The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: A high precission static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi2O6, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around similar to 3.2 and similar to 7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c-P2(1)/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P (tr), thus giving Landau parameters of K (0) = 138.3(2) GPa, K’ = 7.46(5), lambda (V) = 33.6(2) GPa, a = 0.486(3), b = -29.4(6) GPa and c = 551(11) GPa.

💡 Research Summary

The authors present a comprehensive high‑pressure investigation of spodumene (LiAlSi₂O₆) using static compression in a diamond‑anvil cell (DAC) up to 9.3 GPa. The study combines single‑crystal X‑ray diffraction (XRD) and Raman spectroscopy, both performed under hydrostatic conditions provided by a 4:1 methanol‑ethanol pressure medium. A total of 59 pressure points were recorded for the lattice parameters (a, b, c, β) and unit‑cell volume, while Raman spectra were collected at 14 pressures between 1 and 9 GPa.

The primary focus is the well‑known first‑order phase transition from the monoclinic C2/c structure to the higher‑pressure P2₁/c structure near 3.2 GPa. The authors confirm this transition with a 1.2 % volume collapse, a narrow hysteresis of 0.02–0.06 GPa, and a clear increase in the number of Raman‑active modes (from 18 to 26) between 3.4 and 3.6 GPa. The transition pressure determined from compression data (3.19 GPa on compression, 3.18 GPa on decompression) matches previous reports, but the finer pressure steps reveal that an outlying data point reported earlier at 3.19 GPa is not reproducible.

A secondary claim in the literature— a second structural transition around 7.7 GPa based on Raman intensity changes— is examined in detail. The present Raman data show only minor intensity variations for a few modes near 7 GPa, and the XRD data exhibit no discontinuities in lattice parameters or volume. Consequently, the authors argue that no distinct structural phase transition occurs at this pressure.

To quantify the elastic anomalies associated with the 3.2 GPa transition, the authors calculate spontaneous strain components, volume strain, and bulk moduli from the measured lattice parameters. The strain tensor shows pronounced jumps in e₁₁, e₃₃, and the shear component e₁₃, while e₂₂ remains relatively unchanged above the transition, indicating non‑symmetry‑breaking strain components that nevertheless couple to the order parameter.

A modified Landau free‑energy expansion is developed to describe the pressure dependence of the bulk modulus and the observed anomalies. Unlike previous treatments that made the quadratic coefficient linearly dependent on pressure (a(P‑Pc)), the authors treat it as pressure‑independent (a(T‑Tc)), thereby avoiding mixed stress‑strain variables. The simplified Landau functional includes the bulk modulus K₀ of the low‑pressure phase, a volume‑strain coupling λ_V, and a sixth‑order polynomial in the order parameter Q. By minimizing the free energy with respect to Q and the volume strain, analytical expressions for the equilibrium order parameter and the Gibbs free energy are obtained.

Fitting this model to the experimental data yields the following Landau parameters: K₀ = 138.3 (2) GPa, K′ = 7.46 (5), λ_V = 33.6 (2) GPa, a = 0.486 (3), b = ‑29.4 (6) GPa, and c = 551 (11) GPa. These values reproduce the sharp change in bulk modulus at the transition and the large ∂K/∂P observed for the high‑pressure phase (≈8.9) compared with the low‑pressure phase (∂K/∂P < 4). The derived coupling constant a is consistent with earlier work (≈0.5), confirming the validity of the simplified Landau approach.

The authors also discuss the coexistence region between the two phases, estimating a pressure hysteresis width of about 1.09 GPa based on the fitted coefficients, which aligns with the experimentally observed narrow hysteresis. The volume discontinuity at the transition is linked to the order‑parameter jump via the relation Q_tr = √(−c/b), providing a thermodynamic consistency check.

In summary, this study delivers high‑resolution structural and spectroscopic data across the critical pressure range of spodumene, definitively confirms the single first‑order transition at ~3.2 GPa, refutes the existence of a second transition near 7.7 GPa, and offers a robust Landau‑theory framework that quantitatively captures the nonlinear elastic response. The work advances our understanding of pressure‑induced ferroelastic transitions in pyroxene‑type minerals and provides a methodological template for future high‑pressure investigations of elastic anomalies.