Microsoft PowerPoint - MIS_Aziz_08.PPTRichard James University of Minnesota
Thanks: John Ball, Kaushik Bhattacharya, Jun Cui, Traian Dumitrica, Stefan Müller, Ichiro Takeuchi, Rob Tickle, Manfred Wuttig, Jerry Zhang
March 28, 2008 UMD
Ni30.5 Ti49.5 Cu20.0
Cu69 Al27.5 Ni3.5
minimizers...
1
2 1
From analysis of this sequence (= the crystallographic theory of martensite), :
m
March 28, 2008 UMD
H (010)
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Ferromagnetic shape memory materials
Main themes 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
March 28, 2008 UMD
twinned
A rather different hypothesis on the origins of hysteresis
What if we tune the composition of the material to make
March 28, 2008 UMD
Jerry Zhang
Triangles (NiTiCu) from combinatorial measurements of Cui, Chu, Famodu, Furuya, Hattrick- Simpers, James, Ludwig,Theinhaus, Wuttig, Zhang, Takeuchi
March 28, 2008 UMD
φ
There is no existing framework within the calculus of variations for discussing the concept of metastability relevant to the above.
March 28, 2008 UMD
Cub?MonoRhomCubHexRhomCubCubCubHexHexCubCubHexCubCub
March 28, 2008 UMD
Bacteriophage T-4 attacking a bacterium: phage at the right
is injecting its DNA
Wakefield, Julie (2000) The return of the phage. Smithsonian 31:42-6
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Data from Leiman et al., 2005
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describes the molecule
center of mass
M = 1: objective atomic structure
is an objective molecular structure if there are orthogonal transformations such that
Can write the definition using a permutation:
where is a permutation.
March 28, 2008 UMD
Theorem Dayal, Elliott, James
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where
Equilibrium equations (objective atomic structure)
If one atom is in equilibrium then all atoms are in equilibrium
March 28, 2008 UMD
First principles computations of the energy of an objective structure
For full quantum mechanics we do not know how to write a cell problem
For simpler atomic models, e.g., Density Functional Theory (DFT), we do, and this is what underlies the success of DFT: periodic BC for the density
The same simplifications are possible for objective structures – Use density functional theory – Replace periodic boundary conditions
by objective boundary conditions
March 28, 2008 UMD
Objective structures are the natural structures to exhibit collective properties: – Ferromagnetism – Ferroelectricity – Superconductivity
Suggestion: search systematically among objective structures for those with collective properties, using DFT and the formulas for OS based on isometry groups
March 28, 2008 UMD