1. Microstructure-Properties: II Martensitic Transformations
27-302
Lecture 6
Fall, 2002
Prof. A. D. Rollett

2. Materials Tetrahedron
Processing
Performance
Microstructure
Properties

3. Objective
The objective of this lecture is to explain the basic features of martensitic transformations.
Martensitic transformations are the most important type of military transformations, i.e. transformations that do not require diffusion for the change in crystal structure to occur.
Why study martensitic transformations?! They occur in many different metal, ceramic & polymer systems, and are generally important to understand. Steels represent the classical example (and a rate case of a mechanically hard martensite). Also, there are remarkable devices that exploit the shape memory effect (a consequence of martensitic transformation) such as stents that open up once at body temperature. The martensites in this case are generally soft, mechanically speaking.

4. References
Phase transformations in metals and alloys, D.A. Porter, & K.E. Easterling, Chapman & Hall. Porter & Easterling concentrate on the geometrical and crystallographic characteristics of Fe-based martensites.
Materials Principles & Practice, Butterworth Heinemann, Edited by C. Newey & G. Weaver.
Otsuka, K. and C. M. Wayman (1998). Shape Memory Materials. Cambridge, England, Cambridge University Press. This book provides a very thorough description of the scientific and technological basis for the shape memory effect.

5. Notation
T0 := Eq. Temp. for 2 phases at same composition ∆T := undercooling ∆S := entropy of transformation ∆H := enthalpy of transformation ∆G := Gibbs free energy e := transformation strain g := Interface energy

6. Military Transformations
What is a martensitic transformation?
Most phase transformations studied in this course have been diffusional transformations where long range diffusion is required for the (nucleation and) growth of the new phase(s).
There is a whole other class of military transformations which are diffusionless transformations in which the atoms move only short distances in order to join the new phase (on the order of the interatomic spacing).
These transformations are also subject to the constraints of nucleation and growth. They are (almost invariably) associated with allotropic transformations.

7. Massive vs. Martensitic Transformations
There are two basic types of diffusionless transformations.
One is the massive transformation. In this type, a diffusionless transformation takes place without a definite orientation relationship. The interphase boundary (between parent and product phases) migrates so as to allow the new phase to grow. It is, however, a civilian transformation because the atoms move individually.
The other is the martensitic transformation. In this type, the change in phase involves a definite orientation relationship because the atoms have to move in a coordinated manner. There is always a change in shape which means that there is a strain associated with the transformation. The strain is a general one, meaning that all six (independent) coefficients can be different.

8. Classification of Transformations
Civilian
Military
Diffusion Required
Precipitation, Spinodal Decomposition ?
Diffusionless
Massive Transformations
Martensitic Transformations

9. Driving Forces
These transformations require larger driving forces than for diffusional transformations.
Why? In order for a transformation to occur without long range diffusion, it must take place without a change in composition.
This leads to the so-called T0 concept, which is the temperature at which the new phase can appear with a net decrease in free energy at the same composition as the parent (matrix) phase.
As the following diagram demonstrates, the temperature, T0, at which segregation-less transformation becomes possible (i.e. a decrease in free energy would occur), is always less than the solvus (liquidus) temperature.

10. Free Energy - Composition: T0
a, product T1
∆Gga
g, parent G
Common tangent
T1>T2
∆Gga T2
T2 corresponds to figure 6.3b in P&E.
Diffusionless transformation impossible at T1,
Diffusionless transformation possible at T2;
“T0” is defined by no difference in free energy between the phases, ∆G=0. X

11. Driving Force Estimation
The driving force for a martensitic transformation can be estimated in exactly the same way as for other transformations such as solidification.
Provided that an enthalpy (latent heat of transformation) is known for the transformation, the driving force can be estimated as proportional to the latent heat and the undercooling below T0. ∆Gga = ∆Hga ∆T/T0.
Thus P&E estimate the driving force at the temperature at which martensite formation starts in Eq. 6.1 using this relationship.

12. Phase relationships T near T0 equilibrium diffusionless
Note that the Ms line is horizontal in the TTT diagram; also, the Mf line.

