Crystals, vibrations

DIott D D 1988 Dynamics of molecular crystal vibrations Laser Spectroscopy of Solids 7/ed W Yen (Berlin Springer) pp 167-200... 

Applications Although a wide range of metals can be sputtered, the method is often commercially restricted by the low rate of deposition. Applications include the coating of insulating surfaces, e.g. of crystal vibrators, to render them electrically conducting, and the manufacture of some selenium rectifiers. The micro-electronics industry now makes considerable use of sputtering in the production of thin-film resistors and capacitors . ... 

Tables Assignment and wavenumbers (cm ) of the external and torsional vibrations of a-Ss based on polarization dependent studies [106, 107]. In the first two columns the type and symmetry classes of the molecular and crystal vibrations, respectively, are given. The wavenumbers of the vibrations are listed in the columns infrared and Raman corresponding to the order of symmetry species given in the second column (crystal). " S means orthorhombic Sg with natural isotopic composition, while stands for isotopically pure Sg crystals (purity >99.95%)... 

The statistical treatment of the vibrational degrees of freedom of crystals is far more difficult compared to gases. Let us initially consider a monoatomic crystal. An atom in a crystal vibrates about its equilibrium lattice position. In the simplest approach, three non-interacting superimposed linear harmonic oscillators represent the vibrations of each atom. The total energy, given by the sum of the kinetic and potential energies for the harmonic oscillators, is... 

So we understand that as the emf changes with temperature, so the quartz crystal vibrates at a different frequency - all because... 

Such a small crystal behaves like an infinitely expanded crystal. However, if the crystal vibrations remain restricted to the center, one can clamp the outer edge to a crystal holder, without engendering undesired side effects. Moreover, contouring reduces the resonance intensity of undesired anharmonics. This limits the capacity of the resonator to maintain these oscillations considerably. 

Use of a Quartz Crystal Vibrator in Vacuum Destination Invstigations... 

In the 2-level limit a perturbative approach has been used in two famous problems the Marcus model in chemistry and the small polaron model in physics. Both models describe hopping of an electron that drags the polarization cloud that it is formed because of its electrostatic coupling to the enviromnent. This enviromnent is the solvent in the Marcus model and the crystal vibrations (phonons) in the small polaron problem. The details of the coupling and of the polarization are different in these problems, but the Hamiltonian formulation is very similar. ... 

Conducting materials contain large numbers of mobile electrons which are free to move within the bulk of the material. Consequently conductors exhibit such properties as high electrical and thermal conductivity and a resistance which increases with increasing temperature. This is caused by the electrons being slowed down by interaction with the crystal vibrations which increase with temperature. 

DEBYE-SEARS EFFECT. A piezoelectric crystal vibrating in a longitudinal mode in a liquid sets up acoustic waves consisting of regions of compression and regions of rarefaction in the liquid, which alternate at... 

Damped oscillations no yes liquids and some dry products. Employs oscillating dement which is normally a vibrating fork or paddle driven mechanically (Fig. 6.33a) or by a piezoelectric crystal vibrating at its resonant frequency. When immersed in the material there is a frequency or amplitude shift due to viscous damping which is sensed usually by a reluctive transducer (Section 6.3.3). 

This is the correct name for most popular mass sensors, although they are better known as Quartz Crystal Microbalances (QCMs). A piezoelectric crystal vibrating in its resonance mode is a harmonic oscillator. For microgravimetric applications, it is necessary to develop quantitative relationships between the relative shift of the resonant frequency and the added mass. In the following derivation, the added mass is treated as added thickness of the oscillator, which makes the derivation more intuitively accessible. 

The atoms of a crystal vibrate around their equilibrium position at finite temperatures. There are lattice waves propagating with certain wavelengths and frequencies through the crystal [7], The characteristic wave vector q can be reduced to the first Brillouin zone of the reciprocal lattice, 0 < q <7t/a, when a is the lattice constant. 

But if we examine the localized near the donor or the acceptor crystal vibrations or intra-molecular vibrations, the electron transition may induce much larger changes in such modes. It may be the substantial shifts of the equilibrium positions, the frequencies, or at last, the change of the set of normal modes due to violation of the space structure of the centers. The local vibrations at electron transitions between the atomic centers in the polar medium are the oscillations of the rigid solvation spheres near the centers. Such vibrations are denoted by the inner-sphere vibrations in contrast to the outer-sphere vibrations of the medium. The expressions for the rate constant cited above are based on the smallness of the shift of the equilibrium position or the frequency in each mode (see Eqs. (11) and (13)). They may be useless for the case of local vibrations that are, as a rule, high-frequency ones. The general formal approach to the description of the electron transitions in such systems based on the method of density function was developed by Kubo and Toyozawa [7] within the bounds of the conception of the harmonic vibrations in the initial and final states. 

The strong dependence of the layer structure on the nature of the contacting electrolyte has been further investigated by using the electrochemical quartz crystal microbalance (EQCM). As discussed above in Chapter 3, this technique is based on the measurement of the frequency with which a coated quartz crystal vibrates, and this frequency can then be related to the mass of this crystal provided that the material attached to the surface is rigid. In this way, the changes that occur in thin films as a result of redox processes can be monitored. 

Dlott DD. Dynamics of molecular crystal vibrations. In Yen W, ed. Laser Spectroscopy of Solids II. Berlin Springer-Verlag, 1988 167-200. 

When an atom makes a transition from a high-energy quantum state to a lower energy state, electromagnetic radiation with a definite frequency and a definite period is emitted. When properly detected, this frequency, or period, becomes the ticking of an atomic clock, just as the crystal vibration frequency and the swinging frequency are the inaudible ticks of a quartz clock and a pendulum clock. The frequency emanating from the atom, however, is much less influenced by environmental factors such as temperature, pressure, humidity, and acceleration than are the frequencies from quartz crystals or pendula. Thus, atomic clocks hold inherently the potential for reproducibility, stability, and accuracy. 

For an atom to migrate from one position to another within a lattice, an energy barrier must be overcome. The magnitude of this barrier, known as the activation energy Ef), is directly proportional to the rate of atomic diffusion (Figure 2.27). As the temperature of the crystal is increased, the atoms in the crystal vibrate about their equilibrium positions. The Arrhenius equation (Eq. 8) is used to calculate the... 

The mass variation calculated from the variation of the quartz crystal vibration frequency for an iron phthalocyanine catalyst supported on caibon is presented in Fig. 43. In the potential domain over 0.5 V vs RHE, the mass increases during the positive going scan and decreases during the negative going scan. This confirms that the change in oxidation state of the central metal ion is accompanied by an adsorption-desorption process. Furthermore,... 

A more precise measurement of local sample temperature is made possible by the anharmonicity of the crystal vibrational potential energy. Phonon-phonon interactions that reduce individual phonon lifetimes, phonon softening, and thermal expansion give rise to increasing peak width and a change in peak frequency... 

The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment of such diverse phenomena as elasticity, acoustics, AC circuits, molecular and crystal vibrations, electromagnetic fields and optical properties of matter. 

Kitagawa, T., and T. Miyazawa Frequency distribution of crystal vibrations... 

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