Condensed-Matter Physics (1986) / Chapter Skim
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2 Structures and Vibrational Properties of Solids
2 Structures and Vibrational Properties of Solids
Pages 58-74
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From page 58... ...
The vibrational properties of many solids can be understood on the basis of the harmonic approximation, in which the force acting on a given nucleus is assumed to be a linear function of the displacements of that nucleus and of the other nuclei from their average positions. The problem can be solved exactly in this approximation.
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From page 59... ...
There can be stable nonlinear excitations termed solitons, interesting statistical mechanics of thermally excited interacting vibrational states, and phase transitions to structures of different symmetry. Because this field is extensive and closely related to other topics, many of its aspects are considered in separate chapters, in particular, critical phenomena at phase transitions, structures of surfaces and interfaces, defects in crystals, and properties of particular classes of solids.
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From page 60... ...
.0 1.2 1.4 1.6 1.8 2.0 2.2 rS FIGURE 2.1 Ground-state energy of hydrogen as a function of the average proton separation a, in units of the Bohr radius aO calculated by an approximate Monte Carlo simulation of the many-body fermion problem. The solid curve gives the energies for molecular and monatomic metallic phases.
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From page 61... ...
From the restoring forces and stresses, the vibrational properties can be obtained with no input from experiment. Calculations to date include complete phonon dispersion curves Arks, the pressure dependence of phonon frequencies and other enharmonic coefficients, and anomalous soft phonon modes.
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From page 62... ...
There has been an enor mous increase in the number of measurements of extended x-ray absorption fine structure (EXAFSJ spectra, which are being used to determine the local environment of a given type of atom. The most important results have been obtained for alloys, disordered solids, ionic conductors, and liquids, where EXAFS provides detailed information on the correlation functions of different atoms.
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From page 63... ...
Among the recent accomplishments of this technique are measurements of acoustic vibrations in metals through inelastic reflection caused by dynamical rippling of the surface. Low-frequency scattering also plays a crucial role in investigations of nonlinear systems, including such problems as the detection of tunneling modes in glasses, ionic motion in superionic conductors, large increases in quasi-elastic scattering near phase transitions, and dynamics of incommensurate structures described later.
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From page 64... ...
Optical techniques utilizing visible lasers can be used in many transparent solids to generate and detect phonons through coupling to sharp impurity states. State-of-the-art techniques of pulsing and focusing visible lasers make possible complete studies with simultaneous spectral, spatial, and temporal resolution.
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From page 65... ...
An example of this striking anisotropic transport of energy in germanium is shown in Figure 2.2. Other developments include the study of anisotropic phonon winds and their effect on the shape of electron-hole droplets in semiconductors; measurement of the frequency dependence of scattering by defects such as donors and acceptors in semiconductors; stimulated directional emission of phonons; demonstration of phonon mirrors created by superlattices of semiconductors; measurement of lifetimes of optic phonons in the picosecond range; generation and study of high-frequency surface phonons; and observation of anomalous transport in glasses at low temperatures due to coupling to low-frequency tunneling modes.
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From page 66... ...
axis. The dynamics of this transition in Zr have been studied by neutron scattering, which has detected an anomalously low phonon frequency shown in Figure 2.3 and an increase in intensity of the central-peak scattering at zero frequency at the wavelength corresponding to the periodicity of the m-phase.
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From page 67... ...
~1 I '7 I? 0.6 0.8 1.0 FIGURE 2.3 Phonon dispersion curves for the longitudinal (111)
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From page 68... ...
These results have led to new theoretical and experimental work to understand the basic phenomena involved and the role of the interactions in superconductivity and other properties. Other areas in which electron-phonon interactions play a crucial role are inelastic electron tunneling and a new experimental technique termed point-contact spectroscopy.
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From page 69... ...
DISORDERED SOLIDS AND INCOMMENSURATE PHASES A growing area of research is concerned with disordered solids that present intellectual challenges, unique phenomena, and extensive applications. One class of disordered materials is the amorphous or glassy solids, which have no long-range order.
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From page 70... ...
Theoretical studies of vibrational properties of strongly coupled disordered networks, especially with topological disorder, have led to new perspectives on excitations in disordered systems. Experimental measurements of vibration frequencies in glasses, together with the improved theoretical understanding, have motivated new explorations of the topology of glasses, such as silica.
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From page 71... ...
In particular, since it requires no energy to slide or change uniformly the relative phase of one periodicity relative to the other, there may be phason excitations with zero frequency at infinite wavelength. In the harmonic approximation, there is a phason dispersion curve with frequency linear in wave vector k at small k, in addition to the ordinary sound modes present in all solids.
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From page 72... ...
Research on nonlinear excitations involving finite displacements of atoms has become a stimulating area of physics. Although exact solutions to simple nonlinear models and phenomena like solitary waves have been known for many years, a veritable explosion in the study of such excitations has occurred in condensed-matter physics since the mid-1970s.
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From page 73... ...
High pressures achievable in diamond anvil cells open many possibilities for understanding why structures form and creating states of matter never before accomplished in a laboratory, such as metallic hydrogen. Future areas of research in phonon transport will likely include increased emphasis on lower-dimensional systems, superlattices, nonlinear lattices, transport of phonons through interfaces, phonon dynamics in the subpicosecond range, and coherent excitations.
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From page 74... ...
Synthesis of new materials will likely provide unforeseen structures and phenomena as stimulating as those of the recent past, such as organic conductors and superconductors, incommensurate structures, and lower-dimensional systems. The creation of man-made artificial structures, such as semiconductor superlattices, is just beginning to reveal the range of new possibilities.
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