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

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Page 1: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Introduction and point groups

Stereographic projections

Low symmetry systems

Space groups

Deformation and texture

Interfaces, orientation relationships

Martensitic transformations

Crystallography

H. K. D. H. Bhadeshia

Page 2: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Materials, transformation temperatures &

strength

Page 3: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Martensite can form at very low temperatures.

Martensite can grow very rapidly.

No composition change during transformation.

Diffusionless transformation?

Page 4: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Shape of martensite

Page 5: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 6: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Irrational: why?

Page 7: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

[111]

[011]

[111]

[101]

α

α

γ

γ

(011) || (111)γ α

-Kurdjumov Sachs

[111]

[011]

[111] [101]

α

α

γ

γ

(011) || (111)γ α

-Nishiyama Wasserman

[110] γ [110] γ

<001><011><001>

ααγ

Page 8: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Orientation relationships: irrational

Page 9: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Creation of a bi-crystal

cut and rotate by angle about axis normal to diagram

Page 10: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

d

θ

θd

b

Page 11: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Glissile interface

Page 12: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 13: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

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.

Page 14: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 15: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 16: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

50 m

Page 17: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

s

1

s

1

1

uniaxial dilatation

simple shear

general invariant-plane

strain

s=0.26

=0.03

Page 18: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 19: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

c

r

s

1

Christian, 1957

Page 20: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 21: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

body-centred cubic

cubic close-packed

Page 22: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

(a)

BAIN STRAIN

(c) Body-centered tetragonal austenite

(d) Body-centered

cubic martensite

a

a

a1

2

3 b3

b1 b2

(b)

Page 23: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

[100]

[001]

o

aa'

b

b'

o b'

b

a,a'

(a)

(b)

Page 24: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 25: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Austenite

(a)

w

x

y

z

Twinned Martensite

Twin Boundary

Correct macroscopic shape, correct structure

x

w z

y

z

Slipped Martensite

LATTICE -INVARIANT DEFORMATION

x

w

y

Observed shape, wrong structure

P

(b)

w

x

z

y

1

RB

(c)

x

w z

y

P2 Martensite (wrong shape)

Page 26: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 27: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

transformation twins (Wayman)

Page 28: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 29: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Two non-coplanar invariant-plane strains

q

p

d

e

Page 30: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

The Bain Strain

(F B F)

where F is an orthonormal basis parallel to the unit cell of austenite

Page 31: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

Assume that the lattice invariant deformation is on the system

Page 32: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

u deformed to x by (F B F)

Page 33: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 34: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 35: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

lattice invariant deformation is

Page 36: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

h deformed to l by (F B F)

Page 37: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 38: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships
Page 39: Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships

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