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Abstract Although first principles based anharmonic lattice dynamics is one of the most common methods to obtain phonon properties, such method is impractical for high-throughput search of target thermal materials. We develop an elemental spatial density neural network force field as a bottom-up approach to accurately predict atomic forces of ~80,000 cubic crystals spanning 63 elements. The primary advantage of our indirect machine learning model is the accessibility of phonon transport physics at the same level as first principles, allowing simultaneous prediction of comprehensive phonon properties from a single model. Training on 3182 first principles data and screening 77,091 unexplored structures, we identify 13,461 dynamically stable cubic structures with ultralow lattice thermal conductivity below 1 Wm −1 K −1 , among which 36 structures are validated by first principles calculations. We propose mean square displacement and bonding-antibonding as two low-cost descriptors to ease the demand of expensive first principles calculations for fast screening ultralow thermal conductivity. Our model also quantitatively reveals the correlation between off-diagonal coherence and diagonal populations and identifies the distinct crossover from particle-like to wave-like heat conduction. Our algorithm is promising for accelerating discovery of novel phononic crystals for emerging applications, such as thermoelectrics, superconductivity, and topological phonons for quantum information technology. 

Full Heusler compounds have long been discovered as exceptional n-type thermoelectric materials. However, no p-type compounds could match the high n-type figure of merit ( ZT ). In this work, based on first-principles transport theory, we predict the unprecedentedly high p-type ZT = 2.2 at 300 K and 5.3 at 800 K in full Heusler CsK 2 Bi and CsK 2 Sb, respectively. By incorporating the higher-order phonon scattering, we find that the high ZT value primarily stems from the ultralow lattice thermal conductivity ( κ L ) of less than 0.2 W mK −1 at room temperature, decreased by 40% compared to the calculation only considering three-phonon scattering. Such ultralow κ L is rooted in the enhanced phonon anharmonicity and scattering channels stemming from the coexistence of antibonding-induced anharmonic rattling of Cs atoms and low-lying optical branches. Moreover, the flat and heavy nature of valence band edges leads to a high Seebeck coefficient and moderate power factor at optimal hole concentration, while the dispersive and light conduction band edges yield much larger electrical conductivity and electronic thermal conductivity ( κ e ), and the predominant role of κ e suppresses the n-type ZT . This study offers a deeper insight into the thermal and electronic transport properties in full Heusler compounds with strong phonon anharmonicity and excellent thermoelectric performance. 

Zintl phase Mg 3 Sb 2 , which has ultra-low thermal conductivity, is a promising anisotropic thermoelectric material. It is worth noting that the prediction and experiment value of lattice thermal conductivity ( κ ) maintain a remarkable difference, troubling the development and application. Thus, we firstly included the four-phonon scattering processes effect and performed the Peierls–Boltzmann transport equation (PBTE) combined with the first-principles lattice dynamics to study the lattice thermal transport in Mg 3 Sb 2 . The results showed that our theoretically predicted κ is consistent with the experimentally measured, breaking through the limitations of the traditional calculation methods. The prominent four-phonon scatterings decreased phonon lifetime, leading to the κ of Mg 3 Sb 2 at 300 K from 2.45 (2.58) W m −1 K −1 to 1.94 (2.19) W m −1 K −1 along the in (cross)-plane directions, respectively, and calculation accuracy increased by 20%. This study successfully explains the lattice thermal transport behind mechanism in Mg 3 Sb 2 and implies guidance to advance the prediction accuracy of thermoelectric materials. 

The Mg 3 Sb 2− x Bi x family has emerged as the potential candidates for thermoelectric applications due to their ultra-low lattice thermal conductivity ( κ L ) at room temperature (RT) and structural complexity. Here, using ab initio calculations of the electron-phonon averaged (EPA) approximation coupled with Boltzmann transport equation (BTE), we have studied electronic, phonon and thermoelectric properties of Mg 3 Sb 2− x Bi x (x = 0, 1, and 2) monolayers. In violation of common mass-trend expectations, increasing Bi element content with heavier Zintl phase compounds yields an abnormal change in κ L in two-dimensional Mg 3 Sb 2− x Bi x crystals at RT (∼0.51, 1.86, and 0.25 W/mK for Mg 3 Sb 2 , Mg 3 SbBi, and Mg 3 Bi 2 ). The κ L trend was detailedly analyzed via the phonon heat capacity, group velocity and lifetime parameters. Based on quantitative electronic band structures, the electronic bonding through the crystal orbital Hamilton population (COHP) and electron local function analysis we reveal the underlying mechanism for the semiconductor-semimetallic transition of Mg 3 Sb 2-− x Bi x compounds, and these electronic transport properties (Seebeck coefficient, electrical conductivity, and electronic thermal conductivity) were calculated. We demonstrate that the highest dimensionless figure of merit ZT of Mg 3 Sb 2− x Bi x compounds with increasing Bi content can reach ∼1.6, 0.2, and 0.6 at 700 K, respectively. Our results can indicate that replacing heavier anion element in Zintl phase Mg 3 Sb 2− x Bi x materials go beyond common expectations (a heavier atom always lead to a lower κ L from Slack’s theory), which provide a novel insight for regulating thermoelectric performance without restricting conventional heavy atomic mass approach.