oxidation of copper

Oxidation of Metals, Vol. 3, No. 3, 1971

Oxidation of Copper at High Temperatures

S. Mrowec* and A. StokIosa*

Received October 21, 1970--Revised January 13, 1971

The kinetics and mechanism of copper oxidation have been measured over the temperature range 900-1050~ and the pressure range 5 x 10 -3 to 8 • 10-1 arm. It has been shown that, at the pressures lower than the dissociation pressure of CuO, the oxide scale formed on fiat fragments of the copper specimens is compact and composed of a single layer, adhering closely to the metallic base. Growth of the scale proceeds under these conditions by outward diffusion of metal. The rate of the process under the conditions for which single-phase scales are formed increases with increasing oxygen pressure according to the equation :

t t kp = const p1~3.9

the activation energy for oxidation is 24 +_ 2 kcal/mole. On the basis of the Fueki-Wagner method and the method proposed in the present work, the self- diffusion coefficients of copper in cuprous oxide were calculated as a function of oxygen pressure and temperature. It has been shown that distribution of the defect concentration in the growing layer of the scale is linear.

I N T R O D U C T I O N

The mechanism of high-temperature oxidation of copper has been a subject of extensive theoretical and experimental studies. 1-3 Classical works of Wagner *-v published in the 1930's were concerned with the kinetics and mechanism of copper oxidation and with physicochemical properties of cuprous oxide, which was the main product of the oxidation. In the following

* Institute of Solid State Chemistry, School of Mining and Metallurgy, Cracow, Poland.

291

292 Mrowec and Stok]7osa

years studies on the copper-oxygen system were concerned with the elucida- tion of the kinetics and mechanism of scale formation and the physicochemical properties of the two oxides of copper. 1-1~

It has been shown that the scale formed on fiat fragments of the copper specimens is compact and its growth takes place by outward diffusion of the metal. ~~ Hence it may be assumed that the defect structure in cuprous oxide is limited only to the cation sublattice. This conclusion is in full agreement with the results of studies on deviations from stoichiometry in this oxide, conducted at various temperatures and at various oxygen pressures, and is confirmed by the results of Hall effect measurements 13,14 and by the observed dependence of the electrical conductivity on the oxygen pressure, s;15'~6 Specifically, it has been proved that cuprous oxide shows deviations from stoichiometry involving cation defects (Cu2_yO) and that the electrical conductivity of this oxide increases with increasing oxygen pressure, electron holes being the current carriers. Cuprous oxide is thus a p-type, metal-deficit semiconductor, having cationic vacancies and electron holes. These conclusions are also confirmed by the results of studies on. diffusion of copper and oxygen in Cu20, which show that the mobility of the metal in the cuprous oxide is considerably higher than the mobility of oxygen. 11 17 Although much information has been collected, many problems related to the mechanism of copper oxidation and physicochemical properties of Cu20 await solution. In particulaar there exist marked discrepancies between the results obtained by-~arious authors concerning the dependence of the oxidation rate on the oxygen pressure 7'~8'~9 and the dependence of defect concentration on the equilibrium pressure of oxygen. ~6'2~ Accurate data on the mobility of point defects in Cu20 are also lacking. The only data available reported by Moore and Seliks~Sn, 1~ are limited to one pressure of oxygen and were subjected to considerable experimental error because of the very short half-life of 64Cu ('~1/2 ~--- 12 hr).

Because of the discrepancies mentioned above, one cannot formulate unambiguous conclusions about the defect structure of cuprous oxide and in particular about the degree of ionization of cation vacancies and their mobility. Therefore, the mechanism of copper oxidation cannot be described. The present work is an attempt to explain these problems on the basis of precise measurements of parabolic rate constants of copper oxidation as a function of oxygen pressure and temperature.

