Critical behavior at the incommensurate structural phase transition inK2SeO4

${\mathrm{K}}_2$Se${\mathrm{O}}_4$ has a second-order incommensurate structural phase transformation with a two-component order parameter of continuous symmetry. Its critical behavior should therefore be that of a $d=3\mathrm{}$ $\mathrm{XY}$ model. We have measured the critical exponents associated with the growth of primary and secondary diffraction satellites and find them to be $2\beta =0.75(\pm 0.05)$ and $2\tilde{\beta }=1.57(\pm 0.07)$ respectively. These values are in reasonable agreement with the theoretical estimates $2\beta =0.70(\pm 0.04)$ and $2\tilde{\beta }=1.69(\pm 0.09)$ obtained by series expansions. The theoretical value of $2\tilde{\beta }$ is appreciably different from the naive Landau prediction $2\tilde{\beta }=4\mathrm{}\beta$, and is given by $2\tilde{\beta }=2(2-\alpha -\phi )$ where $\phi$ is a crossover exponent associated with a uniaxial perturbation.