The relative static stability of square and triangular dectron lattices (two-dimensional %'igner crystals), the instability against vibrational excitations, and the effect of image-potential-induced screening on the dispersion of the frequency spectra are studied in the inversion layer of a metal-insulator-semiconductor structure. In harmonic approximation the two-dimensional Wigner crystal turns out to be stable against transverse vibrations for a triangular lattice but unstable for a square lattice in the I10] direction in disagreement with previous calculations. In triangular lattices, the transition of the anomalous dispersion (coL~k '") of the two-dimensional longitudinal mode at intermediate wave vectors (D ' & k & a ') to the normal dispersion (el~k) in the extremely-long-wavelength limit (kD & 1) due to screening effects is studied as a function of the ratio of insulator thickness D and lattice constant a.

The temperature dependence of the Debye-Wailer factor (DWF) near the critical point of ferroelectrics, "antiferroelectrics, " 315 structure compounds, etc. , is investigated. Using the compressibility sum rule it is shown that the critical part of the DWF exponent quadratic in the momentum transfer is rigorously determined by the renormalized static phonon frequencies and thus will not be directly affected by the occurrence of a central peak. It is found that the mean-square particle displacement has a cusp at T"rather than the critical divergence predicted by various authors. The critical exponents associated with the cusp are estimated from scaling arguments and related to those of the specific heat. The extent to which this cuspshaped anomaly might be detected experimentally is briefly discussed. The results obtained here are also relevant for the electron-paramagnetic-resonance linewidth in the "slow-motion" regime.

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