Corrosion Science, Vol. 19, pp. 475 to 487 Pergamon Press. 1979. Printed in Great Britain
THE KINETICS OF DIFFUSION
IN POROUS INNER LAYERS*
J. E. CASTLE Department of Metallurgy and Materials Technology, University of Surrey, Guildford, Surrey, England
Abstract--The oxidation of cupro-nickel alloys at temperatures > 160°C produces a duplex oxide structure. In Part I, diffusion of copper across the inner nickel oxide layer was shown to be rate controlling. This conclusion is tested in this paper by examining the oxidation rate curves of a series of nine metals and alloys extending from pure copper to pure nickel. The isochronal curves are found to pass through a maximum at 75 ~oCu which is explained by surface diffusion of the copper through a porous nickel oxide structure extending through the metal consumption zone. The surface diffusion coefficient derived from this model is in the range 0.8-2.0 × 10-14 m 2 s -1 in accord with results of other workers. INTRODUCTION
IN PART 11 it was shown that the segregation of the elements copper and nickel into a duplex oxide structure, which is a feature of the high temperature oxidation of Cu-Ni alloys, also occurs at temperatures as low as 433K. It was shown moreover that diffusion of metallic copper occurs readily across the inner, nickel oxide, layer of the duplex structure even at these low temperatures, and that this flux is rate-controlling. Many authors have utilized the cupro-nickel alloys as a model system for the study of metal oxidation: the mutual solubility of the metals and the lack of miscibility or compound formation in the oxides lends itself well to this purpose. In this part the oxidation of the alloys is again used as a model to gain further understanding of the possible transport mechanisms involved in the formation of duplex layers. For this purpose the most important morphological feature is that which was commented on by Whittle and Wood, 2 that the inner NiO layer appears to just fill the metal consumption zone. This is readily confirmed to be the case at temperatures down to 923K by metallographic section. Since the volume of the metal consumption zone, as well as that of the nickel oxide formed, will depend on the proportion of copper in the alloy, oxidation of a series of alloys at a single temperature should provide an interesting corroboration of this mechanism of formation of the duplex layer and help understanding of the mechanism of mass transport in such cases. EXPERIMENTAL METHOD The alloys were prepared by International Nickel Mond Ltd. : their analyses are given in Table 1. The alloys were progressively rolled from forged bars weighing 500 g to strips ½ m m in thickness with intermediate vacuum annealing as and when necessary, Samples weighing ca. 1 g and of 1200 m m 2 in area were cut from the strip, etched after the method of Sartell e t al. s and finally electro-polished in a mixture containing 670 ral orthophosphoric acid, 300 ml sulphuric acid and 300 ml of water at *Manuscript received 27 May 1978; in revised form 14 September 1978. 475
J. E. CASTLE
TABLE I. Nominal composition
Pure Cu Pure Ni 90/10 C u / N i 85/15 C u / N i 80•20 C u / N i 75/25 C u / N i 70•30 C u / N i 60/40 C u / N i 50/50 C u / N i
0.006 0.016 0.006 0.005 0.009 0.008 0.008 0.008 0.002
THE COMPOSITIONOFTHE BINARYALLOYS
Cr < < < < < < < < <
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
Bal < 0.1 Bal Bal Bal Bal Bal Bal 50.56
N.D. 0.02 < 0.01 < 0.01 < 0.01 < 0.01 c 0.01 0.01 0.03
< 0.01 < 0.01 < 0.01 c0.01 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01
< < < < < < < < <
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
< < < < < < < < <
0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
< < < < < < < < <
0.02 0.04 0.02 0.02 0.02 0.02 0.02 0.02 0.02
c 0.1 Bal 10.70 15.50 21.10 25.70 30.50 40.90 51.00
N . D . = N o t determined; c = Approximately.
