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We report an x-ray diffraction study on the charge-density-wave (CDW) LaTe$_3$ and CeTe$_3$ compounds as a function of pressure. We extract the lattice constants and the CDW modulation wave-vector, and provide direct evidence for a pressure-induced q uenching of the CDW phase. We observe subtle differences between the chemical and mechanical compression of the lattice. We account for these with a scenario where the effective dimensionality in these CDW systems is dependent on the type of lattice compression and has a direct impact on the degree of Fermi surface nesting and on the strength of fluctuation effects.
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