Platinum markers, found at the interface between the compact and porous NiO layers post-oxidation, indicate that the outer layer grows by outward cation migration and the inner layer by inward oxygen migration.

Cold-worked nickel oxidizes faster than annealed nickel, showing lower activation energy due to easier diffusion paths along oxide grain boundaries.

The oxidation rate increases with higher oxygen partial pressure, linked to cation vacancies (V′Ni) that vary with the 1/6 power of oxygen pressure per Equation 4.3.

Point defects (e.g., vacancies) play a key role in oxide layer growth, with intrinsic defects possibly contributing to the overall mechanism.

If oxide plasticity is insufficient (especially in impure nickel with high oxidation rates), the layer separates from the metal, increasing oxygen activity at the inner surface, leading to layer decomposition and new oxide formation.

At 1000°C, high-purity nickel forms a single compact NiO layer, while impurities can produce a dual-layer (compact and porous) structure.

Oxygen partial pressure significantly increases the oxidation rate, as demonstrated in comprehensive studies by Fueki and Wagner.

When pure zinc (Zn) is oxidized, it forms only one oxide, ZnO, which is an n-type cation-excess semiconductor. This characteristic enables the creation of a single-phase, single-layered scale, making it significant for oxidation studies.

The oxidation process of ZnO occurs through the presence of interstitial zinc ions and electrons. These ions and electrons play a primary role in the growth of the oxide layer and facilitate material transport within the structure.

The concentration gradient of defects in the scale is sensitive to oxygen partial pressure, but the overall oxidation rate is less dependent on atmospheric pressure variations, as the internal equilibrium of the system maintains relative stability.

The primary oxide of aluminum, α-Al₂O₃, has a rhombohedral structure characterized by a hexagonal packing of oxide anions and cations occupying two-thirds of the octahedral sites. This oxide grows slowly and serves as a protective layer on high-temperature-resistant alloys and coatings.

Besides α-Al₂O₃, metastable forms such as γ-Al₂O₃ (cubic spinel), δ-Al₂O₃ (tetragonal), and θ-Al₂O₃ (monoclinic) exist, forming under specific conditions.

Aluminum is covered at ambient temperature with a thin amorphous alumina layer (2 to 3 nanometers) that forms naturally in air.

Below 350°C: The amorphous layer grows with inverse logarithmic kinetics.
350 to 425°C: Growth follows parabolic kinetics.
Above 425°C: Kinetics become complex and less predictable.

Iron forms a triple-layer oxide structure in air at high temperatures (above 570°C):
• FeO (Wustite): Closest to the metal
• Fe₃O₄ (Magnetite): Middle layer
• Fe₂O₃ (Hematite): Outer surface
This structure is a classic example of multilayer oxide formation.

Below 570°C: FeO does not form, resulting in a double layer of Fe₃O₄ and Fe₂O₃.
Above 570°C: A complete triple layer forms, with FeO being the thickest (about 95% of total thickness) due to its high defect concentration.

FeO (Wustite): A p-type semiconductor with metal deficit (stoichiometry range Fe₀.₉₃O to Fe₀.₈₈O at 1000°C). Contains cation vacancies and electron holes, enhancing cation and electron mobility.

Fe₃O₄ (Magnetite): An inverse spinel with Fe²⁺ in octahedral sites and half of Fe³⁺ in tetrahedral sites. Defects occur in both sites, allowing iron diffusion in both tetrahedral and octahedral positions. An intrinsic semiconductor with electron transfer via holes.

Fe₂O₃ (Hematite): Rhombohedral structure with a close-packed hexagonal arrangement of oxygen anions. Outward cation diffusion dominates, though anion mobility is also observed.

At low pressures, defects at interfaces remain constant, and the rate is independent of P_O₂. Studies by Pettit, Yinger, and Wagner show that at very low pressures (10⁻¹² atm at 1000°C), the rate remains constant. The CO-CO₂ system is used for testing, but adsorbed CO₂ decomposition keeps the rate steady. Stresses from growth and redox systems (CO/CO₂, H₂/H₂O) can cause layer spalling.

Cobalt forms two primary oxides:
CoO (Cobalt Monoxide): NaCl structure, a p-type semiconductor with cation deficiency, where cations and electrons migrate through cation vacancies and electron holes.
Co₃O₄ (Spinel): A secondary oxide with a spinel structure. At temperatures above 1050°C, intrinsic Frenkel defects (vacancy-interstitial pairs) also appear.

