Elastic and mechanical studies of the transition in LaP5O14: A continuous ferroelastic transition with a classical Landau-type behavior

We report a detailed experimental checking of the phenomenological Landau theory of phase transitions applied to a structural transition involving a homogeneous deformation (ferroelastic transition). We have determined the temperature dependence of 17 physical quantities on both sides of the ferroelastic transition ($\mathrm{mmm}\to \frac{2}{m}$; $T_c=125\mathrm{}$°C) of lanthanum pentaphosphate (La${\mathrm{P}}_5$ ${\mathrm{O}}_{14}$). At each temperature, the thermal-strain-tensor components have been measured by mechanical dilatometry and accurate $\gamma$-ray diffractometry, and the 13 components of the elastic-stiffness tensor have been deduced from Brillouin-scattering measurements performed in seven scattering configurations. The thermal-expansion coefficients are discontinuous at $T_c$ while the monoclinic shear $e_5$ continuously vanishes with the classical critical exponent $\beta =0.500\mathrm{}\pm 0.007$. The associated elastic constant $e_{55}$ is also found to vanish at $T_c$ with the exponents $\gamma ={\gamma }^{\prime }=1.00\mathrm{}\pm 0.02$ in relation with the occurrence of a soft transverse-acoustic mode. The temperature dependence of all the measured quantities is accounted for in the framework of the Landau theory using a free-energy expansion truncated at the fourth-order terms. The ferroelastic transition is assumed to be driven by the softening of a $B_{2g}$ soft optic mode whose normal coordinate is strongly and linearly coupled with $e_5$. This coordinate is also quadratically coupled with the diagonal components of the strain tensor. Thus the set of our experimental data can be satisfactorily fitted with only four coupling coefficients. Furthermore, this model can be quantitatively extended to the other isomorphous ferroelastic rare-earth pentaphosphates, and it predicts correctly the jump of the specific heat at $T_c$ and the pressure dependence of the soft-optic-mode frequency in good agreement with the available experimental data. Finally, the introduction of some corrective terms is discussed.