DOI: 10.1063/1.5064602. Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation

Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation

10.1063/1.5064602

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

A computational framework for predicting phonon frequencies, group velocities, scattering rates, and the resulting lattice thermal conductivity is described. The underlying theory and implementation suggestions are also provided. By using input from first principles calculations and taking advantage of advances in computational power, this framework has enabled thermal conductivity predictions that agree with experimental measurements for diverse crystalline materials over a wide range of temperatures. Density functional theory and density functional perturbation theory calculations are first used to obtain the harmonic and cubic force constants. The harmonic force constants are the input to harmonic lattice dynamics calculations, which provide the phonon frequencies and eigenvectors. The harmonic properties and the cubic force constants are then used with perturbation theory and/or phenomenological models to determine intrinsic and extrinsic scattering rates. The full set of phonon properties is then used to solve the Boltzmann transport equation for the mode populations and thermal conductivity. The extension of the framework to include higher-order processes, capture finite temperature effects, and model alloys is described. A case study on silicon is presented that provides benchmarking and convergence data. Available packages that implement the framework are compared.

Bibliography

McGaughey, A. J. H., Jain, A., Kim, H.-Y., & Fu, B. (2019). Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation. Journal of Applied Physics, 125(1).

Authors 4

Alan J. H. McGaughey (first)
Ankit Jain (additional)
Hyun-Young Kim (additional)
Bo Fu (additional)

