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July 17, 2008
A relation between compatibility and hysteresis and the search for
new active materialsRichard James
University of Minnesota
Postdoc: Vijay Srivastava
Graduate Students: Sakthivel Kasinathan, Xian Chen
Supported by ARO-MURI
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
Rate independent hysteresisC. Chu
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MURI on the Brink - ReviewJuly 17, 2008
Transformation matrix
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
Hysteresis vs. Jerry Zhang
Triangles: combinatorialsynthesis data ofCui, Chu, Famodu,Furuya, Hattrick-Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
Step 1. The bands on the left
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
austenite2 martensite variants 1 martensite variant
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MURI on the Brink - ReviewJuly 17, 2008
Heating and cooling Ni2MnGa
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MURI on the Brink - ReviewJuly 17, 2008
Suggestion: nucleationZhang, Müller, rdj
Possible picture of the “critical nucleus” in austenite
Possible picture of the “critical nucleus” in martensite
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MURI on the Brink - ReviewJuly 17, 2008
Exploratory calculationsZhang, Müller, rdj
I A B
φ
cubic to orthorhombic as in theNiTiX alloys
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MURI on the Brink - ReviewJuly 17, 2008
Minimize energy
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
?From the crystallographic theory
width of the hysteresis H
1
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
12 12
Ti50Ni39Pd11Ti50Ni25Pd25 Ti50Ni30Pd20
Microstructure of Ti50Ni50-xPdx (with Remi Delville and Nick Schryvers)
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MURI on the Brink - ReviewJuly 17, 2008
Ti50Ni27Pd25 λ2=1.007
Lattice invariant shear:(111) type I twins
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
+
[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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MURI on the Brink - ReviewJuly 17, 2008
Ti50Ni39Pd11 λ2=1.0006
Twinless martensite plates Needle of single variant
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MURI on the Brink - ReviewJuly 17, 2008
Ti50Ni40Pd10
λ2 ~ 1
θc ~ RT
Martensitesame variant
“Frozen” growth
of martensite
Austenitematrix
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MURI on the Brink - ReviewJuly 17, 2008
Ti50Ni40Pd10
Retained austenite
λ2 ~ 1
θc ~ RT
MartensiteSingle variant
[011] B2 austenite
[010] B19 martensite
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MURI on the Brink - ReviewJuly 17, 2008
Viewing direction[011] B2[010] B19
4°
b
a
c
b
c
a
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MURI on the Brink - ReviewJuly 17, 2008
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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MURI on the Brink - ReviewJuly 17, 2008
(7 -5 5) trace
(7 5 -5) trace
Comparison
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MURI on the Brink - ReviewJuly 17, 2008
Calculation of the rotation matrix Q that rotates one lattice into the other
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MURI on the Brink - ReviewJuly 17, 2008
rotation axis[011]B2
4°
Comparison with observations
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MURI on the Brink - ReviewJuly 17, 2008
Cofactor conditions
and
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MURI on the Brink - ReviewJuly 17, 2008
Promising systems and initial work
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MURI on the Brink - ReviewJuly 17, 2008
Better calculation of the elastic energy in the transition layer
Ignore branching…
Put on the“B-layers”
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MURI on the Brink - ReviewJuly 17, 2008
Gamma limit of the transition layer energybased on λ~0
Zhang, James, Müller
+ BC