c u r r e n t density o f 7 m A m m -~ for a b o u t 60 s. T h e y were rinsed in a dilute solution o f the electrolyte, distilled water a n d acetone; they h a d a bright but slightly pitted surface. E x a m i n a t i o n o f the prepared surface by X-ray fluorescence indicated that it was identical in chemical c o m p o s i t i o n to that o f a freshly a b r a d e d surface. XPS confirmed this general conclusion but revealed the uptake of s o m e p h o s p h a t e f r o m the bath. This was considered to have a negligible influence o n the results. T h e alloys were oxidized o n a v a c u u m microbalance having a sensitivity of ~ 0.5 Izg in high purity oxygen (B.O.C. Ltd G r a d e X) at a pressure of 1.33 × 104N m -2. All alloys were oxidized in replicate at 773 ~ 0.5 K for periods of up to 5.5 × 106 s. EXPERIMENTAL
The curves for representative samples of all alloys and the metals are given in Fig. 1. They were found to be closer in shape to parabolic than to that required for any other rate law. In the initial period of oxidation there is by no means a mono-
~ . - - f
60 140 II ~ = ' ~ 7 , ~ ,
30 TIME, HOURS
W e i g h t g a i n curves for oxidation o f C u - N i alloys at 773K.
The oxidation of cupro-nickel alloys--II
Weight gain ( ~ g / e m ~) ,150 150"
100 / 5O
T i m e (h)
Composition (~ Cu)
FIG. 2. Triaxial plot of data in Fig. 1 showing dependence on alloy composition.
tonous increase in rate from nickel through to copper: both 90Cu-10Ni and 85Cu15Ni have rates of oxidation which are initially lower than alloys of greater nickel content. However all four samples of 90Cu-10Ni showed an abrupt increase in rate after 1.5 × 104s ( -~ 4 h) oxidation. The samples of 85Cu-15Ni did not increase in rate relative to their neighbours until later but were in line with that expected from the nickel content after 7 × 104s ( _ 20 h). Th]s complex behaviour is more clearly shown by the triaxial plot in Fig. 2. The isochronal lines show the presence of a minimum at c a . 85Cu-15Ni and a maximum at a point between 80Cu-20Ni and 75Cu-25Ni. DISCUSSION The retrogressive dependence of the oxidation rate on the nickel content in the region between 90Cu-10Ni and 70Cu-30Ni alloy composition has been commented on previously4 and it is well known to operators of boiler feed water heat exchangers in power plant that 90Cu-10Ni often has a superior performance to 70Cu-30Ni alloy. 5 The pronounced reduction in rate on addition of 5 - 1 0 ~ of nickel to copper was commented on by Bouillon and Stevens. s There thus seems no doubt that the isochronal curves in Fig. 2 are not artefacts but are typical of the oxidation of the alloy system under moderately low temperature conditions. In Part I of this series it was shown by XPS that, at an early stage of oxidation, the surface layer of nickel oxide is overgrown by copper oxide which in subsequent oxidation forms the outer layer of a duplex structure. Compact NiO, however, acts as a barrier to the diffusion of copper species. For example, the oxidation
PARAMETERS REQUIRED FOR EVALUATION OF
EQUATIONS10, 11 AND 13 0
90 85 80 75 70 60 55
0.23 0.35 0.47 0.58 0.70 0.93 1.00
0.77 0.65 0.53 0.42 0.30 0.07 0
1.23 1.29 1.35 1.41 1.47 1.59 1.64
2.65 3.36 4.02 3.93 3.43 1.79 0
0 = composition of alloy (weight fraction of copper), v = volume fraction of solid phase in metal consumption zone after loss of copper and oxidation of residual nickel, l-v = void fraction of metal consumption zone, 13 = mass of oxygen Mg required to oxidize 1 m s of alloy to CuzO and NiO, A = coefficient in equation (13) (Mg m-3). rate o f 5 0 C u - 5 0 N i is little different from that o f p u r e nickel due, a l m o s t certainly, to the presence o f such a layer. A c o m p a c t inner layer c a n n o t be used to a c c o u n t for the low o x i d a t i o n rate o f alloys o f lower nickel content, however, since the layer o f N i O on alloys o f lower nickel content t h a n 50 ~o c a n n o t be pore-free if, as o b s e r v a t i o n suggests, it also fills the metal c o n s u m p t i o n zone. T h e net p o r o s i t y o f nickel oxide remaining in this zone after o u t w a r d diffusion o f the c o p p e r is equal to the v o l u m e o f the c o p p e r less the expansion on o x i d a t i o n o f the residual nickel to nickel oxide. This porosity, expressed as a fraction o f the v o l u m e o f the m e t a l c o n s u m p t i o n zone, is given in T a b l e 2 u n d e r the h e a d i n g (1 - - v), i.e. v is the solid p h a s e expressed as a fraction o f the t o t a l volume. It is assumed in deriving the p o r o s i t y in this w a y t h a t the a c c u m u l a t i o n o f voids f r o m the o u t w a r d diffusing c o p p e r is n o t c o m p e n s a t e d by an i n w a r d drift o f the outer oxide. There is much evidence t h a t the presence o f pores at the m e t a l - o x i d e interface?, s 500