References 138 Referenced 205

10.1103/PhysRev.120.358 / Phys. Rev. (1960)
10.1103/PhysRev.134.A471 / Phys. Rev. (1964)
10.1016/0038-1101(67)90069-X / Solid State Electron. (1967)
{'volume-title': 'Semiconducting Lead Chalcogenides', 'year': '1970', 'key': '2024042700010890900_c4'} / Semiconducting Lead Chalcogenides (1970)
10.1103/PhysRevB.66.195304 / Phys. Rev. B (2002)
10.1016/S0022-0248(02)01753-0 / J. Cryst. Growth (2002)
10.1002/(ISSN)1521-3951 / Phys. Status Solidi B (2003)
10.1002/(ISSN)1610-1642 / Phys. Status Solidi C (2004)
10.1063/1.2930679 / Appl. Phys. Lett. (2008)
10.1016/j.jeurceramsoc.2013.08.009 / J. Eur. Ceram. Soc. (2014)
10.1103/PhysRevB.80.125203 / Phys. Rev. B (2009)
10.1103/PhysRevB.87.165201 / Phys. Rev. B (2013)
10.7567/APEX.8.071501 / Appl. Phys. Exp. (2015)
10.1103/PhysRevB.85.155203 / Phys. Rev. B (2012)
10.1615/AnnualRevHeatTransfer.v17 / Annu. Rev. Heat Transfer (2014)
10.1063/1.2822891 / Appl. Phys. Lett. (2007)
10.1103/PhysRevB.84.085204 / Phys. Rev. B (2011)
10.1615/AnnualRevHeatTransfer.v17 / Annu. Rev. Heat Transfer (2014)
10.1080/15567265.2016.1218576 / Nanoscale Microscale Thermophys. Eng. (2016)
10.1039/C5CP00437C / Phys. Chem. Chem. Phys. (2015)
10.1137/16M1077325 / Multiscale Model. Simul. (2017)
10.1063/1.1310223 / J. Chem. Phys. (2000)
10.1103/PhysRevB.72.014308 / Phys. Rev. B (2005)
10.1103/PhysRevB.79.104204 / Phys. Rev. B (2009)
10.1103/PhysRevLett.75.1819 / Phys. Rev. Lett. (1995)
10.1103/PhysRevB.53.9064 / Phys. Rev. B (1996)
10.1103/PhysRevB.88.045430 / Phys. Rev. B (2013)
10.1103/PhysRevLett.110.265506 / Phys. Rev. Lett. (2013)
10.1088/0953-8984/26/22/225402 / J. Phys. Condens. Matter (2014)
10.1016/j.cpc.2017.06.023 / Comput. Phys. Commun. (2017)
10.1103/PhysRevB.91.094306 / Phys. Rev. B (2015)
10.1016/j.cpc.2014.02.015 / Comput. Phys. Commun. (2014)
{'volume-title': 'Density Functional Theory of Molecules, Clusters, and Solids', 'year': '1995', 'key': '2024042700010890900_c33'} / Density Functional Theory of Molecules, Clusters, and Solids (1995)
{'volume-title': 'Density Functional Theory: A Practical Introduction', 'year': '2009', 'key': '2024042700010890900_c34'} / Density Functional Theory: A Practical Introduction (2009)
10.1103/RevModPhys.73.515 / Rev. Mod. Phys. (2001)
{'year': '2013', 'key': '2024042700010890900_c36'} (2013)
10.1088/0953-8984/21/39/395502 / J. Phys. Condens. Matter (2009)
10.1103/PhysRevB.71.035109 / Phys. Rev. B (2005)
10.1088/0953-8984/22/25/253202 / J. Phys. Condens. Matter (2010)
10.1103/PhysRevB.47.558 / Phys. Rev. B (1993)
10.1103/PhysRevB.49.14251 / Phys. Rev. B (1994)
10.1103/PhysRevB.54.11169 / Phys. Rev. B (1996)
10.1016/0927-0256(96)00008-0 / Comput. Mater. Sci. (1996)
10.1016/j.cpc.2009.06.022 / Comput. Phys. Commun. (2009)
10.1016/j.cpc.2016.04.003 / Comput. Phys. Commun. (2016)
10.1088/1361-648X/aa680e / J. Phys. Condens. Matter (2017)
10.1103/PhysRev.140.A1133 / Phys. Rev. (1965)
10.1103/PhysRevB.46.6671 / Phys. Rev. B (1992)
10.1103/PhysRevLett.77.3865 / Phys. Rev. Lett. (1996)
10.1063/1.1390175 / AIP Conf. Proc. (2001)
10.1016/j.commatsci.2015.08.014 / Comput. Mater. Sci. (2015)
10.1016/j.commatsci.2018.05.007 / Comput. Mater. Sci. (2018)
10.1063/1.5027619 / J. Appl. Phys. (2018)
{'volume-title': 'Modeling Materials Using Density Functional Theory', 'year': '2008', 'key': '2024042700010890900_c54'} / Modeling Materials Using Density Functional Theory (2008)
A. Togo and I.Tanaka, preprint arXiv:1808.01590 (2018).
10.1103/PhysRevB.77.144112 / Phys. Rev. B (2008)
10.1103/PhysRevB.86.174307 / Phys. Rev. B (2012)
{'volume-title': 'Introduction to Lattice Dynamics', 'year': '1993', 'key': '2024042700010890900_c58'} / Introduction to Lattice Dynamics (1993)
10.1615/AnnualRevHeatTransfer.v17 / Annu. Rev. Heat Transfer (2014)
10.1103/PhysRevB.13.5188 / Phys. Rev. B (1976)
{'volume-title': 'Statistical Mechanics', 'year': '2000', 'key': '2024042700010890900_c61'} / Statistical Mechanics (2000)
10.1140/epjb/e2008-00195-8 / Eur. Phys. J. B (2008)
10.1103/PhysRevLett.79.1885 / Phys. Rev. Lett. (1997)
