Vibrating crystal

In solid state lasers the fluorescence lines are broadened 26) by statistical Stark fields of the thermal vibrating crystal lattice and furthermore by optical inhomogenities of the crystal. The corresponding laser lines are accordinglyjlarge at multimode operation 22)... 

Because of its piezoelectric properties, synthetic CC-quartz is used for frequency control in electrical oscillators and filters and in electromechanical transducers. When mechanically stressed in the correct direction, CC-quartz develops an electric polarization. The opposite is also tme an applied electric field gives rise to a mechanical distortion in the crystal. Thin sections of quartz are cut to dimensions that produce the desired resonance frequency when subjected to an alternating electric field the vibrating crystal then reacts with the driving circuit to produce an oscillation that can be narrowly controlled. Quartz is ideal for this application because it is hard, durable, readily synthesized, and can be tuned to high accuracy, for example, quartz crystal clocks can be made that are stable to one part in 109. 

Figure 21-13 (a) Ultrasonic nebulizer lowers the detection limit for most elements by an order of magnitude, (b) Mist created when sample is sprayed against vibrating crystal. [Courtesy Cetac Technologies,... 

J. Chem. Phys. 23, 1053-6 (1955). IR lattice vibrations, crystal NH3, NHoD, mixed crystals. 

Cady in World War II realized that such a mechanical resonance of a vibrating crystal could be used in frequency control. This discovery had an important influence on radio communications.Alternating electric fields, such as those generated by the radio tubes of the time, were applied to plates of piezoelectric crystals and the expansions and contractions of the plates were caused to react on electrical circuits. If the natural frequency of the mechanical vibration of the quartz plate coincided with the frequency of oscillation of the electric circuit, resonance between the two took place and energy was acquired by the mechanical oscillators. Later. Rochelle salt and barium titanate, which are each both ferroelectric and piezoelectric, were used. ° In ferroelectric crystals, the polarization or dipole moment is reversed or reoriented upon application of an electric field. Ferroelasticity is another property displayed by some crystals in which stress can cause the interconversion between two stable orientational states. These physical properties of crystals are of great use in modern technology. 

Ultrasonic waves have frequencies too high to be detected by the human eag but they can be produced and detected by vibrating crystals. Calculate the wavelength of an ultrasonic wave of frequency 5.0 X 10 s that is propagating through... 

Being the first to reahse the potential of this sensor type he predicted that many more similar sensors would be developed in the future. It is also quite probable that King was the first to investigate the use of Pz crystals as detectors in solution, since he mentions the impaired ability of crystals to vibrate when a solution was placed on the surface. He states the possible reason for this is the dissipation of energy from the vibrating crystal to the liquid. 

Researchers extensively use the Bom-von Karman theory in order to estimate the strength of interatomic bonding [47]. This traditional method is to make a formal expansion of energy of a vibrating crystal in a series and to treat the expansion coefficients as force constants. The main assumptions of this theory are as follows. 

One can easily obtain an expression for the kinetic energy of a vibrating crystal. For this purpose, one should sum up the kinetic energies of all atoms ... 

Conical cooling crystallizer with settling zone according to Howard, vibrated crystallizer to prevent build-up of solid on the heating elements, fluidized-bed crystallizer system Krystal with cooling, evaporation or vacuum crystallization, DP-crystallizer system Escher-Wyss-Tsukishima, evaporation crystallizer with carrier gas by Robinson, vortex crystallizer Standard-MESSO. 

Scientists at the U.S. National Institute of Standards and Technology measured a force of 174 yN exerted by a weak electric field on a vibrating crystal of 60 Be ions cooled to 0.5 mK in an electromagnetic trap. (M. J. Biercuk et al., arXiv.org 1004.0780v3 [quant-ph] 24 Apr 2010.)... 

The Ti sapphire laser is called a vibronic laser, because of the close blending of the Ti electronic and vibrational crystal-host coupling frequencies. A very reduced energy level diagram for the 3d Ti + ion... 

The literature concerning the quartz crystal microbalance (QCM) and its electrochemical analogue, the electrochemical crystal microbalance (EQCM) is wide and diverse. Many reviews are available in the literature, discussing the fundamental properties of this device and its numerous applications, including its use in electrochemistry [1-5], In this chapter we concentrate on electrochemical applications, specifically in studies of submonolayer phenomena and the interaction of the vibrating crystal with the electrolyte in contact with it. 

For a vibrating crystal lattice, the interatomic distances are modulated at the frequency of the lattice vibration to produce an oscillating magnetic field. Suitable vibration with the frequency at the Larmor frequency of the electrons will induce a flip of the elecfron spin. The corresponding relaxation time can be simplified as... 

The physical origin of Raman scattering may be viewed from a simple classical perspective in which the electric field associated with the incident light interacts with the vibrating crystal. In particular, this interaction occurs through the... 

For the same reason of higher amplitude of near-surface atomic vibrations, crystallization cannot start from the liquid-phase surface. Because of this, unlike the melting ptrooess, the crystallization process is homogeneous and needs overcooling of the system by dozens or even hundreds degrees relative to the equilibrium temperature of the phase transition. 

Figure 8.1.13 The MEIS surface peak area, expressed as the number of visible monolayers, as a function of temperature for Pb(lll) (a) [139] and Pb(llO) (b) [135], The experimental conditions for (a) are given in its inset and the ones for (b) in Figure 8.1.12b. The solid curves are the number of visible monolayers calculated by Monte Carlo for a well-ordered thermally vibrating crystal. Curve I in (b) shows the expected behavior from...

With the help of Monte Carlo simulations, the surface peak area can be associated with the number of molten atomic layers. Figure 8.1.13 shows the result for both surfaces. The curve expected from bulk lattice vibrations and bulk interlayer distances is denoted I in Figure 8.1.13b and lies below the data. Curve II accounts, in addition, for the enhanced surface vibration amphtudes and the relaxation of the first two interlayer distances both are manifestations of surface anharmonicity as we have seen above. This curve describes the low-T data quite well. From 500 K on, the number of visible layers is significantly enhanced compared with the expectation from a weU-ordered vibrating crystal. The only way this could be reconciled in the Monte Carlo simulations was to include molten layers on the vibrating soHd. It is seen that the surface has up to 15 such layers at. The surface... 

When a quartz crystal (or any other solid material) vibrates, there is always a resonance frequency, which we denote fo, at which it oscillates with minimum impedance (that is maximum admittance). The resonance frequency depends on the dimensions and on the properties of the vibrating crystal, mostly the density and the shear modulus. A quartz crystal can be made to oscillate at other frequencies, but as the distance, (on the scale of frequency), from the resonance frequency increases, the admittance decreases, until the vibration can no longer be detected. This is the basis for the analysis of the so-called (mechanical) admittance spectrum of the QCM, which is discussed below. 

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