may segregate to grain boundaries, triple points, or voids, which can be fast-transport channels for diffusing ions via surface diffusion. As a consequence, oxygen diffusivity in solid silver is not lower than that in any ceramic oxide, including even the porous YBazCu307 [ 11. Electrochemical measurement of oxygen diffusion in metals has been reviewed by Rickert [ 2 1, and the diffusivities in various metals and alloys have been investigated [ 2-81. The electrochemical measurements were performed primarily by potentiostatic and galvanostatic methods; however, some measurements were performed by ac impedance spectroscopy [ 9 1. Rickert and co-workers [ 41 measured the diffusivity and solubility of oxygen in solid and 0167-577x/90/$
03.50 0 Elsevier Science Publishers
liquid silver with an yttria-stabilized zirconia (YSZ) oxygen sensor. Recently, a gas-tight electrochemical cell has been developed for measuring oxygen transport and thermodynamic behavior at high temperatures [ lo- 13 1. This paper reports the results that were obtained when the diffusivity and solubility of oxygen were measured with the use of this gas-tight electrochemical cell.
2. Transport equation Fig. 1 is a schematic
representation
of the bound-
0-
2
PO,=
I .0 atm
Fig. I. Schematic representation through a silver disc.
B.V. (North-Holland
)
of the permeation
of oxygen
313
Volume 9, number 9
ary conditions for the diffusion process. When the specimen with unit thickness is connected to a gastight chamber with volume V, the rate of oxygen flow through the specimen can be measured by monitoring the change of oxygen partial pressure inside the chamber. If the change is sufficiently small, the change in concentration at the surface, x=0, can be treated as a small perturbation that does not significantly affect the equilibrium concentration at this surface. The boundary conditions of this system can be written as follows: C(X, t=O)=Ci) C(x=O,
bO)=C,
C(x=l,
f>O)=C*.
)
aC/dt= Do a2Cldx2 ,
(2) (3)
(4)
when K/at becomes constant with time after the gas composition in the cell is changed. This implies that oxygen permeation through the specimen reaches a steady state. A plot of C versus t at the inner surface, x=0, asymptotically approaches a line whose intersection at the time coordinate, t, defines the time lag, T. When the boundary conditions tit the pattern Ci >> C, and Ci, 7 could be expressed by Barr [ 141, as (or Do =12/6r) .
(5)
Here, 1 is the sample thickness, and the chemical diffusion coefficient of oxygen in solid silver, Do, is determined by eq. (5 ). A detailed explanation can be found elsewhere [ 11,141.
3. Experimental 3.1. Oxygen permeation cell The gas-tight oxygen permeation cell (fig. 2) consists of a silver-disc sample ( 1 mm thick x 13 mm diameter, obtained from Alfa Products), 8 mol% yttria-stabilized zirconia ( 1.4 mm thickx 13 mm diameter, from Corning, ZDY-2), a stack of two highpurity alumina rings (13 mm outer diameter), and 314
,
Sliver
DISC
Alumina Rings
Sensor’ Porous platinum
_ electrodes
Fig. 2. Gas-tight oxygen permeation cell with attached YSZ oxygen sensor.
(1)
Oxygen diffusivity can be determined by solving Fick’s second law, with the boundary conditions as given above,
r=12/6D0
May 1990
MATERIALS LETTERS
Pyrex glass (Corning, #7740, m.p. = 821 “C) as a sealing material. The whole stacked cell was sealed at 920°C in a flowing 97% Ar-3% O2 gas mixture. The cell volume is 0.56 cm3 and the area of the inner side of the silver disc is 0.56 cm2. Fabrication of these sealing cells has been described elsewhere [ 111. Temperature was measured with a Pt-Pt/ 13% Rh thermocouple. The gas-tight permeation cell was installed in a temperature flat zone of a Kanthal wirewound alumina tube furnace. To avoid pick-up of electrical noise, a heat-resistant alloy tube was installed and grounded inside the alumina tube of the furnace. 3.2. Oxygen permeation measurements Initially, the sample was equilibrated in flowing argon; then the gas was switched quickly to pure oxygen. The gas-switching system was designed so the minimum time to exchange the gas was ~2 s. To avoid temperature fluctuation during switching, the gases were preheated before flowing into the system. After the gas was switched to oxygen, the EMF was monitored with time. The oxygen partial pressure inside the cell was calculated from the Nemst equation, Po, =Pozoefj e-4EF’RT
atm ,
(6)
where PO,crefj= 1.0 atm and F is the Faraday constant. At the onset of the non-steady-state condition, one can record the change m PO, with time. After a given time period, the change in PO, becomes constant, i.e. the amount of oxygen that has diffused into the cell through the specimen becomes constant. At that time, PO, in the cell is still much lower (fig. 3) than the 1 atm of the outside reference gas. In this
Volume 9, number
MATERIALS
9
May 1990
LETTERS
situation, we may have met the boundary condition requirements as described in section 2 for Fick’s second law.
