Richard James Department of Aerospace Engineering and Mechanics University of Minnesota

1. A relation between compatibility and hysteresis and its role in the search for new smart materials Richard James Department of Aerospace Engineering and Mechanics University of Minnesota james@umn.edu Joint work with S. Müller, J. Zhang Thanks: John Ball, Kaushik Bhattacharya, Chunhwa Chu, Jun Cui, Chris Palmstrom, Eckhard Quandt, Karin Rabe, Tom Shield, Ichiro Takeuchi, Manfred Wuttig

2. A biaxial tension experiment C. Chu 1 mm

3. A hysteresis loop C. Chu

4. Main ideas in science on hysteresis in structural phase transformations System gets stuck in an energy well on its potential energy landscape Pinning of interfaces by defects

5. 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

6. Transformation strain matrix

7. 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

8. Step 1. The bands on the left

9. 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.

10. 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 of this idea: tune the composition of the material to make

11. Tuning composition to make NiTiPt NiTiAu Jerry Zhang

12. Data on one graph. Hysteresis = As + Af – Ms – Mf Jerry Zhang

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

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

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

16. Minimize energy

17. 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

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

20. Magnetoelectric materials • Systematic search in the former Soviet Union in the 1950s: replace the cation of ferroelectric perovskites by magnetic cations (Smolensky, Agranovskaya, Isupov, 1959) • Ni3B7O13I the “Rochelle Salt of magnetoelectrics” • Recent: BiMnO3, YMnO3, TbMnO3BiFeO3 BiMnO3, TbMnO3, BiFeO3-SmFeO3, BiScO3,BiFeO3, La0.5Ca0.5MnO3, LuFe2O4, La0.25Nd0.25Ca0.5MnO3. Low Curie temperatures, weak ferromagnetism (or antiferromagnetic) or weak ferroelectricity. • Nice survey: N. Hill, “Density functional studies of multiferroic magnetoelectrics”, 2001 • Physics of BiMnO3, YMnO3 understood pretty well (Hill and Rabe, Phys. Rev. B59 (1999), 8759-8769 Density Functional Theory for magnetoelectrics

21. Simplified explanation energy However, empty d-bands is what typically promotes ferroelectric distortion in perovskites. Hybridization between metal cation(d) and O(2p)

22. Remarks Hill (2001): “Therefore, we should in fact never expect the co-existence of ferroelectricity and ferromagnetism.” Hill and Rabe: BiMnO3, YMnO3 accidents of “directional d0-ness” It is well-known in both ferromagnetism and ferroelectricity that magnetic and electric properties are extremely sensitive to the lattice parameters. • Exchange energy is extremely sensitive to lattice distances (Mn in Ni2MnGa, N2 in rare earth magnets) • R. E. Cohen (2001): “Properties of ferroelectrics are extremely sensitive to volume (pressure), which can cause problems since small errors in volume…can result in large errors in computed ferroelectric properties.”

23. Example of this sensitivity: ferromagnetic shape memory materials: Ni2MnGa austenite martensite Courtesy: T. Shield

24. 100 110 111 60 60 50 50 40 40 M (emu/g) M (emu/g) 30 30 20 20 10 10 0 0 400 600 200 6000 3000 9000 12000 H (Oe) H (Oe) Example, continued, Ni2MnGa magnetization curves austenite martensite c-axis a-axis

25. E&M property Lattice parameter Proposed approach: seek a reversible first order phase transformation between, e.g., ferroelectric and ferromagnetic phases • Rarity predicted by DFT circumvented • The volume fraction of ferroelectric vs. ferromagnetic phases could be changed • High -- low solubility for H2 • High band gap -- low band gap semiconductor • Conductor -- insulator (electrical or thermal) • Opaque -- transparent (at various wavelengths) • High -- low index of refraction (…also nonlinear optical properties) • Luminescent -- nonluminescent • Ferroelectric/magnetic – nonferroelectric/magnetic Other lattice parameter sensitive pairs of properties

26. A way to search for interesting new “smart materials” • Achieve “unlikely properties” by using a martensitic phase transformation and the lattice parameter sensitivity of many electromagnetic properties • Achieve reversibility by tuning lattice parameters to make the phases compatible

27. Other “accidental relations”among lattice parameters Theorem. Suppose in addition to , we have, for a “twin system” a,n Then, there are infinitely many austenite/martensite interfaces, with any volume fraction between 0 and 1. “cofactor conditions”

28. Pictures corresponding to

29. The end