Microsoft PowerPoint - SC_tour_Caltech_07.pptDecember 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
[email protected]
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
December 5, 2007 SC tour - Caltech
A biaxial tension experiment
A hysteresis loop C. Chu
December 5, 2007 SC tour - Caltech
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
December 5, 2007 SC tour - Caltech
Free energy and energy wells
Cu69 Al27.5 Ni3.5
minimizers...
1
2 1
Transformation strain matrix
10 µm
twinned
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 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
20
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Au at. %
H ys
te re
si s(
o C )
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NiTiPt NiTiAu
Jerry Zhang
Data on one graph. Hysteresis = As + Af – Ms – Mf
Jerry Zhang
Hysteresis vs. Jerry Zhang
Triangles: combinatorial synthesis data of Cui, Chu, Famodu,
Furuya, Hattrick- Simpers, James, Ludwig, Theinhaus, Wuttig, Zhang,
Takeuchi
December 5, 2007 SC tour - Caltech
Suggestion: nucleation Zhang, 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 calculations Zhang, Müller, rdj
I A B
December 5, 2007 SC tour - Caltech
Minimize energy
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
?
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
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
Example, continued, Ni2MnGa magnetization curves
0
10
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60
M (
0
10
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M (
12000
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
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
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”
Pictures corresponding to
The end
