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Materials from Mathematics

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DNMW01 - Optimal design of complex materials

We present some recent examples of new materials whose synthesis was guided by some essentially mathematical ideas. They are materials that undergo phase transformations from one crystal structure to another, with a change of shape but without diffusion. They are hard materials, but nevertheless show liquid-like changes of microstructure under a fraction of a degree change of temperature. The underlying mathematical theory was designed to identify alloys that show low hysteresis and exceptional reversibility. The new alloys, of which Zn_45Au_30Cu_25 and Ti_54.7Ni_30.7Cu_12.3Co_2.3 are currently the best examples, do show unprecedented levels of these properties, but also raise fundamental questions for mathematical theory. Magnetoelectric properties of solids are often sensitive to lattice parameters, so they can be switched on and off at a phase transformation: briefly, multiferroism by reversible phase transformation. This switching can be combined with induction in the ferromagnetic case, or capacitance in the ferroelectric case, to yield devices that convert heat directly to electricity, without a separate electrical generator. We describe briefly the associated mathematical theory. The resulting multiferroics provide interesting possible ways to recover the vast amounts of energy stored on earth at small temperature difference. They move heat produced by natural and man-made sources from higher to lower temperature and therefore contribute negatively to global warming.

This talk is part of the Isaac Newton Institute Seminar Series series.

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