Phase transitions in frustrated cobaltite TmBaCo$_4$O$_7$

For the first time, changes in lattice parameters (metrics) during a structural transition in stoichiometric cobaltite TmBaCo$_4$O$_{7+x}$ with $x\approx$ 0 (iodometric titration method) obtained by quenching from 900–950$^\circ$C were investigated by direct X-ray method. It was found that during the structural transition $T_S\approx$ 220–240 K, the $\Delta a/a$ parameter does not detect any features, parameters $b$ and $c$ experience jumps of different sign and different magnitude $\Delta b/b\approx$ 3.5 $\cdot$ 10$^{-3}$ and $\Delta c/c\approx$ -4.0 $\cdot$ 10$^{-3}$, which leads to a jump in the volume of $\Delta V/V\approx$ -0.5 $\cdot$ 10$^{-3}$. The distortion value $\varepsilon_o\approx$ -3.5 $\cdot$ 10$^{-3}$ remains constant with increasing temperature and disappears abruptly during the transition. The distortion of the structure is accompanied by anomalous behavior of the Young's modulus $\Delta E(T)/E_0$ in the $T_S$ region. In the region of the expected magnetic phase transition of the cobalt subsystem, anomalies in the Young's modulus curve $\Delta E(T)/E_0$ were not detected, and a strong absorption peak at $T\approx$ 96 K in the internal friction dependence $q^{-1}(T)$ is, apparently, a sign of a developed short-range order.