1. July 17, 2008 A relation between compatibility and hysteresis and the search for new active materials Richard James University of Minnesota james@umn.edu Postdoc: Vijay Srivastava Graduate Students: Sakthivel Kasinathan, Xian Chen Supported by ARO-MURI

2. MURI on the Brink - Review July 17, 2008 Summary of Progress: 2007-8  Hired postdoc Vijay Srivastava, and graduate students Xian Chen and Sakthivel Kasinathan  A new theoretical understanding of the relation between compatibility and hysteresis  Application of these ideas to thermoelectrics, in collaboration with Jeff Snyder (poster: Xian Chen)  Joint work with Remi Dellville and Nick Schryvers (Antwerp) on observation of interfaces in materials with λ 2 = 1 (this talk and poster: Sakthivel Kasinathan)  Identification and initial results on promising systems to satisfy the cofactor conditions

3. MURI on the Brink - Review July 17, 2008 Plan of talk  Review of experimental data  Qualitative understanding of the role of λ 2 = 1  Quantitative theory  TEM observations of interfaces in alloys near λ 2 = 1 (Joint work with Remi Delville and Nick Schryvers (Antwerp))  Identification and initial results on promising systems in which to satisfy the cofactor conditions

4. MURI on the Brink - Review July 17, 2008 Rate independent hysteresis C. Chu

5. MURI on the Brink - Review July 17, 2008 Transformation matrix

6. MURI on the Brink - Review July 17, 2008 Free energy and energy wells Cu 69 Al 27.5 Ni 3.5  = 1.0619  = 0.9178  = 1.0230 minimizers... 1 U 1 U 2 RU 2 I 3 x 3 matrices 2 2 1

7. MURI on the Brink - Review July 17, 2008 Hysteresis vs. Jerry Zhang Triangles: combinatorial synthesis data of Cui, Chu, Famodu, Furuya, Hattrick- Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi

8. MURI on the Brink - Review July 17, 2008 Size of the hysteresis vs. the determinant of the transformation strain matrix No clear correlation; surprising Cui, Chu, Famodu, Furuya, Hattrick- Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi

9. MURI on the Brink - Review July 17, 2008 10  m austenite two variants of martensite, finely twinned The typical mode of transformation when : The mechanism of transformation: the passage of an austenite/martensite interface

10. MURI on the Brink - Review July 17, 2008 Step 1. The bands on the left

11. MURI on the Brink - Review July 17, 2008 Step 2. A minimizing sequence min n There are four normals to such austenite martensite interfaces. n There are two volume fractions of the twins. From analysis of this sequence (= the crystallographic theory of martensite),, given the twin system:

12. MURI on the Brink - Review July 17, 2008 Hypothesis Hysteresis in martensitic materials is associated with metastability. Transformation is delayed because the additional bulk and interfacial energy that must be present, merely because of co-existence of the two phases, has to be overcome by a further lowering of the well of the stable phase. Experimental test: tune the composition of the material to make

13. MURI on the Brink - Review July 17, 2008 austenite 2 martensite variants1 martensite variant

14. MURI on the Brink - Review July 17, 2008 Heating and cooling Ni 2 MnGa

15. MURI on the Brink - Review July 17, 2008 Suggestion: nucleation Zhang, Müller, rdj Possible picture of the “critical nucleus” in austenite Possible picture of the “critical nucleus” in martensite

16. MURI on the Brink - Review July 17, 2008 Exploratory calculations Zhang, Müller, rdj I A B φ cubic to orthorhombic as in the NiTiX alloys

17. MURI on the Brink - Review July 17, 2008 Minimize energy

18. MURI on the Brink - Review July 17, 2008 Gives a result like classical nucleation energy Introduce the criterion is a given constant. It depends on the material and “defect structure”. Solve for the width of the hysteresis H = 2(θ – θ c ):

19. MURI on the Brink - Review July 17, 2008 ? From the crystallographic theory width of the hysteresis H 1

20. MURI on the Brink - Review July 17, 2008 Remarks n λ 2 is the main parameter affecting hysteresis n Universality of the graph is due to: 1) relative insensitivity to the other parameters, 2) modest variation of the other physical parameters in these alloys, 3) same crystallography of these alloys (cubic to orthorhombic). n Briefly, sharp drop predicted for other alloys, but not the universal graph n Latent heat L in the denominator n Unexpectedly strong dependence of the energy of the transition layer on the twin system (2 orders of magnitude variation) n Г-convergence argument gives a universal problem for determining the transition layer energy (not presented)

21. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 39 Pd 11 Ti 50 Ni 25 Pd 25 Ti 50 Ni 30 Pd 20 Microstructure of Ti 50 Ni 50-x Pd x (with Remi Delville and Nick Schryvers)

22. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 27 Pd 25 λ 2 =1.007 Lattice invariant shear: (111) type I twins

23. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 30 Pd 20 λ 2 =1.006 Banded morphology Some martensite plates show a small twin ratio Some plates have no detectable twins but shows line contrast Twin relation between plates

24. MURI on the Brink - Review July 17, 2008 + [131] B2[121] B19 Inside some martensite plates no twin detected but retained austenite as fine parallel lines Ti 50 Ni 30 Pd 20 λ 2 =1.006

25. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 39 Pd 11 λ 2 =1.0006 Twinless martensite plates Needle of single variant

26. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 40 Pd 10 λ 2 ~ 1 θ c ~ RT Martensite same variant “Frozen” growth of martensite Austenite matrix

27. MURI on the Brink - Review July 17, 2008 Ti 50 Ni 40 Pd 10 Retained austenite λ 2 ~ 1 θ c ~ RT Martensite Single variant [011] B2 austenite [010] B19 martensite

28. MURI on the Brink - Review July 17, 2008 Viewing direction [011] B2 [010] B19 4° b a c b c a

29. MURI on the Brink - Review July 17, 2008 Austenite parent phase Martensite variant 1 Normal Habit Plane 2 numerical solutions in the cubic basis: n Austenite-single variant martensite habit plane [011] B2 [010] B2

30. MURI on the Brink - Review July 17, 2008 (7 -5 5) trace (7 5 -5) trace Comparison

31. MURI on the Brink - Review July 17, 2008 Calculation of the rotation matrix Q that rotates one lattice into the other

32. MURI on the Brink - Review July 17, 2008 rotation axis [011]B2 4° Comparison with observations

33. MURI on the Brink - Review July 17, 2008 Cofactor conditions and

34. MURI on the Brink - Review July 17, 2008 Promising systems and initial work

35. MURI on the Brink - Review July 17, 2008 Better calculation of the elastic energy in the transition layer Ignore branching… Put on the “B-layers”

36. MURI on the Brink - Review July 17, 2008 Gamma limit of the transition layer energy based on λ~0 Zhang, James, Müller + BC