1. MT 610
Advanced Physical Metallurgy
Session : Phase Transformations
in Solids IV
Materials Technology
School of Energy and Materials

2. Contents
 Diffusional transformations
 Long-range diffusion
 Short-range diffusion
 Diffusionless transformations
 Martensitictransformation
 Geometric observation
 Mechanism
2

3. Shear transformation
 Exp. Martensite can be generated by shear on γ
 Both shears are possible
and identical to Bain
distortion if disregarded
the rigid body rotation. 3

4. Shear transformation
 Shear of cooperative movements of atoms can
be in different planes rather than (111)γ plane,
depending on alloy composition and
transformation temp.
 Shear does not have to act along the same
direction on every parallel atomic plane.
4

5. Shear transformation
 Greninger and Troiano (1949) found that
 Observed shear plane in Fe-22% Ni-0.8% C
was not the {111}γ plane and the shear angle
was 10.45°, not 19.5° as predicted by shear
mechanism.
 Theysuggested that another shear had to be
added in order to complete the mechanism.
5

6. Double shear transformation
 The first shear isa macroscopic shear
that contributes the shape change and
change in crystal structure.
 The second shear is a microscopic shear.
 Invariant plane
 Bain distortion has no invariant plane
 Lattice-invariant shear with Bain distortion
6

7. Invariant plane
 During the martensitic transformation
 The interface should be an invariant plane
 Undistorted and unrotated plane
 Any deformation on the invariant plane will
be termed an invariant plane strain.
7

8. From the Bain distortion
 α lattice with bcc can be generated from
an fcc γ lattice by
 Compression about 20% along
one principle axis and
a simultaneous uniform
expansion about 12% along
the other two axes perpendicular to
the first principle axis
8

9. Bain distortion of a sphere
 Due to the Bain distortion
 A unit sphere of the parent crystal
transforms into an oblate spheroid of the
product crystal
 Contraction about 20% along the one
principle axis
 Expansion about 12% along the other
two axes perpendicular to the first
principle axis
9

10. Bain distortion of a sphere
 Initial sphere equation of the parent crystal
x12 + x2 + x3 = 1
2 2
12% expansion 20% contraction
 Ellipsoid equation of the transformed crystal
(x )
' 2
1
+
(x )
' 2
2
+
(x )
' 2
3
=1
( 1.12 ) ( 1.12 ) ( 0.80 )
2 2 2
10

11. Bain distortion of a sphere
 Due to the lattice deformation x12 + x2 + x3 = 1
2 2
 Vectors OA’ and OB’
represent the final
position of vectors
 Vectors OA and OB
represent the initial
position of the same
vectors
 unchanged in
( x1 ) + ( x2 ) + ( x3 ) = 1
' 2 ' 2 ' 2
( 1.12 ) ( 1.12 ) ( 11 )
2 2 2
magnitude 0.80

12. Bain distortion of a sphere
 Vectors unchanged in magnitude during
the lattice deformation
 Corresponding to the
cones AOB and COD and
the cones A’OB’ and C’OD’
 These vectors are termed
unextended lines.
 A homogeneous strain would
result in an undistorted plane
of contact between the initial sphere of
austenite and the ellipsoid of martensite.
12

13. Bain distortion of a sphere
 Allother vectors not involved in the cones
A’OB’ and C’OD’ would be
changed in magnitude.
 Bain distortion would result
in no undistorted plane.
 Hence, there is no invariant plane.
 Very difficult to obtain a coherent planar
interface between the parent and the product
crystals only by the Bain distortion. 13

14. Bain distortion of a sphere
 Therefore,Bain distortion
has no invariant plane.
14

15. Lattice-invariant shear
 Lattice-invariant shear
must be of such
magnitude so as to produce
an undistorted plane
when combined with
the Bain distortion.
 Consider slip or twinning
 Must not make any
change in crystal structure.
15

16. Lattice-invariant shear
 Graphical analysis of a simple shear of
slip or twinning of a unit sphere
 Shear on an equatorial
plane K1 as the shear plane
 d as the shear direction
 α as shear angle Slip
16

17. Lattice-invariant shear
 As a result of shear on K1
 Any vector in the plane AK B is
2
transformed into a vector in
the plane AK’2B, which is
unchanged with length
although rotated relatively
to its original position.
 The plane AK B is the initial Slip
2
position of a plane AK’2B,
which remains undistorted as
a result of the shear. 17

18. Lattice-invariant shear
 As a result ofshear on K1
 The relative positions of
the planes AK2B and AK’2B
depend on the amount of
shear involved.
 The shear plane itself
remains undistorted
after shear. Slip
 Vectors that remain invariant in length
(unextended lines) to this shear operation
are define as potential habit planes. 18

19. Lattice-invariant shear
 As a result ofshear on K1
 The relative positions of
the planes AK2B and AK’2B
depend on the amount of
shear involved.
 The shear plane itself
remains undistorted
after shear. Slip
 Vectors that remain invariant in length
(unextended lines) to this shear operation
are define as potential habit planes. 19

