1. December 5, 2007 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. SC tour - Caltech December 5, 2007 A biaxial tension experiment C. Chu 1 mm

3. SC tour - Caltech December 5, 2007 A hysteresis loop C. Chu

4. SC tour - Caltech December 5, 2007 Main ideas in science on hysteresis in structural phase transformations Pinning of interfaces by defects System gets stuck in an energy well on its potential energy landscape

5. SC tour - Caltech December 5, 2007 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

6. SC tour - Caltech December 5, 2007 Transformation strain matrix

7. SC tour - Caltech December 5, 2007 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

8. SC tour - Caltech December 5, 2007 Step 1. The bands on the left

9. SC tour - Caltech December 5, 2007 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:

10. SC tour - Caltech December 5, 2007 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. SC tour - Caltech December 5, 2007 Tuning composition to make NiTiPt NiTiAu Jerry Zhang

12. SC tour - Caltech December 5, 2007 Data on one graph. Hysteresis = A s + A f – M s – M f Jerry Zhang

13. SC tour - Caltech December 5, 2007 Hysteresis vs. Jerry Zhang Triangles: combinatorial synthesis data of Cui, Chu, Famodu, Furuya, Hattrick- Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi

14. SC tour - Caltech December 5, 2007 Suggestion: nucleation Zhang, Müller, rdj Possible picture of the “critical nucleus” in austenite Possible picture of the “critical nucleus” in martensite

15. SC tour - Caltech December 5, 2007 Exploratory calculations Zhang, Müller, rdj I A B φ cubic to orthorhombic as in the NiTiX alloys

16. SC tour - Caltech December 5, 2007 Minimize energy

17. SC tour - Caltech December 5, 2007 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 ):

18. SC tour - Caltech December 5, 2007 ? width of the hysteresis H 1 From the crystallographic theory

19. SC tour - Caltech December 5, 2007

20. SC tour - Caltech December 5, 2007 Magnetoelectric materials n Systematic search in the former Soviet Union in the 1950s: replace the cation of ferroelectric perovskites by magnetic cations (Smolensky, Agranovskaya, Isupov, 1959) n Ni 3 B 7 O 13 I the “Rochelle Salt of magnetoelectrics” n Recent: BiMnO 3, YMnO 3, TbMnO 3 BiFeO 3 BiMnO 3, TbMnO 3, BiFeO 3 -SmFeO 3, BiScO 3,BiFeO 3, La 0.5 Ca 0.5 MnO 3, LuFe 2 O 4, La 0.25 Nd 0.25 Ca 0.5 MnO 3. Low Curie temperatures, weak ferromagnetism (or antiferromagnetic) or weak ferroelectricity. n Nice survey: N. Hill, “Density functional studies of multiferroic magnetoelectrics”, 2001 n Physics of BiMnO 3, YMnO 3 understood pretty well (Hill and Rabe, Phys. Rev. B59 (1999), 8759-8769 Density Functional Theory for magnetoelectrics

21. SC tour - Caltech December 5, 2007 Simplified explanation energy However, empty d-bands is what typically promotes ferroelectric distortion in perovskites. Hybridization between metal cation(d) and O(2p)

22. SC tour - Caltech December 5, 2007 Remarks Hill (2001): “Therefore, we should in fact never expect the co-existence of ferroelectricity and ferromagnetism.” Hill and Rabe: BiMnO 3, YMnO 3 accidents of “directional d 0 -ness” It is well-known in both ferromagnetism and ferroelectricity that magnetic and electric properties are extremely sensitive to the lattice parameters. n Exchange energy is extremely sensitive to lattice distances (Mn in Ni 2 MnGa, N 2 in rare earth magnets) n 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. SC tour - Caltech December 5, 2007 Example of this sensitivity: ferromagnetic shape memory materials: Ni 2 MnGa austenitemartensite Courtesy: T. Shield

24. SC tour - Caltech December 5, 2007 Example, continued, Ni 2 MnGa magnetization curves 0 10 20 30 40 50 60 M (emu/g) 200 400600 H (Oe) 0 10 20 30 40 50 60 M (emu/g) 3000 6000 9000 H (Oe) 12000 100 110 111 c-axisa-axis austenitemartensite

25. SC tour - Caltech December 5, 2007 Proposed approach: seek a reversible first order phase transformation between, e.g., ferroelectric and ferromagnetic phases n Rarity predicted by DFT circumvented n The volume fraction of ferroelectric vs. ferromagnetic phases could be changed E&M property Lattice parameter High -- low solubility for H 2 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. SC tour - Caltech December 5, 2007 A way to search for interesting new “smart materials” n Achieve “unlikely properties” by using a martensitic phase transformation and the lattice parameter sensitivity of many electromagnetic properties n Achieve reversibility by tuning lattice parameters to make the phases compatible

27. SC tour - Caltech December 5, 2007 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. SC tour - Caltech December 5, 2007 Pictures corresponding to

29. SC tour - Caltech December 5, 2007 The end