The oxidation of metals, needless to say, is of great technological and economic importance as well as of interest scientifically. One of the initial things to consider about the oxidation of a given metals is, “Does the oxide provide a coherent protective, or passive, layer that reduces the rate of continued oxidation?” This is best summarized by the Piling–Bedworth ratio, which is the ratio of the volume of the oxide compared to that of the volume of the metal consumed (West 1986; Kofstad 1988). If the ratio is less than 1, then the oxide layer is under tension and cracks form exposing the surface to further oxidation—the oxide layer does not cover the metal surface completely and is not protective:
not passive. For the oxidation of magnesium to MgO, the ratio is 0.8 and, as a result, magnesium oxidation does not provide a protective oxide layer. On the other hand, the ratio is greater than 1 for nickel, silicon, iron, and a number of other metals that do form protective layers. For example, the ratio is 1.6 for nickel. However, too large of a positive ratio can lead to compressive stresses in the oxide layer that can also lead to cracking—spalling of the oxide—and increase the complexity of the oxidation process. Here, only oxidation with the formation of a protective layer is considered.
Most of the time, the rate of metal oxidation is determined by either the diffusion of the metal out to the surface or oxygen in from the atmosphere as shown in Figure 14.1. In either case, it is diffusion through the oxide layer that determines the rate of oxidation. In fact, much of the under- standing of diffusion in oxide compounds has been generated mainly to understand oxidation of metals. It was seen in Chapter 10 that in the oxidation of silicon—or silicon-containing compounds such as SiC, Si3N4, and silicides—interstitial diffusion of oxygen through the SiO2 layer controls the rate of oxidation. In that case, as shown in Figure 14.1, any inert markers* placed at the silicon–
oxygen atmosphere would end up at the top of the oxide layer. However, in the oxidation of transi- tion metals such as iron, nickel, and titanium, which is of significant commercial and industrial importance, the diffusing species move via a vacancy mechanism and, for all practical purposes, the composition of the oxide is constant throughout the thickness of the oxide layer. In other words, there is no concentration gradient—ignoring possible point defect gradients—but there is a large Gibbs energy gradient that drives the diffusion-controlled oxidation process. In reality, however, for many of these oxides, there is the small deviation from stoichiometry discussed in Chapter 9 that
* An inert marker is some nonreactive material such as tungsten wires in copper or zirconia particles in alumina that do not react with the bulk phase at elevated temperatures and serve as a spatial reference point.
Me + 1/2 O2(g) = MeO Metal
Oxide, MeOMe2+ O2− Me2+ O2−
2e−
4e−
2e− Oxygen
Inert markers
(a) (b) (c)
FIGURE 14.1 Possible marker motion during the oxidation of metals. In all cases, the diffusion of electrons is fast compared to that of the ions. (a) The cation, Me+2, diffuses much faster than the oxygen anion, so the markers remain at the metal–oxide interface. (b) The diffusion rates of cations and anions are about the same so the markers end up somewhere inside the oxide layer. (c) The oxygen anion diffusion is much faster than that of the cation, so the markers are on top at the oxide–oxygen interface.
produces the requisite electronic charge flux, and this small electron or hole concentration differ- ence will indeed vary from one side of the oxide layer to the other. For example,
NiO s x O g Ni O s Fe O s Fe O s x O g TiO
x x
( ) / ( ) ( )
( ) ( ) / ( )
( +
+
−
−
2
2
2 1
2 3 2 3 2
2
ss)TiO2−x( )s +x/2O g2( ).
As was seen in Chapter 10, this concentration difference, 1 – x, is usually quite small (~10–3) com- pared to the very large Gibbs energy gradient that drives diffusion and mass transport and the oxida- tion process. In both cases, there must also be a flux of electronic charge or oxidation will not take place according the Wagner theory of oxidation (Wagner 1951), which is modeled in the Appendix in terms of the electrical conductivities of the oxide layer. This is in the Appendix to simply reduce the amount of algebra here to minimize the possibility of “losing sight of the forest for the trees.”
