1 MTE 585 Oxidation of Materials Part 1 Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield
2 Introduction To illustrate the case of high temperature oxidation, we will use Ni-base superalloys. Ni-base superalloys contain Ni, Al, Cr, and a number of other elements. Originally they were based on NiChrome (80Ni-20Cr) the material that is used for toaster heating wire. Al was added later for precipitation hardening. It h s ls b n p d t b l bl It has also been proved to be a valuable addition for other reasons; primarily oxidation and hot corrosion resistance.
3 Simple Oxidation (1) Let s start with the case of a single crystal of a pure metal (M) in an oxidizing environment. Air or other Oxygen containing atmosphere O -2 oxide x metal metal M +2 Oxidation takes place at the surface. M + O MO As soon as the surface is completely oxidized, further oxidation will only occur if: 1. metal atoms must diffuse through the oxide layer to get to the surface to react with oxygen at the air/oxide interface or 2. oxygen must diffuse through the oxide layer to react with the metal at the metal/oxide interface. Therefore, oxidation is diffusion controlled.
4 Simple Oxidation (2) air air O -2 oxide x metal metal M +2 Oxidation rate can be represented as follows: dx dt k x where k is the parabolic rate constant with units of cm 2 /s. Integration yields: x x 2k t t 2 2 t t o o where t o is the time at which diffusion control begins. Wagner (1933) has provided a theoretical way to find k based on the idealized model for oxide formation making a few assumptions. C. Wagner, Z. Phys. Chem. B21 (1933) 25.
5 Simple Oxidation (3) The extent of reaction can be expressed in terms of mass change per unit area (Δm/A) as: 2 2 m m 2 k t t A A where k t In this expression, V is the equivalent volume of the oxide. The units of k are g 2 /cm 4 s. t o 8 V 2 k o Wagner s theories predict parabolic oxide Wagner s theories predict parabolic oxide growth kinetics!
6 Wagner s Oxidation Theory Assumes that lattice diffusion of reacting atoms or ions or the transport of electrons through the oxide scale is the rate determining step in oxidation. Fig (a) Transport processes through a dense, single phase oxide scale growing via lattice diffusion. (b) Transport processes in growing scales in terms of lattice and electronic defects. Figure from P. Kofstad, High Temperature Corrosion (Elsevier, New York, 1988) p.163.
7 Wagner s Oxidation Theory cont d The parabolic rate constant, k, can be found by making certain assumptions (there are 6) and performing a mass balance. The assumptions are: 1. Oxide layer is compact and perfectly adherent 2. Migration of ions or electrons across the oxide is the rate controlling process 3. Thermodynamic equilibrium exists at both boundaries 4. The oxide is stoichiometric (e.g., Al 2 O 3, NiO, etc.) 5. Thermodynamic equilibrium exists throughout 6. Oxygen is insoluble in the metal The mass balance is detailed in Chapter 3 of N. Birks, G.H. GH Meier, and FS F.S. Petit, Introduction to the High-Temperature Oxidation of Metals, 2 nd Edition (Cambridge University Press, 2006).
8 Oxide scale formation according to Wagner s model Metal Oxide Gas M MO O 2 Cations Cation vacancies Anions electrons a 1 M p O 2 o GMO 2 M MO RT po exp / M = M e - Or M + O 2- = MO + 2e - o 1 GMO a M exp 2 RT p 1/2 O O 2 M e - + ½ O 2 = MO Or ½ O 2 + 2e - = O 2- OVERALL RXN.: 2M + O 2 = 2MO; ΔG o MO Do mass balance through oxide scale & solve for k
9 Simple Oxidation (3) With these assumptions, it can be shown via mass balance and diffusion theory that: 1 O Z D M M O Z O k D do RT O DM DO Zm ZO O O diffusivity of metal in the oxide diffusivity of oxygen in the oxide valence of metal valence of oxygen chemical potential of oxygen at the M/oxide interface chemical potential of oxygen at the gas/oxide interface Parabolic oxide growth according to Wagner s model rarely happens in real systems WHY? one or more of the assumptions is not satisfied; in particular assumption (2), which states that migration of ions or electrons across the oxide is the rate controlling process.
