Thermodynamic grounds for the invar and ellinvar effects in ferromagnets

In terms of the standard thermodynamic approach (the Debye-Grüneisen model of solid and the Landau theory of second-order phase transitions), approximate conditions providing the constancy of the volumetric thermal expansion coefficient (the Invar effect) and of the bulk modulus (the Ellinvar effect) of a ferromagnet are established. Conditions under which a ferromagnet may exhibit Invar and Ellinvar properties simultaneously are found. Interaction between the magnetic, phonon, and electron subsystems of a ferromagnet is shown to be a crucial factor in the occurrence of the Invar and Ellinvar effects.