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

Using the Hartree approximation, a high-temperature expansion, and the molecular-dynamics technique, we study some properties of the one-particle probability distribution F1(Ux1→) of the displacement Ux 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 F1(Ux1→) or its symmetrized analog F1(Ux1→)=12[F1(Ux1→)+F1(-Ux1→)], being a very useful property to elucidate the regime to which a particular antiferrodistortive transition belongs. In the displacive regime, the ratio as= ddUx1→F1(Ux1→)maxddUx1→F1(Ux1→)min, for Ux1→ either negative or positive, is shown to diverge at some temperature T*, because F1(Ux1→) exhibits for T<T* a double-peak structure disappearing at T=T*. In the order-disorder regime, the ratio TTc is infinite and decreases in the displacive regime by approaching the displacive limit to some value TTc<1. As Müller and Berlinger have shown, the key quantity as can be measured, close to Tc by means of the electron-paramagnetic-resonance technique. © 1974 The American Physical Society.