EXPERIMENTAL

Kinetics Measurement

The kinetics of copper oxidation were studied with the continuous gravimetric method in an apparatus containing a spiral microbalance, a

Oxidation of Copper at High Temperatures 293

constant

gas o1.1,

~er

8 F

10

Fig. 1. Vacuum microbalance. 1, Hooks for hanging the spiral; 2, tungsten spiral; 3, thermostatic cooler; 4, damping device ; 5, window to measure the spiral elongation with a microscope; 6, water cooler; 7, quartz plates ; 8, asbestos shield ; 9, ceramic casing ; 10, heating elements ; 11, thermo- couple controlling the furnace temperature.

schematic diagram of which is shown in Fig. 1. A detailed description of this apparatus is given elsewhere. 21 The sensitivity of the microbalance was 26 mg/cm, which was equivalent to measuring the mass gains with the accuracy of _+ 2 x 10- 6 g at a load not exceeding 700 mg. The oxidation was

294 Mrowec and StokJcosa

conducted in a constant stream of gas, the flow rate of which was varied between 5 and 15 ml/min. The oxygen pressure ranged from 6.6 x 10 -3 to 0.8 atm and the temperature from 900 to 1050~ The lower limit of the pressure range was set by evaporation of cuprous oxide which under these conditions began to affect the results of the kinetics. The upper value of the pressure was determined by the dissociation pressure of cupric oxide (CuO). The experiments were carried out on spectrally pure copper (Matthey and Johnson). The flat specimens, 12.5 x 8.00 x 0.45 ram, were cut from sheet obtained by cold rolling of 5 mm diameter rods of copper. The surface of the specimens was polished with emery paper through 4/0, and then washed successively with water, acetone, and methanol. After fixing, the specimen in the reaction chamber, purified argon was passed through the apparatus. The reaction chamber was then evacuated down to the pressure of the order of 10-6 mm Hg, which, taking into account the preliminary purification of the system with argon, enabled the partial pressure of oxygen to be reduced to about 10- lo atm. Under these conditions the specimen was not oxidized in the temperature range applied. After the pressure was reduced to 10-6 mm Hg, the reaction chamber was heated to the desired temperature. After the desired temperature was attained, the specimen was further heated for 20 min, and then oxygen was admitted, its pressure and flow rate being controlled by Alpert-type valves. The oxidation kinetics were followed by registering the mass gains of the oxidized samples as a function of reaction time. The required pressure of oxygen was established within 2 min, and this time was regarded as the zero on the time scale.

Calculation of Parabolic Rate Constants

To determine accurately the values of parabolic rate constants of metal oxidation by the gravimetric method, the reaction conditions must ensure that a single-layer scale forms which adheres to the metallic substrate throughout the entire test. If scale growth proceeds by outward diffusion of metal, full contact between the reaction product and the metal is preserved by plastic deformation of the scale. 22-24 However, plastic deformation is possible only on the fiat regions of the oxidized specimen. However, plasticity occurs only for reaction times for which the ratio of the scale thickness to the size of the flat surface is considerably less than one. 25'26 The specimen edges make the scale rigid, acting subsequently as an obstacle to plastic deformation.22 26 Due to this behavior one must estimate the duration for which the scale remains adherent to the metallic core. It was shown by preliminary measurements that the scale adhered well when its thickness did not exceed 0.17 ram. This was equivalent to a reaction time of about 3 hr at 900~ and of 1 hr at 1050~


Another essential factor affecting the value of a parabolic rate constant is the surface area by which the mass gains are divided when calculating kp from the Pilling and Bedworth equation 27 :

(Am/q) 2 = k~t + C (1)

where Am is a mass gain after a time t, q is the surface area of metal, k~ is the parabolic rate constant, and C is a constant.

Most studies do not take into account the decrease of surface area during the reaction and, thus, the division of successive mass gains by the initial surface area leads to larger and larger errors. In precise experiments this fact is reflected in distinct departures from the parabolic rate law (Fig. 2). These departures were usually considered as inherent in the oxidation process and not as a result of systematic experimental errors. This problem has been

2

I

!

20 30 5O 7O

t m m

Fig. 2. Kine t ics of copper ox ida t ion at 1000~ at Po2 = 2.6 x 10 2 a tm (parabol ic plot). Curve 1, us ing the in i t ia l surface a rea ; 2, using an average surface area.

296 Mrowec and StoMosa

discussed by the present authors in a separate paper. 28 Correct results are obtained if one uses the mean surface area qi, which is the average of the initial surface area and the instantaneous area. This is obtained by measuring the initial and final surface area and assuming that the change is a linear function oflthe change in the mass gain:

que = qo -- P Am (2)

�9 ~here qM~ is the instantaneous surface area, q0 is the initial surface area, p is a constant. This equation was used to calculate gh. An example of kinetic curves for copper oxidation at a pressure of 2.6 x 10 -3 a tm is shown in Fig. 3. Values of the parabolic rate constants obtained are given in Table I.

