AbstractThe thermal behaviour of a natural allanite-(Ce) has been investigated up to 1073 K (at room pressure) by means of in situ synchrotron powder X-ray diffraction and single-crystal neutron diffraction. Allanite preserves its crystallinity up to 1073 K. However, up to 700 K, the thermal behaviour along the three principal crystallographic axes, of the monoclinic β angle and of the unit-cell volume follow monotonically increasing trends, which are almost linear. At T > 700–800 K, a drastic change takes place: an inversion of the trend is observed along the a and b axes (more pronounced along b) and for the monoclinic β angle; in contrast, an anomalous increase of the expansion is observed along the c axis, which controls the positive trend experienced by the unit-cell volume at T > 700–800 K. Data collected back to room T, after the HT experiments, show unit-cell parameters significantly different with respect to those previously measured at 293 K: allanite responds with an ideal elastic behaviour up to 700 K, and at T > 700–800 K its behaviour deviates from the elasticity field. The thermo-elastic behaviour up to 700 K was modelled with a modified Holland–Powell EoS; for the unit-cell volume, we obtained the following parameters: VT0 = 467.33(6) Å3 and αT0(V) = 2.8(3) × 10–5 K−1. The thermal anisotropy, derived on the basis of the axial expansion along the three main crystallographic directions, is the following: αT0(a):αT0(b):αT0(c) = 1.08:1:1.36. The T-induced mechanisms, at the atomic scale, are described on the basis of the neutron structure refinements at different temperatures. Evidence of dehydroxylation effect at T ≥ 848 K are reported. A comparison between the thermal behaviour of allanite, epidote and clinozoisite is carried out.
Black rubber and the non-linear elastic response of scale invariant solids