{'volume-title': 'Thermodynamics of Crystals', 'year': '1972', 'key': '2024042700010890900_c64'} / Thermodynamics of Crystals (1972)
10.1080/0892702031000104887 / Mol. Simul. (2003)
10.1103/PhysRevB.39.5261 / Phys. Rev. B (1989)
{'volume-title': 'The Physics of Phonons', 'year': '1973', 'key': '2024042700010890900_c67'} / The Physics of Phonons (1973)
A. Ward , Ph.D. thesis (Boston College, Boston, MA, 2009).
A. Jain , Ph.D. thesis (Carnegie Mellon University, Pittsburgh, PA, 2015).
10.1088/0953-8984/20/16/165209 / J. Phys. Condens. Matter (2008)
10.1103/PhysRevB.79.064301 / Phys. Rev. B (2009)
10.1103/PhysRevB.82.115427 / Phys. Rev. B (2010)
10.1103/PhysRevX.6.041013 / Phys. Rev. X (2016)
10.1021/acs.nanolett.7b01202 / Nano Lett. (2017)
10.1038/srep15640 / Sci. Rep. (2015)
10.1063/1.4993601 / J. Appl. Phys. (2017)
10.1098/rstl.1864.0004 / Philos. Trans. R. Soc. London (1864)
{'volume-title': 'Electrons and Phonons', 'year': '2001', 'key': '2024042700010890900_c78'} / Electrons and Phonons (2001)
10.1063/1.4821117 / Appl. Phys. Lett. (2013)
10.1103/PhysRevB.92.235206 / Phys. Rev. B (2015)
10.1103/PhysRevB.27.858 / Phys. Rev. B (1983)
10.1103/PhysRevB.81.045408 / Phys. Rev. B (2010)
10.1103/PhysRevB.90.094117 / Phys. Rev. B (2014)
10.1103/PhysRevLett.119.075902 / Phys. Rev. Lett. (2017)
10.1021/acs.nanolett.6b04756 / Nano Lett. (2017)
10.1088/1367-2630/aaa383 / New. J. Phys. (2018)
10.1103/PhysRevLett.114.115901 / Phys. Rev. Lett. (2015)
10.1063/1.4962010 / J. Appl. Phys. (2016)
10.1103/PhysRevB.76.165108 / Phys. Rev. B (2007)
{'volume-title': 'Many-Particle Physics', 'year': '2013', 'key': '2024042700010890900_c90'} / Many-Particle Physics (2013)
10.1016/j.cpc.2016.07.028 / Comput. Phys. Commun. (2016)
10.1103/PhysRevB.93.081206 / Phys. Rev. B (2016)
10.1063/1.4953366 / J. Appl. Phys. (2016)
10.1063/1.3644163 / Appl. Phys. Lett. (2011)
10.1063/1.4918703 / Appl. Phys. Lett. (2015)
10.1016/S0031-8914(38)80162-2 / Physica (1938)
10.1063/1.3683539 / Appl. Phys. Lett. (2012)
10.1103/PhysRevB.87.195301 / Phys. Rev. B (2013)
10.1103/PhysRevB.34.5058 / Phys. Rev. B (1986)
10.1103/PhysRevB.49.16223 / Phys. Rev. B (1994)
10.1063/1.4893185 / J. Appl. Phys. (2014)
10.1103/PhysRevB.56.9431 / Phys. Rev. B (1997)
10.1063/1.5040887 / Appl. Phys. Lett. (2018)
10.1103/PhysRevB.93.045202 / Phys. Rev. B (2016)
10.1103/PhysRevB.96.161201 / Phys. Rev. B (2017)
10.1103/PhysRevB.97.045202 / Phys. Rev. B (2018)
10.1103/PhysRevB.98.085205 / Phys. Rev. B (2018)
10.1126/science.aat7932 / Science (2018)
10.1126/science.aat5522 / Science (2018)
10.1126/science.aat8982 / Science (2018)
10.1103/PhysRevB.92.144308 / Phys. Rev. B (2015)
10.1103/PhysRevB.84.180301 / Phys. Rev. B (2011)
10.1103/PhysRevB.87.104111 / Phys. Rev. B (2013)
10.1103/PhysRevB.88.144301 / Phys. Rev. B (2013)
10.1103/PhysRevB.95.014302 / Phys. Rev. B (2017)
10.1103/PhysRevLett.119.185901 / Phys. Rev. Lett. (2017)
10.1016/j.commatsci.2008.06.016 / Comput. Mater. Sci. (2009)
10.1103/PhysRevB.92.054301 / Phys. Rev. B (2015)
10.1063/1.5048799 / J. Appl. Phys. (2018)
10.1103/PhysRevLett.106.045901 / Phys. Rev. Lett. (2011)
10.1209/0295-5075/102/46002 / EPL (Europhys. Lett.) (2013)
M. Arrigoni , J.Carrete, N.Mingo, and G. K. H.Madsen, Phys. Rev. B98, 115205 (2018). 10.1103/PhysRevB.98.115205 (10.1103/PhysRevB.98.115205)
10.1103/PhysRevB.89.144303 / Phys. Rev. B (2014)
{'key': '2024042700010890900_c124'}
10.7566/JPSJ.87.041015 / J. Phys. Soc. Jpn. (2018)
10.1002/wcms.1360 / Wiley Interdiscip. Rev. Comput. Mol. Sci. (2018)
10.1103/PhysRevLett.68.1858 / Phys. Rev. Lett. (1992)
10.1103/PhysRevB.54.5586 / Phys. Rev. B (1996)
10.1006/jcph.1995.1039 / J. Comput. Phys. (1995)
10.1103/PhysRevB.85.235149 / Phys. Rev. B (2012)
{'key': '2024042700010890900_c131'}
10.1126/science.aar8072 / Science (2018)
10.1103/PhysRevB.48.12581 / Phys. Rev. B (1993)
10.1103/PhysRevB.48.12589 / Phys. Rev. B (1993)
10.1088/1367-2630/18/1/013028 / New J. Phys. (2016)
10.1103/PhysRevB.81.205441 / Phys. Rev. B (2010)
10.1038/s41524-017-0026-y / NPJ Comput. Mater. (2017)
10.1063/1.5020611 / J. Appl. Phys. (2018)

