Oxidation at high temperatures

9.2.1 Oxidation at high temperatures

9.2.1.1 Thermodynamics of oxidation

The tendency for a metal to oxidize, like any other spontaneous reaction, is indicated by the free

G is negative for oxide formation. The free energy released by the combination of a fixed amount ◦ and is usually termed the standard free

◦ , the standard change in entropy, by the Gibbs equation. The variation of the standard free energy change

with absolute temperature for a number of metal oxides is shown in Figure 9.1. The noble metals, which are easily reduced, occur at the top of the diagram and the more reactive metals at the bottom. Some of these metals at the bottom (Al, Ti, Zr), however, resist oxidation at room temperature owing to the impermeability of the thin coherent oxide film which first forms.

482 Physical Metallurgy and Advanced Materials

2 ⫽ 2NiO 2Co ⫹O 2 ⫽ 2CoO

PbO

4Cu

⫹O 2 ⫽ 2PbO 12 S 2 ⫹O 2 ⫽ SO 2 2 2Pb O 2H 2 ⫹O 2 ⫽ 2H

FeO (2Fe ⫹ O 2 ⫽ 2FeO)

C⫹O 2 ⫽ CO 2 O 2Si ⫹ O 2 2 ⫽ 2SiO

⫹O 2 ⫽ 2MnO

2 O 3 ⫹O 2 ⫽ 2TiO) Li 2 45 O Ta ⫹ 23 Ti

Ba 2 ⫽ 2CaO

23 Changes of state

Th

43 La ⫹O

Melting point Boiling point

1000 1200 1400 1600 1800 Temperature, T (⬚C)

Figure 9.1 Standard free energies of formation of oxides.

◦ for oxidation reactions decreases with increase in temperature, i.e. the oxides become less stable. This arises from the decreased entropy accompanying the reaction, solid

(metal) + gas (oxygen) → solid (oxide). The metal and oxide, being solids, have roughly the same

mol −1 transitions through the boiling point (e.g. ZnO at 970 ◦

C) and sublimation (e.g. Li 2 O at 1330 ◦

C) have

Oxidation, corrosion and surface treatment 483 CO or CO 2 . In both cases the oxide product is gaseous and thus also has a high free energy. In the

reaction 2C + O 2 → 2CO, two moles of gas are produced from one of oxygen so that S = (S oxide −S carbon −S oxygen )

(9.1) = (2S ◦ oxide −S ◦ carbon −S ◦ oxygen ) ≃S ◦ oxide .

The CO free energy versus temperature line has a downward slope of approximately this value. For the C+O 2 → CO 2 reaction, one mole of CO 2

≈ 0; the CO 2 free energy line is thus almost horizontal. The carbon monoxide reaction is favored at high temperatures and consequently carbon is a very effective reducing agent, having a greater affinity for

oxygen than most oxides.

◦ tends to zero at some elevated temperature. This is known as the standard dissociation temperature when the

oxide is in equilibrium with the pure element and oxygen at 1 atm pressure. In the case of gold, the oxide is not stable at room temperature, for silverAg 2 O dissociates when gently heated to about 200 ◦ C, and the oxides of the Pt group of metals around 1000 ◦

C. The other oxides dissociate at much higher temperatures. However, the temperature is affected by pressure since the free energy per mole of any gaseous phase varies with pressure P (atm) according to G(P) =G ◦ + RT ln P, whereas that for the solid phase is relatively unaffected. Thus, for the metal + oxygen → metal oxide reaction under stan-

◦ =G ◦

oxide −G ◦ metal −G ◦ oxygen

◦ − RT ln P O 2 .

= 0 and hence

P O 2 ◦ /RT ] (9.2) is the equilibrium dissociation pressure of the oxide at the temperature T . If the pressure is lowered

below this value the oxide will dissociate, if raised above the oxide is stable. The common metal oxides have very low dissociation pressures ≈10 −10 Nm −2 ( ∼10 −15 atm) at ordinary annealing temperatures and thus readily oxidize in the absence of reducing atmospheres.

◦ is also related to the equilibrium constant K of the reaction. For the reaction discussed above, i.e.

