Magnetocaloric features of the NiMn$_{1-x}$Сr$_x$Ge system due to the diffuse nature of the first-order structural transitions $P6_3/mmc$ $\leftrightarrow$ $Pnma$

An approach is proposed to describe the magnetostructural features of the Mn$_{1-x}$Сr$_x$NiGe system within the concept of diffuse first-order phase transitions. The approach is based on the combination of two models for describing first-order structural transitions hex$(P6_3/mmc)$ $\leftrightarrow$ orth$(Pnma)$. The microscopic model of first-order point transitions is used to describe the phase state of a homogeneous medium of an orthorhombic phase nucleus. The thermodynamic model of redistribution of nuclei of both phases of a heterogeneous medium of a sample under the action of the entropy of mixing is used to describe the macroscopic phase state. Within the framework of the model used, an explanation is given for three types of phase transitions observed in systems with structural instability. It is shown that the reversible and first-order magnetostructural transitions observed in samples $x$ = 0.18, $x$ = 0.25, respectively, can be realized in sample $x$ = 0.11 with an isostructural second-order magnetic transition when the sample is subjected to hydrostatic pressure.