Mechanical Coupling Coefficient

This scattering mode occurs only in piezoelectric materials, i.e., in crystals without inversion symmetry, and is caused by the electric field associated with acoustical phonons. Zinc oxide exhibits very high electro-mechanical coupling coefficients P (see later), exceeding that of quartz [42,59], which is one of the mostly used piezoelectric materials. Zook [60] has calculated the piezoelectrically limited mobility on the basis of the elastic and piezoelectric constants as (see also Rode [54]) ... 

Electrospinning technique has been used not only for the deposition of polymeric nanofibres but also for the production of ceramic nanofibres of PZT. PZT is commonly used in micro- and macro-scale piezoelectric energy harvesting devices due to its high electro-mechanical coupling coefficient of -500-600pC ) as compared... 

At room temperature the crystals of M(C6H5)4 (M = Si to Pb) are temperature-insensitive insulators having a relative dielectric constant of 10 and an electric resistivity over 10 ° ohm-cm. The electrical-mechanical coupling coefficient parallel to the c axis is 5 to 10%. The crystals exhibit moderately strong piezoelectric resonances [24]. 

This provides us the electro-mechanical coupling coefficient d for the measured tip displacement (F = 0 in Fig. 2.36) ... 

The picture here is of uncoupled Gaussian functions roaming over the PES, driven by classical mechanics. The coefficients then add the quantum mechanics, building up the nuclear wavepacket from the Gaussian basis set. This makes the treatment of non-adiabatic effects simple, as the coefficients are driven by the Hamiltonian matrices, and these elements couple basis functions on different surfaces, allowing hansfer of population between the states. As a variational principle was used to derive these equations, the coefficients describe the time dependence of the wavepacket as accurately as possible using the given... 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

Donor doping in PZT would be expected to reduce the concentration of oxygen vacancies, leading to a reduction in the concentration of domain-stabilizing defect pairs and so to lower ageing rates. The resulting increase in wall mobility causes the observed increases in permittivity, dielectric losses, elastic compliance and coupling coefficients, and reductions in mechanical Q and coercivity. 

If we consider a membrane having the same solute concentration on both sides, we have All 0 However, a hydrostatic pressure difference AP exists between the two sides, and we have a flow Jv that is a linear function of AP. The term Lp is called the mechanical filtration coefficient, which represents the velocity of the fluid per unit pressure difference between the two sides of the membrane. The cross-phenomenological coefficient Ldp is called the ultrafiltration coefficient, which is related to the coupled diffusion induced by a mechanical pressure of the solute with respect to the solvent. Osmotic pressure difference produces a diffusion flow characterized by the permeability coefficient, which indicates the movement of the solute with respect to the solvent due to the inequality of concentrations on both sides of the membrane. 

We have seen how the molecular properties in nonlinear optics are defined by the expansion of the molecular polarization in orders of the external electric field, see Eq. (5) beyond the linear polarization this definition introduces the so-called nonlinear hyperpolarizabilities as coupling coefficients between the two quantities. The same equation also expresses an expansion in terms of the number of photons involved in simultaneous quantum-mechanical processes a, j3, y, and so on involve emission or absorption of two, three, four, etc. photons. The cross section for multiphoton absorption or emission, which takes place in nonlinear optical processes, is in typical cases relatively small and a high density of photons is required for these to occur. 

If the film cannot be freely deformed in its plane, the piezoelectric current is called t/33 or dj. If the variation in the electric field is measured per unit of stress, g coefficients are obtained that are connected by the correlation of g = d/e where e is the dielectric constant depending on the film thickness. Constants g and tf are most widely used in the design of electromechanical transducers. The yield from the conversion of mechanical energy into electrical energy is represented by the electromechanical coupling coefficient ATjby Eq. (3.3). 

Because of the conservation of the total angular momentum (J = j -f-1), we have to search for a proper combination of spherical harmonics. Introducing then the coupling coefficients of quantum mechanical angular momenta (the Clebsch-Gordan coefficients), we obtain a bipolar harmonic... 

Lewontin s coupling coefficient Ibid, p. 294), represent things we look for and find mechanisms for, but general or context-independent translations at a molecular level seem absurd - both impossible and pointless. a context-dependent translation is not a translation (1976 682). 

Actual calculation of the RRS spectra and excitation profiles of a PH dimer are not yet available, and we are currently working on that. One interesting qualitative feature is worth mentioning, though. The relative importance of the A-type and C-type enhancement mechanisms is determined by the coefficients [P22(c) — J liW] and Pi2(c) respectively. Using the explicit expressions for these coupling coefficients in terms of the basic electronic interactions t and U (Eq. (19)), one can see that the C-type non-Condon mechanism is induced by the on-site Coulomb correlation U, Analysis of possible interference phenomena in the excitation profiles and in the polarization dispersion could therefore provide information on the electron correlations. 

Returning now to uniaxial fibre orientation, we can use the same models of mechanical coupling to predict thermoelastic properties of the composite. If the coefficients of linear expansion of fibres and matrix respective) are a/ and a , the coefficients aj and 02 for the composite parallel to axes 1 and 2 can be shown to be... 

The piezoelectric generator coefficient d indicates the mechanical strains that are induced by electric potentials and the piezoelectric motorcoefficient e is a measure of the dipole moments that are created by strains. These two parameters are similar in nature and proportional to one another. The electromechanical coupling coefficient k is proportional to both d and e, its square giving the efficiency of conversion between mechanical and electrical energy that can be achieved with the ferroelectric... 

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