Structural phase transition below 250 K in superconducting K$_{0.75}$Fe$_{1.75}$Se$_{2}$

Vibrational properties of iron-chalcogenide superconductor K$_{0.75}$Fe$_{1.75}$Se$_{2}$ with $T_{c}\sim$ 30 K have been measured by Raman and optical spectroscopies over temperature range of 3-300 K. Sample undergoes \textit{I4/m} $\to$ \textit{I4} structural phase transition accompanied by loss of inversion symmetry at $T_{1}$, below 250 K, observed as appearance of new fully-symmetric Raman mode at $\sim$ 165 cm$^{-1}$. Small vibration mode anomalies are also observed at $T_{2}\sim$ 160 K. From first-principles vibrational analysis of antiferromagnetic K$_{0.8}$Fe$_{1.6}$Se$_{2}$ utilizing pseudopotentials all observed Raman and infrared modes have been assigned and the displacement patterns of the new Raman mode identified as involving predominantly the Se atoms.