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

July 17, 2008

A relation between compatibility and hysteresis and the search for

new active materialsRichard James

University of Minnesota

james@umn.edu

Postdoc: Vijay Srivastava

Graduate Students: Sakthivel Kasinathan, Xian Chen

Supported by ARO-MURI

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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

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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

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Rate independent hysteresisC. Chu

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Transformation matrix

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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

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Hysteresis vs. Jerry Zhang

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

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Size of the hysteresis vs. the determinant of the transformation strain matrix

Det(U)0.90 0.95 1.00 1.05 1.10 1.15 1.20

10

20

30

40

50

60

70

Hys

tere

sis

(oC

) No clear correlation;surprising

Cui, Chu, Famodu,Furuya, Hattrick-Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi

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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

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Step 1. The bands on the left

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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:

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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

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austenite2 martensite variants 1 martensite variant

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Heating and cooling Ni2MnGa

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Suggestion: nucleationZhang, Müller, rdj

Possible picture of the “critical nucleus” in austenite

Possible picture of the “critical nucleus” in martensite

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Exploratory calculationsZhang, Müller, rdj

I A B

φ

cubic to orthorhombic as in theNiTiX alloys

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Minimize energy

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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):

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?From the crystallographic theory

width of the hysteresis H

1

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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)

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12 12

Ti50Ni39Pd11Ti50Ni25Pd25 Ti50Ni30Pd20

Microstructure of Ti50Ni50-xPdx (with Remi Delville and Nick Schryvers)

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Ti50Ni27Pd25 λ2=1.007

Lattice invariant shear:(111) type I twins

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Ti50Ni30Pd20 λ2=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

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+

[131] B2 [121] B19

Inside some martensite plates no twin detected but retained

austenite as fine parallel lines

Ti50Ni30Pd20 λ2=1.006

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Ti50Ni39Pd11 λ2=1.0006

Twinless martensite plates Needle of single variant

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Ti50Ni40Pd10

λ2 ~ 1

θc ~ RT

Martensitesame variant

“Frozen” growth

of martensite

Austenitematrix

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Ti50Ni40Pd10

Retained austenite

λ2 ~ 1

θc ~ RT

MartensiteSingle variant

[011] B2 austenite

[010] B19 martensite

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Viewing direction[011] B2[010] B19

4°

b

a

c

b

c

a

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naIQU

1Austenite

parent phaseMartensitevariant 1

NormalHabit Plane

2 numericalsolutionsin the cubicbasis:

5

5

7

006.5

006.5

063.7

5

5

7

006.5

006.5

063.7

n

Austenite-single variant martensite habit plane

[011] B2

[010] B2

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(7 -5 5) trace

(7 5 -5) trace

Comparison

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

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rotation axis[011]B2

4°

Comparison with observations

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Cofactor conditions

and

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Promising systems and initial work

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Better calculation of the elastic energy in the transition layer

Ignore branching…

Put on the“B-layers”

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Gamma limit of the transition layer energybased on λ~0

Zhang, James, Müller

+ BC