�9 The temperature dependence of the oxidation rate is plotted in Fig. 4 for various pressures of oxygen. Curves 1-5 correspond to the oxygen pressures below the dissociation pressure of CuO. These conditions are those for which single-phase scales of cuprous oxide are formed. Curve 6 corresponds to the oxygen pressure in air. This latter pressure exceeds the dissociation pressure of CuO except at 1050~ This curve represents the temperature dependence

2 2

/

25 50 '75

t m/n

Fig. 3. Kinetics of copper oxidation at Po2 = 2.6 x 10 -2 a tm for several temperatures (parabolic plot). Curves 1-5 correspond, respectively, to 900, 950, 980, 1000, and 1050~


Table I. Parabolic Rate Constants of Copper Oxidation in the Temperature Range 900 1050~ (k~ x 108 g2 cm-4sec-1)

Temperature (~

900 950 980 1000 1050 Pressure \ .

(Po2 X 10 3 atm)

6.6 1.83 2.87 3.8 3.9 5.7 13.2 2.22 3.47 4.6 4.9 7.0 19.7 2.47 - - 4.8 - - - - 26.3 2.67 4.08 5.2 5.9 7.8 39.5 2.82 4.57 5.7 6.5 9.3 52.6 - - 4.58 6.3 7.0 9.8 79.5 2.80 - - 6.7 7.7 11,1

100.0 2.80 4.58 6.8 8.1 - - 134 - - - - - - 12.5 144 - - - - 6.7 - - - - 180 - - - - - - 8.2 13.8 265 - - - - 6.7 - - 14.5 400 - - - - 8.1 17.1 500 - - - - 17.0 600 - - - - - - 16.8

Error Ak~ +0.03 -+0.08 -+0.1 -+0.1 -+0.3

of the ox ida t ion rate for a duplex scale. The act ivat ion energy of oxida t ion is 24 _+ 2 kcal /mole for the monophase scale (curves 1-5) and 33.5 kcal /mole for the duplex scale (curve 6).

Da ta for the tempera ture dependence of the rate of fo rmat ion of the m o n o p h a s e scale on copper are lacking in the l i terature ; therefore, the value of the ac t iva t ion energy ob ta ined in the present work canno t be compared with other data. The compar i son may be made, however, for the duplex scale formed at ambien t oxygen pressure 0.21 atm. In Table II the values of

the ac t iva t ion energy of copper oxida t ion in air avai lable in the literature 19'z9-32 are compared with those ob ta ined in the present work (curve 6).

The values ob ta ined by different au thors vary considerably. This may be due

to the different degrees of pur i ty of the copper sample and also to the errors made in the de te rmina t ion of the parabol ic rate constants . 26'zs

The dependence of the rate of ox ida t ion on the oxygen pressure is plot ted in Fig. 5. The react ion rate increases with increasing oxygen pressure up to a point , above which it remains constant , and at 1050~ it decreases slightly. In the range of pressures below the dissociat ion pressure of cuprous oxide, the vacancy concen t ra t ion gradient in the growing scale, C u 2 0 , is

dependen t on the oxygen pressure, increasing with increasing oxygen

298 Mrowec and Stokr

Table II. Activation Energy of Copper Oxidation in Air

Activation energy Temperature range Literature (kcal/mole) (~

Tylecote 29 29.4 600- 900 Valensi 3~ 37.7 700-1000 Kofstad 31 35 750-1000 Bridges e t a l . 19 31.5 700-1000 Czerski e t a l ) 2 38 900-1050 Present work 33.5 901~1050 Present work (at the oxygen pressure 2.6 x 10 .2 atm) 24 +_ 2 900-1050

r ~ f050 ~ 1000 o 950 ~ 900 *

~za

G

07~ QSO O.e4

r "K

Fig, 4, Temperature dependence of the rate of copper oxidation for several oxygen pressures. Curves i -5 correspond, respectively, to 6.6 x 10 -3a t m , 1.3 x 10 -2a tm, 2.6 x 10 -2a tm, 3.9 x 10-2a tm, and 7.9 x 10 -2 atm. Curve 6 corresponds to the oxygen pressure of air.