Dates

Type	When
Created	6 years, 7 months ago (Jan. 3, 2019, 11:31 a.m.)
Deposited	1 year, 4 months ago (April 26, 2024, 8:01 p.m.)
Indexed	3 days, 1 hour ago (Aug. 23, 2025, 9:38 p.m.)
Issued	6 years, 7 months ago (Jan. 3, 2019)
Published	6 years, 7 months ago (Jan. 3, 2019)
Published Online	6 years, 7 months ago (Jan. 3, 2019)
Published Print	6 years, 7 months ago (Jan. 7, 2019)

Funders 2

National Science Foundation 10.13039/100000001
Region: Americas
gov (National government)
Labels4
1. U.S. National Science Foundation
2. NSF
3. US NSF
4. USA NSF
Awards1
1. DMR-1507325
China Scholarship Council 10.13039/501100004543
Region: Asia
gov (National government)
Labels1
1. CSC
Awards1
1. 201706280251

BibTeX

@article{McGaughey_2019, title={Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation}, volume={125}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.5064602}, DOI={10.1063/1.5064602}, number={1}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={McGaughey, Alan J. H. and Jain, Ankit and Kim, Hyun-Young and Fu, Bo}, year={2019}, month=jan }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        24
      ]
    ],
    "date-time": "2025-08-24T01:38:00Z",
    "timestamp": 1755999480541,
    "version": "3.41.2"
  },
  "reference-count": 138,
  "publisher": "AIP Publishing",
  "issue": "1",
  "funder": [
    {
      "DOI": "10.13039/100000001",
      "name": "National Science Foundation",
      "doi-asserted-by": "publisher",
      "award": [
        "DMR-1507325"
      ],
      "id": [
        {
          "id": "10.13039/100000001",
          "id-type": "DOI",
          "asserted-by": "publisher"
        }
      ]
    },
    {
      "DOI": "10.13039/501100004543",
      "name": "China Scholarship Council",
      "doi-asserted-by": "publisher",
      "award": [
        "201706280251"
      ],
      "id": [
        {
          "id": "10.13039/501100004543",
          "id-type": "DOI",
          "asserted-by": "publisher"
        }
      ]
    }
  ],
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2019,
        1,
        7
      ]
    ]
  },
  "abstract": "<jats:p>A computational framework for predicting phonon frequencies, group velocities, scattering rates, and the resulting lattice thermal conductivity is described. The underlying theory and implementation suggestions are also provided. By using input from first principles calculations and taking advantage of advances in computational power, this framework has enabled thermal conductivity predictions that agree with experimental measurements for diverse crystalline materials over a wide range of temperatures. Density functional theory and density functional perturbation theory calculations are first used to obtain the harmonic and cubic force constants. The harmonic force constants are the input to harmonic lattice dynamics calculations, which provide the phonon frequencies and eigenvectors. The harmonic properties and the cubic force constants are then used with perturbation theory and/or phenomenological models to determine intrinsic and extrinsic scattering rates. The full set of phonon properties is then used to solve the Boltzmann transport equation for the mode populations and thermal conductivity. The extension of the framework to include higher-order processes, capture finite temperature effects, and model alloys is described. A case study on silicon is presented that provides benchmarking and convergence data. Available packages that implement the framework are compared.</jats:p>",
  "DOI": "10.1063/1.5064602",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2019,
        1,
        3
      ]
    ],
    "date-time": "2019-01-03T16:31:12Z",
    "timestamp": 1546533072000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 205,
  "title": "Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation",
  "prefix": "10.1063",
  "volume": "125",
  "author": [
    {
      "ORCID": "https://orcid.org/0000-0001-8777-9923",
      "authenticated-orcid": false,
      "given": "Alan J. H.",
      "family": "McGaughey",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Mechanical Engineering, Carnegie Mellon University 1 , Pittsburgh, Pennsylvania 15213, USA"
        }
      ]
    },
    {
      "ORCID": "https://orcid.org/0000-0002-8963-7774",
      "authenticated-orcid": false,
      "given": "Ankit",
      "family": "Jain",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Mechanical Engineering, Carnegie Mellon University 1 , Pittsburgh, Pennsylvania 15213, USA"
        }
      ]
    },
    {
      "given": "Hyun-Young",
      "family": "Kim",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Mechanical Engineering, Carnegie Mellon University 1 , Pittsburgh, Pennsylvania 15213, USA"
        }
      ]
    },
    {
      "given": "Bo",
      "family": "Fu",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2019,
        1,
        3
      ]
    ]
  },
  "reference": [
    {
      "key": "2024042700010890900_c1",
      "doi-asserted-by": "publisher",
      "first-page": "358",
      "DOI": "10.1103/PhysRev.120.358",
      "volume": "120",
      "year": "1960",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024042700010890900_c2",
      "doi-asserted-by": "publisher",
      "first-page": "A471",
      "DOI": "10.1103/PhysRev.134.A471",
      "volume": "134",
      "year": "1964",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024042700010890900_c3",
      "doi-asserted-by": "publisher",
      "first-page": "161",
      "DOI": "10.1016/0038-1101(67)90069-X",
      "volume": "10",
      "year": "1967",
      "journal-title": "Solid State Electron."
    },
    {
      "volume-title": "Semiconducting Lead Chalcogenides",
      "year": "1970",
      "key": "2024042700010890900_c4"
    },
    {
      "key": "2024042700010890900_c5",
      "doi-asserted-by": "publisher",
      "first-page": "195304",
      "DOI": "10.1103/PhysRevB.66.195304",
      "volume": "66",
      "year": "2002",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c6",
      "doi-asserted-by": "publisher",
      "first-page": "287",
      "DOI": "10.1016/S0022-0248(02)01753-0",
      "volume": "246",
      "year": "2002",
      "journal-title": "J. Cryst. Growth"
    },
    {
      "key": "2024042700010890900_c7",
      "doi-asserted-by": "publisher",
      "first-page": "447",
      "DOI": "10.1002/(ISSN)1521-3951",
      "volume": "240",
      "year": "2003",
      "journal-title": "Phys. Status Solidi B"
    },
    {
      "key": "2024042700010890900_c8",
      "doi-asserted-by": "publisher",
      "first-page": "2995",
      "DOI": "10.1002/(ISSN)1610-1642",
      "volume": "1",
      "year": "2004",
      "journal-title": "Phys. Status Solidi C"
    },
    {
      "key": "2024042700010890900_c9",
      "doi-asserted-by": "publisher",
      "first-page": "191911",
      "DOI": "10.1063/1.2930679",
      "volume": "92",
      "year": "2008",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c10",
      "doi-asserted-by": "publisher",
      "first-page": "307",
      "DOI": "10.1016/j.jeurceramsoc.2013.08.009",
      "volume": "34",
      "year": "2014",