The growth of the CoO layer occurs via outward cation diffusion, indicating the formation of a compact, uniform layer. Platinum markers are found at the metal-layer interface after oxidation, confirming cation migration. The oxidation rate depends on oxygen partial pressure (P_O₂) and temperature but becomes complex due to intrinsic defects.

The theory of multi-layered scale growth refers to the oxidation process of metals at high temperatures in oxidizing environments (e.g., air), leading to the formation of multiple oxide layers with different compositions. This phenomenon is observed in metals like iron, cobalt, copper, and zirconium, and depends on crystal structure, temperature, and oxygen partial pressure (P_O₂).

Layers, from inner to outer, consist of different oxides with distinct properties:
• Example for iron: FeO (wüstite) near the metal, Fe₃O₄ (magnetite) middle, Fe₂O₃ (hematite) outer
• Example for cobalt: CoO (inner) and Co₃O₄ (outer)
• Example for copper: Cu₂O and CuO
Each layer has a specific crystal structure (e.g., NaCl for CoO, spinel for Co₃O₄), and the interfaces between layers are sites of chemical equilibrium and growth.

Layer growth occurs through the migration of species, such as cations or anions:
• Cation migration: e.g., Ni²⁺ in NiO or Fe²⁺ in FeO moving outward
• Anion diffusion: e.g., oxygen in ZrO₂ moving inward
Platinum markers in experiments indicate the metal-layer interface location and confirm the type of migration. Interfacial equilibrium between layers controls the growth of each layer.

The overall growth of layers is described by the parabolic rate law: x² = kp × t, where x is the layer thickness, kp is the parabolic rate constant, and t is time. The growth rate depends on the mobility of defects (e.g., cation or anion vacancies) and oxygen partial pressure (P_O₂). The thicker layer (e.g., FeO in iron, comprising 95% of total thickness) typically has more defects and grows faster.

Cr₂O₃ oxide forms; under specific conditions, complications like volatilization arise, which is important for pure chromium and alloys relying on the Cr₂O₃ layer.

Occurs through the formation of CrO₃ (Equation 4.24); significant at high temperatures and high oxygen pressures.

Initially follows parabolic kinetics; volatilization affects scale thickness (Equations 4.25, 4.27).

Higher temperatures increase volatilization impact; chromium oxidation at 900°C is independent of oxygen pressure (kp).

At high temperatures and high oxygen pressures, molybdenum and tungsten form oxides; unlike chromium, which has a limited scale thickness, complete oxide volatilization may occur.

Investigated by Gulbransen and Meier; the impact of oxide volatilization on the oxidation process is evident at 1250 K (refer to Figures 4.14 and 4.15).

For molybdenum, above 725°C, gas-phase diffusion becomes the primary rate-limiting factor, leading to catastrophic oxidation; this behavior is also observed for tungsten at higher temperatures.

At high temperatures, only volatile oxides form for platinum and platinum-group metals, leading to continuous mass loss (refer to Figure 4.16).

PtO₂ and RhO₂ species have been identified; mass loss at 1400°C is proportional to the partial pressure of oxygen.

Platinum and platinum-rhodium wires are used as supports, influencing mass-change measurements.

Between 650 and 1000°C, Rh₂O₃ forms with logarithmic kinetics; above 800°C, only the orthorhombic Rh₂O₃ phase is observed; at 1000°C, power-law kinetics (near parabolic) and significant volatilization occur.

This process results in a very low oxidation rate for silicon, silicon-containing alloys, and silicon-based ceramics. However, the system is influenced by oxide vapor species, which alter its behavior.

The SiO diagram (refer to Figure 4.17) shows that SiO is in equilibrium with solid SiO₂ (s) and pure silicon (s), especially near the volatilization pressure. This condition leads to a rapid SiO flux and the formation of non-protective SiO₂ smoke that detaches from the specimen surface.

This pressure is defined by the formula pO₂(crit) ≈ pSiO/2 or its more precise version (Equation 4.39). It determines the distinction between active (destructive) and passive (protective) oxidation.

Stable oxides: TiO, Ti₂O₃, TiO₂.
High oxygen solubility in titanium.
Dependence on temperature and oxygen weight percentage.

