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# Combined ab initio and empirical model of the thermal conductivity of uranium, uranium-zirconium, and uranium-molybdenum

TL;DR: In this article, the authors developed a practical and general modeling approach for thermal conductivity of metals and metal alloys that integrates ab initio and semi-empirical physics-based models to maximize the strengths of both techniques.

Abstract: In this work we developed a practical and general modeling approach for thermal conductivity of metals and metal alloys that integrates ab initio and semiempirical physics-based models to maximize the strengths of both techniques. The approach supports creation of highly accurate, mechanistic, and extensible thermal conductivity modeling of alloys. The model was demonstrated on {\alpha}-U and U-rich U-Zr and U-Mo alloys, which are potential fuels for advanced nuclear reactors. The safe use of U-based fuels requires quantitative understanding of thermal transport characteristics of the fuel. The model incorporated both phonon and electron contributions, displayed good agreement with experimental data over a wide temperature range, and provided insight into the different physical factors that govern the thermal conductivity under different temperatures. This model is general enough to incorporate more complex effects like additional alloying species, defects, transmutation products, and noble gas bubbles to predict the behavior of complex metallic alloys like U-alloy fuel systems under burnup.

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01 Jan 2002

TL;DR: It is suggested that by 2020, the number of students attending classes at the University of Southern California will have risen to about 20,000, up from about 10,000 in 1980.

Abstract: ?? ????? ??????? ??? ????????????? ?????? ??????? ???? ??????? ????????????? ??? ???????? ?? 1978 ??? ?? ????? ?????? ???? ??? ?? 1980. ??????, ??????????? ??? 2020, ??????? 17 ???? ??? ??? ??????? 25 ?????????. ?? 1995 ?? ????? ??????????? ??? ????????? ?????? ???? ??????? ??? ??????, ???? ????????????????? ??? ???????? ??? ?????? ??? ????????? ?????? 8 ??? ??????????? ??? ??? ???? ??? ?????????. ?? ???????? ??? ????? ?????? ??? ????? ????????? ?? ????? ??????? ???? ?? ?? ????? ????????? ??????????? [1] ??? ?? ?????? ??????????? ???? ???????? [2], ???????? ??? Univ. of Southern California (???).

311 citations

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TL;DR: In this article, the thermophysical properties of the U3Si2 compound were investigated using a semi-empirical modified Embedded-Atom Method (MEAM) potential and density functional theory.

18 citations

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15 citations

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01 Jan 2020TL;DR: In this article, the authors present a review, demonstration, and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale, focusing primarily on the development and implementation of a unified methodology to enable predictive heat transport.

Abstract: We present a review, demonstration, and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the self-adjoint angular flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity (κeff), using Bose–Einstein source terms coupled through an average material temperature. This method provides a way of obtaining temperature using the linearized Boltzmann transport equation, without the necessary nonlinear outer iteration on temperature used in many approaches. Our thermal conductivity and heat flux results are consistent with existing research. We introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system and serves as an indicator of the amount of nonequilibrium behavior occurring in the system. We predict thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.

7 citations

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TL;DR: In this paper, a computational model of thermal conductivity based on density functional theory (DFT) calculations, physics rules, and experimental data, for concentrated binary metal alloys was developed.

4 citations

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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

146,533 citations

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TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.

Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

81,985 citations

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IBM

^{1}TL;DR: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way and can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function.

Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

61,450 citations

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TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.

Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

57,691 citations

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TL;DR: In this article, a method for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector is given, where the integration can be over the entire zone or over specified portions thereof.

Abstract: A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.

51,059 citations