Ab initio variational approach for evaluating lattice thermal conductivity

By G. Fugallo, M. Lazzeri, L. Paulatto, F. Mauri. 2012

235 citations recorded by the source corpus.

We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us with an algorithm faster than the one previously used in literature and able to always converge to the exact solution [Omini and Sparavigna, Physica B: Condens. Matter 212, 101 (1995)]. Three-phonon normal and umklapp collisions, isotope scattering, and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than those commonly observed in isotopically enriched diamond samples with 99.93% C12 and 0.07 C13.

Subfields: Geophysics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/bb3a4b8dcdbcf4209fc5e0949749041631343b27

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In Geophysics

1. Wu Li
2. C. Hua
3. S. Lee
4. L. Lindsay
5. Natalio Mingo
6. Nicola Marzari
7. Jesús Carrete
8. X. Ruan

In Materials Chemistry

1. Xiaokun Gu
2. Ronggui Yang
3. Baowen Li
4. Xiaobo Yin
5. Yujie Wei
6. X. Ruan
7. C. Hua
8. S. Lee

Citations in the corpus

• Survey of ab initio phonon thermal transport (2018, background): “(2) is necessary, for example, by self-consistent iteration [16] or variational methods [17].”
• Colloquium: Phononic thermal properties of two-dimensional materials (2017, methodology): “To analyze the thermal conductivity of infinitely large 2D crystals through PBTE, ideally one needs to employ either the iterative approach (Omini and Sparavigna, 1996; Broido, Ward, and Mingo, 2005) or a variational method (Fugallo et al., 2013, 2014).”
• Phonon hydrodynamics and its applications in nanoscale heat transport (2015, unknown): “The full solution needs complicated numerical iteration [71] or ab initio variational approach [75].”
• Wigner Formulation of Thermal Transport in Solids (2021, methodology): “The LWTE conductivity (47) reduces to the LBTE conductivity in the limit of a simple crystal [14] (i.e. characterized by interband spacings much larger than the linewidths) and to the Allen–Feldman conductivity in the limit of a harmonic glass; most importantly, the LWTE conductivity (47) is more ge”
• ShengBTE: A solver of the Boltzmann transport equation for phonons (2014, background): “To date, ab-initio calculations of thermal conductivity have been applied to many bulk systems such as Si and Ge [12,16], diamond [17,18], MgO [15], SixGe1−x [19], PbSe, PbTe, and PbSexTe1−x [20], Ga–V compounds [21], Mg2Si, Mg2Sn and Mg2SixSn1−x [22], Al–V and In–V compounds [23], MgSiO3 [24,25], a”
• Lattice thermal conductivity of penta-graphene (2016, methodology): “In addition, this method only describes the depopulation of the phonon states rigorously, but entirely neglects the effect of the corresponding repopulation, which is assumed to have no memory of the initial phonon distributions [15,16].”