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The temperature dependences of the heat capacity (Cp(T)) and crystal lattice parameters (a(T) and Vu(T)) of barium difluoride, BaF2, as well as the heterovalent (BaF2)0.59(TmF3)0.41 solid solution, in the temperature range of 2–300 K are experimentally studied. Anomalous deviations of the dependences of Cp(T), a(T) and Vu(T) of the solid solution at low temperatures (2–20 K) both in the direction of higher and lower values, due to the rearrangement of the crystal field, as well as the appearance of two-level systems in the metal sublattice of the solution, are revealed. At elevated temperatures (150–300 K), an anomalous feature of the studied characteristics with a deviation towards lower values is also observed, which we attribute to the increased influence of the anharmonicity of the vibrations of the solution lattice. It is established that the occurrence of the mechanisms of the revealed anomalies may be attributed to the structural disorder of the solid solution due to the random nature of the placement of Tm3+ ions when replacing Ba2+ ions in the metal sublattice, as well as the appearance of F− ions in the interstitial spaces of the barium difluoride structure. [ABSTRACT FROM AUTHOR]