The existence of optical second harmonic generation has been shown to be a highly reliable and sensitive physical test for the detection of crystalline non-centrosymmetry. A second harmonic analyzer has been constructed which can resolve space group ambiguities arising from Friedel's Law with a confidence level greater than 99%. The system has been optimized for use with powdered crystalline samples so as to obviate the need for large single crystals and thus facilitates rapid determination of crystalline non-centrosymmetry. The present analyzer can routinely detect second harmonic generation at levels 1/1000 of that generated in a quartz standard, this is about an order ofmagnitude increase over previously reported systems. Data are reported on several materials including dibenzyldisulfide, and [(C6H5)3 P] 3CuBF,~. The detection of structural phase transitions with the second harmonic analyzer is reported for BaTiO3, colemanite and phenanthrene. Second harmonic generation in the 'cubic' phase of BaTiO3 promises to be a powerful tool for determining the dynamics of the ferroelectric phase transition. It is the most direct method for establishing the existence or nonexistence of microscopic polar regions well above the Curie point in a nominally centrosymmetric phase.* A comparison of the Giebe Scheibe and SHG methods (Kurtz, 1972a), encompassing 86 non-centrosymmetric materials, found 31 cases where the SHG technique detected the lack of centrosymmetry while the piezoelectric test gave a null result. In no case was the converse true.
A model Fokker-Planck equation for a single species of particles in a plasma is discussed. This equation has several properties in common with the real equation, and ascribes an approximately correct behavior to most of the particles, though incorrect for the high-energy tail in the thermal distribution. It is shown that the equation can be solved completely, for the small perturbations of a uniform plasma by electric fields harmonic in space and time, in an external magnetic field. Applications to ionospheric radar scattering are briefly discussed; it is shown that in certain circumstances, ion-ion collisions can have a profound effect on the scattering even though the collision frequency is much smaller than the ion gyrofrequency, and this appears to agree with observation.
The theory of incoherent scattering in a plasma is extended to include the effect of ions and electrons colliding with neutral molecules, an effect that could be important in the ionosphere below perhaps 150 km for experiments at frequencies of the order of 50 Mc/s or less. We find, first of all, that the total scattered power is completely independent of collisions; the collisions only affect the shape of the spectrum. If, as is usually the case, the Debye length [6.9 (T/N)1/2 cm] is small compared to λ/4π. (λ is the radio wavelength), the spectrum begins to become narrower and peaked at the center when the mean free path of the ions becomes comparable to λ/4π. Any possible ion gyroresonant effects on the spectrum due to the presence of a magnetic field will be prevented if the collision frequency of the ions is greater than or equal to their gyrofrequency. If the Debye length should happen to be greater than λ/4π, the above comments would apply to the mean free path, collision frequency, and gyrofrequency of the electrons; however, such electron effects are not likely to be important in the ionosphere. It does seem that perhaps we might be able to measure ion collision rates by means of incoherent scattering. The principal difficulty would be in obtaining, from low altitudes, incoherent scattering signals uncontaminated by other types of scattering.
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