[Paper Review] An unlikely route to low lattice thermal conductivity: small atoms in a simple layered structure

Wanyue Peng, Guido Petretto+3 more|arXiv (Cornell University)|Apr 4, 2018

Advanced Thermoelectric Materials and Devices41 references3 citations

TL;DR

This study reveals that Mg₃Sb₂ achieves exceptionally low lattice thermal conductivity (κₗ ~1.5 W/mK) not through structural complexity or high density, but due to intrinsic anharmonicity caused by undersized Mg²⁺ cations in octahedral sites, leading to soft, unstable interlayer bonding and highly anharmonic shear acoustic phonons. Ab initio calculations and resonant ultrasound spectroscopy confirm giant Grüneisen parameters and strong temperature-dependent softening of elastic moduli, identifying cation size mismatch as a novel route to low κₗ in simple, low-density materials.

ABSTRACT

In the design of materials with low lattice thermal conductivity, compounds with high density, low speed of sound, and complexity at either the atomic, nano- or microstructural level are preferred. The layered compound Mg$_3$Sb$_2$ defies these prevailing paradigms, exhibiting lattice thermal conductivity comparable to PbTe and Bi$_2$Te$_3$, despite its low density and simple structure. The excellent thermoelectric performance ($zT$ $\sim$ 1.5) in $n$-type Mg$_3$Sb$_2$ has thus far been attributed to its multi-valley conduction band, while its anomalous thermal properties have been largely overlooked. To explain the origin of the low lattice thermal conductivity of Mg$_3$Sb$_2$, we have used both experimental methods and ab initio phonon calculations to investigate trends in the elasticity, thermal expansion and anharmonicity of $A$Mg$_2Pn_2$ Zintl compounds with $A$ = Mg, Ca, Yb, and $Pn$ = Sb and Bi. Phonon calculations within the quasi-harmonic approximation reveal large mode Grüneisen parameters in Mg$_3$Sb$_2$ compared with isostructural compounds, in particular in transverse acoustic modes involving shearing of adjacent anionic layers. Measurements of the elastic moduli and sound velocity as a function of temperature using resonant ultrasound spectroscopy provide a window into the softening of the acoustic branches at high temperature, confirming their exceptionally high anharmonicity. We attribute the anomalous thermal behavior of Mg$_3$Sb$_2$ to the diminutive size of Mg, which may be too small for the octahedrally-coordinated site, leading to weak, unstable interlayer Mg-Sb bonding. This suggests more broadly that soft shear modes resulting from undersized cations provide a potential route to achieving low lattice thermal conductivity low-density, earth-abundant materials.

Motivation & Objective

• To explain the anomalously low lattice thermal conductivity (κₗ) of Mg₃Sb₂, which defies conventional design rules for low-κₗ materials.
• To investigate whether structural instability from cation size mismatch underlies the high anharmonicity and low κₗ in Mg₃Sb₂ and related AMg₂Pn₂ compounds.
• To determine the role of interlayer bonding and elastic softening in phonon scattering and thermal transport reduction.
• To establish a new design principle for low-κₗ materials based on cation size mismatch in layered ionic structures.

Proposed method

• Ab initio phonon calculations within the quasi-harmonic approximation to compute mode Grüneisen parameters and predict anharmonicity in AMg₂Pn₂ compounds (A = Mg, Ca, Yb; Pn = Sb, Bi).
• Resonant ultrasound spectroscopy (RUS) to measure temperature-dependent elastic moduli and sound velocity in Mg₃Sb₂ and reference compounds.
• Analysis of crystal structure distortions, bond angle variances, and coordination geometries to assess lattice instability from ionic radius mismatch.
• Comparison of κₗ values across AMg₂Pn₂ compounds using experimental data and calculated sound velocities to isolate structural effects.
• Use of Materials Project database for elastic moduli and density inputs to estimate mean sound velocity and κₗ scaling.
• Examination of high-temperature phase transitions in Mg₃Sb₂ and Mg₃Bi₂ to link structural instability with anharmonic behavior.

Experimental results

Research questions

• RQ1 Why does Mg₃Sb₂ exhibit lattice thermal conductivity comparable to PbTe and Bi₂Te₃ despite its low density and simple structure?
• RQ2 What is the origin of the high anharmonicity in Mg₃Sb₂’s acoustic phonon modes, particularly in transverse shear modes?
• RQ3 How does the undersized Mg²⁺ cation in the octahedral site affect interlayer bonding and elastic softening?
• RQ4 To what extent does cation size mismatch alone induce sufficient phonon scattering to achieve low κₗ in layered materials?
• RQ5 Can the instability of Mg²⁺ in octahedral coordination be linked to the observed high-temperature phase transition in Mg₃Sb₂?

Key findings

• Mg₃Sb₂ exhibits a lattice thermal conductivity (κₗ) of ~1.5 W/mK at room temperature, comparable to PbTe and Bi₂Te₃, despite having roughly half the density of these materials.
• Ab initio calculations reveal large, both positive and negative, mode Grüneisen parameters in Mg₃Sb₂, especially in transverse acoustic modes involving shearing of anionic layers, indicating strong anharmonicity.
• Resonant ultrasound spectroscopy shows a rapid decrease in elastic moduli and sound velocity with increasing temperature in Mg₃Sb₂, confirming strong softening of acoustic modes.
• The bond angle variance in Mg₃Sb₂’s Mg(1)Sb₆ octahedra (26.53°) is significantly higher than in CaMg₂Sb₂ (1.77°), indicating severe distortion and instability of the octahedral site.
• Mg₃Sb₂ undergoes a high-temperature phase transition (~900 °C) to a cubic structure with tetrahedral Mg coordination, confirming lattice instability from cation size mismatch.
• The study identifies cation size mismatch in layered ionic structures as a new mechanism for achieving low lattice thermal conductivity via soft shear modes and enhanced phonon scattering.