Me +O 2 → MeO 2 , the equilibrium constant K = [MeO 2 ]/[Me][O 2 ] derived from the law of mass action. The active

masses of the solid metal and oxide are taken equal to unity and that of the oxygen as its partial pressure under equilibrium conditions. The equilibrium constant at constant pressure, measured in

atmospheres, is thus K P = 1/P O 2 ◦ = −RT ln K P . To illustrate the use of these concepts, let us consider the reduction of an oxide to metal with the aid of a reducing agent (e.g. Cu 2 O by steam). For the oxidation reaction,

4Cu +O 2 → 2Cu 2 O ◦ = −0.195 MJ mol −1 = 1/P O 2 , giving P O 2 = 6.078 × 10 −6 Nm −2 .

At 1000 K the equilibrium constant for the steam reaction 2H 2 O → 2H 2 +O 2 is K

H 2 / P H 2 O = 1.013 × 10 Nm . Thus, to reduce Cu 2 O the term P O 2 < 6 × 10 −11 in the steam reaction gives P H 2 / P H 2 O > 10 −5 , so

=P 2 O 2 P 2 −15

that an atmosphere of steam containing 1 in 10 5 parts of hydrogen is adequate to bright-anneal copper.

484 Physical Metallurgy and Advanced Materials In any chemical reaction, the masses of the reactants and products are decreasing and increasing

respectively during the reaction. The term chemical potential µ ( =dG/dn) is used to denote the change of free energy of a substance in a reaction with change in the number of moles n, while the temperature, pressure and number of moles of the other substances are kept constant. Thus,

i =μ i + RT ln P i (9.3) and the free energy change of any reaction is equal to the arithmetical difference of the chemical

potentials of all the phases present. So far, however, we have been dealing with ideal gaseous com- ponents and pure metals in our reaction. Generally, oxidation of alloys is of interest and we are then dealing with the solution of solute atoms in solvent metals. These are usually non-ideal solutions which behave as if they contain either more or less solute than they actually do. It is then convenient to use the activity of that component, a i , rather than the partial pressure, P i , or concentration, c i . For an ideal solution P i

i c i , whereas for non-ideal solutions P i =P i a i , such that a i is an effective concentration equal to the ratio of the partial, or vapor, pressure of the ith component above the

0 =P 0

solution to its pressure in the standard state. The chemical potential may then be rewritten

i + RT ln a i , (9.4) where for an ideal gas mixture a i

μ i =μ 0

i and by definition P i = 1. For the copper oxide reaction, the law of mass action becomes

where a n i is replaced by unity for any component present in equilibrium as a pure solid or liquid. Some solutions do behave ideally (e.g. Mn in Fe), obeying Raoult’s law with a i =c i . Others tend to in dilute solution (e.g. Fe in Cu), but others deviate widely with a i approximately proportional to c i (Henry’s law).

9.2.1.2 Kinetics of oxidation

Free energy changes indicate the probable stable reaction product but make no prediction of the rate at which this product is formed. During oxidation the first oxygen molecules to be absorbed on the metal surface dissociate into their component atoms before bonding chemically to the surface atoms of the metal. This process, involving dissociation and ionization, is known as chemisorption. After the build-up of a few adsorbed layers the oxide is nucleated epitaxially on the grains of the base metal at favorable sites, such as dislocations and impurity atoms. Each nucleated region grows, impinging on one another until the oxide film forms over the whole surface. Oxides are therefore usually composed of an aggregate of individual grains or crystals, and exhibit phenomena such as recrystallization, grain growth and creep involving lattice defects, just as in a metal.

If the oxide film initially produced is porous the oxygen is able to pass through and continue to react at the oxide/metal interface. Usually, however, the film is not porous and continued oxidation involves diffusion through the oxide layer. If oxidation takes place at the oxygen/oxide surface, then metal ions and electrons have to diffuse through from the underlying metal. When the oxidation reaction occurs at the metal/oxide interface, oxygen ions have to diffuse through the oxide and electrons migrate in the opposite direction to complete the reaction.