"t, Ii

-7,o

-~'8

/ /

///z////

ii g / o o

-2.0 ~2,5 -ZO -0~5

(og Po~ otto

Fig. 5. Dependence of the copper oxidation rate on oxygen pressure. Curves 1-5 correspond, respectively, to 900, 950, 980, 1000, and 1050"C. The broken line shows the boundary between the single-phase scale (region I) and the two-phase scale (region II).

pressure. Since the reaction rate is determined by the diffusion of cation vacancies in the scale, the parabolic rate constant for oxidation increases with an increase in the defect concentration gradient in the scale. In region II, at pressures exceeding the dissociation pressure of CuO, there always exists a thin layer of CuO on the exterior scale surface which separates the Cu~O from the oxidizing atmosphere. The partial pressure of oxygen at the Cu~O-CuO boundary, which determines the value of the concentration gradient in the Cu20 phase, is thus independent of the external oxygen pressure and is equal to the dissociation pressure of CuO. Because nearly the whole scale consists of Cu20 (CuO represents about 1% of the scale), the oxidation rate at a given temperature should be independent of the external oxygen pressure

300 Mrowec and Stok4osa

whenever CuO exists. This conclusion is verified by the results presented in Fig. 5. In order to confirm the above conclusions, the dissociation pressures of CuO at various temperatures were calculated from the thermodynamic data reported by various authors 33-36 and compared with the values of the oxygen pressures at which the break of the curves in Fig. 5 was observed. The results of these calculations are presented in Fig. 6. As expected, the values of the oxygen pressures at which the break in the straight lines of Fig. 5 is observed correspond to the values of the dissociation pressures of cupric oxide derived from thermodynamic data.

Metallographie Studies

The measurements of oxidation kinetics were supplemented by studies on material transport through the scale using the marker method. A platinum

r ~

E]

.~ -/.0

-/.5

f 050 �9 fO00 �9 950 �9 900 �9

-0.5

0.78 0.80 0.'8/~

- / - / 0 3 , / ( T

Fig. 6. Dependence of the dissociation pressure of cupric oxide (CuO) on temperature. (D, Kubashevski31; A, Landolt32; [], Charotta3; Z~, Bidwell 3s ;0 , present work.


wire, 30 g in diameter, was used as a marker. Sections of this wire, 2 mm long, were placed on the sample surface which was then oxidized in a horizontal position. The sample was subsequently mounted in polyester resin and then cut perpendicularly to the surface covered with the markers. The location of the marker in the scale was determined microscopically. Marker studies were performed for some extreme temperatures and oxygen pressures. The studies proved that the scale was compact and single-layered in its entire cross section and that the platinum markers were located at the metal-scale phase boundary. It follows from these facts that scale growth in this case takes place exclusively by outward diffusion of metal.

DISCUSSION

The kinetic data obtained allow us to formulate a number of important conclusions concerning the mechanism of high-temperature oxidation of copper, the mobility of point defects in cuprous oxide, and the degree of ionization of cation vacancies in this oxide. It has been found, that under suitably selected conditions the oxidation of copper produces a single- layered compact scale adherent to the metal. Scale growth proceeds under these conditions by outward diffusion of metal. These facts corroborated by strictly following the parabolic rate law imply that the slowest process determining the rate of scale growth is diffusion of cation vacancies according to the theoretical model of Wagner. 37 Good contact of the scale with the metallic core during the determination of the kinetics and strict parabolic behavior suggest that, under the conditions described above, there are no perturbations of local thermodynamic equilibria at either phase boundary. The results of the kinetics may be thus employed in calculations of self- diffusion coefficients of copper in cuprous oxide from the general equation of Wagner 37 :

--.--(a'~/zx ) (3) kr=ceq j~k l -~D~e + Dx dlnax

where k r is a rational oxidation constant expressed in gram equivalents per centimeter per second; Ceq is the concentration of metal ions in gram equivalents per cm 2 of the scale; z 1 and z2 are the valences of metal and an oxidant in the reaction product, respectively; a~ and a~ are the thermodynamic activities of the oxidant at the metal scale and scale-oxidant phase boundaries; and DM, and D x are the self-diffusion coefficients of metal and anions in the scale. Since in the case under consideration Dcu >> Do2,17 the general equation of Wagner can be simplified to the following form :