13. Heterogeneous Nucleation
Why does martensite not form until well below the T0 temperature? The reason is that a finite driving force is required to supply the energy needed for (a) the interfacial energy of the nucleus and (b) the elastic energy associated with the transformation strain. The former is a small quantity (estimated at 0.02 J.m-2) but the elastic strain is large (estimated at 0.2 in the Fe-C system), see section for details. Therefore the following (standard) equation applies.
∆G* = 16πg3 / 3(∆GV - ∆GS)2
Why does martensite require heterogeneous nucleation? The reason is the large critical free energy for nucleation outlined above.

14. Microstructure of Martensite
The microstructural characteristics of martensite are: - the product (martensite) phase has a well defined crystallographic relationship with the parent (matrix). - martensite forms as platelets within grains. - each platelet is accompanied by a shape change - the shape change appears to be a simple shear parallel to a habit plane (the common, coherent plane between the phases) and a uniaxial expansion (dilatation) normal to the habit plane. The habit plane in plain-carbon steels is close to (225), for example (see P&E fig. 6.11). - successive sets of platelets form, each generation forming between pairs of the previous set. - the transformation rarely goes to completion.

15. Microstructures
Martensite formation rarely goes to completion because of the strain associated with the product that leads to back stresses in the parent phase.

16. Self-accommodation by variants
A typical feature of martensitic transformations is that each colony of martensite laths/plates consists of a stack in which different variants alternate. This allows large shears to be accommodated with minimal macroscopic shear.

17. Mechanisms
The mechanisms of military transformations are not entirely clear. The small length scales mean that the reactions propagate at high rates - close to the speed of sound. The high rates are possible because of the absence of long range atomic movement (via diffusion).
Possible mechanisms for martensitic transformations include (a) dislocation based (b) shear based
Martensitic transformations strongly constrained by crystallography of the parent and product phases.
This is analogous to slip (dislocation glide) and twinning, especially the latter.

18. Atomic model - the Bain Model
For the case of fcc Fe transforming to bct ferrite (Fe-C martensite), there is a basic model known as the Bain model.
The essential point of the Bain model is that it accounts for the structural transformation with a minimum of atomic motion.
Start with two fcc unit cells: contract by 20% in the z direction, and expand by 12% along the x and y directions.

19. Bain model
Orientation relationships in the Bain model are: (111)g <=> (011)a’ [101]g <=> [111]a’ [110]g <=> [100]a’ [112]g <=> [011]a’

20. Crystallography, contd.
Although the Bain model explains several basic aspects of martensite formation, additional features must be added for complete explanations (not discussed here).
The missing component of the transformation strain is an additional shear that changes the character of the strain so that an invariant plane exists. This is explained in fig. 6.8.

21. Role of Dislocations
Dislocations play an important, albeit hard to define role in martensitic transformations.
Dislocations in the parent phase (austenite) clearly provide sites for heterogeneous nucleation.
Dislocation mechanisms are thought to be important for propagation/growth of martensite platelets or laths. Unfortunately, the transformation strain (and invariant plane) does not correspond to simple lattice dislocations in the fcc phase. Instead, more complex models of interfacial dislocations are required.

22. Why tetragonal Fe-C martensite?
At this point, it is worth stopping to ask why a tetragonal martensite forms in iron. The answer has to do with the preferred site for carbon as an interstitial impurity in bcc Fe.
Remember: Fe-C martensites are unusual for being so strong (& brittle). Most martensites are not significantly stronger than their parent phases.
Interstitial sites: fcc: octahedral sites radius= nm tetrahedral sites radius= nm bcc: octahedral sites radius= nm tetrahedral sites radius= nm
Carbon atom radius = 0.08 nm.
Surprisingly, it occupies the octahedral site in the bcc Fe structure, despite the smaller size of this site (compared to the tetrahedral sites) presumably because of the low modulus in the <100> directions.