4I 5I 6I 7I 8I 9I I0] TIME,HOURS
t I I I 30 40 50 60 70
FIG. 3. Data obtained for the oxidationof ~v~ral samplesof 90Cu]0Ni ahoy showing
the transient rate increase at
4 h. (Data of Fig. 1 replotted on logarithmic time-scale for clarity.)
FIG. 4. Optical micrograph showing the oxide blistering associated with the rate change in 90Cu-10Ni alloy. The bright areas are uppermost in this micrograph.
The oxide formed on 70Cu-30Ni alloy at 923K (a) the NiO layer; (b) the copper oxide structure at the interface with NiO.
The oxidation of cupro-nickel alloys--II
will be as effective as second-phase particles in reducing the cross-sectional area available for solid state diffusion in the major oxide and in reducing the rate of oxidation, if this be diffusion controlled. Thus the sharp fall in oxidation ~ate at low, c a . 10 ~ , alloying additions is probably a consequence of the condensation of vacancies around the small volume of NiO particles within the metal consumption zone. These particles in effect act as props preventing the outer copper oxide layers from maintaining contact with the underlying alloy. The inner layer may thus be represented as the metal consumption zone mechanically stabilized by nickel oxide particles. Circumstantial evidence for this is found in the transient increases in rate shown by the most dilute alloy studied: 90Cu-10Ni. The initial increase in rate tended always to start after c a . 4 h of oxidation as is shown by the results for several specimens of the alloy in Fig. 3. When runs were arrested after the rate transition the surface oxide was found to have formed blisters (e.g. as shown by optical microscopy in Fig. 4). These are very similar in appearance to those described by Cohen e t al. s as forming when vacancies condense to voids at the metal-oxide interface. In the present instance they would correspond to the collapse of the highly porous inner layer giving either localized contact between the metal interface and the copper oxide layer or cracking and ingress of the molecular oxygen. In either case the enhanced rate of oxidation is short-lived although further rate accelerations were observed after a period of normal growth. The underlying reasons for the low oxidation rates at 90Cu-10Ni and 50Cu-50Ni compositions thus seem clear: the former has an almost complete void at the interface whilst the latter has art almost complete nickel oxide barrier layer. Between these extremes the voidage steadily decreases as the proportion of nickel oxide increases (Table 2). The oxidation rate over the same range however passes through a distinct maximum. The one physical feature of the oxide which should parallel this behaviour is the surface area of the inner layer per unit area of specimen. Assuming that the nickel oxide particles are approximately equiaxed, as is suggested by the microstructure of the inner layer formed at 923K in Fig. 5(a), and that the size distribution does not vary with alloy composition, then their'area will increase with the volume of nickel oxide particles in the metal consumption zone, reach a maximum at the greatest packing density of the particles, and then decline to zero as the particles intergrow to fill the residual volume. This process is complete at c a . 55 ~oNi. Surface diffusion of copper ions across this surface, bridging the metal consumption zone, would account for all kinetic features: the near parabolic oxidation rate, the inner layer rate control and finally the dependence on alloy composition. The next section is devoted to a derivation of a rate equation for the alloy series, based on surface diffusion across oxide bridges which will enable the model to be checked in quantitative terms. MODEL EQUATION There is no doubt that a model equation ought to be based on stereological interpretation of micrographs of the inner, porous, oxide layer. Microscopy of the inner layer formed at 773K is not practicable but Fig. 5 showing the layer formed on 70Cu-30Ni alloy at 923K gives some idea of the probable structure. Interpretation of this would be beyond the scope of this paper but Katan and Bourman, 9 discussing transport processes in porous electrodes, have shown that assemblies of cylinders can
Bulk Cu diffusion
Outer oxide layer
Cu Surface diffusion
~ NiO particles equaled to cylinder of radius r F I G . 6.