4. Results and discussion
T (“Cl 950
650
900
600
750
s $
Fig. 3 shows a plot of PO, versus time at 863°C after switching the gas to pure oxygen. The two different shapes in one isothermal run are the curvature associated with the shorter time period and the linear portion associated with the longer times. For the longer time period, we can consider oxygen permeation to be steady state and eq. (2) can be used to calculate the parameters in table 1. Fig. 4 shows the I 030-
-4.7-
0” H
-4
6---
RAMANARAYANAN AND RAPP
-4.9------RICKERT 0
MIZIKAR -PRESENT
6.0
6.2
64
et al. WORK
6.6
6.6
9.0
92
9.4
9.6
96
100
104/T (KI
Fig. 4. Temperature dependence of oxygen diffusion for solid silver, as found in the literature and determined in this study.
I 2
T=663’C
_E
’
-0.06
0.05
temperature dependence of oxygen diffusivity given in the literature along with the results for this study. The diffusion coeffkient can be represented as Do = 3.2 x low3 e-“-50eV’kT cm2/s ,
0 2
Fig. 3. PO, (atm) to pure oxygen.
Table 1 Experimental Run no.
3
4 TIME
versus time (min)
5 lminl
6
7
after switching
where k is the Boltzmann constant and T the absolute temperature. The steady-state oxygen flux can be obtained from the slope of linear portion of the curves in fig. 3 and by employing the ideal gas law, pV=nRT. The steady-state oxygen flux, jo, for unit area of the silver disc is given by
6
j. = An/t=
( V/RT)AP,,/t
Temp.( “C)
914.5 906.5 863 841.5 835 807 804 764 740
Do, flux jol, and solubility
(8)
in moles of oxygen in the ._
Co in solid silver
r (s)
Diffusivity, Do (IO’ cm’/s)
Flux, jol ( 10” mol O/cm
69 72.6 96 102 102 114 103.2 153 168
2.42 2.30 1.74 1.63 1.63 1.46 I .62 I .09 0.996
6. I7 5.92 3.91 3.07 3.21 2.40 2.52 1.68 1.36
Time lag,
,
from argon
where An is the difference
data for time lag r, oxygen diffusivity
(7)
s)
Solubility, Co ( 10’ mol O/cm’
Ag)
2.55 2.58 2.25 1.88 1.96 1.64 1.56 1.54 1.37
315
MATERIALS LETTERS
Volume 9, number 9
May 1990 T PC)
E-* :: -9.5
ov,
* N’
s
-9.6 -4.9-
4 *
4 -9.7 -co-
RICKERT (800°C
104/T
6.4
6.6
0.8
9.0
9.2 104/T
9.4
9.6
9.9
10.0
DATA1
IKI
Fig. 6. Temperature dependence of oxygen solubility for solid silver.
(KI
Fig. 5. Temperature dependence of oxygen permeation flux for solid silver.
cell that are being permeated through the sample, and correspond to APo,, which is the difference in PO, at two different times. Table 1 and fig. 5 represent the log jo versus 1/T, which can be represented as jol=4.4x
10-6e-o~goeV~krmol
The solubility
O/cm3Ag.
of oxygen was calculated
Acknowledgement This work was supported by the US Department of Energy under Contract W-3 I- 109-Eng-38.