The growth of the oxide film may be followed by means of a thermobalance in conjunction with metallographic techniques. With the thermobalance it is possible to measure to a sensitivity of 10 −7 g

Oxidation, corrosion and surface treatment 485

Parabolic Logarithmic

Thickness

Time t

Figure 9.2 Different forms of oxidation behavior in metals. in an accurately controlled atmosphere and temperature. The most common metallographic technique

is ellipsometry, which depends on the change in the plane of polarization of a beam of polarized light on reflection from an oxide surface; the angle of rotation depends on the thickness of the oxide. Interferometry is also used, but more use is being made of replicas and thin films in the transmission electron microscope and the scanning electron microscope.

The rate at which the oxide film thickens depends on the temperature and the material, as shown in Figure 9.2. During the initial stages of growth at low temperatures, because the oxygen atoms acquire electrons from the surface metal atoms, a strong electric field is set up across the thin oxide film, pulling the metal atoms through the oxide. In this low-temperature range (e.g. Fe below 200 ◦

C) the thickness increases logarithmically with time (x ∝ ln t), the rate of oxidation falling off as the field strength diminishes.

C in Fe) the oxidation develops with time according to a parabolic law (x 2 ∝ t) in nearly all metals. In this region the growth is a thermally activated process and ions pass through the oxide film by thermal movement, their speed of migration depending on the nature of the defect structure of the oxide lattice. Large stresses, either compressive or tensile, may often build up in oxide films and lead to breakaway effects when the protective oxide film cracks and spalls. Repeated breakaway on a fine scale can prevent the development of extensive parabolic growth and the oxidation assumes an approximately linear rate or even faster. The stresses in oxide film are related to the Pilling–Bedworth (P–B) ratio, defined as the ratio of the molecular volume of the oxide to the atomic volume of the metal from which the oxide is formed (Table 9.1). If the ratio is less than unity, as for Mg, Na and K, the oxide formed may be unable to give adequate protection against further oxidation right from the initial stages and, under these conditions, commonly found in alkali metals, linear oxidation (x ∝ t) is obeyed. If, however, the P–B ratio is very much greater than unity, as for many of the transition metals, the oxide is too bulky and may also tend to spall.

At intermediate temperatures (e.g. 250–1000 ◦

At high temperatures oxide films thicken according to the parabolic rate law, x 2 ∝ t, and the mechanism by which thickening proceeds has been explained by Wagner. As shown in Figure 9.3, point defects (see Chapter 3) diffuse through the oxide under the influence of a constant-concentration gradient. The defects are annihilated at one of the interfaces, causing a new lattice site to be formed. Specifically, zinc oxide thickens by the diffusion of zinc interstitials created at the metal/oxide interface through the oxide to the oxide/oxygen interface, where they are removed by the reaction

2Zn 2 i + + 4e + O 2 → 2ZnO. The concentration of zinc interstitials at the metal/oxide interface is maintained by the reaction Zn

2 (metal) → Zn + i + 2e,

486 Physical Metallurgy and Advanced Materials Table 9.1 Some Pilling–Bedworth ratios.

Metal and oxide

Pilling–Bedworth ratio Mg–MgO

Density of oxide (Mg m −3 )

3.6 0.8 Al–Al 2 O 3 4.0 1.3 Ti–TiO 2 5.1 1.5 Zr–ZrO 2 5.6 1.5 Fe–Fe 2 O 3 5.3 2.1 Cr–Cr 2 O 3 5.1 2.1

Cu–Cu 2 O

Ni–NiO

6.9 1.6 Si–SiO 2 2.7 1.9 U–UO 2 11.1 1.9 W–WO 3 7.3 3.3

Oxide Air

O 2⫺ 2e⫹O M

(b) Figure 9.3 Diffusion processes leading to oxide growth at: (a) oxide/air interface, e.g. Cu, Fe, and

(a)

(b) metal/oxide interface, e.g. Ti, Zr (after Ashby and Jones, 2005).

with the creation of vacancies in the zinc lattice. The migration of charged interstitial defects is accompanied by the migration of electrons and for thick oxide films it is reasonable to assume that the concentrations of the two migrating species are constant at the two surfaces of the oxide, i.e. oxide/gas and oxide/metal, governed by local thermodynamic equilibria. There is thus a constant

dx/dt and the film thickens parabolically according to the relation x 2 = kt,

(9.6) where k is a constant involving several structural parameters. Wagner has shown that the oxida-

tion process can be equated to an ionic plus an electronic current, and obtained a rate equation for oxidation in chemical equivalents cm −2 s −1 involving the transport numbers of anions and elec- trons respectively, the conductivity of the oxide, the chemical potentials of the diffusing ions at the interfaces and the thickness of the oxide film. Many oxides thicken according to a parabolic law over some particular temperature range. It is a thermally activated process and the rate constant