      "journal-title": "J. Eur. Ceram. Soc."
    },
    {
      "key": "2024042700010890900_c11",
      "doi-asserted-by": "publisher",
      "first-page": "125203",
      "DOI": "10.1103/PhysRevB.80.125203",
      "volume": "80",
      "year": "2009",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c12",
      "doi-asserted-by": "publisher",
      "first-page": "165201",
      "DOI": "10.1103/PhysRevB.87.165201",
      "volume": "87",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c13",
      "doi-asserted-by": "publisher",
      "first-page": "071501",
      "DOI": "10.7567/APEX.8.071501",
      "volume": "8",
      "year": "2015",
      "journal-title": "Appl. Phys. Exp."
    },
    {
      "key": "2024042700010890900_c14",
      "doi-asserted-by": "publisher",
      "first-page": "155203",
      "DOI": "10.1103/PhysRevB.85.155203",
      "volume": "85",
      "year": "2012",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c15",
      "doi-asserted-by": "publisher",
      "first-page": "205",
      "DOI": "10.1615/AnnualRevHeatTransfer.v17",
      "volume": "17",
      "year": "2014",
      "journal-title": "Annu. Rev. Heat Transfer"
    },
    {
      "key": "2024042700010890900_c16",
      "doi-asserted-by": "publisher",
      "first-page": "231922",
      "DOI": "10.1063/1.2822891",
      "volume": "91",
      "year": "2007",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c17",
      "doi-asserted-by": "publisher",
      "first-page": "085204",
      "DOI": "10.1103/PhysRevB.84.085204",
      "volume": "84",
      "year": "2011",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c18",
      "doi-asserted-by": "publisher",
      "first-page": "9",
      "DOI": "10.1615/AnnualRevHeatTransfer.v17",
      "volume": "17",
      "year": "2014",
      "journal-title": "Annu. Rev. Heat Transfer"
    },
    {
      "key": "2024042700010890900_c19",
      "doi-asserted-by": "publisher",
      "first-page": "67",
      "DOI": "10.1080/15567265.2016.1218576",
      "volume": "20",
      "year": "2016",
      "journal-title": "Nanoscale Microscale Thermophys. Eng."
    },
    {
      "key": "2024042700010890900_c20",
      "doi-asserted-by": "publisher",
      "first-page": "31360",
      "DOI": "10.1039/C5CP00437C",
      "volume": "17",
      "year": "2015",
      "journal-title": "Phys. Chem. Chem. Phys."
    },
    {
      "key": "2024042700010890900_c21",
      "doi-asserted-by": "publisher",
      "first-page": "29",
      "DOI": "10.1137/16M1077325",
      "volume": "15",
      "year": "2017",
      "journal-title": "Multiscale Model. Simul."
    },
    {
      "key": "2024042700010890900_c22",
      "doi-asserted-by": "publisher",
      "first-page": "6888",
      "DOI": "10.1063/1.1310223",
      "volume": "113",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024042700010890900_c23",
      "doi-asserted-by": "publisher",
      "first-page": "014308",
      "DOI": "10.1103/PhysRevB.72.014308",
      "volume": "72",
      "year": "2005",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c24",
      "doi-asserted-by": "publisher",
      "first-page": "115201",
      "DOI": "10.1103/PhysRevB.79.104204",
      "volume": "79",
      "year": "2009",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c25",
      "doi-asserted-by": "publisher",
      "first-page": "1819",
      "DOI": "10.1103/PhysRevLett.75.1819",
      "volume": "75",
      "year": "1995",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c26",
      "doi-asserted-by": "publisher",
      "first-page": "9064",
      "DOI": "10.1103/PhysRevB.53.9064",
      "volume": "53",
      "year": "1996",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c27",
      "doi-asserted-by": "publisher",
      "first-page": "045430",
      "DOI": "10.1103/PhysRevB.88.045430",
      "volume": "88",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c28",
      "doi-asserted-by": "publisher",
      "first-page": "265506",
      "DOI": "10.1103/PhysRevLett.110.265506",
      "volume": "110",
      "year": "2013",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c29",
      "doi-asserted-by": "publisher",
      "first-page": "225402",
      "DOI": "10.1088/0953-8984/26/22/225402",
      "volume": "26",
      "year": "2014",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "2024042700010890900_c30",
      "doi-asserted-by": "publisher",
      "first-page": "351",
      "DOI": "10.1016/j.cpc.2017.06.023",
      "volume": "220",
      "year": "2017",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "2024042700010890900_c31",
      "doi-asserted-by": "publisher",
      "first-page": "094306",
      "DOI": "10.1103/PhysRevB.91.094306",
      "volume": "91",
      "year": "2015",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c32",
      "doi-asserted-by": "publisher",
      "first-page": "1747",
      "DOI": "10.1016/j.cpc.2014.02.015",
      "volume": "185",
      "year": "2014",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "volume-title": "Density Functional Theory of Molecules, Clusters, and Solids",
      "year": "1995",
      "key": "2024042700010890900_c33"
    },
    {
      "volume-title": "Density Functional Theory: A Practical Introduction",
      "year": "2009",
      "key": "2024042700010890900_c34"
    },
    {
      "key": "2024042700010890900_c35",
      "doi-asserted-by": "publisher",
      "first-page": "515",
      "DOI": "10.1103/RevModPhys.73.515",
      "volume": "73",
      "year": "2001",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "year": "2013",
      "key": "2024042700010890900_c36"
    },
    {
      "key": "2024042700010890900_c37",
      "doi-asserted-by": "publisher",
      "first-page": "395502",
      "DOI": "10.1088/0953-8984/21/39/395502",
      "volume": "21",
      "year": "2009",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "2024042700010890900_c38",
      "doi-asserted-by": "publisher",
      "first-page": "035109",
      "DOI": "10.1103/PhysRevB.71.035109",
      "volume": "71",
      "year": "2005",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c39",
      "doi-asserted-by": "publisher",
      "first-page": "253202",
      "DOI": "10.1088/0953-8984/22/25/253202",
      "volume": "22",
      "year": "2010",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "2024042700010890900_c40",
      "doi-asserted-by": "publisher",
      "first-page": "558",
      "DOI": "10.1103/PhysRevB.47.558",
      "volume": "47",
      "year": "1993",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c41",
      "doi-asserted-by": "publisher",
      "first-page": "14251",
      "DOI": "10.1103/PhysRevB.49.14251",
      "volume": "49",
      "year": "1994",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c42",
      "doi-asserted-by": "publisher",
      "first-page": "11169",
      "DOI": "10.1103/PhysRevB.54.11169",
      "volume": "54",
      "year": "1996",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c43",
      "doi-asserted-by": "publisher",
      "first-page": "15",
      "DOI": "10.1016/0927-0256(96)00008-0",
      "volume": "6",
      "year": "1996",
