Thermal dependence of the x-ray white-line interference effect for charge-density waves in alloys of organic conductors

A few years ago a new diffraction effect was discovered in solid solutions of quasi-one-dimensional organic conductors exhibiting a charge-density-wave (CDW) instability at the critical wave vector q₀=2k_F or 4k_F. It corresponds to an asymmetry between the +q₀ and -q₀ x-ray diffuse scattering intensities and it is due to interferences between the CDW displacive contribution and the Laue scattering produced by the substitutional disorder. The asymmetry is so strong that negative diffuse lines (``white lines'') are formed at the expense of the Laue scattering at either the +q₀ or the -q₀ reduced wave vectors. Being of first order in lattice displacement, the interference effect is sensitive to the relative phase of the CDW with respect to the substituant. Such a phase can be deduced from the simple observation of the sign of the asymmetry. Here we present experimental data for the TTF/TSF-TCNQ alloys and the relevant theory of the temperature dependence of this effect in the one-dimensional regime. In the weak impurity case, the theoretical calculation accounts well for the order of magnitude and for the thermal dependence of the 4k_F white-line effect experimentally observed. There are two microscopic contributions to the asymmetry term. The first contribution, which is proportional to the electronic susceptibility, corresponds to the formation of Friedel oscillations enhanced by the electron-electron correlations, in the vicinity of the impurity. The second contribution corresponds to the so-called size effect of the impurity. In the weak impurity case both contributions are enhanced, when the temperature decreases, by a factor proportional to the inverse of the square of the frequency of the Kohn anomaly associated to the CDW lattice instability.