Oxidation, corrosion and surface treatment 487 k =k 0 × exp [−Q/RT ], with Q equal to the activation energy for the rate-controlling diffusion

process. At low temperatures and for thin oxide films, a logarithmic rate law is observed. To account for this the Wagner mechanism was modified by Cabrera and Mott. The Wagner mechanism is only applicable when the concentrations of point defects and electrons are equal throughout the film; for thin oxide films this is not so, a charged layer is established at the oxide/oxygen interface. Here the oxygen atoms on the outer surface become negative ions by extracting electrons from the metal underneath the film and so exert an electrostatic attraction on the positive ions in the metal. When the oxide thickness is $ < 10 nm this layer results in an extremely large electric field being set up, which pulls the diffusing ions through the film and accelerates the oxidation process. As the film thickens the field strength decreases as the distance between positive and negative ions increases, and the oxidation rate approximates to that predicted by the Wagner theory.

As the scale thickens, according to a parabolic law, the resultant stress at the interface increases and eventually the oxide layer can fail either by fracture parallel to the interface or by a shear or tensile fracture through the layer. In these regions the oxidation rate is then increased until the build-up in stress is again relieved by local fracture of the oxide scale. Unless the scale fracture process occurs at the same time over the whole surface of the specimen, then the repeated parabolic nature of the oxidation rate will be smoothed out and an approximately linear law observed. This breakaway parabolic law is sometimes called paralinear, and is common in oxidation of titanium when the oxide reaches a critical thickness. In some metals, however, such as U, W and Ce, the linear rate process is associated with an interface reaction converting a thin protective inner oxide layer to a non-protective porous oxide.

Worked example

Zirconium oxidizes to ZrO 2 . Given the density of Zr is 6.5 Mg m −3 and that of ZrO 2

5.9 Mg m −3 , calculate the Pilling–Bedworth ratio for the oxidation and indicate whether it would be protective.

Solution

The Pilling–Bedworth ratio Volume of oxide M o ρ M = Volume of metal = ρ o M M , where M o is the molecular weight of ZrO 2 ,M M is the weight of Zr, ρ M is the density of Zr and ρ o is the density of the oxide.

Since P–B > 1, the oxidation is protective.

Worked example

Corrosion of a galvanized steel sheet with a zinc coating 0.1 mm thick generates a corrosion current of 6 × 10 −3 Am −2 . Determine if the coating is sufficient to give rust-free protection for 10 years (density of Zn = 7.13 Mg m −3 , atomic weight = 65.4).

Solution

Zn → Zn 2 + + 2e.

488 Physical Metallurgy and Advanced Materials Number of electrons to produce 6 × 10 −3 Am −2 for 10 years

= 6 × 10 7 −3 × 10 × 3.15 × 10 / 1.6 × 10 −19 = 1.18 × 10 25 = 5.89 × 10 24 atoms of Zn

Mass of Zn

24 = 5.89 × 10 23 × 65.4/6.02 × 10 = 0.64 kg m −2

Thickness

= 0.64/7130 = 9 × 10 −5 m = 0.09 mm.

This is just smaller than the thickness of the coating (0.1 mm), so galvanizing is sufficient.

9.2.1.3 Parameters affecting oxidation rates

The Wagner theory of oxidation and its dependence on the nature of the defect structure has been successful in explaining the behavior of oxides under various conditions, notably the effects of small alloying additions and oxygen pressure variations. The observed effects can be explained by reference to typical n- and p-type semiconducting oxides. For oxidation of Zn to ZnO the zinc atoms enter the oxide interstitially at the oxide/metal interface (Zn

i + 2e), and diffuse to the oxide/oxygen interface. The oxide/oxygen interface reaction (2Zn 2 i + + 4e + O 2 → 2ZnO) is assumed to be a rapid (equilibrium) process and, consequently, the concentration of defects at this interface is very small, and

2 → Zn +

independent of oxygen pressure. This is found to be the case experimentally for oxide thicknesses in the Wagner region. By considering the oxide as a semiconductor with a relatively small defect concentration, the law of mass action can be applied to the defect species. For the oxide/oxygen interface reaction this means that

[Zn 2 + ] 2 [e] 4 = constant.

