Properties of the one-particle-displacement probability distribution in systems undergoing antiferrodistortive structural phase transitions

Abstract

Using the Hartree approximation, a high-temperature expansion, and the molecular-dynamics technique, we study some properties of the one-particle probability distribution $F_1\left(U_x^{\overrightarrow{1}}\right)$ of the displacement $U_x$ of particle one in a model system. The system is two dimensional and subjected to constraints in such a way that it exhibits antiferrodistortive structural phase transitions. It covers the displacive and order-disorder regime, including the Ising and displacive limit. We present evidence that $F_1\left(U_x^{\overrightarrow{1}}\right)$ or its symmetrized analog ${\tilde{F}}_1\left(U_x^{\overrightarrow{1}}\right)=\frac{1}{2}\left[F_1\right(U_x^{\overrightarrow{1}})+F_1(-U_x^{\overrightarrow{1}}\left)\right]$, being a very useful property to elucidate the regime to which a particular antiferrodistortive transition belongs. In the displacive regime, the ratio $a_s=\frac{{\left(\frac{d}{d{U}_x^{\overrightarrow{1}}}{\tilde{F}}_1\left(U_x^{\overrightarrow{1}}\right)\right)}_{max}}{{\left(\frac{d}{d{U}_x^{\overrightarrow{1}}}{\tilde{F}}_1\left(U_x^{\overrightarrow{1}}\right)\right)}_{min}},$ for $U_x^{\overrightarrow{1}}$ either negative or positive, is shown to diverge at some temperature $T^{*}$, because ${\tilde{F}}_1\left(U_x^{\overrightarrow{1}}\right)$ exhibits for $T<\mathrm{}{T}^{*}$ a double-peak structure disappearing at $T=T^{*}$. In the order-disorder regime, the ratio $\frac{T^{*}}{T_c}$ is infinite and decreases in the displacive regime by approaching the displacive limit to some value

Keywords

• STRUCTURAL
• MSUBSUP
• MATH
• MROW
• MOVER
• XMLNS

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