Metal consuml)lim~ zone
Internal oxidation ~one
Model for mass transport calculation.
be used as models of complex porous solids. We envisage two cases: either the nickel oxide is distributed as tortuous cylinders bridging the void between metal and cuprous oxide, or the void is distributed as tortuous pipes in a continuous layer of nickel oxide. The models give identical areas at the alloy composition producing a maximum packing density of the cylinders and it is convenient to use cylindrical columns in the high voidage (low nickel) alloys region and cylindrical pipes in the low voidage region. Figure 6 gives the essential features of the simplified model. The volume of the copper consumption zone depends on the volume fraction of copper in the alloy 01, which is related to the weight fraction 0w by O~ =
pNiOw pNiOw + PCu (1 -- Ow)
However, since Pcu = 1.002 PNi, 0v ~- 0w = 0. The volume of solid NiO remaining the metal consumption zone expressed as a fraction of the volume of the zone and after outward diffusion of the copper and oxidation of the remaining nickel, v is given by v = (1 -- 0)
The data given in Table 2 are derived from this equation. If the solid fraction is assumed to be distributed as n cylindrical bridges each having a volume of ~r~rx, where r = mean radius, x ---- thickness of copper consumption zone and T is the tortuosity factor, then and
vAx = n~r%x,
n = vA/grZr,
where A is the area of alloy oxidized. The total periphery, !, of these cylinders, perpendicular to the direction of surface diffusion is then i = n 2or,
T h e oxidation of cupro-nickel a l l o y s - - l I
2vA l = --
Thus the flux, per unit area of alloy surface, of surface diffusing ions, J J / A is given by: 10
J~# = 2v Ds (no - - n,<) , A r~ zx
where D, = the surface diffusion coefficient of copper on nickel-oxide, n x = the planar concentration of copper on the surface at the nickel oxide--copper oxide interface, and no = the planar concentration of copper at the metal-oxide interface. Thus the rate of extension of the metal consumption zone = d x / d t is given by d x _ J, lt2 1 _
2v D , f2 (no - - nx)
rz 2 0 N
A N O
in which f2 is the molar volume of copper and N is Avagadro's number. This may be integrated to give the familiar parabolic rate law in terms of the thickness of rrietal oxidized, i.e. x~_
4 v D sf~(n 0 _ n x ) t . rz z 0 N
However: 1V :
where w is the weight gained per unit area and time and ~ is the mean mass of oxygen required for total oxidation of the metal within unit volume of the copper consumption zone, i.e. 13 =
Mo] + (1 -- O) P N , ~
--- 2.25 for all compositions, assuming CuO and NiO to be the final states. Mo, Mcu and MNi are defined as the megagramme atomic weight of oxygen, copper and nickel in CuO and NiO. If Cu20 is formed than Mcu should be replaced by 2Mc~ and the range of [~values given in Table 2 is obtained. Thus, for pure surface diffusion, the isochronal relationship is .,
This will apply for the composition range 0 = 1.0-0.78, the boundary composition
for close packing of the cylindrical columns. The corresponding relationship for pipe diffusion which applies from 0 = 0.77-0.55, the boundary for zero porosity is
This function (11) decreases to zero at 55 yoCu whereas the actual oxidation rate only falls to that determined by grain boundary or solid state diffusion through the compact nickel oxide. This residual oxidation rate is seen in that of the 50Cu-50Ni alloy which is close to that of pure nickel. There is thus a rising background of grain boundary diffusion to be added to that arising from surface diffusion. The correction used was a simple proportion, c, of the weight gained in the same time by the 50 % alloy, i.e.
