Crystallography H. K. D. H. Bhadeshia Introduction and point groups

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Presentation transcript:

Crystallography H. K. D. H. Bhadeshia Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships Martensitic transformations

Materials, transformation temperatures & strength

Olson and Hartman, 1982

Olson and Hartman, 1982

Olson and Hartman, 1982

Diffusionless transformation? Martensite can form at very low temperatures. Martensite can grow very rapidly. No composition change during transformation.

Shape of martensite ?

Irrational: why?

Orientation relationships: irrational

athermal transformation

Creation of a bi-crystal cut and rotate by angle q about axis normal to diagram q

Glissile interface

Glissile interface cannot contain more than one set of dislocations. Martensitic transformation only possible if the deformation which changes the parent into the product leaves one line undistorted and unrotated, i.e. an invariant-line. Deformation is an invariant-line strain.

50 mm

general invariant-plane strain d s 1 uniaxial dilatation simple shear general invariant-plane strain s=0.26 d=0.03

s d c r 1 Christian, 1957

body-centred cubic cubic close-packed

b a a b b a 3 3 2 1 2 1 (a) (b) BAIN STRAIN (c) (d) Body-centered tetragonal cubic martensite austenite

[001] b b' o [100] a' a b (a) o b' (b) a,a'

RB P P 1 2 (c) x w z y Martensite (wrong shape) Austenite (a) w x y z Observed shape, wrong structure P (b) w x z y 1 Twinned Martensite Twin Boundary Correct macroscopic shape, correct structure x w z y z Slipped Martensite LATTICE -INVARIANT DEFORMATION x w y

transformation twins (Wayman)

hexagonal close-packed cubic close-packed

P 1 Austenite (a) w x y z Observed shape, correct structure (b) w x z

Brooks, Loretto and Smallman, 1979

a + strain a Free Energy g a ag ga x x x Carbon Concentration