Commensurate charge-density wave

Commensurate Charge Density Wave a static modulation of the charge density in the system with a periodicity equal to a rational number multiplied by the underlying periodicity of the lattice. Due to the charge density wave, a gap is opened at the Fermi level which lowers the total energy of the system. 

Incommensurate Charge Density Wave similar to a commensurate charge density wave except that the periodicity of the charge density modulation does not equal a rational number multiplied by the periodicity of the underlying lattice. 

The Peierls169 metal-to-semiconductor phase transition in TTFP TCNQ p was detected in an oscillation camera these streaks became bona fide X-ray spots only below the phase transition temperature of 55 K this transition is incommensurate with the room-temperature crystal structure, due to its partial ionicity p 0.59, and the "freezing" of the concomitant itinerant charge density waves (this effect was missed by four-circle diffractometer experiments, which had been set to interrogate only the intense Bragg peaks of either the commensurate room-temperature metallic structure, or the commensurate low-temperature semiconducting structure). 

Let the period of the basic structure be a and the modulation wavelength be the ratio a/X may be (1) a rational or (2) an irrational number (Fig. 1.3-7). In case (1), the structure is commensurately modulated we observe a qa superstructure, where q= /X. This superstructure is periodic. In case (2), the structure is incommensurately modulated. Of course, the experimental distinction between the two cases is limited by the finite experimental resolution, q may be a function of external variables such as temperature, pressure, or chemical composition, i. e. = f T, p, X), and may adopt a rational value to result in a commensurate lock-in stmcture. On the other hand, an incommensurate charge-density wave may exist this can be moved through a basic crystal without changing the internal energy U of the crystal. 

On superposition of the implied wave structure, the TF-like arrangement is transformed into a periodic curve that now resembles a distribution with the same periodic structure as a typical HF simulation of a many-electron unitary atom. To bring this result into register with actual HF models only needs a set of screening constants that regulates contraction of the density function in the field of a nuclear charge of -l-Ze. Rather than random variables, these screening constants are small numbers that reflect a variability commensurate with the periodic table. 

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