(9) from References
jo = -Do
dCo/dx
,
(10)
where Co is the oxygen solubility and x the sample thickness. Eq. ( 10) can be written as
jojdx=DojdCo, 0
(11) Cl
where C, and C, indicate the oxygen concentrations (or the equilibrium oxygen solubility values) in the sample corresponding to the surface on each side. At steady-state oxygen penetration, eq. ( 11) becomes jol=Do(C,-Cl). When C, B Cr, we obtain
jol=DoCo ,
(12) the following
relation: (13)
where Co= C,. Thus we can obtain the solubility of oxygen, Co =jol/Do. Table 1 and fig. 6 show the oxygen solubility obtained by this method at various temperatures. On the basis of these results, we represent oxygen solubility at 1 atm O2 as 316
[ 1 ] J.-H. Park, P. Kostic and J.P. Singh, Mater. Letters 6 ( 1988) 393. [2] H. Rickert, Electrochemistry of solids, an introduction (Springer, Berlin, 1982). [3] W. Eichenauer andG. Muller, Z. Metallkd. 53 (1962) 321, 700. [4] H. Rickert and R. Steiner, Z. Physik. Chem. NF 49 (1966) 127. [ 51 H. Rickert, H. Wagner and R. Steiner, Chem. Ing. Tech. 38 (1966) 618. [6] E.A. Mizikar, R.E. Grace and N.A.D. Parlee, Trans. ASM 56 (1963) 101. [ 71 H. Rickert and A.A. Miligy, Z. Metallkd. 59 (1968) 635. [ 81 T.A. Ramanarayanan and R.A. Rapp, Metal. Trans. 3 ( 1972) 3239. [ 91 EA. Moghadam and D.A. Stevenson, J. Electrochem. Sot. 133 (1986) 1329. [lo] J.-H. Park, R.N. Blumenthal and M.A. Panhans, J. Electrochem. Sot. 135 (1988) 855. [ 111 J.-H. Park and R.N. Blumenthal, J. Electrochem. Sot. 136 (1989) 2867. [ 121 J.-H. Park, Physica B 150 (1988) 80. [ 131 J.-H. Park and P. Kostic, Mater. Letters 6 ( 1988) 327. [ 141 R.M. Barr, Trans. Faraday Sot. 35 (1939) 628; Phil. Mag. 28 (1939) 148.
MATERIALS
9
May 1990
LETTERS
MEASURING OXYGEN DIFFUSIVITY AND SOLUBILITY WITH A GAS-TIGHT ELECTROCHEMICAL CELL Jong-Hee
IN SOLID SILVER
PARK
Materials and Components Technology Division, Argonne National Laboratory, Argonne, IL 60439. USA Received
20 February
1990
The diffusivity and solubility of oxygen in solid silver were determined in the temperature range 740-9 15°C by means of a gastight yttria-stabilized zirconia electrochemical cell. The diffusivity of oxygen, Do, in solid silver can be represented by Do = 3.2 x 10W3e-0~5”cV’*T cm*/s, where k is the Boltzmann constant, and T the absolute temperature, and the solubility of oxygen, Co, at 1 atm O2 is given by Co = 1.2~ 10W3e-0.40cV/k’ mol O/cm3 Ag. Results are compared with earlier data obtained by various techniques.
1. Introduction The diffusion and solubility of oxygen in solid and liquid metals is relevant to several problems. For example, it is frequently necessary to remove oxygen from Cu, Ag, Au, Na, and Li to improve specific properties of these materials such as conductivity and corrosivity. Another example is the use of these metals in electrodes for solid-state electrochemical oxygen cells, where a reaction involving oxygen species, oxide ions, and electrons occurs. Transport of oxygen to the electrolyte interface is related to electrode kinetics. Recently, attention has focused on a silver-doped or composite superconducting ceramic oxide, YBa2Cu307, because silver may segregate to grain boundaries, triple points, or voids, which can be fast-transport channels for diffusing ions via surface diffusion. As a consequence, oxygen diffusivity in solid silver is not lower than that in any ceramic oxide, including even the porous YBazCu307 [ 11. Electrochemical measurement of oxygen diffusion in metals has been reviewed by Rickert [ 2 1, and the diffusivities in various metals and alloys have been investigated [ 2-81. The electrochemical measurements were performed primarily by potentiostatic and galvanostatic methods; however, some measurements were performed by ac impedance spectroscopy [ 9 1. Rickert and co-workers [ 41 measured the diffusivity and solubility of oxygen in solid and 0167-577x/90/$
03.50 0 Elsevier Science Publishers
liquid silver with an yttria-stabilized zirconia (YSZ) oxygen sensor. Recently, a gas-tight electrochemical cell has been developed for measuring oxygen transport and thermodynamic behavior at high temperatures [ lo- 13 1. This paper reports the results that were obtained when the diffusivity and solubility of oxygen were measured with the use of this gas-tight electrochemical cell.
2. Transport equation Fig. 1 is a schematic
representation
of the bound-
0-
2
PO,=
I .0 atm
Fig. I. Schematic representation through a silver disc.
