Correlated Local Atomic Displacements: The Microscopic Origins for Macroscopic Phenomena
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Correlated Local Atomic Displacements: The Microscopic Origins For Macroscopic Phenomena. Frank Bridges1 , Daliang Cao1 , and Corwin H. Booth2 1 Department of Physics, University of California, Santa Cruz, CA 95064 2 Lawrence Berkeley National Laboratory, Berkeley, CA 94720 ABSTRACT In many systems for which there are several atoms in the unit cell, the displacements of the atoms may be locally correlated even though there is no long range coherence. Such displacements can play an important role in determining various macroscopic properties. We consider several examples to demonstrate this phenomena - the local distortions in the colossal magneto-resistive (CMR) and charge-ordered manganites, magnetic field induced distortions in CMR materials that are connected to macroscopic magnetostriction, and correlated displacements of tetrahedral units within the negative thermal expansion material ZrW 2 O8 . The distortions in the CMR materials observed using XAFS change rapidly just below T c and are attributed to the formation of polarons as the temperature is increased through Tc . In the ferromagnetic state, the lattice is more ordered for CMR systems; consequently applying a magnetic field for T T c should decrease the local distortions. Such an effect has been observed and is a much larger effect than the measured macroscopic magnetostriction. Finally, in ZrW 2 O8 the tetrahedral and octahedral units are found to be very rigid as expected. More surprising is that the width of the pair-distance distribution for the W-Zr atom-pair is also quite small, indicating that the W-Zr linkage is stiff. In contrast, for the W-W pair, the distribution width grows rapidly with T, indicating correlated displacements of two WO4 tetrahedral units. INTRODUCTION Correlations of the motions and displacements of the constituent atoms in a crystal occur for all materials, but their relevance in determining some of the macroscopic properties of a material have only recently begun to be understood. For simple materials such as the alkali halide salts, the dominant vibrational modes at low temperatures are the acoustic phonons. For these modes, particularly for long wavelength modes, the displacements of the neighboring atoms are highly positively correlated - that is at any instant in time, these atoms are moving in the same direction[1]. At higher temperatures, the optical phonons become excited; for these modes the motions of the atoms are negatively correlated[2, 3], particularly for short wavelength modes near the Brillouin zone boundary. In this case, the neighboring atoms move towards or away from each other and if charged (ionic), couple strongly to electromagnetic radiation (i.e. visible and infrared light). Eventually at high enough temperatures that a large number of short wavelength modes of various types are excited, the net motions of the neighboring atoms should become essentially uncorrelated. For simple systems, apart from the coupling to optical radiation, the correlated motions of the atoms do not appear to play a major r
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