Oxidation behavior changes with temperature.

Governing law: Parabolic rate.

Zirconium (Zr) and Hafnium (Hf) exhibit similar behavior to titanium.

Niobium oxidation at high temperatures occurs through the inward diffusion of oxygen via the scale layer. Initially, a protective layer forms, but as the scale grows, oxide formation at the scale-metal interface causes stress, leading to cracking and "breakaway" linear oxidation.

Copper markers are found at the scale-gas interface after oxidation, indicating continuous growth of the Nb₂O₅ layer over lower oxides due to inward oxygen migration. Over time, copper fills cracks in the outer scale portion, accelerating the oxidation rate.

At 600°C, initial oxidation follows parabolic growth kinetics. After this initial period, the kinetics typically shift to linear behavior as protective properties are compromised due to scale cracking, resulting in accelerated oxidation rates.

The volume ratio of Nb₂O₅ to Nb is approximately 2.68, creating substantial compressive stresses within the oxide layer. These stresses cause cracking, particularly at the scale-metal interface, allowing direct oxygen access to the metal surface.

Multiple oxide phases form during niobium oxidation: NbO, NbO₂, and Nb₂O₅. The outermost layer consists primarily of Nb₂O₅, which is less protective due to its tendency to crack under thermal and growth stresses.

Tantalum exhibits oxidation behavior similar to niobium but with better resistance at moderate temperatures. The primary oxide formed is Ta₂O₅, which initially provides some protection but eventually cracks due to growth stresses.

The oxidation process transitions from parabolic to linear kinetics as the oxide scale thickens and cracks. This transition occurs later than in niobium, indicating tantalum's superior oxidation resistance in the Group V metals.

At temperatures below 500°C, tantalum forms a relatively protective oxide layer. Above this temperature, rapid oxidation occurs due to scale cracking, with the rate increasing substantially above 750°C.

The linear rate law is expressed as: x = k_l·t, where x is the oxide thickness or mass gain, k_l is the linear rate constant, and t is time. This law applies when a surface or phase-boundary process controls the overall reaction rate.

Linear oxidation occurs when:
• The oxide scale is porous or cracked, allowing direct gas access to the metal
• Surface reactions (adsorption, dissociation, or incorporation of oxygen) are rate-limiting
• A steady-state oxide thickness is maintained due to simultaneous formation and volatilization

Linear oxidation is observed in:
• Initial stages of oxidation for many metals
• Niobium and tantalum at high temperatures after scale breakdown
• Metals forming volatile oxides (e.g., Mo, W) under certain conditions

The parabolic rate law follows: x² = k_p·t, where k_p is the parabolic rate constant. This law indicates that the oxidation rate is inversely proportional to the scale thickness, suggesting diffusion-controlled growth.

Carl Wagner's theory explains parabolic oxidation through:
• Solid-state diffusion of ions and electrons through the scale
• Establishment of a chemical potential gradient across the oxide
• Equilibrium at both metal-oxide and oxide-gas interfaces

Parabolic oxidation is common in:
• Nickel forming NiO
• Iron at high temperatures (>570°C)
• Copper forming Cu₂O
• Many other metals forming compact, adherent scales

The parabolic rate constant depends on:
• Temperature (following Arrhenius relationship)
• Oxygen partial pressure
• Defect structure and concentration in the oxide
• Impurities in both metal and gas

The logarithmic rate law is expressed as: x = k_log·log(at + 1), where k_log and a are constants. This law describes rapid initial oxidation followed by substantial rate reduction, typically observed at low temperatures.

The inverse logarithmic law follows: 1/x = A - B·log(t), where A and B are constants. This behavior is also observed at low temperatures and thin films.

These laws may result from:
• Electric field effects across thin oxide films
• Space charge development within the oxide
• Progressive blocking of low-resistance diffusion paths
• Chemisorption processes

Logarithmic or inverse logarithmic behavior is observed in:
• Aluminum oxidation below 350°C
• Copper, iron, and zinc at room temperature
• Many metals during the initial stages of oxidation at low to moderate temperatures

The cubic rate law follows: x³ = k_c·t, where k_c is the cubic rate constant. This intermediate behavior between parabolic and logarithmic laws may result from multiple diffusion mechanisms operating simultaneously.

