An official website of the United States government
Abstract We present a phase-field crystal model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.
more »
« less
Thermoelastic modeling of cubic lattices from granular materials to atomic crystals
When a cubic lattice is confined by a surface layer, the effective thermoelastic properties can be tailored by the prestress produced by the surface. The thermal expansion coefficient, temperature derivative of elasticity, and the equation of state (EOS) of the solid depend on the potential of each bond and the lattice structure, which can be predicted by the recently developed singum model. This paper first uses a granular lattice confined by a spherical shell to demonstrate singum modeling of the thermoelastic behavior of the cubic lattices and then extends it to atomic crystal lattices by considering the surface tension and long-range interactions. Given the elasticity and the EOS of a cubic crystal, the interatomic potential can be inversely derived. As the bond length changes with thermal expansion and pressure, the singum model predicts the temperature- and pressure-dependent elasticity. Using the orientational average, isotropic elastic constants can be obtained for polycrystals. The case study of copper (Cu) demonstrates the versatility of the model for different cubic lattices and predicts the experimental results of pressure- and temperature-dependent elasticity. The singum model is general for different lattice types and EOS forms and provides clear physical and mechanical meanings to correlate the interatomic potential, EOS, and elasticity in the closed-form formulation, which is very useful in engineering design and analysis of metal structural members in fire, geothermal, and space applications without the needs of large-scale numerical simulations.
more »
« less
- PAR ID:
- 10593826
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 135
- Issue:
- 7
- ISSN:
- 0021-8979
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Mixed-space cluster expansion (MSCE), a first-principles method to simultaneously model the configuration-dependent short-ranged chemical and long-ranged strain interactions in alloy thermodynamics, has been successfully applied to binary FCC and BCC alloys. However, the previously reported MSCE method is limited to binary alloys with cubic crystal symmetry on a single sublattice. In the current work, MSCE is generalized to systems with multiple sublattices by formulating compatible reciprocal space interactions and combined with a crystal-symmetry-agnostic algorithm for the calculation of constituent strain energy. This generalized approach is then demonstrated in a hypothetical HCP system and Mg-Zn alloys. The current MSCE can significantly improve the accuracy of the energy parameterization and account for all the fully relaxed structures regardless of lattice distortion. The generalized MSCE method makes it possible to simultaneously analyze the short- and long-ranged configuration-dependent interactions in crystalline materials with arbitrary lattices with the accuracy of typical first-principles methods.more » « less
-
We present the combined results of single crystal X-ray diffraction, physical properties characterization, and theoretical assessment of EuSnP under high pressure. Single crystals of EuSnP prepared using Sn self-flux crystallize in the tetragonal NbCrN-type crystal structure (S.G. P 4/ nmm ) at ambient pressure. Previous studies have shown that for Eu ions, seven unpaired electrons impart a 2+ oxidation state. Assuming the oxidation states of Eu to be +2 and P to be −3, each Sn will donate one electron, with one p valence electron left for forming a weak Sn–Sn bond. According to the high-pressure single crystal X-ray diffraction measurements, no structural phase transition was observed up to ∼6.2 GPa. Temperature-dependent resistivity measurements up to 2.15 GPa on single crystals indicate that the phase-transition temperature occurring at the Néel temperature ( T N ) is significantly enhanced under high pressure. The robust crystallography and enhanced antiferromagnetic transition temperatures can be rationalized by the electronic structure calculations and chemical bonding analysis. The increasing Eu–P bonding interaction is consistent with the lattice parameter changing and enhanced T N . Moreover, the molecular orbital diagram shows that the weak Sn–Sn bond can be squeezed under pressure, acting as a compression buffer to stabilize the structure.more » « less
-
Abstract The elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli—directly tied to sound velocity—is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high‐temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.more » « less
-
A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Grüneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.more » « less
