Phase Transformations Exam 2

Interfaces, Nucleation, Groth

Three types of crystal interfaces

free surfaces (solid/vapor), grain boundaries, interphase interfaces

Interfacial free energy

excess free energy of a system containing an interface

L_s

latent heat of melting and vaporization

The close-packed surface plane orientations occur at the minimum E_sv (the cusp)

True

E_sv

solid-vapor interface energy

Vicinal surface

a terraced surface alternating between 2 planes

Wulff plane

a plot in which the free energy of the plane is equal to the distance between the surface and the origin, used to predict the equilibrium shape of crystals

Equilibrium shapes maximize surface energy

False- they minimize excess surface energy

For Wulff construction, planes are perpendicular to the radius vector to each point closest to the origin (and these planes form the equilibrium shape)

True

The shape of crystals becomes spheroidal (instead of faceted) above the recrystallization temperature

False- this occurs above the roughening temperature

Pure tilt grain boundaries

disorientation/rotation axis is contained in the boundary plane

Pure twist grain boundaries

disorientation/rotation axis is perpendicular to the boundary plane

Low-angle GBs

structure can be described by dislocation arrays, surface energy is linearly proportional to theta

High-angle GBs

structure of a configurationally disordered condensed state with excess free volume, surface energy is independent of theta

Theta ranges for LAGB, transition regime, and HAGB

theta<10, 10<theta<15, 15<theta

LAGBs have special angles with cusps of minimized energy

False- HAGBs have these!

Special HAGB angles depend on the disorientation axis and crystal structure

True!

D (plus LAGB equation)

dislocation spacing, D = b/theta

Geometrically necessary dislocations

dislocations required to accommodate LAGB misorientation

Why is HAGB energy constant with theta?

As theta increases, the strain fields overlap and partially cancel

All HAGB have cusps in energy

False- they’re observed in coherent (symmetric tilt GB) and incoherent twins

Symmetric LA tilt GBs are made up of edge dislocations with a single Burgers vector

True

Asymmetric LA tilt GBs are made up of edge dislocations with a single Burgers vector

False- the edge dislocations have multiple Burgers vectors

Coincident site lattice

The overlapping lattice points from overlaid, rotated lattices

Sigma # (CSL) meaning

the number of original lattice sites in the CSL motif

Coherent twin boundaries have the lowest interfacial energy

True!

Asymmetric incoherent twins have terrace-ledge structures

True

CTB, SITB, AITB

coherent twin boundary, symmetric incoherent twin boundary, asymmetric incoherent twin boundary

Grain shapes reduce G by reducing curvature

True!

Grains with less than 4 sides shrink, while grains with more than 4 sides grow (4 is the stable number of sides)

False- 6 is the stable number of sides

Grain growth occurs through the migration of GB

True!

Equation for growth rate (v)

v = MF, M = mobility, F = driving force (proportional to GB energy)

GB segregation

Solute atoms exert lattice strain and concentrate in the GB

Segregation (X_b) increases as T ______ and solubility ______

decreases, decreases

Solutes at GB can exert a drag force to increase GB velocity

False- this decreases GB velocity

CSLs with large sigma values indicate preferred misorientation angles

False- low sigma values are preferred due to their decreased excess energy

In equilibrium, up to 3 grains can meet at the same edge

True- 4 or more grains will be separated by a new edge

interfacial energy of special HAGB is ______ than that of general HAGB

less

GB migration velocity of special HAGB is ______ than that of general HAGB

greater

Zener pinning effect

particles exert a restraining force on GB

Fully coherent

perfect matching of atomic planes at the interface

The interfacial energy of all interfaces is equal to the chemical energy

False- this is only true for fully coherent interfaces

Coherent interfaces can have small geometric mismatches

True- mismatch under 5% is common, and it introduces strain energy!

Semi-coherent interfaces

have a larger mismatch in lattice parameter and use dislocations to reduce strain energy

Interfacial energy for semi-coherent interfaces comes from a chemical contribution and a structural misfit contribution

True

Incoherent interfaces

have a large misfit (>25%), interfacial energy is insensitive to orientation

Fully coherent precipitate shape

matching orientation, spherical

Incoherent precipitate shape

spherical (but other shapes are possible)

Semi-coherent precipitate shape

plane

Coherency is independent of precipitate size

false- coherent precipitates become semi-coherent above the critical radius

Two types of solid-liquid interfaces

flat, diffuse

Interface control

low interface mobility, relative fast diffusion

Diffusion control

high interface mobility, local equilibrium at interface

Nucleation

creation of interface

Growth

migration of interface

Military transformations (thermal sensitivity, interface glissile?, diffusion, rate limiting step)

athermal, glissile, no diffusion, interface control

Civilian transformations (thermal sensitivity, interface glissile?, diffusion, rate limiting step)

thermally activated, non-glissile, short/long-range diffusion, interface/diffusion/mixed control)

Military transformation examples (2)

martensite, twinning

Civilian transformation examples (4)

grain growth, bainite, solidification, eutectoid

Homogeneous nucleation

uniform throughout material, needs large driving force

Heterogeneous nucleation

occurs at special locations, needs small driving force

Critical radius

The radius above which free energy decreases and the nucleus grows

delta G_v

driving force, change in free energy per precipitate volume

delta G*

energy barrier, the maximum increase in energy before decreasing to the minimum G

N

nucleation rate

Embryos exist when T is ____ than T_N and r is ____ than r*

less, less

Nuclei exist when T is ____ than T_N and r is ____ than r*

greater, greater

The energy barrier for homogeneous nucleation is _______ than that of heterogeneous nucleation

greater

Diffuse surface

macroscopically flat, most metals, lower bonding energy, random growth of solid into liquid (continuous growth)

Flat surface

stepped/zig-zagged features, nonmetals, higher bonding energy, growth of solid into liquid at specific sites (lateral growth)

Solid growing into a superheated liquid

heat flow against interface velocity, planar interface

Solid growing into a supercooled liquid

heat flow with interface velocity, cellular/dendritic interface

Three cases of alloy solidification

equilibrium solidification; no diffusion in solid/perfect mixing in liquid; no diffusion in solid/diffusion mixing in liquid

Equilibrium solidification

assumes straight solidus and liquidus lines, infinitely slow cooling, compositions follow phase diagram

No diffusion in solid, perfect mixing in liquid

uniform liquid composition at any time, liquid composition follows liquid line, solid composition changes with position, average solid composition is lower than the solidus line

No diffusion in solid, diffusional mixing in liquid

liquid composition decreases from liquidus line to bulk concentration, system can reach steady state with stable solidification rate, coring in solid

Zones in ingot solidification

chill zone, columnar zone, central zone

Chill zone

rapid undercooling, heterogeneous nucleation at surface defects on mold wall, high nucleation rate

Columnar zone

crystals grow in direction of heat transfer, favors tertiary dendrites to form new primary arms

Occlusion in the chill zone leads to selective growth

True

Equiaxed zone

randomly oriented grains, cavity pipe is formed in narrow freezing ranges

Macrosegregation

composition changes over distance

Inverse segregation

solute-rich liquid flows back between dendrites to compensate for shrinkage

Microsegregation

composition changes on the scale of secondary dendrite arm spacing, mitigated by homogenization heat treatment

Segregation

non-uniform distribution of impurities and alloying elements, depends on chemical composition and rate of cooling

Seeded crystal growth

growth of a crystal with the same structure as the heterogeneous interface

Order of increasing weld speed (tap picture to see the entire thing)

a, b, c

L_s/T_m (delta S) is around ___ for diffuse surfaces and ___ for flat surfaces

R, 4R