B.V. (North-Holland
)
of the permeation
of oxygen
313
Volume 9, number 9
ary conditions for the diffusion process. When the specimen with unit thickness is connected to a gastight chamber with volume V, the rate of oxygen flow through the specimen can be measured by monitoring the change of oxygen partial pressure inside the chamber. If the change is sufficiently small, the change in concentration at the surface, x=0, can be treated as a small perturbation that does not significantly affect the equilibrium concentration at this surface. The boundary conditions of this system can be written as follows: C(X, t=O)=Ci) C(x=O,
bO)=C,
C(x=l,
f>O)=C*.
)
aC/dt= Do a2Cldx2 ,
(2) (3)
(4)
when K/at becomes constant with time after the gas composition in the cell is changed. This implies that oxygen permeation through the specimen reaches a steady state. A plot of C versus t at the inner surface, x=0, asymptotically approaches a line whose intersection at the time coordinate, t, defines the time lag, T. When the boundary conditions tit the pattern Ci >> C, and Ci, 7 could be expressed by Barr [ 141, as (or Do =12/6r) .
(5)
Here, 1 is the sample thickness, and the chemical diffusion coefficient of oxygen in solid silver, Do, is determined by eq. (5 ). A detailed explanation can be found elsewhere [ 11,141.
3. Experimental 3.1. Oxygen permeation cell The gas-tight oxygen permeation cell (fig. 2) consists of a silver-disc sample ( 1 mm thick x 13 mm diameter, obtained from Alfa Products), 8 mol% yttria-stabilized zirconia ( 1.4 mm thickx 13 mm diameter, from Corning, ZDY-2), a stack of two highpurity alumina rings (13 mm outer diameter), and 314
,
Sliver
DISC
Alumina Rings
Sensor’ Porous platinum
_ electrodes
Fig. 2. Gas-tight oxygen permeation cell with attached YSZ oxygen sensor.
(1)
Oxygen diffusivity can be determined by solving Fick’s second law, with the boundary conditions as given above,
r=12/6D0
May 1990
MATERIALS LETTERS
Pyrex glass (Corning, #7740, m.p. = 821 “C) as a sealing material. The whole stacked cell was sealed at 920°C in a flowing 97% Ar-3% O2 gas mixture. The cell volume is 0.56 cm3 and the area of the inner side of the silver disc is 0.56 cm2. Fabrication of these sealing cells has been described elsewhere [ 111. Temperature was measured with a Pt-Pt/ 13% Rh thermocouple. The gas-tight permeation cell was installed in a temperature flat zone of a Kanthal wirewound alumina tube furnace. To avoid pick-up of electrical noise, a heat-resistant alloy tube was installed and grounded inside the alumina tube of the furnace. 3.2. Oxygen permeation measurements Initially, the sample was equilibrated in flowing argon; then the gas was switched quickly to pure oxygen. The gas-switching system was designed so the minimum time to exchange the gas was ~2 s. To avoid temperature fluctuation during switching, the gases were preheated before flowing into the system. After the gas was switched to oxygen, the EMF was monitored with time. The oxygen partial pressure inside the cell was calculated from the Nemst equation, Po, =Pozoefj e-4EF’RT
atm ,
(6)
where PO,crefj= 1.0 atm and F is the Faraday constant. At the onset of the non-steady-state condition, one can record the change m PO, with time. After a given time period, the change in PO, becomes constant, i.e. the amount of oxygen that has diffused into the cell through the specimen becomes constant. At that time, PO, in the cell is still much lower (fig. 3) than the 1 atm of the outside reference gas. In this
Volume 9, number
MATERIALS
9
May 1990
LETTERS
situation, we may have met the boundary condition requirements as described in section 2 for Fick’s second law.
4. Results and discussion
T (“Cl 950
650
900
600
750
s $
Fig. 3 shows a plot of PO, versus time at 863°C after switching the gas to pure oxygen. The two different shapes in one isothermal run are the curvature associated with the shorter time period and the linear portion associated with the longer times. For the longer time period, we can consider oxygen permeation to be steady state and eq. (2) can be used to calculate the parameters in table 1. Fig. 4 shows the I 030-
-4.7-
0” H
-4
6---
RAMANARAYANAN AND RAPP
-4.9------RICKERT 0
MIZIKAR -PRESENT
6.0
6.2
64
et al. WORK
6.6
6.6
9.0
92
9.4
9.6
96
100
104/T (KI
Fig. 4. Temperature dependence of oxygen diffusion for solid silver, as found in the literature and determined in this study.
I 2
T=663’C
_E
’
-0.06
0.05
temperature dependence of oxygen diffusivity given in the literature along with the results for this study. The diffusion coeffkient can be represented as Do = 3.2 x low3 e-“-50eV’kT cm2/s ,
0 2
Fig. 3. PO, (atm) to pure oxygen.
