Phase transformation

Phase transformation

Phase Transformation Topics o Basic principles relating to transformations o Kinetics of phase transformation: Nucleation and growth o Metastable and equilibrium state o Shape memory alloys

Phase Transformation Terminology Transformation rate reaction progress on time Phase transformation alteration of one or more phases to other phase(s) types of phase transformation: diffusion-independent transformations diffusion-dependent transformations diffusionless transformations

Phase Transformation Diffusion-independent transformations No change in either the number or composition of the phases present. solidification of a pure metal allotropic transformations (e.g.: α phase β phase) recrystallization and grain growth

Phase Transformation Diffusion-dependent transformations Some alteration in phase compositions and often in the number of phases present. The final microstructure ordinarily consists of two phases. e.g.: eutectoid reaction

Phase Transformation Diffusionless transformations The phase transformation occours without diffusion. A metastable phase is produced. Martensitic transformation

nucleation formation of numerous small particles new phase(s) Liquid phase Liquid phase growth increase in size until the transformation has reached completion Grain boundaries nuclei Growing crystals Grains (crystals) Liquid-to-solid and solid-state transformations

Nucleation Two types: homogeneous: heterogeneous: The new phase forms uniformly throughout the parent phase. The new phase(s) prefers structural inhomogeneities, such as container surfaces, insoluble impurities, grain boundaries, dislocations, etc. homogeneous heterogeneous

Homogeneous nucleation G: Gibbs free energy (G=H-TS) ΔG: change in free energy A transformation will occur spontaneously only when G has a negative value. Nuclei of the solid phase form in the interior of the liquid, atoms cluster together. Assumption: each nucleus is spherical with a radius r Gibbs free energy difference between the two states: liquid phase ΔG Solid phase + small crystals within liquid nucleus

Homogeneous nucleation 2 component of G: G v the energy difference between the liquid and solid phase ΔG v < 0 if T < T solidification γ 4 surface free energy 3 πr3 volume of the spherical nucleus 4πr 2 surface area of the nucleus G = 4 3 πr3 G v + 4πr 2 γ difference between the solid and liquid phases X volume formation of the solid liquid phase boundary

G = 4 3 πr3 G v + 4πr 2 γ

G = 4 3 πr3 G v + 4πr 2 γ critical radius r* r < r* Shrink and redissolve r > r* growth nucleus energy barrier to the nucleation process: critical free energy, ΔG* (activation free energy)

Homogeneous nucleation Critical radius and free energy: G = 4 3 πr3 G v + 4πr 2 γ d G dr = 4πr 2 G v + 8πr γ = 0 r = 2γ G v Critical radius of a stable solid particle G = 16πγ3 3 G v 2 Energy required for the formation of a stable nucleus

Homogeneous nucleation G v is a function of temperature G v = H f(t m T) T m H f is the latent heat T m melting temperature in K Lowering of temperature at temperatures below the equilibrium solidification temperature (T m ), nucleation occurs more readily. r = 2γT m H f (T m T) G = 16πγ 3 T m 2 3 H f 2 (T m T) 2

Homogeneous nucleation The number of stable nuclei n* (r > r*) is a function of temperature n = K 1 e G kt K 1 - constant 1) If T lowered below T m, the magnitude of n* increases. 2) Short-range diffusion during the formation of nuclei: temperature s effect on the rate of diffusion (D diffusion coefficient) D = D 0 e Q RT the frequency at which atoms from the liquid attach themselves to the solid nucleus, v d. v d = K 2 e Q kt

supercooling Nr of stable nuclei * diffusion = Nucleation rate n = K 1 e G kt v d = K 2 e Q kt

Homogeneous nucleation Nucleation rate The small activation driving force suppresses the nucleation rate The low atomic mobility suppresses the nucleation rate

Heterogeneous nucleation Nuclei form on a surfaces or interfaces Activation energy for nucleation is lowered when nuclei form on preexisting surfaces or interfaces, because the surface free energy is reduced. surface tension force balance: γ IL = γ SI +γ SL cos(θ) θ - wetting angle γ IL - Interface-liquid surface energy γ SI - Solid-Interface surface energy γ SL - Solid-liquid surface energy

Heterogeneous nucleation r = 2γ SL G v G = 16πγ SL 3 2 3 G v S(θ)=0 1 S(θ) G het = G hom S(θ)

Growth growth of the new phase particles long-range atomic diffusion Growing nucleus diffusion through the original phase The growth process stops in any region where particles of the new phase meet the transformation is completed The growth rate is determined by the diffusion rate G = Ce Q kt

Growth Liquid phase Liquid phase Grain boundaries nuclei Growing crystals Grains (crystals)

Overal transformation rate

Solid-solid transformation The same general principles Time dependency Avrami equation typical kinetic behavior for most solid-state reactions y = 1 e ktn T=constant k, n parameters f(t,p)

Solid-solid transformation Percent recrystallization as a function of time and at constant temperature for pure copper.

Metastable vs equilibrium states Equilibrium states Infinite slow cooling / heating Phase diagrams Metastabele states supercooling or superheating For other than infinite slow cooling / heating, transformations are shifted to lower / higher temperatures than indicated by the phase diagram Isothermal transformation diagrams Continuous cooling transformation diagrams

Metastable vs equilibrium states Isothermal transformation diagrams Isothermal diagram for an eutectoid iron carbon alloy

Metastable vs equilibrium states Continuous transformation diagrams cooling Continuous cooling diagram for an eutectoid iron carbon alloy

Martensitic transformation Diffusionless transformation Martensite: non-equilibrium single-phase structure (iron alloys) Face centered cubic phase transforms to a body-centered tetragonal (BCT) martensite. Cooperative movements of atom without diffusion, very fast, when the material is cooled to the transformation temperature

Martensitic transformation Model of the transformation

Martensitic transf. Shape Memory alloys Diffusionless transformation shape-memory alloy: shape-memory effect: may have two crystal structures (or phases) involves phase transformation. One phase (austenite phase) body-centered cubic structure that exists at elevated Temperatures. Upon cooling, the austenite transforms to a (a body-centered tetragonal) martensite phase. Martensite is heavily twinned, deformation occurs by the migration of twin boundaries. Twin boundary: atoms on one side of the boundary are located in mirror-image positions

Shape Memory alloys