chapter4

chapter4 - SOUND WAVES LATTICE VIBRATIONS OF 1D CRYSTALS...

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SOUND WAVES LATTICE VIBRATIONS OF 1D CRYSTALS chain of identical atoms chain of two types of atoms LATTICE VIBRATIONS OF 3D CRYSTALS PHONONS HEAT CAPACITY FROM LATTICE VIBRATIONS ANHARMONIC EFFECTS THERMAL CONDUCTION BY PHONONS
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Crystal Dynamics Concern with the spectrum of characteristics vibrations of a crystalline solid. Leads to; consideration of the conditions for wave propagation in a periodic lattice, the energy content, the specific heat of lattice waves, the particle aspects of quantized lattice vibrations (phonons) consequences of an harmonic coupling between atoms.
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Crystal Dynamics These introduces us to the concepts of forbidden and permitted frequency ranges, and electronic spectra of solids
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Crystal Dynamics In previous chapters we have assumed that the atoms were at rest at their equilibrium position . This can not be entirely correct (against to the HUP); Atoms vibrate about their equilibrium position at absolute zero. The energy they possess as a result of zero point motion is known as zero point energy. The amplitude of the motion increases as the atoms gain more thermal energy at higher temperatures. In this chapter we discuss the nature of atomic motions, sometimes referred to as lattice vibrations. In crystal dynamics we will use the harmonic approximation , amplitude of the lattice vibration is small . At higher amplitude some unharmonic effects occur .
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Crystal Dynamics Our calculations will be restricted to lattice vibrations of small amplitude. Since the solid is then close to a position of stable equilibrium its motion can be calculated by a generalization of the method used to analyse a simple harmonic oscillator.The small amplitude limit is known as harmonic limit. In the linear region (the region of elastic deformation), the restoring force on each atom is approximately proportional to its displacement (Hooke’s Law). There are some effects of nonlinearity or ‘anharmonicity’ for larger atomic displacements. Anharmonic effects are important for interactions between phonons and photons.
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Crystal Dynamics Atomic motions are governed by the forces exerted on atoms when they are displaced from their equilibrium positions. To calculate the forces it is necessary to determine the wavefunctions and energies of the electrons within the crystal. Fortunately many important properties of the atomic motions can be deduced without doing these calculations.
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Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law.
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chapter4 - SOUND WAVES LATTICE VIBRATIONS OF 1D CRYSTALS...

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