10 Examples of different oxidation kinetics
11 Parabolic rate constants still provide a convenient method for comparing relative oxidation rates where nearly parabolic growth is observed (see below). Grows fastest Grows slowest
12 Simple Oxidation (4) Since parabolic growth rarely occurs in real systems, what is the rate limiting step? ANSWER Migration of atoms (either metal or oxygen) through the oxide is the only way for oxygen or metal to reach each other. THUS self-diffusion ff must be the rate limiting step. we should only need to calculate self-diffusion rates and we will get the oxide growth rates. HOWEVER Reviews of literature t show that t the calculations l are several orders of magnitude too low. This has been attributed to structural defects in the oxide layer.
13 Influence of lattice defects (1) Diffusion coefficients are higher in the vicinity of lattice defects such as dislocations and grain boundaries.
14 Influence of lattice defects (2) Diffusion coefficients are higher in the vicinity of impurities as well.
15 Influence of lattice defects (3) Comparison of calculated and measured parabolic rate constants for the oxidation of Ni to NiO. Defects f (in particular grain boundaries) shift the experimental results away from the calculated values. Clearly diffusion involving defects is very important.
16 Structures of Grain Boundary & Line Defects
17 Diffusion Having recognized the importance of lattice defects in oxidation, you should realize that the entire process is complicated when alloying elements are present. We implied this fact three slides ago.
18 What are Alloys? Combination of elements (always) Combination of phases (sometimes) Properties that are different from those of the elemental l constituents Mechanical (yes) Electrical (yes) Corrosion resistance??? Let s consider some generic examples.
19 Oxidation of a Binary Alloy Noble Metal A + Reactive Metal B Noble metal A does not react with O 2 while less noble alloying element B reacts with O 2. Dilute solution of B in A x(t) Co onc. of B, C B C Bo A(B) A+BO air Depletion of element B Distance, x Internal oxidation of B in A Simplest case, when BO is very stable and D B << D O, the depth of internal oxidation is: ( ) 2C s O ( O) x t C B D Ot 1/2 ( s ) CO 2 C DO t ( O) B oxygen solubility of O in A (at.%) bulk alloy concentration of B in A (at.%) Diffusivity of oxygen time As the %B in A is increased, x(t) decreases. Case 1(a)
20 Oxidation of a Binary Alloy Noble Metal A + Reactive Metal B Noble metal A does not react with O 2, while less noble alloying element B reacts with O 2. Concentrated solution of B in A. Conc c. of B, C B Once again, if BO is very stable and D B << D O, if we increase the concentration of element B; a continuous oxide BO will form on the metal surface when %B is high enough. x(t) A(B) Depletion of element B BO air Distance, x That critical concentration of B is given by: g DV C C DV * crit ( s) O m B O 2 DV B O 1/2 * g V V m O critical volume fraction of oxide for transition 0.3 molar volume of metal molar volume of oxide Case 1(b)
21 Oxidation of Alloys cont d In general, oxidation of alloys is more complicated than pure metals. Why? 1. The metals will have different affinities iti for O 2. This is reflected in different free energies of formation for different oxides. 2. Ternary and higher level oxides can form. 3. Different oxides may exhibit a degree of solid solubility. For example, Cr 2 O 3 in Al 2 O Each alloying component will have a different diffusion rate in the metal alloy. 5. Each species of metal ion will have a different mobility in the oxide phase. 6. Dissolution of the oxygen into the alloy may result in sub-surface surface precipitation of oxides of one or more alloying elements (internal oxidation).