Specifically, for NiO formation the flux of nickel from the nickel–nickel oxide interface to the nickel oxide–oxygen interface is given by (Wagner 1951)
J t t dG
Ni= − 1 i e dxNi
4F2σ (14.1)
where:
σ = total electrical conductivity = ionic conductivity + electronic conductivity ti = the transference number for ionic conductivity
te = the transference number for the electronic conductivity F = faraday or one mole of electron charges = 96,485 C/mol.
The transference numbers are simply the fractions of the total conductivity (current) by either the ions or electrons, ti= σ σi total. So if te = 0 and th = 0—no electronic conduction—then there is no oxidation, which is implied in Figure 14.1.
The principles applied to oxidation can be equally applied to the formation of other compounds or reaction products between a metal and a gas such as sulfides or fluorides. Finally, oxidation can become quite complex if there is more than one oxidation state of the oxide or if an alloy is being oxidized. The modeling of these complexities is best left to studies focused on metals and/or their oxidation and corrosion. Only simple oxidation is covered here to illustrate the general principles involved in a nonideal, diffusion-controlled reaction. These same principles apply to more complex cases but require some modifications. There are many good sources for information on the oxidation of metals that summarize both complex and simple reactions (e.g., West 1986; Kofstad 1988).
14.2.2 o
xIdatIonofn
Ickel14.2.2.1 Introduction
For the sake of concreteness, the oxidation of nickel in pure oxygen, pO2=1bar, is examined at 1200°C. The melting point of nickel is 1455°C and that of NiO is 1957°C (Haynes 2013). From the diffusion data in Table 9.5,
DNi D e e cm s
Q
= 0 −RT = × −4 − = × −
184 900
8 314 1473 10 2
4 4 10. 1 22 10. /
,
( . )( ) (14.2)
DO D e e cm s
Q
= 0 −RT = × −4 − = × −
240 600
8 314 1473 12 2
6 2 10. 1 82 10. / .
,
( . )( ) (14.3)
The diffusion coefficient of oxygen is about two orders of magnitude smaller than that of nickel. So for all practical purposes, the oxidation rate is controlled by the faster of the diffusing species, the nickel ion, which is the situation depicted in Figure 14.1a. Any inert markers at the original nickel surface should remain there because all of the diffusion will be from the nickel through the oxide. This, of
14.2 Oxidation of Metals 483 course, assumes that the transference number for electrons is large enough for oxidation to take
place. As pointed out, the electronic conductivity arises because of the nonstoichiometric NiO, which is a fairly good conductor at elevated temperatures due to the formation of point defects by oxidation in oxygen to produce the nonstoichiometric Ni O1−x , essentially a solid solution of Ni2O3 in NiO:
2 1
2 2 2
NNix O g Ni O V
Ni Ox
+ ( ) i + + ′′Ni (14.4)
where the electronic conductivity comes from the electrons on the Ni2+ ions (NiNix
) moving to the Ni3+ ions (Ni⋅Ni), the so-called hopping electron conductivity or small polaron conductivity. A litera- ture value of the electrical conductivity of NiO at 1200°C in 1 atm of pure oxygen is σ ≅ 1 S/cm making it a very good semiconductor (Smyth 2000). For now, it is assumed that telectronic≅1 so only the flux density of Ni2+ ions needs to be considered (see Exercises).
14.2.2.2 Calculation of the Parabolic Rate Constant Again invoking the Nernst–Planck equations,
′ = − −
′ + = −
+ +
J D
k T N
dG dx eE
J D
k T N
dG
e e e
B A
e
Ni Ni Ni
B A
Ni
η
η 1
1
2
2 2 2++
+
dx 2eE
(14.5)
which, after some tedious algebra in the Appendix, if the oxidation is being carried out in pure oxy- gen at one bar pressure, leads to
′ = −
(
+)
+
+ + − −
+ + − −
J D D
N k T D D
G
Ni Ni Ni e e L
A B Ni Ni e e
NiOo 2
2 2
2 2
4
η η
η η
∆ (14.6)
where:
∆GNiOo
is the Gibbs energy of formation of NiO from pure nickel and 1 bar (atmosphere) oxygen L is the thickness of the oxide layer as shown in Figure 14.2.