The effect of small alloying additions can be explained (Wagner–Hauffe rule) by considering this equation. Suppose an alloying element is added to the metal that enters the oxide on the cation lattice. Since there are associated with each cation site, only two electron sites available in the valence band of the oxide, if the element is trivalent the excess electrons enter the conduction band, increasing the concentration of electrons. For a dilute solution the equilibrium constant remains unaffected and, hence, from the above equation, the net effect of adding the element will be to decrease the concentration of zinc interstitials and thus the rate of oxidation. Conversely, addition of a monovalent element will increase the oxidation rate. Experimentally it is found that Al decreases and Li increases the oxidation rate.

For Cu 2 O, a p-type semiconductor, the oxide formation and cation vacancy (Cu + ) creation take place at the oxide/oxygen interface, according to

O 2 + 4Cu = 2Cu 2 O + 4(Cu + ) + 4(e ).

The defect diffuses across the oxide and is eliminated at the oxide/metal interface; the equilibrium concentration of defects is at the metal/oxide interface and the excess at the oxide/oxygen interface. It follows therefore that the reaction rate is pressure dependent. Applying the law of mass action to the oxidation reaction gives

[Cu + ] 4 [e ] 4 = const P O 2

Oxidation, corrosion and surface treatment 489 and, since electrical neutrality requires [Cu + W] = [eW], then

(9.7) and the reaction rate should be proportional to the 1/8th power of the oxygen pressure. In practice, it

[Cu + ] = const P 1/8

varies as P 1/7 O 2 , and the discrepancy is thought to be due to the defect concentration not being sufficiently low to neglect any interaction effects. The addition of lower valency cations (e.g. transition metals) would contribute fewer electrons and thereby increase the concentration of holes, decreasing the vacancy concentration and hence the rate. Conversely, higher valency cations increase the rate of oxidation.

Worked example

Estimate the corrosion rate of iron in units of mm year −1 if the corrosion rate in an unstirred solution is controlled by the diffusion of oxygen. (F is 96 500 C mol −1 , the molar mass of iron is 55.8 g mol −1 , and its density is 7.9 g cm −3 .)

Solution

Fick’s first law of diffusion: diffusion rate

Diffusion-limited current density i L =

D, diffusion coefficient: ∼2 × 10 −5 cm 2 s −1 for oxygen in room temperature in water.

C, concentration difference: room temperature concentration of oxygen in water is ∼0.25 mM (0.25 × 10 −3 mol l −1 ); it is assumed that the concentration is zero at the metal surface. δ , diffusion distance: ∼200 µm for natural convection in an unstirred solution.

This gives a value of i L ∼ 100 µA cm −2 for the diffusion-limited reduction of oxygen at a metal surface in an aqueous solution at room temperature. Number of electrons to give a current of 100 µA cm −2 for one year

1.6 = 1.97 × 10 = 9.84 × 10 × 10 Fe atoms. −19

Mass of Fe

6.02 × 10 23 = 0.912 g cm

Thickness =

7.9 = 0.115 cm = 1.15 mm.

9.2.1.4 Oxidation resistance

The addition of alloying elements according to the Wagner–Hauffe rule just considered is one way in which the oxidation rate may be changed to give increased oxidation resistance. The alloying element may be added, however, because it is a strong oxide former and forms its own oxide on the metal surface in preference to that of the solvent metal. Chromium, for example, is an excellent additive,

forming a protective Cr 2 O 3 layer on a number of metals (e.g. Fe, Ni) but is detrimental to Ti, which forms an n-type anion-defective oxide. Aluminum additions to copper similarly improve the oxidation behavior by preferential oxidation to Al 2 O 3 . In some cases, the oxide formed is a compound oxide of both the solute and solvent metals. The best-known examples are the spinels with cubic structure

490 Physical Metallurgy and Advanced Materials

CrS Sulfidation threshold

Oxidation threshold

Cavity in scale

(d) Figure 9.4 Reaction paths for oxidation and sulfidation of chromium.