22 Oxidation of a Binary Alloy Reactive Metal A + More Reactive Metal B Alloy of B in A, but both are reactive but metal B forms the more stable oxide. In superalloys: A = Co or Ni; B = Al, Ti, Cr, X Dilute solution of B in A of B, C B Conc. A(B) Depletion of more reactive element B until gone A + BO AO air Distance, x D A & D B << D O Stable oxide BO usually forms first (it is more stable and forms readily) resulting in a mixed layer of A (depleted in B) with BO oxide precipitates. Once B is depleted, an external oxide AO will form above the mixed zone as component A is available to react with oxygen. What happens if we increase the %B? Case 2(a)
23 Oxidation of a Binary Alloy Reactive Metal A + More Reactive Metal B Alloy of B in A, but both are reactive. Assuming that B forms the more stable oxide. In superalloys: A = Co or Ni; B = Al, Ti, Cr, X Concentrated solution of B in A of B, C B A(B) Depletion of more reactive element B BO air Conc. (1) Distance, x D A & D B << D O A continuous external layer of oxide BO forms. Oxidation rate is parabolic but the rate constant is the same as B s s. Thus, to increase oxidation resistance you must increase the concentration of elements that form very stable or slow-growing oxides. What can happen after a long time? Depletion of B at point (1), i.e., low C B, leads to the formation of AO within BO. At this point, the rate constant increases towards that of oxide AO and the oxidation rate increases. Case 2(b)
24 Comparison of Cases 2(a) and 2(b) Reactive Metal A + More Reactive Metal B DILUTE A(B) A + BO AO CONCENTRATED A(B) BO After long time A(B) BO + AO precipitation inside scale
25 How Parabolic Growth Occurs
26 Summary of Oxide Formation in Binary Alloys
27 Breakdown of Parabolic Growth Eventually, we will deplete the concentration of the reactive element so much that parabolic oxidation will break down. The time for transition away from parabolic oxidation kinetics depends on many factors. Temperature Specimen size Diffusivity of elements in alloy and scale Initial concentration of B in A.
28 Breakdown of Parabolic Growth cont d Also hastened by any process that reduces the protectiveness of layer BO. Examples include: Evaporation of volatile oxides which thin the protective layer (e.g., CrO 3 from Cr 2 O 3 ). Mechanical damage of the oxide such as erosion, cracking, or spalling. Stresses during gformation or service
29 Some Sources for Stresses in Scales Growth stresses: Can arise from epitaxial growth of crystalline oxides on metal surface. Limits epitaxy to first ~50 nm of oxide. Polycrystalline lli oxides develop stresses along grain boundaries due to more rapid grain growth in those regions and increased rates of short-circuit diffusion. Compositional variation across scale due to deviation from stoichiometry. Etc. Transformation stresses: Phase transformation leading to change in volume. Thermal stresses: Difference in CTE Read pages from Heat Resistant Materials for a short summary.
30 Growth Stresses Volume change induces biaxial stress at metal/oxide interface Quite significant in epitaxial oxide ae (1 ) xx yy a o
31 Growth Stresses cont d In absence of epitaxy, stress depends on: lattice parameters, oxide microstructure, and local diffusive fluxes. For simplicity and visualization purposes, we can assume that oxide growth occurs at: (1) steps on the metal/oxide interface (2) ledges on the oxide surface. (2) air oxide (1) metal
32 Growth Stress Limiting case #1 Inward flux of oxygen atoms through the oxide layer. An in-plane elastic stress σ xx develops on ledge where new oxide forms resulting in a stress gradient. The stress gradient induces a vacancy flux in alloy and along the interface in the direction of the ledge. This reduces the density of metal atoms along the y f g plane of the ledge and reduces the strain there placing the oxide in compression.
33 Stress Limiting case #2 When the oxide forms at the surface due to metal atom diffusion (outward) through the oxide layer. Removal of metal atoms at the oxide/metal interface places the oxide in tension. Stress differential contributes towards spallation of the oxide. Most of the time things are a bit more complicated!
34 Continuous loss of material. - Cyclic exposure is worse. Th t ki d lli The stresses cause cracking and spalling leading to accelerated oxidation.
36 Determination of Oxidation Kinetics
38 Summary Oxidation is the most important hightemperature corrosion reaction. Oxidation takes place whenever the oxygen content and oxygen activity are suitable. It can even occur in reducing atmospheres or vacuum. Oxide scale morphology depends upon alloy concentration, solute diffusivity, and related factors.
Hot Corrosion Focus on superalloys as examples of high temperature materials F. Petit, Hot Corrosion of Metals and Alloys, Oxidation of Metals 76 (2011) 1-21. Ref. Ch. 12 in Superalloys II Ch. 14 in Tien
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