Phase diagrams are essential tools for understanding alloy systems. They show how temperature and composition affect the equilibrium phases in materials, helping predict microstructures and properties.
The Gibbs phase rule links components, phases, and degrees of freedom in a system. It's crucial for interpreting phase diagrams and understanding the stability of different phases in alloys under various conditions.
Phase Diagrams and Alloy Systems
Interpretation of phase diagrams
- Binary phase diagrams graphically represent equilibrium phases in two-component systems (Cu-Ni) with composition on x-axis and temperature on y-axis
- Distinct regions separated by phase boundaries denote different phases
- Tie lines connect phases in equilibrium at given temperature and composition (liquid + solid)
- Ternary phase diagrams depict equilibrium phases in three-component systems (Fe-Cr-Ni) using an equilateral triangle for composition and isothermal sections or vertical temperature axis
- Microstructure evolution determined by equilibrium phases at specific composition and temperature
- Slow cooling enables formation of equilibrium phases
- Rapid cooling may yield non-equilibrium phases (martensite) or supersaturated solid solutions
Application of Gibbs phase rule
- Gibbs phase rule $F = C - P + 2$ relates degrees of freedom $F$ to number of components $C$ and phases in equilibrium $P$
- Degrees of freedom represent independent variables (composition, temperature) that can vary without changing number of equilibrium phases
- In binary systems, maximum degrees of freedom is 2
- Single-phase regions have $F = 2$, phase boundaries have $F = 1$, and invariant points (eutectic) have $F = 0$
- Ternary systems have maximum degrees of freedom of 3
- Single-phase regions have $F = 3$, phase boundaries have $F = 2$, and invariant points have $F = 0$
Thermodynamics of intermetallics and solutions
- Intermetallic compounds are ordered phases with specific stoichiometry (NiAl) and crystal structure
- Form when Gibbs free energy of compound is lower than constituent elements
- Negative enthalpy of formation $\Delta H_f < 0$ due to strong bonding between unlike atoms
- Negative entropy of formation $\Delta S_f < 0$ from ordered atomic arrangement
- Stability governed by Gibbs free energy $\Delta G_f = \Delta H_f - T\Delta S_f$
- Solid solutions are single-phase solids with solute elements dissolved in solvent matrix (Cu in Ni)
- Form when Gibbs free energy of mixing is negative $\Delta G_{mix} < 0$
- Enthalpy of mixing $\Delta H_{mix}$ depends on relative bond strengths between like and unlike atoms
- Entropy of mixing $\Delta S_{mix}$ is always positive due to increased system disorder
- Stability determined by Gibbs free energy of mixing $\Delta G_{mix} = \Delta H_{mix} - T\Delta S_{mix}$
- Solid solubility affected by atomic size difference (Hume-Rothery rules), electronegativity difference, and valence electron concentration
Factors in alloy phase transformations
- Composition determines equilibrium phases, their relative amounts, solubility limits, and invariant reaction temperatures and compositions (eutectic point)
- Temperature influences stable equilibrium phases, solid solution solubility limits (higher temperature increases solubility), and kinetics of phase transformations (faster diffusion at higher temperatures)
- Pressure has less impact compared to composition and temperature but can affect stability of phases with different densities (high-density phases favored at high pressures) and shift equilibrium lines and invariant points
- Phase transformations alter properties:
- Mechanical properties (strength, ductility) depend on phases present, their amounts, and microstructural features (grain size)
- Physical properties (density, conductivity) determined by crystal structure and bonding of present phases
- Corrosion resistance affected by phase composition, distribution, and galvanic couples between phases