~f ~ Z1 kr = C~q -- D~e d In a x (4)

k Z2

302 Mrowec and Stok4"osa

The rational rate constant in Eqs. (3) and (4) may be replaced by the parabolic rate constant kp expressed in g2 • cm-4 x sec i.

kr = ~Mox(z2/Ax) 2 k~ (5)

Substituting the oxidant activity by its partial pressure, one obtains the following relation between the parabolic rate constant of oxidation and the cation self-diffusion coefficient in the scale :

,, A~zl fpk k p - -2 3 Duedlnpx (6)

V~MeXZ2 p,.

where Pr denotes the oxidant pressure at the metal-scale phase boundary and Px is the oxidant pressure at the outer phase boundary. To integrate Eq. (6) we should know a priori the dependence of self-diffusion coefficient of metal in the scale on the oxidant pressure. Fueki and Wagner 39 have proposed the solution of this problem which does not require the knowledge of the dependence of DMe on the oxidant pressure. They drew attention to the fact that Pr is, at a given temperature, independent of the oxidant pressure. According to the assumptions of the Wagner theory, 37 a local thermodynamic equilibrium is attained at the metal-scale phase boundary, and hence the partial pressure at this phase boundary is very close to the dissociation pressure of the scale. The above-mentioned assumption of the Wagner theory was proved in a number of experiments. 4~ Taking this fact into account we may integrate Eq. (6) to give:

zt~ Ax ] ~dtnpx]p.

In the case of copper oxidation to Cu20, Eq. (7) assumes the form :

I dk" Dc~ = 1.818| ---'~p | (8)

ld log Po2]v,

To calculate the self-diffusion coefficient of metal in the scale, it is necessary to determine the dependence of the oxidation rate on oxygen pressure. Having determined this function, one can calculate the value of DM~ by finding the differential of the function for a given pressure. Fueki and Wagner 39 performed these calculations for the Ni-NiO-Oz system and Mrowec, Walec, and Werber 42 for the Co-CoO-O 2 system. The results reported were in agreement with the data obtained with the use of radioisotopes of nickel and cobalt. Analogous agreement was also found by Mrowec 43'4~ for the Fe-FeS-S2 system. Equation (8) has been employed in the present work for calculations of the self-diffusion coefficients of copper in Cu20 at selected oxygen pressures and at a temperature of 1000~


However, owing to the comparatively narrow range of oxygen pressures, over which the oxidation of copper was studied, the accurate determination of k~ = f( log Po2) and its differentiation were difficult, and the values of Dcu were associated with considerable error.

Considering this problem, we have observed that the self-diffusion coefficient of a metal in a p-type semiconductor scale may be calculated in a much simpler way if log k~ is a linear function of log Po2. In this case the reaction rate increases with an increase in the oxidant pressure according to the equation :

t t kp = const plx/" (9)

It follows from the above relationship that the self-diffusion coefficient of a metal should be an analogous function of the oxidant pressure, because diffusion of cation vacancies in the scale is in this case the slowest partial process determining the oxidation rate:

DMe = DoP~/n (10)

Substituting Eq. (10) into Eq. (6) and integrating, one gets:

A2xzl D n ~-I/n k p - iv~__3 o ~ex - p ~ l , ) (11) ghieXZ2

r162

The above equation may be simplified, if the measurements of kp were performed at pressures considerably above the oxidant pressure at the Me-MeX boundary (Px >> Pr) :

A~-zl t ! - - kp ~2 3 Donpx/" (12)

VMeXZ2

An analogous equation was reported much earlier by Wagner 37 in a discussion of the possibilities of simplifying the solution of his general equation. However the simplification used by Wagner has a form identical to Eq. (9), and hence it does not define the proportionality coefficient of this equation. This excludes the possibility of employing this relation for the calculation of other physicochemical parameters, in particular in determining D o and 1In.

