[Paper Review] Simulation study of negative thermal expansion in yttrium tungstate Y2W3O12

Leila H. N. Rimmer, Martin T. Dove|PubMed|Nov 25, 2014

Thermal Expansion and Ionic Conductivity34 references3 citations

TL;DR

This study investigates negative thermal expansion (NTE) in yttrium tungstate (Y₂W₃O₁₂) using density functional perturbation theory to compute phonon dispersion curves and mode Grüneisen parameters. It reveals that NTE arises from low-frequency phonons involving rigid-body rotations of WO₄ tetrahedra and Y–O rods, despite the absence of traditional rigid unit modes (RUMs), offering a new mechanism for NTE in non-RUM materials.

ABSTRACT

A simulation study of negative thermal expansion in Y2W3O12 was carried out using calculations of phonon dispersion curves through the application of density functional perturbation theory. The mode eigenvectors were mapped onto flexibility models and results compared with calculations of the mode Grüneisen parameters. It was found that many lower-frequency phonons contribute to negative thermal expansion in Y2W3O12, all of which can be described in terms of rotations of effectively rigid WO4 tetrahedra and Y-O rods. The results are strikingly different from previous phonon studies of higher-symmetry materials that show negative thermal expansion.

Motivation & Objective

• To understand the atomic-scale origin of negative thermal expansion (NTE) in Y₂W₃O₁₂, a material that exhibits strong NTE but lacks traditional rigid unit modes (RUMs).
• To investigate whether NTE in Y₂W₃O₁₂ arises from phonon modes involving rigid-body motions of structural units, despite the absence of RUMs.
• To compare the contributions of different phonon modes to NTE using Grüneisen parameters and flexibility models.
• To provide a mechanism for NTE in framework materials that do not support RUMs, expanding the theoretical understanding of NTE beyond the RUM model.

Proposed method

• Employed density functional perturbation theory (DFPT) to calculate phonon dispersion curves and eigenvectors for Y₂W₃O₁₂.
• Mapped phonon eigenvectors onto flexibility models using harmonic bond and angle potentials (E_bond = ½k(r−r₀)², E_angle = ½K(θ−θ₀)²) to identify rigid and flexible regions.
• Used eigenvector continuity across wave vectors (via e_k · e_{k+δk}) to track phonon modes and plot dispersion curves in reciprocal space.
• Calculated mode Grüneisen parameters by comparing phonon frequencies at different volumes, using eigenvector matching (e_k · e'_k) to ensure mode correspondence.
• Visualized results with color-coded dispersion curves: red for negative Grüneisen parameters, blue for positive, white for near-zero.
• Implemented models in the GULP lattice simulation program to assess structural flexibility independently of real-force constants.

Experimental results

Research questions

• RQ1 What phonon modes are responsible for negative thermal expansion in Y₂W₃O₁₂, a material that does not support rigid unit modes (RUMs)?
• RQ2 How do the eigenvectors of low-frequency phonons in Y₂W₃O₁₂ relate to the structural units (WO₄ tetrahedra and Y–O rods) and their collective motion?
• RQ3 To what extent do Grüneisen parameters of phonon modes correlate with NTE behavior in this system?
• RQ4 Can flexibility models based on rigid-body motion explain the observed NTE, even in the absence of RUMs?
• RQ5 How does the mechanism of NTE in Y₂W₃O₁₂ differ from that in conventional RUM-driven NTE materials like ZrW₂O₈ or ScF₃?

Key findings

• Many low-frequency phonons in Y₂W₃O₁₂ contribute to negative thermal expansion, with the dominant mechanism involving rotations of effectively rigid WO₄ tetrahedra and Y–O rods.
• The NTE in Y₂W₃O₁₂ is driven by phonons with negative Grüneisen parameters, indicating that increased thermal energy leads to reduced average unit cell volume.
• Despite the absence of RUMs, the structural units (WO₄ and Y–O) behave as rigid entities in the relevant low-frequency modes, supporting a modified RUM-like mechanism.
• The flexibility model analysis confirms that the dominant NTE-driving modes involve minimal bond stretching or angle distortion, consistent with rigid-body motion.
• The volumetric thermal expansion coefficient of Y₂W₃O₁₂ is approximately −21 MK⁻¹, with a linear expansion coefficient of −7.0 MK⁻¹, confirming strong NTE behavior.
• The results demonstrate a distinct mechanism for NTE that differs fundamentally from previous studies on high-symmetry RUM materials, highlighting the role of anisotropic, low-frequency rotations in non-RUM systems.