20. Lattice-invariant shear
 When initial sphere → ellipsoid
by lattice deformation using
Bain distortion is distorted by
simple shear into another ellipsoid
+
and the lattice is left invariant,

 The simple shear is termed
a lattice-invariant shear.
shear
20

21. Stereographic projection
21

22. Stereographic representation
of the Bain distortion
 Any vector lying on the initial
cone AOB with a semiapex
of φ moves radially onto the
final cone A’OB’ with a
semiapex of φ’.
 Vectors in the cones of
unextended lines do not
change their length,
but only the angle ∆φ.
22

23. Stereographic representation
of the lattice-invariant shear
 An unextended line C
moves to the final position
along the circumference
of the great circle
defined by d*
(dash line).
23

24. Stereographic representation
of the lattice-invariant shear
 Vectors in K’2 plane do not
change their length due to
shear, and the line OC’ in
the plane represents the final
position of an unextended line.
 Line OC in K2 plane
represents the
initial position
of OC’.
24

25. Requirement for habit plane
 Both Bain distortion and lattice
invariant shear provide an undistorted
plane for the habit plane.
 Additional requirement is that the habit
plane be unrotated.
 A rigid body rotation must be able to
return the undistorted plane to its
original position before
transformation.
25

26. 3 important components
 Bain distortion
 Lattice invariant shear
 Rigid body rotation
26

27. Bain distortion with slip #1
 Vectors b and c are defined
by the intersections of the
initial Bain cone with K1 plane
 1.Apply a complementary shear
 Vectors b and c become b’ and c’ and still lie
in the K1 plane and remain unchanged in
both direction and magnitude.
 They are invariant lines.
27

28. Bain distortion with slip #1
 Vectors b and c are defined
by the intersections of the
initial Bain cone with K1 plane
 2.Apply a Bain distortion
 Vectors b’ and c’ become b’’ and c’’ lie on the
initial and final Bain cones, respectively,
without changing their magnitude.
28

29. Bain distortion with slip #1
 Complementary shear
b and c to b’ and c’
 Bain distortion
b’ and c’ to b’’ and c’’
 Angle btw b and c ≠ angle btw b” and c”
 Appropriate rotation cannot be applied to
return b” and c” to initial positions of b and c.
 Plane defined by b and c cannot be an invariant
plane. 29

30. Bain distortion with slip #2
 To obtainan invariant plane,
must have other extended lines
 Ifassumed to know
the shear angle α,
vectors a and d obtained from the intersections
of the K2 plane change to a’ and d’ along the
great circles.
 Bain distortion,
vectors a’ and d’ become a” and d”, respectively
30

31. Bain distortion with slip #2
 Through the transformation of
the complementary shear and
the Bain distortion
 Sequences of a→a’→a”
and sequences d→d’→d”
reveal no change in length
 However, angle btw a & d ≠ angle btw a” & d”
 Plane defined by a and d cannot be an invariant
plane. 31

32. Complete transformation
process
 Possible invariant planes will
depend on the choice of
combination of b or c
with a or d such as
 Vectors a and b
 Vectors a and c
 Vectors b and d
 Vectors c and d
32

33. Complete transformation
process
 If theinvariant plane is the
plane defined by vectors a & c
 Angle btw a & c = angle btw a’’ & c’’
 Let the axis required for rotation
be at point u
 Determine the amount of rotation
stereographically by intersection
of a great circle bisecting a-a”
with another great circle bisecting c-c” 33

34. Complete transformation
process
 Once a” and c” coincide simultaneously
with a and c, respectively
 Angle btw a & c = angle btw a’’ & c’’
 Therefore, orientation relationship btw γ plane
(defined by the vectors a and c) and α’ plane
(defined by the vectors a” and c”) can be
determined for a specific variant of the Bain
distortion (B), lattice invariant shear (P), and
rotation operation (R).
T = BPR
34

35. Complete transformation
process T = BPR
Bain distortion (B)
Lattice invariant shear (P)
Rotation operation (R)
35

36. Bain distortion with twinning
 Twinned martensite can take place by having
alternate regions in the parent phase undergo
the lattice deformation along different
contraction axes, which are initially at right
angles to each other.
 In the first region, contraction occurs along
the x3 [ 001] f axis.
 In the adjacent region, contraction direction
can be either x1 [100] f or x2 [ 010] f axis.
 Two rigid body rotations are also involved in
the twinning analysis. 36

37. Nucleation and growth
 It only takes about 10-5 to 10-7 seconds for a plate
of martensite to grow to its full size.
 The nucleation during the martensitic
transformation is extremely difficult to study
experimentally.
 Average number of martensite is as large as 104
nuclei/mm3
 Number of martensite nuclei can be
increased by increasing ∆T prior to Ms.
 It is too small in term of number of
nucleation sites for homogeneous nucleation.
37