Because the kinetics of copper oxidation were determined at pressures considerably higher than the oxygen pressure at the Cu-Cu20 phase boundary, the function

log kp = f( log Po2) (13)

was obtained by the least-squares method, and then the values of D o and 1/n were calculated from the constants obtained. Substituting these data

304 Mrowec and Stokt'osa

Table IlL Self-Diffusion of Copper in Cuprous Oxide

Temperature Pressure range Dc. = ~0vo~n .1/, (~ (atm) (cm 2 sec- 1)

900 6.6- 26.3 950 6.6- 39.3 980 6.6- 79.5

1000 6.6-105 1050 6.6-400

Dcu = (6.8 • 0.1) x 10-8pl/2(4"~176

Dcu = (1.10 • 0.02) x 10-Tp~/~ 3"9-+0"1)

Dcu = (1.39 • 0.03) x 10-Tp~ 3'9-+~ DCu = (1.55 • 0.03) x 10-Tp~ 3"9+-~ Dc. = (2.27 + 0.09) x 10 -7-1/(3"9-+~

- - /vO 2

in to Eq. (13) we o b t a i n e d the empi r ica l fo rmulas for the self-diffusion coefficients of coppe r in C u 2 0 as a funct ion of oxygen pressure. The results of the ca lcu la t ions are given in Tab le III . The values of Dc, ca lcu la ted by the F u e k i - W a g n e r m e t h o d are c o m p a r e d with those o b t a i n e d by the m e t h o d desc r ibed a b o v e (columns 1 and 2 of Tab le IV). G o o d ag reemen t (within the l imits of expe r imen ta l error) be tween the two sets of values is observed. However , the e r ro r m a d e in the ca lcu la t ions with the F u e k i - W a g n e r m e t h o d is cons ide rab ly h igher t han tha t o b t a i n e d with the presen t a u t h o r s ' me thod . The la t te r m e t h o d m a y be used only for pressures which are cons ide rab ly h igher t han the ox idan t pressure at the meta l - sca le phase b o u n d a r y . One

Table IV. Self-Diffusion Coefficients of Copper in CU20 at 1000~ (Calculated by Various Methods from Kinetic Data of Copper Oxidation as a Function

of Oxygen Pressure)

Pressure P o z • 103

(atm)

Self-diffusion coefficient Dcu x lO s cm z sec-I

Values derived with equations

(8) (12) (19)

6,6 4.6 4.3 4.2 13,2 5.4 5.2 5.2 26.3 6.1 6.2 6.3 39.5 7.3 6.8 8.9 53.8 7.6 7.4 7.5 79.5 8.0 8.1 8.3

100 8.3 8.6 8.7 ErrorADcu • • - -


may thus conclude that the Fueki-Wagner method is more general, and the results may be equally accurate when the measurements are carried out over a suitably wide pressure range. If this is not possible, however, the method proposed by the present authors appears to yield more accurate results.

To compare the results of calculations of Dcu with the values obtained by Moore and Selikson 11 by radioisotope methods, the results of the present work were extrapolated to an oxygen pressure of 1.3 x 10 .4 atm making use of the equations given in Table III. Moore and Selikson determined the diffusion coefficients of copper in Cu20 in the temperature range 800- 1050~ at only one value of oxygen pressure (1.3 • 10 -4 atm). In Fig. 7 the results of the present work and the data obtained by Moore and Selikson are presented graphically. As already mentioned, the results obtained with the radioisotope method show considerable scatter of the experimental points which may be due to serious experimental difficulties resulting from the short half-life of radiocopper. As seen from the plot, the results of the present

-7.6

g

r ' c

i

o

0

o o

8 o .

8 ~

176 ~gO I I O,84 O,00

~. . 3 o K 10

O ~

Fig. 7. The temperature dependence of the self-diffusion coefficient of copper at Po2 = 1.3 • 10 -'~ atm. Open circles denote the experimental values obtained from radioisotope measurements; open triangles are the values extrapolated from the results of the present work.

306 Mrowec and Stok]'osa

calculations are essentially in agreement with the results of the isotopic studies. It should be noted, however, that the value of the activation energy of copper diffusion in Cu20, 36 kcal/mole, reported by Moore and Selikson is considerably higher than that obtained in the present work, 24 _+ 2 kcal/mole, the latter value being practically independent of the oxygen pressure over the pressure range studied (Fig. 8). Although the pressure range in our experiments was relatively narrow, it seems improbable that a further decrease of pressure of one order of magnitude could cause such a marked increase in the activation energy of diffusion. In addition, the temperature dependence of Dcu (Fig. 7) cannot be determined accurately from the Moore and Selikson data as the scatter of experimental points is too large.

