Peter Sondergeld

Displacive components of the low-temperature phase transitions in lawsonite

Abstract The phase transitions in deuterated lawsonite were investigated with high-resolution, time-offlight neutron diffraction between 2 and 500 K. From the analysis of spontaneous strain data, the thermodynamics of the phase transition at 273 K are not changed by the deuteration process. Shifts in atomic positions with temperature indicate continuous changes for a framework oxygen and for one of the deuterium atoms, whereas for the other deuterium atom, a more discontinuous behavior was observed in the average structure. Comparison of O···D and O···O bond lengths with IR data from a non-deuterated lawsonite permits a detailed analysis of assignments of O-H stretching modes

Local and macroscopic order parameter variations associated with low temperature phase transitions in lawsonite, CaAl2Si2O7(OH)2·H2O

The temperature dependence of lattice parameters and dilatation data of natural lawsonite shows anomalies at 265 K and 130 K. The spontaneous strains are relatively small (a few per mill) and the components of the strain tensor allowed in the respective point groups show almost tricritical behaviour. At temperatures below ∼100 K order parameter saturation is observed. IR spectra of lawsonite were investigated at temperatures between 50 and 500 K in the range from 150–4500 cm −1 . The autocorrelation function has been used to quantify the decrease in line widths, which occurs with falling temperature due to phase transitions. Changes in frequency, Δω, due to ordering and changes of the line width have been used to characterise the state of local order over the temperature range. The IR data reveal an almost tricritical behaviour for the square of the effective line width of (δΔcorr) 3800 . (δΔcorr) 2 3800 , (Δω) 2 3650 and (δω) 2 900 correlate to the square of the e 1 strain component. (δΔcorr) 2 900 , and (Δω) 2 3550 seem to follow a more complex behaviour of the strain components e 2 2 and e 3 2 . The findings from IR and strain analysis allow the transitions to be understood as strain mediated ordering processes of protons in a channel parallel to the crystallographic c-axis. Close adherence to a Landau pattern of order parameter evolution suggests that the main driving force may be a displacive lattice distortion with a soft mode origin, however.

Ordering behaviour of the mineral lawsonite

Abstract Lawsonite crystals have been investigated by dilatometry and dynamic mechanical analysis as well as by measurements of the optical birefringence and the dielectric constant in the temperature range 90K ≤T ≤ 633K. Two successive phase transitions have been found at low temperatures. The analysis of the spontaneous strain and the excess birefringence data reveals that the transition around 273 K (T 1) is tricritical. The other transition around 120K. (T 2) is of second order and proper ferroelectric. The mineral shows remarkable pretransitional effects in a temperature range up to 200 K. above T 1. The data below T 2 are interpreted in terms of a mutual interference of the two different ordering processes associated with T 1 and T 2, respectively.

Discontinuous evolution of single‐crystal elastic constants as a function of pressure through the C2/c ↔ P21/c phase transition in spodumene (LiAlSi2O6)

A Landau free energy expansion in one order parameter has been developed to describe the first-order C2/c ↔ P21/c phase transition at high pressures in spodumene (LiAlSi2O6). The complete set of elastic constants required for this model was determined at ambient conditions by resonant ultrasound spectroscopy. Other coefficients in the 246 expansion were calibrated using lattice parameter data from the literature, which had been collected by following the transition in a diamond anvil cell. The complete calibration leads to predictions of significant, abrupt changes in elastic constants at the transition point, 3.19 GPa, which have then been tested against ultrasonic data obtained in situ at high pressures in a uniaxial split cylinder apparatus. Velocities of compressional waves in three mutually perpendicular directions through single crystals of spodumene were measured and used to extract elastic constant data. The transition, indeed, causes large, abrupt changes of single-crystal elastic constants with increasing pressure. Steep increases in attenuation were also observed in the vicinity of the transition point for two directions and over a broader pressure interval in the third direction. The Landau expansion reproduces the general form of the elastic anomalies, even though it does not do as well for spontaneous strain variations. If this type of transition occurred in mantle pyroxenes (or in any other mantle phase), it would be expected to leave a distinctive signature in seismic velocity profiles of the Earths interior.

Ordering and elasticity associated with low-temperature phase transitions in lawsonite

Abstract The two low-temperature phase transitions of lawsonite have been studied using single-crystal X-ray diffraction from 86 to 318 K and a single-crystal high-frequency continuous-wave resonance technique from 323 to 102 K. While recently published data of the variations of strains, birefringence, and IR line widths are consistent with the (271 K) Cmcm-Pmcn transition being simply tricritical, our investigation of critical X-ray reflections and the six diagonal elastic constants of lawsonite reveals, consistently, a more complex crossover pattern in the temperature range of 205.225 K. Below 205 K the overall pattern is again in good agreement with a tricritical solution of the Cmcm-Pmcn transition and a second-order behavior of the (120 K) Pmcn-P21cn transition. The structure determination from single-crystal X-ray data at 215 K reveals a possible orientational disorder of some of the hydroxyl groups in the Pmcn phase. From this and a recent strain analysis of deuterated and hydrogenated lawsonite we conclude that down to 205 K the Cmcm-Pmcn transition is driven by a displacive component, as observed in strain and birefringence data, plus an order/disorder component or dynamical effects associated with proton ordering. Below 205 K only the displacive component plays a role, and the (120 K) Pmcn-P21cn transition is driven by a single order parameter. The remarkable elastic softening of C66 ahead of the Cmcm-Pmcn transition indicates another orthorhombic-monoclinic transition, which is suppressed on cooling through the low-temperature phase sequence Cmcm-Pmcn-P21cn, but can be observed on applying pressure to the mineral.

Crossover from classical to 3d-Ising critical behaviour near the antiferrodistortive phase transition of lawsonite.

Abstract Results of X-ray scattering intensities and peak profiles of lawsonite single crystals are presented in a wide temperature range including the antiferrodistortive phase transition Cmcm – (Tc ∼ 270 K) → Pmcn. In the integrated intensities of the superlattice reflections above Tc pronounced pretransitional tails similar to those detected recently in birefringence [P. Sondergeld et al., Phys. Rev. B62, 6143 (2000)] and in excess entropy data [S. A. Hayward et al., Eur. J. Min. 14, 1145 (2002)] are observed. These tails correspond to diffuse Lorentzian shaped scattering peaks. The temperature variation of the diffuse scattering intensity and profile can be well described within a Landau-Ginzburg model. In combination with entropy data we obtain a complete set of free energy parameters. Using these coefficients we are able to fit the spontaneous part and the precursor tails of the integrated intensities, the excess birefringence and entropy in a broad temperature range outside a temperature interval of about ±3 K around Tc. In the vicinity of Tc the experimental data are in excellent agreement with the predictions of a crossover model, the effective critical exponent αeff(τ) varying from the classical (αeff = 0.5) to the 3d Ising limit (αeff = 0.11). Lawsonite therefore represents an ideal system to study the crossover from classical to critical behavior.