Phase transition at 434 K, independent strain coupling in second transition at 400 K, and thermal expansivity in ferroelastic K2TeBr6

摘要

Xhyphen;ray diffraction and specific heat measurements have identified two independent strainhyphen;coupled processes in a broad phase transition at about 400 K and a normal lambdahyphen;type phase transition at 434 K in K2TeBr6between 20 K and decomposition at 590 K. Phase I is cubicFm3mwith four K2TeBr6per unit cell,a435=10.7456(14) Aring;, and expansion coefficients to thirdhyphen;order of agr;=0.134(3)times;10minus;3Aring;thinsp;Kminus;1, bgr;=0.198(17)times;10minus;6Aring;thinsp;Kminus;2, and ggr;=0.162(27)times;10minus;9Aring;thinsp;Kminus;3: it transforms on cooling to phase II at 434 K with an entropy change of 1.3 Jthinsp;molminus;1thinsp;Kminus;1. Phase II is tetragonal,P4/mnc, with two K2TeBr6per unit cell,a410=7.5755(10) andc410=10.7702(22) Aring;, with expansion coefficients to thirdhyphen;order for the tetragonalaaxis identical to those of the cubicaaxis, and linear coefficient agr;c=minus;0.103(12) times;10minus;3Aring;thinsp;Kminus;1: it transforms on cooling to phase III at about 400 K with an entropy change of 2.9 Jthinsp;molminus;1thinsp;Kminus;1. Phase III is monoclinic,P21/n, with two K2TeBr6per unit cell,a295=7.4908(10),bthinsp;295=7.5492(7),c295=10.6984(11) Aring;, bgr;thinsp;295=90.307(6)deg;, with monoclinicaaxis expansion coefficients to thirdhyphen;order identical to those of the cubicaaxis, linear coefficient agr;b=minus;0.308(6)times;10minus;4Aring;thinsp;Kminus;1, secondhyphen;order coefficients agr;c=0.711(14) times;10minus;4Aring;thinsp;Kminus;1, bgr;c=0.290(99)times;10minus;7Aring;thinsp;Kminus;2. The monoclinic angle follows a Landau critical power law with bgr;minus;90prop;(400minus;T)1/2, whereasaminus;bprop;(359minus;T). Group theoretical analysis of the phase II symmetry operators predicts two independent softEgmodes for the K and Br atom special positions at the transition to phase III, leading to independent proportionality constants for the thermal variation of bgr; andaminus;b, as observed. By contrast, the transition from phase I to phase II has only a single softA2gmode, leaving the K atom special position unchanged. A simple model predicts 1.52 Jthinsp;molminus;1thinsp;Kminus;1for the phase transition at 434 K and 2.64 Jthinsp;molminus;1thinsp;Kminus;1for that at 400 K. Dynamical shorthyphen;range tetragonal order may set in above 359 K. Ferroelastic transformation in phase III at room temperature is shown to be accompanied by atomic displacements no larger than about 0.6 Aring; as theaandbaxes are exchanged under applied compressive stress.