Metallurgy and solid-state transformations study guide

H. K. D. H. Bhadeshia

This study guide provides a comprehensive review of solid-state transformations, focusing on twinning mechanisms and martensitic transformations in metals and alloys.

Part 1: Short-answer quiz

A pair of grains is twinned when the atomic arrangement of one grain can be generated from the other by reflection across a common plane. While the orientations differ in space, their underlying crystal structures remain identical.

Mechanical twin shape is governed by the minimisation of long-range elastic strain energy (lenticular shape). Annealing twins are shaped by the minimisation of interfacial energy (faceted shape with flat ends).

The standard ...ABCABC... sequence becomes a mirror reflection, ...ABCABACBA..., where the central "B" layer is the low-energy interface.

This suggests annealing twins form during recrystallisation due to random errors in the stacking of {111} planes, favoured by high grain boundary velocity or low stacking fault energy.

The system is {111}⟨112⟩. Displacement occurs by a/6⟨112⟩, resulting in a twinning shear (s) of 1/2.

Mechanical twinning proceeds at the speed of sound, creating acoustic emissions.

Preferred when few slip systems are available or during high strain rates.

Compression along the z-axis and uniform expansion along x and y axes to convert c.c.p. to b.c.c..

Reconstructive requires diffusion; displacive (martensitic) involves coordinated, diffusionless atom movement.

Achieved by martensite variants growing under stress; lost via defects from cycling or irreversible strain.

Part 2: essay questions

Instructions: Click each prompt to reveal writing hints and key technical points.

Key Points to Include:
  • Describe the lenticular morphology of mechanical twins vs. faceted annealing twins.
  • Discuss dislocation density differences: recrystallised grains are "clean" compared to deformed regions.
  • Explain why strain field contrast is absent at annealing twin tips but present in mechanical twins.
Key Points to Include:
  • Define the "growth-accident hypothesis".
  • Incorporate the mathematical relationship: ρ=(b/d)log(d/d0).
  • Address the anomaly of high stacking fault energy metals like Nickel.
Key Points to Include:
  • Detail the z-axis compression and x/y expansion of the Bain strain.
  • Explain how transformation twinning accommodates the macro-scale shape change.
  • Compare c.c.p. to h.c.p. (coordinated shear) vs. c.c.p. to b.c.c. transformations.
Key Points to Include:
  • Discuss the role of {111} planes as the coherent, low-energy boundary.
  • Define the "invariant plane" concept as a plane unaffected by deformation.
  • Relate faceted appearance to interfacial energy minimisation.
Key Points to Include:
  • Contrast deformed matrix contrast with uniform recrystallised grain contrast in TEM.
  • Reference specific steel grades like "302AA" and "NF709".
  • Explain the sequence: cold-rolling → heating → grain nucleation → growth accidents.

Part 3: Glossary of terms

Annealing Twin
A twin formed during the recrystallisation of a deformed metal, characterised by a faceted shape and a growth mechanism that minimises interfacial energy.
Bain Strain
The specific deformation—consisting of compression along one axis and expansion along the others—required to convert a c.c.p. lattice into a b.c.c. lattice.
Cubic Close-Packed (c.c.p.)
A crystal structure with an ABCABC stacking sequence of {111} planes; commonly found in metals like copper, nickel, and austenite.
Displacive Transformation
A diffusionless transformation involving the coordinated motion of atoms, where the parent structure is deformed into the product phase.
Invariant Plane
A specific plane within a crystal structure that remains unaffected by the deformation or shear during twinning or martensitic transformation.
Lenticular
Lens-shaped with sharp edges; the characteristic morphology of mechanical twins aimed at minimising long-range elastic strains.
Martensitic Transformation
A diffusionless, displacive transformation where the change in crystal structure is achieved through a coordinated shear of the parent phase.
Mechanical Twinning
A deformation process involving the coordinated movement of atoms to reorient a portion of a crystal into a mirror orientation, typically in response to stress.
Recrystallisation
The process by which deformed grains are replaced by a new set of defect-free grains that nucleate and grow until the original structure is consumed.
Stacking Fault Energy
The energy associated with an interruption in the normal stacking sequence of crystal planes; lower energy generally favours the formation of twins and stacking faults.
Twinning Shear
The ratio of the atomic displacement distance on close-packed planes to the spacing between those planes ( 1/2 for c.c.p. systems).