Assuming that te ≅ 1 is the same as assuming 4ηNi2+DNi2+ ηe−De− because the term in the paren- theses in Equation 14.6 is proportional to the total electrical conductivity. Therefore, Equation 14.6 becomes
′ + = −
+ +
J D
RT G
Ni L
Ni Ni NiOo
2
2 2
η ∆ . (14.7)
Again, the left-hand side of this equation needs to be expressed in terms of the change in the oxide thickness with time, dL/dt. Doing this and dividing the number flux density to get the molar flux density of JNi2+,
Nickel
L NiO
PO2
GoNi
GNi = ΔGoNiO −1RTlnpO2 2
Ni2+ 2e−
FIGURE 14.2 Schematic for the oxidation of nickel where the nickel diffusion is much faster than that of oxygen. The oxide layer thickness is L and there is a Gibbs energy difference across the oxide layer of
∆GNiOo RT p
−( / )1 2 ln O2. If the oxidation is in pure oxygen, then it is simply ∆GNiOo .
ρNiO η
NiO
NiO Ni Ni
A
Ni Ni A
NiOo
Ni
M dL
dt J J J
N
D N RT
G L C
= = = ′
= −
+
+ + +
2
2 2 2 ∆
O
OdL Ni Ni NiOo
dt
C D
RT G
= − 2+ 2+ ∆ L where
C M
g cm
g mol mol cm C
NiO= ρ = 6 72 = × − = Ni+
74 692 9 00 10
3 2 3
2
. /
. / . /
there is one mole of nickel ions in every mole of NiO. Integration gives the desired result of the oxide thickness as a function of time:
L D G
RT t kt
Ni NiOo
2 2 2
= − +∆ = (14.8)
again, the parabolic oxidation rate with the rate constant k. The negative sign remains because ∆GNiO0
is negative and, in fact, ∆GNiOo
(
1200°C)
= −107 878, J mol/ (Roine 2002).14.2.2.3 Comparison to Experiment
Data on oxidation of nickel, a very oxidation resistant metal, are summarized in the literature (Kofstad 1988). From these data, it can be estimated that the weight gained by nickel during oxida- tion is ΔW ≅ 6 mg/cm2 in 10 h at 1200°C. The weight gain is all oxygen so the total thickness of the oxide layer is
L W g cm
mol cm A O g mol L
=
( )
= ×
×
( )
−
−
∆ ( / )
/ ( ) /
2 3
3 2
6 10 9 10 16 where A(O) is the atomic weight of oxygen, so
L=4 17 10. × −3cm.
This oxidation was carried out in air so pO2 ≅0 21. bar, so the value for ∆GNiO to be used in Equation 14.8 is
∆ ∆
∆
G G RT p
G
NiO NiOo
O
NiO
= −
= − −
( )( )
1 2 107 878 1
2 8 314 1473 0 21 ln 2
, . ln .
(( )
= −
∆GNiO 98 322, J mole/ as shown in Figure 14.2. From Equation 14.8
L D G
RT t
L
Ni NiO
2
2
10
2
2 1 22 10 98 322 8 314 1473 1
= − 2
= −
(
×) (
−)
( )( )
+
−
∆
. ,
. 00 3600
7 05 10
2 5 2
h s h
L cm
(
×)
= × −
/ .
14.2 Oxidation of Metals 485
or
L=8 40 10. × −3cm
roughly about a factor of 2 greater than what is observed. This is close enough to validate the model given all the assumptions, and a factor of 2 error could easily be introduced by the uncertainties in the experimentally derived values: for example, value for the calculated diffusion coefficient can vary by a factor of 2 just by an error of 5% in the activation energy.