T ~ 1060 �9 tO00 * 950 ~ 900 o

- 7 , 0

- 7 , ~

- 7 6

- 7 , 8

i - - i _ _ i ~TG 0,80 O.B/~

-lr.lOJ o E

Fig. 8. The temperature dependence of the self-diffusion coefficient of copper in Cu;O. Curves 1-5 correspond, respectively, to 6.6 x 10 -3 atm, 1.3 x 10 2atm, 2.6 x 10-2atm, 3.9 x 10-2atm, and 7.9 x 10-Zatm.


The activation energy of copper self-diffusion in Cu 2 0 is the sum of the energy of formation of cation vacancies and the energy of movement of these vacancies. By studying deviations from stoichiometry in Cu20 as a function of oxygen pressure and temperature, Moore and O'Keeffe 2~ found the following relationship between the concentration of cation vacancies and oxygen pressure :

,,1/3J (14) y = const zo2

The exponent in Eq. (14) is very close to 1/4, implying that the cation vacancies are practically nonionized. The latter conclusion follows from considerations on the defect equilibria in the crystal lattice of cuprous oxide. 45'46

This conclusion is in agreement with the results of investigations on the rate of copper oxidation as a function of oxygen pressure, shown in Fig. 5, which is the basis for calculations of self-diffusion coefficients of copper in cuprous oxide. It has been found that the pressure dependence of the parabolic rate constant is described by

kp = const p ~ (15)

where the exponent 1/n varies, depending on the temperature, between 1/3.9 and 1/4. An analogous dependence was obtained for the self-diffusion coefficient of copper in Cu20 (Table IV and Fig. 8).

Bearing in mind the fact that the exponent of Eq. (10) has a value close to 1/4, the general relationship between the coefficient of self-diffusion of copper in Cu20 and temperature and the oxygen pressure may be described a s

Dcu = const p ~ e x p { [ - ( A H f + AHm)?/RT } (16)

where A/-/m is the energy for the movement of defects. It follows from Fig. 8 that the temperature dependence of the self-diffusion coefficient obeys the Arrhenius law and may be described by the equation:

Dcu = const p ~ e x p ( - E/RT) (17)

where E is the experimental activation energy of diffusion. Comparison of Eqs. (16) and (17) shows that the measured activation energy of diffusion of 24 _+ 2 kcal/mole is the sum of the heat of defect formation in the crystal lattice of Cu20 and the energy of the defect motion :

E = A H z + A H m (18)

The " t rue" activation energy of diffusion of cation vacancies in the crystal lattice of Cu20 is thus equal to the difference between the value of E and the activation energy of the defect formation (AHf). Results of Moore and O'Keeffe 2~ give the value of 21.7 kcal/mole for AHf. On the other hand,

308 Mrowec and Stoldosa

Wagner and Hammen 6 report the value o fAH I as 13 kcal/mole at an oxygen pressure of 6.6 x 10 .3 atm. Such discrepancies in these values make it impossible to evaluate the energy for the movement of cation vacancies. Nevertheless, it may be stated with a high degree of certainty that the energy for defect motion in cuprous oxide is markedly smaller than the energy of this process in other transition metal oxides. If the value obtained by Wagner and Hammen is substituted into Eq. (18), then AH,, = 11 kcal/mole, whereas substitution of the value of Moore and O'Keeffe yields AH m = 3 kcal/mole. Both these values are considerably smaller than the energy of defect motion in oxides of iron, nickel, and cobalt, which like Cu20 are metal-deficit, p-type semiconductors. AH m for the latter oxides is about 28-30 kcal/mole. 47 The cation vacancies in these oxides are, over the range of pressures and temperature in which A H m was determined, singly ionized. In the case of cuprous oxide, as it follows from the above discussion, the activation energy was determined for the case in which the majority o fvacancies were un-ionized. It can then be supposed that the low energy of defect motion in Cu20 can be related to the absence of ionization of cation vacancies. The problem requires further studies ; in particular it is necessary to measure the activation energy of diffusion and the heat of formation of defects at low oxygen pressures, at which pressures ionized vacancies may occur.

