Third-order elastic constants of orthorhombic calcium formate

All 20 independent third-order elastic constants (TOEC) of orthorhombic calcium formate, Ca(HCOO)₂, Ca²⁺. C₂H₂O^2-₄, space group Pcab, have been determined with the aid of stress-induced shifts of ultrasonic resonance frequencies. Longitudinal and transverse effects possess negative values indicating the high stability of calcium formate over a wide pressure range. The anisotropy of TOEC, characterized by --c₁₁₁ > --c₃₃₃ > --c₂₂₂, corresponds with the anisotropy of second-order elastic constants (c₁₁ > c₃₃ > c₂₂). The value 5.22 for the pressure derivative of the inverse bulk compressibility coincides with the quasi- invariant value of ca 5 observed in most stable cubic crystals so far investigated. There exists a pronounced departure from third-order Cauchy relations: the 'transverse' constants exceed the corresponding 'shear' components considerably in absolute magnitude in accordance with the behaviour of the second-order Cauchy relations. These effects are explained as originating from the non-centrosymmetric formate ions. A comparison of TOEC of calcium formate and cubic calcium fluoride confirms the typical contribution of the formate ions to the third-order elastic behaviour.