The general power law is expressed as: x^n = k·t, where n can take various values depending on the controlling mechanism. For example, n = 2 for parabolic, n = 3 for cubic, and n = 1 for linear kinetics.

Many real oxidation processes follow mixed kinetics, with different rate laws dominating at different stages or under changing conditions. The transition between laws often indicates a change in the rate-controlling mechanism.

Oxidation rate constants typically follow the Arrhenius equation: k = A·exp(-E_a/RT), where E_a is the activation energy, R is the gas constant, T is absolute temperature, and A is the pre-exponential factor. This relationship indicates exponential increase in oxidation rates with temperature.

Temperature can induce phase transformations in both the metal and oxide, altering defect structures and diffusion rates. For example, iron forms different oxide phases above and below 570°C, drastically changing its oxidation behavior.

Higher temperatures promote sintering of the oxide scale, reducing porosity and potentially improving protective properties. However, excessive temperatures can also increase defect mobility and concentration, accelerating oxidation.

For p-type oxides (e.g., NiO, FeO), the oxidation rate typically increases with oxygen partial pressure raised to a positive power (e.g., P_O₂^(1/n), where n depends on the defect structure). For n-type oxides (e.g., ZnO), the dependence may be negative.

Some systems exhibit critical oxygen pressures that mark transitions between different oxidation mechanisms. For example, silicon transitions from passive to active oxidation below a critical P_O₂, while chromium experiences accelerated oxidation above certain pressures due to volatile oxide formation.

Surface roughness affects the initial oxidation rate, with rougher surfaces generally showing higher rates due to increased surface area and defect density. However, the long-term effect diminishes as the oxide scale thickens.

Cold-worked metals typically oxidize faster than annealed ones due to higher defect density and stored energy. For example, cold-worked nickel shows lower activation energy for oxidation compared to annealed nickel.

Surface impurities, including residual polishing compounds, oils, or environmental contaminants, can significantly alter initial oxidation behavior by affecting adsorption sites and nucleation processes.

Specimen geometry influences stress development in the oxide scale. Edges and corners are particularly susceptible to scale cracking due to higher stress concentration, potentially accelerating local oxidation rates.

Specimens with high surface-to-volume ratios (e.g., thin foils, fine powders) may exhibit different oxidation kinetics compared to bulk materials due to limited metal supply and enhanced stress effects.

Pure metal oxidation involves several fundamental mechanisms:
• Adsorption and initial oxide nucleation: Oxygen adsorbs on the metal surface and forms initial oxide nuclei
• Lateral growth and film formation: Nuclei grow laterally to form a continuous film
• Diffusion-controlled growth: Further oxidation requires solid-state diffusion of reactants through the scale
• Stress development and mechanical effects: Growth and thermal stresses can cause scale cracking or spallation

Different metals exhibit characteristic oxidation behaviors:
• Single-layer formers (Ni, Al, Zn): Form protective single-phase oxide scales with relatively simple diffusion mechanisms
• Multi-layer formers (Fe, Co, Cu): Form complex layered structures with different defect types and diffusion mechanisms in each layer
• Volatile oxide formers (Cr, Mo, W): Form oxides that can volatilize under certain conditions, complicating the oxidation process
• Oxygen dissolvers (Ti, Zr, Hf): Dissolve significant oxygen in the metal substrate, affecting mechanical properties and oxidation kinetics
• Scale crackers (Nb, Ta): Form non-protective scales that crack due to high growth stresses, leading to accelerated oxidation

Understanding pure metal oxidation provides a foundation for selecting materials for high-temperature applications. Metals forming stable, adherent oxide scales (e.g., Ni, Cr, Al) are preferred for oxidation resistance.

Pure metal oxidation mechanisms inform alloy design strategies. For example, chromium and aluminum are added to many high-temperature alloys to promote the formation of protective Cr₂O₃ or Al₂O₃ scales.

Knowledge of oxidation mechanisms guides the development of protective coatings. For instance, aluminide coatings promote the formation of slow-growing Al₂O₃ scales, while chromium-rich coatings form protective Cr₂O₃ layers.

Current research focuses on:
• Advanced in-situ characterization techniques to observe oxidation processes in real-time
• Atomic-scale modeling of defect formation and migration in oxides
• Development of novel alloys and coatings with enhanced oxidation resistance
• Understanding the effects of complex environments (water vapor, salt deposits, etc.) on oxidation mechanisms