A relation between compatibility and hysteresis and the search for new active materials

1. 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. 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 λ2 = 1 (this talk and poster: Sakthivel Kasinathan) • Identification and initial results on promising systems to satisfy the cofactor conditions

3. Plan of talk • Review of experimental data • Qualitative understanding of the role of λ2 = 1 • Quantitative theory • TEM observations of interfaces in alloys near λ2 = 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. Rate independent hysteresis C. Chu

5. Transformation matrix

6. U 3 x 3 matrices 1 2 1 2 1 I U 2 RU 2 Free energy and energy wells minimizers... Cu69 Al27.5 Ni3.5  = 1.0619  = 0.9178  = 1.0230

7. Hysteresis vs. Jerry Zhang Triangles: combinatorial synthesis data of Cui, Chu, Famodu, Furuya, Hattrick- Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi

8. 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. The mechanism of transformation: the passage of an austenite/martensite interface The typical mode of transformation when : austenite 10 m two variants of martensite, finely twinned

10. Step 1. The bands on the left

11. Step 2. A minimizing sequence min From analysis of this sequence (= the crystallographic theory of martensite), , given the twin system: • There are four normals to such austenite martensite interfaces. • There are two volume fractions of the twins.

12. 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. austenite 1 martensite variant 2 martensite variants

14. Heating and cooling Ni2MnGa

15. Possible picture of the “critical nucleus” in austenite Possible picture of the “critical nucleus” in martensite Suggestion: nucleation Zhang, Müller, rdj

16. φ I A B cubic to orthorhombic as in the NiTiX alloys Exploratory calculations Zhang, Müller, rdj

17. Minimize energy

18. energy is a given constant. It depends on the material and “defect structure”. Solve for the width of the hysteresisH = 2(θ – θc): Gives a result like classical nucleation Introduce the criterion

19. width of the hysteresis H 1 ? From the crystallographic theory

20. Remarks • λ2 is the main parameter affecting hysteresis • 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). • Briefly, sharp drop predicted for other alloys, but not the universal graph • Latent heat L in the denominator • Unexpectedly strong dependence of the energy of the transition layer on the twin system (2 orders of magnitude variation) • Г-convergence argument gives a universal problem for determining the transition layer energy (not presented)

21. Microstructure of Ti50Ni50-xPdx (with Remi Delville and Nick Schryvers) Ti50Ni30Pd20 Ti50Ni25Pd25 Ti50Ni39Pd11

22. Ti50Ni27Pd25λ2=1.007 Lattice invariant shear: (111) type I twins

23. Ti50Ni30Pd20λ2=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. Ti50Ni30Pd20λ2=1.006 + Inside some martensite plates no twin detected but retained austenite as fine parallel lines [131] B2 [121] B19

25. Ti50Ni39Pd11 λ2=1.0006 Needle of single variant Twinless martensite plates

26. Ti50Ni40Pd10 λ2 ~ 1 θc ~ RT “Frozen” growth of martensite Martensite same variant Austenite matrix

27. Ti50Ni40Pd10 λ2 ~ 1 θc ~ RT Martensite Single variant [010] B19 martensite Retained austenite [011] B2 austenite

28. a a 4° c b c b Viewing direction [011] B2 [010] B19

29. Austenite-single variant martensite habit plane [011] B2 Normal Habit Plane Martensite variant 1 Austenite parent phase 2 numerical solutions in the cubic basis: n [010] B2

30. Comparison (7 -5 5) trace (7 5 -5) trace

31. Calculation of the rotation matrix Q that rotates one lattice into the other

32. Comparison with observations rotation axis [011]B2 4°

33. Cofactor conditions and

34. Promising systems and initial work

35. Put on the “B-layers” Better calculation of the elastic energy in the transition layer Ignore branching…

36. Gamma limit of the transition layer energybased on λ~0 Zhang, James, Müller + BC