Theory of the Structural Phase Transformations in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ)

An order parameter theory is derived and used to explain the observed structural phase transformations in tetrathiafulvalene tetracyanoquinodimethane. It is shown that there should be three transitions. One set of chains orders at 54 K, the other at 47 K. The modulation wave vector in the ${\overrightarrow{a}}^{*}$ direction is equal to $\frac{a^{*}}{2}$ between 54 and 47 K, increases as $\frac{a^{*}}{2}+\lambda {\mathrm{}(47-T)\mathrm{}}^{\frac{1}{2}}$ between 47 and 38 K, and locks to a value of $\frac{a^{*}}{4}$ below 38 K as a consequence of Umklapp terms in the free energy.