      "journal-title": "Comput. Mater. Sci."
    },
    {
      "key": "2024042700010890900_c44",
      "doi-asserted-by": "publisher",
      "first-page": "2175",
      "DOI": "10.1016/j.cpc.2009.06.022",
      "volume": "180",
      "year": "2009",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "2024042700010890900_c45",
      "doi-asserted-by": "publisher",
      "first-page": "106",
      "DOI": "10.1016/j.cpc.2016.04.003",
      "volume": "205",
      "year": "2016",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "2024042700010890900_c46",
      "doi-asserted-by": "publisher",
      "first-page": "273002",
      "DOI": "10.1088/1361-648X/aa680e",
      "volume": "29",
      "year": "2017",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "2024042700010890900_c47",
      "doi-asserted-by": "publisher",
      "first-page": "A1133",
      "DOI": "10.1103/PhysRev.140.A1133",
      "volume": "140",
      "year": "1965",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024042700010890900_c48",
      "doi-asserted-by": "publisher",
      "first-page": "6671",
      "DOI": "10.1103/PhysRevB.46.6671",
      "volume": "46",
      "year": "1992",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c49",
      "doi-asserted-by": "publisher",
      "first-page": "3865",
      "DOI": "10.1103/PhysRevLett.77.3865",
      "volume": "77",
      "year": "1996",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c50",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1063/1.1390175",
      "volume": "577",
      "year": "2001",
      "journal-title": "AIP Conf. Proc."
    },
    {
      "key": "2024042700010890900_c51",
      "doi-asserted-by": "publisher",
      "first-page": "115",
      "DOI": "10.1016/j.commatsci.2015.08.014",
      "volume": "110",
      "year": "2015",
      "journal-title": "Comput. Mater. Sci."
    },
    {
      "key": "2024042700010890900_c52",
      "doi-asserted-by": "publisher",
      "first-page": "153",
      "DOI": "10.1016/j.commatsci.2018.05.007",
      "volume": "151",
      "year": "2018",
      "journal-title": "Comput. Mater. Sci."
    },
    {
      "key": "2024042700010890900_c53",
      "doi-asserted-by": "publisher",
      "first-page": "215105",
      "DOI": "10.1063/1.5027619",
      "volume": "123",
      "year": "2018",
      "journal-title": "J. Appl. Phys."
    },
    {
      "volume-title": "Modeling Materials Using Density Functional Theory",
      "year": "2008",
      "key": "2024042700010890900_c54"
    },
    {
      "key": "2024042700010890900_c55",
      "unstructured": "A.\n            Togo\n           and I.Tanaka, preprint arXiv:1808.01590 (2018)."
    },
    {
      "key": "2024042700010890900_c56",
      "doi-asserted-by": "publisher",
      "first-page": "144112",
      "DOI": "10.1103/PhysRevB.77.144112",
      "volume": "77",
      "year": "2008",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c57",
      "doi-asserted-by": "publisher",
      "first-page": "174307",
      "DOI": "10.1103/PhysRevB.86.174307",
      "volume": "86",
      "year": "2012",
      "journal-title": "Phys. Rev. B"
    },
    {
      "volume-title": "Introduction to Lattice Dynamics",
      "year": "1993",
      "key": "2024042700010890900_c58"
    },
    {
      "key": "2024042700010890900_c59",
      "doi-asserted-by": "publisher",
      "first-page": "49",
      "DOI": "10.1615/AnnualRevHeatTransfer.v17",
      "volume": "17",
      "year": "2014",
      "journal-title": "Annu. Rev. Heat Transfer"
    },
    {
      "key": "2024042700010890900_c60",
      "doi-asserted-by": "publisher",
      "first-page": "5188",
      "DOI": "10.1103/PhysRevB.13.5188",
      "volume": "13",
      "year": "1976",
      "journal-title": "Phys. Rev. B"
    },
    {
      "volume-title": "Statistical Mechanics",
      "year": "2000",
      "key": "2024042700010890900_c61"
    },
    {
      "key": "2024042700010890900_c62",
      "doi-asserted-by": "publisher",
      "first-page": "381",
      "DOI": "10.1140/epjb/e2008-00195-8",
      "volume": "62",
      "year": "2008",
      "journal-title": "Eur. Phys. J. B"
    },
    {
      "key": "2024042700010890900_c63",
      "doi-asserted-by": "publisher",
      "first-page": "1885",
      "DOI": "10.1103/PhysRevLett.79.1885",
      "volume": "79",
      "year": "1997",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "volume-title": "Thermodynamics of Crystals",
      "year": "1972",
      "key": "2024042700010890900_c64"
    },
    {
      "key": "2024042700010890900_c65",
      "doi-asserted-by": "publisher",
      "first-page": "291",
      "DOI": "10.1080/0892702031000104887",
      "volume": "29",
      "year": "2003",
      "journal-title": "Mol. Simul."
    },
    {
      "key": "2024042700010890900_c66",
      "doi-asserted-by": "publisher",
      "first-page": "5261",
      "DOI": "10.1103/PhysRevB.39.5261",
      "volume": "39",
      "year": "1989",
      "journal-title": "Phys. Rev. B"
    },
    {
      "volume-title": "The Physics of Phonons",
      "year": "1973",
      "key": "2024042700010890900_c67"
    },
    {
      "key": "2024042700010890900_c68",
      "unstructured": "A.\n            Ward\n          , Ph.D. thesis (Boston College, Boston, MA, 2009)."
    },
    {
      "key": "2024042700010890900_c69",
      "unstructured": "A.\n            Jain\n          , Ph.D. thesis (Carnegie Mellon University, Pittsburgh, PA, 2015)."
    },
    {
      "key": "2024042700010890900_c70",
      "doi-asserted-by": "publisher",
      "first-page": "165209",
      "DOI": "10.1088/0953-8984/20/16/165209",
      "volume": "20",
      "year": "2008",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "2024042700010890900_c71",
      "doi-asserted-by": "publisher",
      "first-page": "064301",
      "DOI": "10.1103/PhysRevB.79.064301",
      "volume": "79",
      "year": "2009",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c72",
      "doi-asserted-by": "publisher",
      "first-page": "115427",
      "DOI": "10.1103/PhysRevB.82.115427",
      "volume": "82",
      "year": "2010",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c73",
      "doi-asserted-by": "publisher",
      "first-page": "041013",
      "DOI": "10.1103/PhysRevX.6.041013",
      "volume": "6",
      "year": "2016",
      "journal-title": "Phys. Rev. X"
    },
    {
      "key": "2024042700010890900_c74",
      "doi-asserted-by": "publisher",
      "first-page": "4675",
      "DOI": "10.1021/acs.nanolett.7b01202",
      "volume": "17",
      "year": "2017",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2024042700010890900_c75",
      "doi-asserted-by": "publisher",
      "first-page": "15640",
      "DOI": "10.1038/srep15640",
      "volume": "5",
      "year": "2015",
      "journal-title": "Sci. Rep."
    },
    {
      "key": "2024042700010890900_c76",
      "doi-asserted-by": "publisher",
      "first-page": "125101",
      "DOI": "10.1063/1.4993601",
      "volume": "122",
      "year": "2017",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024042700010890900_c77",
      "doi-asserted-by": "publisher",
      "first-page": "167",