(c)

(e.g. NiO · Cr 2 O 3 and FeO · Cr 2 O 3 ). It is probable that the spinel formation is temperature dependent, with Cr 2 O 3 forming at low temperatures and the spinel at higher ones. Stainless steels (ferritic, austenitic or martensitic) are among the best oxidation-resistant alloys and are based on Fe–Cr. When iron is heated above about 570 ◦

C the oxide scale which forms consists of wüstite, FeO (a p-type semiconductor) next to the metal, magnetite Fe 3 O 4 (a p-type semiconductor) next and hematite Fe 2 O 3 (an n-type semiconductor) on the outside. When Cr is added at low concen- trations the Cr forms a spinel FeO · CrO 3 with the wüstite and later with the other two oxides. However,

a minimum Cr addition of 12% is required before the inner layer is replaced by Cr 2 O 3 below a thin outer layer of Fe 2 O 3 . Heat-resistant steels for service at temperatures above 1000 ◦

C usually contain 18% Cr or more, and austenitic stainless steels 18% Cr, 8% Ni. The growth of Cr 2 O 3 on austenitic

stainless steels containing up to 20% Cr appears to be rate-controlled by chromium diffusion. Kinetic factors determine whether Cr 2 O 3 or a duplex spinel oxide form. The nucleation of Cr 2 O 3 is favored by higher Cr levels, higher temperatures and by surface treatments (e.g. deformation), which increase the diffusivity. Surface treatments which deplete the surface of Cr promote the formation of spinel

oxide. Once Cr 2 O 3 is formed, if this film is removed or disrupted, then spinel oxidation is favored because of the local lowering of Cr. When chromium-bearing alloys, such as austenitic stainless steels, are exposed to the hot com- bustion products of fossil fuels, the outer layer of chromium oxide which forms is often associated with an underlying sulfide phase (Figure 9.4a). This duplex structure can be explained by using phase (stability) diagrams and the concept of ‘reaction paths’. Accordingly, an isothermal section from the full phase diagram for the Cr–S–O system is shown in Figure 9.4b. The chemical activities of sulfur and oxygen in the gas phase are functions of their partial pressures (concentration). If the partial pressure of sulfur is relatively low, the composition of the gas phase will lie within the chromium oxide field and the alloy will oxidize (Figure 9.4b). Sulfur and oxygen diffuse through the growing

Oxidation, corrosion and surface treatment 491

NiS LIQ

NiSO 4

Ni 3 S 2LIQ CrS

Figure 9.5 Superimposition of isothermal sections from Cr–S–O and Ni–S–O systems. layer of oxide scale but S 2 diffuses faster than O 2 ; accordingly, the composition of the gas phase in

contact with the alloy follows a ‘reaction path’, as depicted by the dashed line. Figure 9.4c shows the reaction path for gases with a higher initial partial pressure of sulfur. Its slope is such that first chromium oxide forms, and then chromium sulfide (i.e. Cr + S = CrS). Sometimes the oxide scale

may crack or form voids. In such cases, the activity of S 2 may rise locally within the scale and far exceed that of the main gas phase. Sulfidation of the chromium then becomes likely, despite a low concentration of sulfur in the main gas stream (Figure 9.4d).

Relative tendencies of different metallic elements to oxidize and/or sulfidize at a given temperature may be gauged by superimposing their isothermal pS 2 –pO 2 diagrams, as in Figure 9.5. For example, with the heat-resistant 80Ni–20Cr alloy (Nichrome), it can be reasoned that (1) Cr 2 O 3 scale and CrS subscale are both stable in the presence of nickel, and (2) Cr 2 O 3 forms in preference to NiO; that is, at much lower partial pressures of oxygen. The physical state of a condensed phase is extremely important because liquid phases favor rapid diffusion and thus promote corrosive reactions. Although nickel has a higher sulfidation threshold than chromium, the Ni–NiS eutectic reaction is of particular concern with Ni-containing alloys because it takes place at the relatively low temperature of 645 ◦ C.