A dimerized quantum Heisenberg or XY antiferromagnetic chain has a gap in the spectrum. We show that a weak incommensurate modulation around a dimerized chain produces a zero-temperature quantum critical point. As the incommensuration wavelength is varied, there is a transition to a modulated gapless state. The critical behaviour is in the universality class of the classical commensurate-incommensurate (Pokrovsky-Talapov) transition. An analogous metal-insulator transition can also take place for an incommensurate chain. §

Rutile crystals, groan in vacuum-deposited amorphous films by electron beam heating, have been investigated by high-resolution transmission electron microscopy with the aid of computer image simulation. A new type of ordered (110) CS structum with +[Or11 shear has been found in reduced TinOz,,-l crystals with n = 1.

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The localized density of states g(E) near midgap for undoped, B2H6-doped, and PH3-doped hydrogenated amorphous silicon is evaluated from the electrophotographic (xerographic) method. The density of hole traps decreases with increasing B2H6 concentration and that of electron traps decreases with increasing PH3. These features are qualitatively similar to those deduced from the deep-level transient spectroscopy, the photothermal deflection spectroscopy, the time-of-flight measurements, and the isothermal capacitance transient spectroscopy. The energy positions of neutral dangling bonds D0 and doubly occupied D− are estimated to be 0.85–0.88 eV from the valence band and 0.62–0.67 eV from the conduction band, respectively. Comparison of the energy peaks of electron and hole traps shows that the positive correlation energy of dangling bonds is about 0.3–0.4 eV.

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