= r (1.00 -- O) 1 c
L I-~-~C_~O.'f5g Wso •
Of the parameters required for evaluation of (10) and (11), N and f2 are fixed constants taken as 6.14 × 102a and 7.13 mS/Mg mol respectively, ~ is also fixed at 2.25 Mg since SEM evidence is that the greater proportion of copper oxide is in the cupric form. The parameters no and nx, 3, r and Ds are within limits, disposable. It is a reasonable assumption that n,, at the oxide-oxide interface will be zero and that no at the metal-oxide interface will be at saturation coverage, i.e. 2 × 10t9 atoms m -2. It is further assumed that a.tortuosity of n/2 corresponding to a path increased by diffusion across hemispherical surfaces, is appropriate for testing the model. However the most serious difficulty in interpreting this model quantitatively is that the metallographic observations, from which data relating to particle size or surface area could be obtained, were only possible with the thicker films formed at 923K (Fig. 5). However, at this temperature the period of oxidation control exercised by the inner layer is short-lived. Microprobe analysis of cross-sections showed that copper accumulated at the alloy-nickel oxide interface after a few hours' oxidation. This is a natural consequence of the presence of a barrier layer. However, this enrichment was inevitably followed by oxidation of the metal interface to give a conglomerate oxide, presumably because the oxygen pressure within the pores grew to a value exceeding the decomposition pressure of cuprous oxide. Thus tests of the model by, for example, interruption of oxidation, showed it to be inapplicable after about 5 h. Nevertheless, use of particle size data from the 923K samples enables the relative oxidation rates of the alloys at 773K to be compared. The radius of these particles is thus taken as r = 0.25 ~m. The value of D, remains the final unknown. This may be obtained, and the model tested, by plotting all the data in the form
w = D. t A t ~.
Where A is evaluated using the above parameters for each of the aUoys. This plot is shown in Fig. 7 and achieves a marked condensation of the data of Figs. 1 and 2. The parabolic rate law is not obeyed by all alloys, but the most common deviation is a breakaway to higher rates of oxidation. Excluding the obvious breaks of this type,
The oxidation of cupro-nickel alloys--II
o . . . . .
. . . . . .
60 c .
At-" (Mg m'3s ~)
FIG. 7. Data of Fig. 1 plotted in accord with equation (13).