      "DOI": "10.1098/rstl.1864.0004",
      "volume": "154",
      "year": "1864",
      "journal-title": "Philos. Trans. R. Soc. London"
    },
    {
      "volume-title": "Electrons and Phonons",
      "year": "2001",
      "key": "2024042700010890900_c78"
    },
    {
      "key": "2024042700010890900_c79",
      "doi-asserted-by": "publisher",
      "first-page": "113103",
      "DOI": "10.1063/1.4821117",
      "volume": "103",
      "year": "2013",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c80",
      "doi-asserted-by": "publisher",
      "first-page": "235206",
      "DOI": "10.1103/PhysRevB.92.235206",
      "volume": "92",
      "year": "2015",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c81",
      "doi-asserted-by": "publisher",
      "first-page": "858",
      "DOI": "10.1103/PhysRevB.27.858",
      "volume": "27",
      "year": "1983",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c82",
      "doi-asserted-by": "publisher",
      "first-page": "045408",
      "DOI": "10.1103/PhysRevB.81.045408",
      "volume": "81",
      "year": "2010",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c83",
      "doi-asserted-by": "publisher",
      "first-page": "094117",
      "DOI": "10.1103/PhysRevB.90.094117",
      "volume": "90",
      "year": "2014",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c84",
      "doi-asserted-by": "publisher",
      "first-page": "075902",
      "DOI": "10.1103/PhysRevLett.119.075902",
      "volume": "119",
      "year": "2017",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c85",
      "doi-asserted-by": "publisher",
      "first-page": "1587",
      "DOI": "10.1021/acs.nanolett.6b04756",
      "volume": "17",
      "year": "2017",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2024042700010890900_c86",
      "doi-asserted-by": "publisher",
      "first-page": "023010",
      "DOI": "10.1088/1367-2630/aaa383",
      "volume": "20",
      "year": "2018",
      "journal-title": "New. J. Phys."
    },
    {
      "key": "2024042700010890900_c87",
      "doi-asserted-by": "publisher",
      "first-page": "115901",
      "DOI": "10.1103/PhysRevLett.114.115901",
      "volume": "114",
      "year": "2015",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c88",
      "doi-asserted-by": "publisher",
      "first-page": "095104",
      "DOI": "10.1063/1.4962010",
      "volume": "120",
      "year": "2016",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024042700010890900_c89",
      "doi-asserted-by": "publisher",
      "first-page": "165108",
      "DOI": "10.1103/PhysRevB.76.165108",
      "volume": "76",
      "year": "2007",
      "journal-title": "Phys. Rev. B"
    },
    {
      "volume-title": "Many-Particle Physics",
      "year": "2013",
      "key": "2024042700010890900_c90"
    },
    {
      "key": "2024042700010890900_c91",
      "doi-asserted-by": "publisher",
      "first-page": "116",
      "DOI": "10.1016/j.cpc.2016.07.028",
      "volume": "209",
      "year": "2016",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "2024042700010890900_c92",
      "doi-asserted-by": "publisher",
      "first-page": "081206",
      "DOI": "10.1103/PhysRevB.93.081206",
      "volume": "93",
      "year": "2016",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c93",
      "doi-asserted-by": "publisher",
      "first-page": "225109",
      "DOI": "10.1063/1.4953366",
      "volume": "119",
      "year": "2016",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024042700010890900_c94",
      "doi-asserted-by": "publisher",
      "first-page": "131904",
      "DOI": "10.1063/1.3644163",
      "volume": "99",
      "year": "2011",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c95",
      "doi-asserted-by": "publisher",
      "first-page": "171901",
      "DOI": "10.1063/1.4918703",
      "volume": "106",
      "year": "2015",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c96",
      "doi-asserted-by": "publisher",
      "first-page": "495",
      "DOI": "10.1016/S0031-8914(38)80162-2",
      "volume": "5",
      "year": "1938",
      "journal-title": "Physica"
    },
    {
      "key": "2024042700010890900_c97",
      "doi-asserted-by": "publisher",
      "first-page": "061911",
      "DOI": "10.1063/1.3683539",
      "volume": "100",
      "year": "2012",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c98",
      "doi-asserted-by": "publisher",
      "first-page": "195301",
      "DOI": "10.1103/PhysRevB.87.195301",
      "volume": "87",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c99",
      "doi-asserted-by": "publisher",
      "first-page": "5058",
      "DOI": "10.1103/PhysRevB.34.5058",
      "volume": "34",
      "year": "1986",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c100",
      "doi-asserted-by": "publisher",
      "first-page": "16223",
      "DOI": "10.1103/PhysRevB.49.16223",
      "volume": "49",
      "year": "1994",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c101",
      "doi-asserted-by": "publisher",
      "first-page": "073503",
      "DOI": "10.1063/1.4893185",
      "volume": "116",
      "year": "2014",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024042700010890900_c102",
      "doi-asserted-by": "publisher",
      "first-page": "9431",
      "DOI": "10.1103/PhysRevB.56.9431",
      "volume": "56",
      "year": "1997",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c103",
      "doi-asserted-by": "publisher",
      "first-page": "073901",
      "DOI": "10.1063/1.5040887",
      "volume": "113",
      "year": "2018",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2024042700010890900_c104",
      "doi-asserted-by": "publisher",
      "first-page": "045202",
      "DOI": "10.1103/PhysRevB.93.045202",
      "volume": "93",
      "year": "2016",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c105",
      "doi-asserted-by": "publisher",
      "first-page": "161201",
      "DOI": "10.1103/PhysRevB.96.161201",
      "volume": "96",
      "year": "2017",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c106",
      "doi-asserted-by": "publisher",
      "first-page": "045202",
      "DOI": "10.1103/PhysRevB.97.045202",
      "volume": "97",
      "year": "2018",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c107",
      "doi-asserted-by": "publisher",
      "first-page": "085205",
      "DOI": "10.1103/PhysRevB.98.085205",
      "volume": "98",
      "year": "2018",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c108",
      "doi-asserted-by": "publisher",
      "first-page": "582",
      "DOI": "10.1126/science.aat7932",
      "volume": "361",
      "year": "2018",
      "journal-title": "Science"
    },
    {
      "key": "2024042700010890900_c109",
      "doi-asserted-by": "publisher",
      "first-page": "575",
      "DOI": "10.1126/science.aat5522",
      "volume": "361",
      "year": "2018",
      "journal-title": "Science"
    },
    {
      "key": "2024042700010890900_c110",
      "doi-asserted-by": "publisher",
      "first-page": "579",
      "DOI": "10.1126/science.aat8982",
      "volume": "361",
      "year": "2018",