14.2.2.4 Other Considerations
How good was the assumption that the transport of electrons is much more rapid than that of the ions so that the transference number for electrons could be assumed to be te ≅ 1.0? This can be checked by calculating the ionic conductivity—in this case, that of Ni2+—with the Nernst–Einstein equation:
σ η
Ni Ni Ni
B
Ni Ni
e D
k T
C D
2 RT
2 2 2 2
2 2 2 2
+
+ + + +
=
( )
=( )
F(14.9) where the latter part of the equation is obtained by multiplying both the numerator and denomina- tor by NA2
and compare it to that of the electronic conductivity which was found in the literature to be σ ≅ 1 S/cm. Inserting values into Equation 14.9,
σ σ
Ni
Ni 2
2
2 96472 9 00 10 1 22 10 8 314 1473
2 2 10
+
+
=
(
×) (
×) (
×)
( )( )
=
− −
. .
. 33 34 10. × −5S cm/ .
The ionic conductivity is almost five orders of magnitude smaller than the electronic conductivity so the assumption that telectronic ≅ 1 is certainly justified.
One inevitable result of metal oxidation—such as that of nickel where the metal is diffusing through the oxide layer—is the disappearance of the original nickel: it is being used up. One way of looking at this process is illustrated in Figure 14.3. For every nickel atom that enters the oxide as a Ni2+ ion and two negative electrons, a vacancy in the nickel is created. This vacancy can be destroyed by diffusing to the end of a dislocation causing dislocation climb, which, in essence, is removing atomic planes from the nickel and replacing them with vacancies. For thin oxide layers on large pieces of metal, this is a satisfactory way of taking care of the volume of the metal that has gone to cre- ate the oxide. However, for smaller pieces of metal for which most of the metal ends up as oxide, then ultimately porosity will replace the volume of the metal that has been oxidized as illustrated in Figure 14.4a. If a small sphere is oxidized and the oxide cannot plastically deform as easily as the
Vacancy diffusion NiO
Ni Ni2+
2e−
Vacancy creation
Nickel
planes Dislocation
climb
Vacancy flux
FIGURE 14.3 Schematic that shows the oxidation of a metal such as nickel generates vacancies in the metal that are destroyed at dislocations or at grain boundaries. This means that planes of metal are being removed from the metal and placed into the oxide.
metal, then a pore or pores will form in the metal. In Figure 14.4a, a single pore is formed in the center and when the oxidation is complete, all that will remain is the shell of oxide with an empty center.
Figure 14.4b illustrates a more likely case in which pores form throughout the metal. However, if the oxidation is taken to completion, the net result is the same: the pores will coalesce into one single large pore leaving only the empty oxide shell. Sometimes this porosity is referred to as the “Kirkendall porosity.” The Kirkendall porosity, discussed later, is caused by differences in diffusion coefficients in alloys. Naming the porosity that is the result of oxidation the same as that produced by interdiffusion is confusing at a minimum. The mechanisms of the porosity formation are really quite different even though they are both produced by differences in diffusion coefficients of two different atomic or ionic species. Calling this oxidation-induced porosity the “Kirkendall porosity” seems ill-advised.
Another way to form porosity is at the metal–oxide interface as shown in Figure 14.4c. An alternative way of tracing the disappearance of the nickel metal is that the metal–oxide interface simply moves with the disappearing metal. However, this requires that, for a finite-size piece of metal, the oxide must plastically deform to keep up with the shrinking nickel. In some cases, the compressive stresses on a plane surface may become large enough to cause the oxide layer to buckle and debond from the nickel and form a pore at the interface. At a corner, where even greater defor- mation of the oxide is necessary to take care of shrinking Ni–NiO interfaces, debonding and pores are even more likely to form. In both of these situations, pores form and oxidation stops at these points unless cracks actually form in the oxide layer.