Richard James Department of Aerospace Engineering and Mechanics University of Minnesota

December 5, 2007

A relation between compatibility and hysteresis and its role in the search for new smart materials

Richard JamesDepartment of Aerospace Engineering and Mechanics

University of [email protected]

Joint work with S. Müller, J. ZhangThanks: John Ball, Kaushik Bhattacharya, Chunhwa Chu, Jun Cui, Chris Palmstrom,

Eckhard Quandt, Karin Rabe, Tom Shield, Ichiro Takeuchi, Manfred Wuttig

December 5, 2007 SC tour - Caltech

A biaxial tension experiment

C. Chu

1 mm


A hysteresis loopC. Chu


Main ideas in science on hysteresis in structural phase transformations

Pinning of interfaces by defectsSystem gets stuck in an energy

well on its potential energy landscape


Free energy and energy wells

Cu69

Al27.5

Ni3.5

= 1.0619 = 0.9178 = 1.0230

minimizers...

1

U1 U2

RU2

I

3 x 3 matrices 2

2

1


Transformation strain matrix


10 m

austenite

two variants ofmartensite, finely

twinned

The typical mode of transformation when :

The mechanism of transformation: the passage of an austenite/martensite interface


Step 1. The bands on the left


Step 2. A minimizing sequence

min

There are four normals to such austenite martensite interfaces. There are two volume fractions of the twins.

From analysis of this sequence (= the crystallographic theory of martensite), , given the twin system:


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


Tuning composition to make

Pt at. %

Hys

tere

sis(

o C)

0 5 10 1510

20

30

40

50

60

70

80

90

100

A f - M f

A s + A f - M s - M f

Au at. %

Hys

tere

sis(

oC

)

0 5 10 15 200

10

20

30

40

50

60

70

80

90

100

A f - M f

A s + A f - M s - M f

NiTiPt NiTiAu

Jerry Zhang


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

Jerry Zhang


Hysteresis vs. Jerry Zhang

Triangles: combinatorialsynthesis data ofCui, Chu, Famodu,Furuya, Hattrick-Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi


Suggestion: nucleationZhang, Müller, rdj

Possible picture of the “critical nucleus” in austenite

Possible picture of the “critical nucleus” in martensite


Exploratory calculationsZhang, Müller, rdj

I A B

φ

cubic to orthorhombic as in theNiTiX alloys


Minimize energy


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 – θc):


?

width of the hysteresis H

1

From the crystallographic theory



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, TbMnO3 BiFeO3 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


Simplified explanation

energy

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


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.”


Example of this sensitivity: ferromagnetic shape memory materials: Ni2MnGa

austenite martensite

Courtesy:T. Shield


Example, continued, Ni2MnGa magnetization curves

0

10

20

30

40

50

60

M (

emu/

g)

200 400 600H (Oe)

0

10

20

30

40

50

60

M (

emu/

g)

3000 6000 9000H (Oe)

12000

100110111

c-axis a-axis

austenite martensite


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

E&M property

Lattice parameter

High -- low solubility for H2

High band gap -- low band gap semiconductorConductor -- insulator (electrical or thermal)Opaque -- transparent (at various wavelengths)High -- low index of refraction (…also nonlinear optical properties)Luminescent -- nonluminescentFerroelectric/magnetic – nonferroelectric/magnetic

Other lattice parametersensitive pairs of properties


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


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”


Pictures corresponding to


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Richard James Department of Aerospace Engineering and Mechanics University of Minnesota