[Paper Review] Multihyperuniform Long-Range Order in Medium-Entropy Alloys

Duyu Chen, Xinyu Jiang+3 more|arXiv (Cornell University)|Nov 22, 2021

Thermal properties of materials4 citations

TL;DR

This paper presents strong numerical evidence for multihyperuniform long-range order (MHLRO) in SiGeSn medium-entropy alloys, where infinite-wavelength composition fluctuations for all three elements are fully suppressed. The MHLRO naturally induces short-range order, leading to lower-energy states, enhanced electronic band gaps (~0.50 eV), and superior low-temperature thermal conductivity (1.53 W/m·K) compared to random or SQS structures, enabling ideal mixing behavior consistent with Vegard’s law.

ABSTRACT

We provide strong numerical evidence for a hidden multihyperuniform long-range order (MHLRO) in SiGeSn medium-entropy alloys (MEAs), in which the normalized infinite-wavelength composition fluctuations for all three atomic species are completely suppressed as in a perfect crystalline state. We show this MHLRO naturally leads to the emergence of short-range order (SRO) recently discovered in MEAs, which results in stable lower-energy states compared to alloy models with random or special quasi-random structures (SQSs) possessing no atomic SROs. The MHLRO MEAs approximately realize the Vegard's law, which offers a rule-of-mixture type predictions of the lattice constants and electronic band gap, and thus can be considered as an ideal mixing state. The MHLRO also directly gives rise to enhanced electronic band gaps and superior thermal transport properties at low temperatures compared to random structures and SQSs, which open up novel potential applications in optoelectronics and thermoelectrics. Our analysis of the SiGeSn system leads to the formulation of general organizing principles applicable in other medium- and high-entropy alloys (HEAs), and a highly efficient computational model for rendering realistic large-scale configurations of MEAs and HEAs.

Motivation & Objective

• To investigate whether medium-entropy alloys (MEAs) with observed short-range order (SRO) also exhibit hidden long-range order.
• To determine if such long-range order suppresses large-scale composition fluctuations, akin to hyperuniformity.
• To evaluate the impact of this order on electronic structure, thermal transport, and energy stability in MEAs.
• To develop a computationally efficient model for generating realistic large-scale MEA and HEA configurations beyond random or SQS assumptions.
• To establish general organizing principles applicable to other MEAs and high-entropy alloys (HEAs).

Proposed method

• Numerical generation of multihyperuniform realizations of SiGeSn MEAs using a stochastic optimization framework to enforce suppression of infinite-wavelength composition fluctuations.
• Employment of density functional theory (DFT) and classical molecular dynamics (MD) with the Stillinger-Weber potential to compute energies and structural properties.
• Calculation of the static structure factor S(k) and local number variance σ²_N(R)/N(R) to verify hyperuniformity via lim_{k→0} S(k) = 0 and lim_{R→∞} σ²_N(R)/N(R) = 0.
• Comparison of band structures, phonon density of states (PDOS), and thermal conductivity between multihyperuniform, SQS, and random configurations.
• Analysis of atomic clustering and SRO using radial distribution functions and coordination number statistics.
• Validation of Vegard’s law compliance by comparing lattice constants and band gaps to weighted averages of pure elements.

Experimental results

Research questions

• RQ1 Does the presence of short-range order in medium-entropy alloys imply the existence of hidden multihyperuniform long-range order?
• RQ2 To what extent does multihyperuniform long-range order suppress composition fluctuations across all atomic species in MEAs?
• RQ3 How does MHLRO affect the electronic band gap and thermal conductivity of SiGeSn MEAs compared to random or SQS structures?
• RQ4 Can MHLRO explain the observed stability and lower energy states in MEAs with SRO?
• RQ5 To what extent does the MHLRO configuration approximate ideal mixing behavior as described by Vegard’s law?

Key findings

• The multihyperuniform SiGeSn MEA exhibits a direct band gap of 0.50 eV at the Γ point, significantly higher than the 0.28 eV in random and 0.36 eV in SQS structures.
• The band gap of the MHLRO structure is nearly the average of the pure elements (0.59 eV), indicating approximate realization of Vegard’s law and ideal mixing.
• Low-temperature thermal conductivity reaches 1.53 W/m·K for the multihyperuniform structure, exceeding the 0.87 W/m·K of the random structure at 10 K.
• The phonon density of states for the MHLRO system shows a gap-like feature near 280 cm⁻¹, reducing phonon partition ratio and contributing to lower thermal conductivity at high temperatures.
• The MHLRO configuration results in lower total energy compared to both random and SQS structures, indicating greater thermodynamic stability.
• The multihyperuniform model successfully suppresses large-scale composition fluctuations and generates SRO consistent with recent experimental observations.