Table 1 Experimental Run no.
3
4 TIME
versus time (min)
5 lminl
6
7
after switching
where k is the Boltzmann constant and T the absolute temperature. The steady-state oxygen flux can be obtained from the slope of linear portion of the curves in fig. 3 and by employing the ideal gas law, pV=nRT. The steady-state oxygen flux, jo, for unit area of the silver disc is given by
6
j. = An/t=
( V/RT)AP,,/t
Temp.( “C)
914.5 906.5 863 841.5 835 807 804 764 740
Do, flux jol, and solubility
(8)
in moles of oxygen in the ._
Co in solid silver
r (s)
Diffusivity, Do (IO’ cm’/s)
Flux, jol ( 10” mol O/cm
69 72.6 96 102 102 114 103.2 153 168
2.42 2.30 1.74 1.63 1.63 1.46 I .62 I .09 0.996
6. I7 5.92 3.91 3.07 3.21 2.40 2.52 1.68 1.36
Time lag,
,
from argon
where An is the difference
data for time lag r, oxygen diffusivity
(7)
s)
Solubility, Co ( 10’ mol O/cm’
Ag)
2.55 2.58 2.25 1.88 1.96 1.64 1.56 1.54 1.37
315
MATERIALS LETTERS
Volume 9, number 9
May 1990 T PC)
E-* :: -9.5
ov,
* N’
s
-9.6 -4.9-
4 *
4 -9.7 -co-
RICKERT (800°C
104/T
6.4
6.6
0.8
9.0
9.2 104/T
9.4
9.6
9.9
10.0
DATA1
IKI
Fig. 6. Temperature dependence of oxygen solubility for solid silver.
(KI
Fig. 5. Temperature dependence of oxygen permeation flux for solid silver.
cell that are being permeated through the sample, and correspond to APo,, which is the difference in PO, at two different times. Table 1 and fig. 5 represent the log jo versus 1/T, which can be represented as jol=4.4x
10-6e-o~goeV~krmol
The solubility
O/cm3Ag.
of oxygen was calculated
Acknowledgement This work was supported by the US Department of Energy under Contract W-3 I- 109-Eng-38.
(9) from References
jo = -Do
dCo/dx
,
(10)
where Co is the oxygen solubility and x the sample thickness. Eq. ( 10) can be written as
jojdx=DojdCo, 0
(11) Cl
where C, and C, indicate the oxygen concentrations (or the equilibrium oxygen solubility values) in the sample corresponding to the surface on each side. At steady-state oxygen penetration, eq. ( 11) becomes jol=Do(C,-Cl). When C, B Cr, we obtain
jol=DoCo ,
(12) the following
relation: (13)
where Co= C,. Thus we can obtain the solubility of oxygen, Co =jol/Do. Table 1 and fig. 6 show the oxygen solubility obtained by this method at various temperatures. On the basis of these results, we represent oxygen solubility at 1 atm O2 as 316
[ 1 ] J.-H. Park, P. Kostic and J.P. Singh, Mater. Letters 6 ( 1988) 393. [2] H. Rickert, Electrochemistry of solids, an introduction (Springer, Berlin, 1982). [3] W. Eichenauer andG. Muller, Z. Metallkd. 53 (1962) 321, 700. [4] H. Rickert and R. Steiner, Z. Physik. Chem. NF 49 (1966) 127. [ 51 H. Rickert, H. Wagner and R. Steiner, Chem. Ing. Tech. 38 (1966) 618. [6] E.A. Mizikar, R.E. Grace and N.A.D. Parlee, Trans. ASM 56 (1963) 101. [ 71 H. Rickert and A.A. Miligy, Z. Metallkd. 59 (1968) 635. [ 81 T.A. Ramanarayanan and R.A. Rapp, Metal. Trans. 3 ( 1972) 3239. [ 91 EA. Moghadam and D.A. Stevenson, J. Electrochem. Sot. 133 (1986) 1329. [lo] J.-H. Park, R.N. Blumenthal and M.A. Panhans, J. Electrochem. Sot. 135 (1988) 855. [ 111 J.-H. Park and R.N. Blumenthal, J. Electrochem. Sot. 136 (1989) 2867. [ 121 J.-H. Park, Physica B 150 (1988) 80. [ 131 J.-H. Park and P. Kostic, Mater. Letters 6 ( 1988) 327. [ 141 R.M. Barr, Trans. Faraday Sot. 35 (1939) 628; Phil. Mag. 28 (1939) 148.