      "journal-title": "Science"
    },
    {
      "key": "2024042700010890900_c111",
      "doi-asserted-by": "publisher",
      "first-page": "144308",
      "DOI": "10.1103/PhysRevB.92.144308",
      "volume": "92",
      "year": "2015",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c112",
      "doi-asserted-by": "publisher",
      "first-page": "180301",
      "DOI": "10.1103/PhysRevB.84.180301",
      "volume": "84",
      "year": "2011",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c113",
      "doi-asserted-by": "publisher",
      "first-page": "104111",
      "DOI": "10.1103/PhysRevB.87.104111",
      "volume": "87",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c114",
      "doi-asserted-by": "publisher",
      "first-page": "144301",
      "DOI": "10.1103/PhysRevB.88.144301",
      "volume": "88",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c115",
      "doi-asserted-by": "publisher",
      "first-page": "014302",
      "DOI": "10.1103/PhysRevB.95.014302",
      "volume": "95",
      "year": "2017",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c116",
      "doi-asserted-by": "publisher",
      "first-page": "185901",
      "DOI": "10.1103/PhysRevLett.119.185901",
      "volume": "119",
      "year": "2017",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c117",
      "doi-asserted-by": "publisher",
      "first-page": "888",
      "DOI": "10.1016/j.commatsci.2008.06.016",
      "volume": "44",
      "year": "2009",
      "journal-title": "Comput. Mater. Sci."
    },
    {
      "key": "2024042700010890900_c118",
      "doi-asserted-by": "publisher",
      "first-page": "054301",
      "DOI": "10.1103/PhysRevB.92.054301",
      "volume": "92",
      "year": "2015",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c119",
      "doi-asserted-by": "publisher",
      "first-page": "145101",
      "DOI": "10.1063/1.5048799",
      "volume": "124",
      "year": "2018",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024042700010890900_c120",
      "doi-asserted-by": "publisher",
      "first-page": "045901",
      "DOI": "10.1103/PhysRevLett.106.045901",
      "volume": "106",
      "year": "2011",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c121",
      "doi-asserted-by": "publisher",
      "first-page": "46002",
      "DOI": "10.1209/0295-5075/102/46002",
      "volume": "102",
      "year": "2013",
      "journal-title": "EPL (Europhys. Lett.)"
    },
    {
      "key": "2024042700010890900_c122",
      "doi-asserted-by": "crossref",
      "unstructured": "M.\n            Arrigoni\n          , J.Carrete, N.Mingo, and G. K. H.Madsen, Phys. Rev. B98, 115205 (2018). 10.1103/PhysRevB.98.115205",
      "DOI": "10.1103/PhysRevB.98.115205"
    },
    {
      "key": "2024042700010890900_c123",
      "doi-asserted-by": "publisher",
      "first-page": "144303",
      "DOI": "10.1103/PhysRevB.89.144303",
      "volume": "89",
      "year": "2014",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c124"
    },
    {
      "key": "2024042700010890900_c125",
      "doi-asserted-by": "publisher",
      "first-page": "041015",
      "DOI": "10.7566/JPSJ.87.041015",
      "volume": "87",
      "year": "2018",
      "journal-title": "J. Phys. Soc. Jpn."
    },
    {
      "key": "2024042700010890900_c126",
      "doi-asserted-by": "publisher",
      "first-page": "e1360",
      "DOI": "10.1002/wcms.1360",
      "volume": "8",
      "year": "2018",
      "journal-title": "Wiley Interdiscip. Rev. Comput. Mol. Sci."
    },
    {
      "key": "2024042700010890900_c127",
      "doi-asserted-by": "publisher",
      "first-page": "1858",
      "DOI": "10.1103/PhysRevLett.68.1858",
      "volume": "68",
      "year": "1992",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024042700010890900_c128",
      "doi-asserted-by": "publisher",
      "first-page": "5586",
      "DOI": "10.1103/PhysRevB.54.5586",
      "volume": "54",
      "year": "1996",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c129",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1006/jcph.1995.1039",
      "volume": "117",
      "year": "1995",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "2024042700010890900_c130",
      "doi-asserted-by": "publisher",
      "first-page": "235149",
      "DOI": "10.1103/PhysRevB.85.235149",
      "volume": "85",
      "year": "2012",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c131"
    },
    {
      "key": "2024042700010890900_c132",
      "doi-asserted-by": "publisher",
      "first-page": "1455",
      "DOI": "10.1126/science.aar8072",
      "volume": "360",
      "year": "2018",
      "journal-title": "Science"
    },
    {
      "key": "2024042700010890900_c133",
      "doi-asserted-by": "publisher",
      "first-page": "12581",
      "DOI": "10.1103/PhysRevB.48.12581",
      "volume": "48",
      "year": "1993",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c134",
      "doi-asserted-by": "publisher",
      "first-page": "12589",
      "DOI": "10.1103/PhysRevB.48.12589",
      "volume": "48",
      "year": "1993",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c135",
      "doi-asserted-by": "publisher",
      "first-page": "013028",
      "DOI": "10.1088/1367-2630/18/1/013028",
      "volume": "18",
      "year": "2016",
      "journal-title": "New J. Phys."
    },
    {
      "key": "2024042700010890900_c136",
      "doi-asserted-by": "publisher",
      "first-page": "205441",
      "DOI": "10.1103/PhysRevB.81.205441",
      "volume": "81",
      "year": "2010",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024042700010890900_c137",
      "doi-asserted-by": "publisher",
      "first-page": "27",
      "DOI": "10.1038/s41524-017-0026-y",
      "volume": "3",
      "year": "2017",
      "journal-title": "NPJ Comput. Mater."
    },
    {
      "key": "2024042700010890900_c138",
      "doi-asserted-by": "publisher",
      "first-page": "085109",
      "DOI": "10.1063/1.5020611",
      "volume": "123",
      "year": "2018",
      "journal-title": "J. Appl. Phys."
    }
  ],
  "container-title": "Journal of Applied Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.5064602/19905527/011101_1_1.5064602.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.5064602/19905527/011101_1_1.5064602.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        4,
        27
      ]
    ],
    "date-time": "2024-04-27T00:01:25Z",
    "timestamp": 1714176085000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jap/article/125/1/011101/155527/Phonon-properties-and-thermal-conductivity-from"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2019,
        1,
        3
      ]
    ]
  },
  "references-count": 138,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          2019,
          1,
          7
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.5064602",
  "relation": {},
  "ISSN": [
    "0021-8979",
    "1089-7550"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2019,
        1,
        7
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2019,
        1,
        3
      ]
    ]
  },
  "article-number": "011101"
}