Phase Transformation of alloys

Explore the driving force of phase transformations in alloys, from unstable initial states to final states, using thermodynamic principles that relate energy content, enthalpy, and internal energy.

Explain how enthalpy and entropy drive phase transformations and Gibbs free energy g equals h minus t s is formed, with entropy vanishing at zero kelvin; specific heat measures changes.

Explain how Gibbs free energy drives phase transformations and how temperature-dependent specific heat links enthalpy and entropy to the Clausius-Clapeyron relation dG = v dp - s dT.

Subtract the t d s term from h versus t to obtain g versus t, yielding a negative slope and crossing of solid and liquid curves at the melting point.

Show how the solid-liquid free-energy difference drives solidification, with delta g zero at the melting temperature and delta g = L delta t / tm away from tm.

Examine Gibbs free energy as a function of pressure, link dG to phase volume, and apply Clausius–Clapeyron to predict P–T slopes for iron's alpha, gamma, delta, and epsilon phases.

The lecture derives the free energy of mixing for a binary ideal solution, with delta g_mix = -T delta s_mix from configurational entropy, and notes the non-linear xb dependence.

Learn how regular solutions exhibit nonzero enthalpy of mixing captured by the interaction parameter omega; analyze how delta g mix, temperature, and composition shape phase behavior and phase diagrams.

Examine how free energy changes with temperature, pressure, and composition in multicomponent systems. Define partial molar free energy as chemical potential and relate mu_A, mu_B to mole fractions in mixing.

explains phase equilibrium in a binary a-b alloy with alpha and beta phases, deriving that mu_a in alpha equals mu_a in beta at equilibrium.

Apply the Gibbs phase rule to phase equilibrium in alloys. Find that f = c - p + 2, with c as components, and chemical potentials are equal across phases.

Construct an isomorphous phase diagram for a binary alloy by analyzing free energy curves and the common tangent as temperature changes, revealing solidus and liquidus boundaries.

Explains how positive delta h mix in solids creates a miscibility gap in the phase diagram, with alpha prime and alpha double prime phases and a pseudo eutectic region.

Explore the eutectic phase diagram by analyzing alpha, beta, and liquid equilibria, using Gibbs free energy and common tangents to determine compositions and a tie line at the eutectic temperature.

Construct a peritectic phase diagram by mapping common tangents among liquid, alpha, beta, and gamma phases at temperatures t1 through t5, identifying peritectic and eutectic compositions and stability regions.

describe how solid forms from liquid via homogeneous nucleation, where a critical nucleus radius arises from balancing volume free energy decrease and interfacial (surface) free energy increase.

Analyze homogeneous nucleation and how surface energy, interfacial energy, and volume free energy shape the critical radius. Explore how undercooling affects delta g and the ease of nucleation.

Lower the energy barrier for nucleation on a delta substrate, forming a spherical-cap beta phase with interfacial energy balance at the contact angle and lower heterogeneous free energy than homogeneous.

Explain how pure metals solidify, driven by undercooling, cooling rate, and temperature gradient, shaping the solid–liquid interface. Show how latent heat release and conductivities control heat flow and growth direction.

Explore how a spherical solid particle grows into dendritic structures during solidification, with primary, secondary, and tertiary arms, and perpendicular growth directions. Note this covers thermal dendrites in pure metals.

Examine equilibrium solidification of a single-phase binary alloy with a simplified straight liquidus and solidus diagram. Define the partition coefficient k and solid–liquid compositions, and discuss solute conservation.

Explore the Scheil equation for non-equilibrium solidification: rapid cooling, no solid diffusion, a homogeneous liquid, and solute rejected into the liquid, enriching it toward eutectic composition.

unidirectional solidification without stirring causes solute to accumulate at the solid–liquid boundary, creating initial and final transient states; diffusion balances rejection to sustain a constant rate and yield aligned microstructure.

Explore constitutional supercooling during alloy solidification, where compositional gradients shift the liquidus temperature and cause planar fronts to break into cells and form secondary and tertiary dendrites.

Explore solid-state transformations in alloys, including diffusional and non diffusional paths, such as martensitic transformation, precipitation, eutectoid and ordering reactions, and polymeric transformations.

Examine solid-state precipitation in aluminum-copper alloys, from supersaturated alpha after quenching to GP zones and evolving theta, theta prime, and theta double prime, via the common tangent line.

Explain the eutectoid transformation in the iron–carbon system, where FCC austenite becomes bcc ferrite and cementite as pearlite forms, guided by TTT diagram and cooling rate effects on bainite morphologies.

Explore spinodal decomposition in diffusion-controlled solid-state transformations within a miscibility-gap phase diagram, where negative free-energy curvature triggers downhill diffusion to equilibrium compositions, contrasting nucleation-and-growth outside the spinodal.

Analyze diffusion in solid solutions driven by chemical potential gradients, including downhill diffusion down the concentration gradient and uphill diffusion in miscibility gaps, with spinodal and phase separation implications.

Explore short range diffusional transformation in a 38% zinc copper alloy, where alpha m forms at the alpha beta boundary, and study ordering and disordering, first and second order characteristics.