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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 [email protected] Joint work with S. M üller, J. Zhang - PowerPoint PPT Presentation
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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
December 5, 2007 SC tour - Caltech
A hysteresis loopC. Chu
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
Transformation strain matrix
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
Step 1. The bands on the left
December 5, 2007 SC tour - Caltech
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:
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
Data on one graph. Hysteresis = As + Af – Ms – Mf
Jerry Zhang
December 5, 2007 SC tour - Caltech
Hysteresis vs. Jerry Zhang
Triangles: combinatorialsynthesis data ofCui, Chu, Famodu,Furuya, Hattrick-Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang, Takeuchi
December 5, 2007 SC tour - Caltech
Suggestion: nucleationZhang, Müller, rdj
Possible picture of the “critical nucleus” in austenite
Possible picture of the “critical nucleus” in martensite
December 5, 2007 SC tour - Caltech
Exploratory calculationsZhang, Müller, rdj
I A B
φ
cubic to orthorhombic as in theNiTiX alloys
December 5, 2007 SC tour - Caltech
Minimize energy
December 5, 2007 SC tour - Caltech
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):
December 5, 2007 SC tour - Caltech
?
width of the hysteresis H
1
From the crystallographic theory
December 5, 2007 SC tour - Caltech
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
Simplified explanation
energy
However, empty d-bands is what typically promotes ferroelectric distortion in perovskites. Hybridization between metal cation(d) and O(2p)
December 5, 2007 SC tour - Caltech
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.”
December 5, 2007 SC tour - Caltech
Example of this sensitivity: ferromagnetic shape memory materials: Ni2MnGa
austenite martensite
Courtesy:T. Shield
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
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”
December 5, 2007 SC tour - Caltech
Pictures corresponding to
December 5, 2007 SC tour - Caltech
The end