38. Nucleation and growth
 Less likely to occur by homogeneous nucleation
process, but heterogeneous.
 Surfaces and grain boundaries are not
significantly contributing to nucleation.
 Most likely types of defect that could produce
the observed density of martensite nuclei are
dislocations (> 105 dislocation/mm2).
 C. Zener (1948): movement of partial dislocations
during twinning could generate a thin bcc region
of lattice from an fcc region.
38

39. Nucleation and growth
 Dissociation of a dislocation
into 2 partials is favorable
→ lower strain energy.
r r r
 To generate b1 = b2 + b3
bcc structure, a a a
[ 110] = [ 211] + 121
the requirements are that all 2 6 6 
green atoms move (shear)
a
forward by 12 [ 211] and an
additional dilatation
to correct lattice spacings. 39

40. Nucleation and growth
 Growth of lath martensite with dimension
a > b >> c growing on a {111}γ planes
 Thickening mechanism would involve the
nucleation and glide of transformation
dislocations moving on discrete ledges
behind the growing front.
 Due to large misfit between
bct and fcc lattice,
dislocations could be
self-nucleated at the
lath interface as the lath moves forward.
40

41. Nucleation and growth
 In medium and high carbon steels,
 Morphology of martensite turns to change
from a lath to a plate-like shape.
 As carbon concentration decreases,
 Decrease lath structure
 Decrease martensitic temperature
 Increase twinning
 Increase retained austenite
 Depending on compositions, the habit plane
changes from {111}γ → {225}γ → {259}γ
41

42. Effect of pressure to martensite
 As pressure increases
 In Fe unary system, the equilibrium
temperature decreases
 In Fe-C binary system, the phase region
around γ phase shifts to the left and
downward.
 Similar to adding austenite stabilizer
42

43. Effect of alloying element to
martensite
 Each alloying element will effect the martensitic
transformation differently.
 If initially Hγ = Hα
 When adding C
 The ē of C will decrease Hα and cause α to
be less stable.
 ∆H = Hγ – Hα > 0, stabilize the γ
 When adding X
 Increase Hα and ∆H < 0, stabilize the α
43

44. Effect of external stress to
martensite
 As martensite prefers to nucleate and grow
along the dislocation
 Expected that an externally applied shear
stress will assist and accelerate the
generation of dislocations and hence the
growth of martensite.
 An external shear stress can aid martensite
nucleation if the external elastic strain
components play as a part of the Bain strain.
 This can also help by raising the M
s
temperature. 44

45. Effect of external stress to
martensite
 Once the plastic deformation occurs
 There is an upper limit value of M that the
s
stress can be applied.
 The limit temp. of M is called M (highest
s d
temperature that stress helps to form
martensite)
 Too much plastic deformation will
suppress the transformation.
45

46. Effect of external stress to
martensite
 If a tensile
stress is applied
 M temperature can be suppressed to lower
s
temperature
 Transformation may be reversed from α’ →
γ
 Presence of large magnetic field may favor the
formation of the ferromagnetic phase and
therefore raise Ms temp.
46

47. Effect of external stress to
martensite
 Plastic deformation of γ before transformation
will assist on increasing number of nucleation
sites.
 Once the transformation occurs
 Result in very fine plate size of martensite
(Called the ausforming process)
 Combined effect of very fine martensite plates,
1
2
solution hardening of carbon, and 3dislocation
hardening
 Very high strength ausformed steel 47

48. Shape-memory alloys (SMA)
 Unique property of some alloys
 After being deformed at one temperature,
they recover the original undeformed shape
when heated to a higher temperature.
48

49. Shape-memory alloys (SMA)
 Unique property of some alloys
 After being deformed at one temperature,
they recover the original undeformed shape
when heated to a higher temperature.
 Fundamental to the shape-memory effect
(SME) is the occurrence of a martensitic phase
transformation and its subsequent reversal.
 Alloys: Ni-Ti (called NiTiNOL), Ni-Al, Fe-Pt,
Cu-Al-Ni, Cu-Au-Zn, Cu-Zn-(Al,Ga,Sn,Si),
Ni-Mn-Ga 49

50. SMA
 Common characteristics
 Atomicordering transformation from
ordered parent phase to ordered martensite
phase
 Thermoelastic martensitic transformation
that is crystallographic reversible
 Martensite
phase that forms in a self-
accommodating manner (slip or twinning)
50

51. SMA
 Typical plot of property changes versus temp.
 A hysteresis is usually on the order of 20°C
51

52. One-way SMA
 Sample is cooled from above Af to
below Mf → martensite forms
 Sample has no shape change
 Sample is deformed below Mf
 Sample remains deformed
until heated.
 Begin shape recovery at A and complete at A
s f
 No shape change when cooled below Mf
 Deforming the 52
martensite again will reactivate SME

53. Two-way SMA
 Sample is cooled from above Af to
below Mf → martensite forms
 Sample has no shape change
 Sample is deformed below Mf
 Sample remains deformed
until heated.
 Begin shape recovery at A and complete at A
s f
 Returnsto the deformed shape when cooled
below Mf 53