the data lie on lines with slopes ranging from 0.9-1.4 × 10-7 m s-~. Thus the'surface diffusion coefficient implied by use of this data is in the range 0.8-2.0 × 10-14 m 2 s -1. Comparable literature values for the same temperature are 0.97-15 x 10-14 m 2 s -1 (Kuczynskin), 7.8 × 10-t4-4.1 × 10-la m 2 s -1 (Nichols and Mullins 1~) and 9 × 10-14 (Stobbs13). The most recent result in this list (Stobbs, 1973) was derived by measurement of the spheroidization of SiO~. in internally oxidized silicon-copper alloys and is thus perhaps the most relevant. The other results are obtained from copper-oncopper diffusion in hydrogen atmospheres. Results in oxygen atmospheres are usually at least in order of magnitude greater in value3 ° APPLICATION OF THE MODEL The reasonable agreement with the literature values suggests that the model gives a correct description of the factors controlling the oxidation of the cupro-nickel alloys. Nevertheless the isochronals (Fig. 8) obtained by use of equations (10), (1 l) and (12), taking D s from the best fitting parabola (Ds70Cu-30Ni -- 1.25 x l0 -14 m ~ s-X), are not as sharply peaked as those derived from experiment. A more accurate representation of the porous structure would tend to give a better match. For example the tortuosity factor has been treated as a constant, whereas it would almost certainly vary with particle or void density. The better match in the isochronals on making a function of 1/i, or 1/l -- v in the high or low voidage region respectively9 is shown by the dashed lines in Fig. 8. This shows that the model would be improved by better representation of the porous structure. However, such sophistication is unjustified by the data available. The temperature range over which this mechanism is applicable extends down to at least 573K. The data already published 14 show close parallels with those given here,
FIG. 8. Calculated isochronal curves plotted with observed results.
i.e. a parabolic rate showing a retrogressive dependence on nickel content between the 90Cu-10Ni and 70Cu-30Ni alloys. It is shown to be inapplicable at times longer than a few hours at 923K and above by the evidence of interrupted oxidation experiments as described in Part I. SEM evidence shows that at least part of the nickel oxide is produced in an internally oxidized zone within the alloy. This demonstrates that the inward diffusion of molecular oxygen takes place. As long as this does not exceed the decomposition pressure of Cu~O then the surface diffusing copper species will not be oxidized within the inner layer. Thus the thermodynamic requirements for two-way transport across a porous inner layer are satisfied in this particular model. On the extension of this type of model to other duplex growths which may be found to occur on single metals as well as alloys, the satisfactory explanation of why counter diffusing species do not react may be more onerous. CONCLUSION The oxidation of cupro-nickel alloys at 773K is controlled by surface diffusion of copper atoms across a porous inner layer of nickel oxide. The surface diffusion coe~cient is in the range 0.8-2.0 × l0 -x4 m 2 s -a. Acknowledgements--The author acknowledges the generous provision of the metals and alloys by International Nickel Ltd, and thanks the Director of CERL, Leatherhead for permission to test the model using data obtained whilst employed by CERL. REFERENCES I. J. E. CASTLE and M. NASSERIAN-RIABI, Corros. Sci. 15, 537 (1975). 2. D. P. Wl-nTr~ and G. C. WOOD, Corros. Sci. 8, 295 (1968). 3. J. A. Sha~a~LL and C. H. LI, Am. Soc. Metals, Q. Trans. 55, 1023 (1962).
The oxidation of cupro-rtickel alloys--II
4. J. E. CASTLE,J. T. HARRISONand H. G. MASTERSON,Br. Corros. J. 1, 143 (1966). 5. J. E. CASTLE, J. T. HARRISON and H. G. MASTERSON,Proc. 2rid Congr. Metal Corros. NACE (1966) p. 822. 6. F. BOUILLONand J. STEVENS,Industrie chem. beige 24, 1335 (1959). 7. W. E. Boc,Gs and R. H. KACHIK, J. electrochem. Soc. 116, 424 (1969). 8. D. CAPLAN, M. J. GRAHAMand M. COHEN, Corros. Sci. 10, 1 (1970). 9. T. KATAN and H. F. BAUMAN,J. electrochem. Soc. 122, 77 (1975). 10. D. B. BUTRYMOWICZ,J. R. MANNINGand M. E. READ, J. phys. Chem. R e f Data 2, 643 (1974). 11. G. C. KUCZYNSKI,Traits. Metall. Soc. A.I.M.E. 185, 169 (1949). 12. F. A. NICHOLSand W. A. MULLINS,J. appl. Phys. 36, 1826 (1965). 13. W. M. STOBBS,Phil. Mag. 27, 1073 (1973). 14. J, E. CASTLEand H. G. MASTERSON,Anti. Corrosion 3 (1966).