23. Interstitial sites for C in Fe
fcc: carbon occupies the
octahedral sites bcc: carbon occupies the octahedral sites
[Leslie]

24. Carbon in ferrite
One consequence of the occupation of the octahedral site in ferrite is that the carbon atom has only two nearest neighbors.
Each carbon atom therefore distorts the iron lattice in its vicinity.
The distortion is a tetragonal distortion.
If all the carbon atoms occupy the same type of site then the entire lattice becomes tetragonal, as in the martensitic structure.
Switching of the carbon atom between adjacent sites leads to strong internal friction peaks at characteristic temperatures and frequencies.
[P&E]

25. Shape Memory Effect (SME)
General phenomenon associated with martensitic transformations.
Characteristic feature = strain induced martensite (SIM), capable of thermal reversion.
Ferroelasticity and Superelasticity also possible.
Md,Af,As,Ad,Ms,Mf temperatures.
[Shape Memory Materials]

26. Temperatures Md T0 Ad Mf Af As Ms
The Md and Ad temperatures bracket T0 because they define the on-cooling and on-heating temperatures at which the transformation is possible with allowance for the effect of strain energy.

27. SME Definitions Md: SIM possible below Md.
Af: reversion of SIM complete above Af (heating).
As: reversion of SIM starts above As (heating).
Ad: formation of parent phase possible above Ad.
Ms: martensite start temperature (cooling).
Mf: martensite finish temperature (cooling).

28. SME, contd. Classic alloy = Nitinol = NiTi
alloying for control of Ms.
Stress for SIM must be less than yield stress for plastic deformation.
SME depends on incomplete transformation and elastic back stresses to provide memory (>MS).
SME more effective in single xtals.
Alloying permits variations in the equilibrium transformation temperature, for example (critical for bio applications, for example). Also variations in the maximum strain that can be recovered are possible.

29. Super-elasticity
Super-elasticity is simply reversible (therefore “elastic”) deformation over very large strain ranges (many %).
Example: Ti-50.2%Ni.
[Shape Memory Materials]

30. Role of Ordering
A key feature of the Ni-Ti alloys for shape memory applications is that their compositions are all in the vicinity of 50Ni-50Ti and that the high temperature phase is an ordered B2 structure. The low temperature B19’ monoclinic structure is therefore also ordered (as is the other, intermediate R phase which is trigonal).
The ordered structure (recall the discussion of ordered particle strengthening) means that there is an appreciable resistance to dislocation motion. This is critical for favoring strain accommodation via transformation and twinning as opposed to dislocation glide.

31. Self-accommodation
Micrograph with diagram shows how different variants of a given martensitic phase form so as to minimize macroscopic shear strains in a given region.

32. Shape Memory Effect
Demonstration of shape memory effect (SME) in a spring
Mechanism of SME: 1) transformation; 2) martensite, self-accommodated; 3) deformation by variant growth; 4) heating causes re-growth of parent phase in original orientation

33. Surface Relief
Micrographs show a sequence of temperatures with surface relief from the martensite plates.

34. Stress versus Temperature
The stress applied to the material must be less than the critical resolved shear stress for dislocation motion, because the latter is not recoverable; SME= Shape Memory Effect; SE = Superelasticity
d/dT = ∆S/ = ∆H/(Te
Critical Stress for Martensite Formation As Mf
Stress
SME SE
Critical Stress for Slip
Temperature Ms Af

35. Ni-Ti Alloys X Ms Mf As Af V > 25 < -140 < -64 Cr -100
[Wasilewski, SME in Alloys, p245] X Ms Mf As Af V
> 25
< -140
< -64 Cr
-100
< -180
< -58 Mn
-116
< -63
> 10 Fe
No information
-30 Co Cu
< -100 ?
TiNi0.95 70 60
108
113
TiNi 52 71 77
Ti0.95Ni
-50
20 (?)

36. SME Requirements
For achieving a strong or technologically useful SME, the following characteristics are required.
High resistance to dislocation slip (to avoid irreversible deformation).
Easy twin motion in the martensitic state so that variants can exchange volume at low stresses.
Crystallographically reversible transformation from product phase back to parent phase. Ordered structures have this property (whereas for a disordered parent phase, e.g. most Fe-alloys, multiple routes back to the parent structure exist.)

37. Photo-stimulated SME!

38. Summary
Martensitic transformations are characterized by a diffusionless change in crystal structure.
The lack of change in composition means that larger driving forces and undercoolings are required in order for this type of transformation to occur.
The temperature below which a diffusionless transformation is possible is known as “T0”.
Martensitic transformations invariably result in significant strains with well defined (if irrational, in terms of Miller indices) crystallography.
Technological applications abound - quenched and tempered steels, Nitinol shape memory alloys etc.