Making use of the Pettit theory, 48 the kinetic data were used to determine the oxygen activity gradient in the scale during growth at various temperatures and pressures. The results obtained, supplemented by results of studies on deviations from stoichiometry in Cu20 obtained by Moore and O'Keeffe, 2~ were then employed to determine the distribution of cation vacancies in the oxide. These calculations proved that the gradient of the defect concentration was linear (Fig. 9). Analogous results were obtained by Pettit 48 and Mrowec 42'43 for other systems.

The linear distribution of the concentration of cation vacancies in the scale indicates that the self-diffusion coefficient of defects, D v, is independent of defect concentration.

It is also possible to derive the self-diffusion coefficient of copper in Cu20 from kinetic data by making use of the modified Mot t -Gurney equation 49 :

t kp = (p + 1)Die (19)

t where kp is a parabolic rate constant for the reaction in cm 2 sec- 1 and p is the degree of defect ionization.

As already mentioned, the dependence of the cation vacancy concentra- t t tion in Cu20 on the oxygen pressure [Eq. (14)J and the dependence kp

f (Po2) [Eq. (15)1 imply that the vacancies in the cation sublattice are probably


/ / /

1 1 1 "+

I f

I /

I /I

/ I

/ I"

/

x xo

Fig. 9. Defect concentration gradient in Cu20 during oxidation at 1000~

un-ionized, and thus p = 0. The value obtained is in good agreement with those derived from Eqs. (8) and (12). The results of these calculations are given in column 3 of Table IV.

The agreement of the values of Dcu calculated from Eqs. (8), (12), and (19) confirms the hypothesis stated earlier, according to which cation vacancies in Cu~O are un-ionized. If the singly ionized vacancies were predominant, then one should substitute p = 1 in Eq. (19) which would double the value of Dcu obtained from Eqs. (8) and (12).

CONCLUSIONS

The results of studies on the kinetics and mechanism of copper oxidation, under conditions for which the formation of a single-phase scale of cuprous oxide forms, allow us to formulate the following conclusions.

1. The oxide scale on copper, formed over a range of oxygen pressures below that of the dissociation pressure of CuO, is compact and adheres

310 Mrowec and Stokt~osa

closely to the metal on the flat portions of the sample. Growth of the scale, consisting solely of Cu20, occurs by the outward diffusion of the metal. The rate-determining step of oxidation is the diffusion of cation vacancies in the scale.

2. When interpreting kinetic data, one should take into account the changes in surface area of the metal during oxidation. Neglecting this factor may give rise to erroneous conclusions, with respect to the rate law followed and the absolute values of the rate constants of this process.

3. Under the conditions for which CuzO is the sole product of oxidation, the rate of copper oxidation increases with an increase in oxygen pressure according to the assumptions of the Wagner theory. It follows from this dependence that in the temperature range 900-1050~ and at pressures close to 1 atm, cuprous oxide contains mainly un-ionized cation vacancies. This conclusion is confirmed by the results of calculations of Dco performed with the use of Eqs. (8), (12), and (19).

4. The activation energy of copper oxidation when a single-phase scale forms is different than that observed when a duplex scale forms (Table II). This difference is due to the dependence of the rate of growth of Cu20 phase on oxygen pressure.

5. The self-diffusion coefficient of copper in cuprous oxide as a function of oxygen pressure and temperature was derived from kinetic data by the Fueki-Wagner method as well as by the new method proposed in the present work. The agreement between the results obtained with these two methods is good. This agreement is observed also between calculated results and data obtained by Moore and Selikson who used radioisotopes.

6. The defect concentration gradient in the growing scale was analyzed by the Pettit equations. This distribution was linear (Fig. 9). This enabled us to employ the modified Mot t -Gurney equation [Eq. (19)] to calculate the self-diffusion coefficients of copper in Cu20 as a function of temperature and oxygen pressure. The agreement between values obtained in these calculations and those derived by other methods (Table IV) enabled the degree of ionization to cation vacancies in Cu20 to be determined.

R E F E R E N C E S

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oxidation of copper

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