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arxiv: 2402.02787 · v1 · pith:ZIICUX36new · submitted 2024-02-05 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Ab initio Investigation of Thermal Transport in Insulators: Unveiling the Roles of Phonon Renormalization and Higher-Order Anharmonicity

Soham Mandal , Manish Jain , Prabal K. Maiti This is my paper

Pith reviewed 2026-05-24 04:14 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph
keywords thermal transportphonon renormalizationanharmonic effectslattice thermal conductivityPeierls-Boltzmann equationfirst-principles calculationsinsulatorssemiconductors
0
0 comments X

The pith

Self-consistent phonon renormalization treats phonons as quasiparticles and extends renormalization to third- and fourth-order force constants.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a numerical framework using self-consistent phonon renormalization to calculate thermal and thermodynamic properties of insulators and semiconductors. It addresses limitations of traditional perturbative methods by treating phonons as temperature-dependent quasiparticles instead of bare normal modes. The method renormalizes interatomic force constants up to fourth order and uses the Peierls-Boltzmann transport equation to find thermal conductivity including anharmonicity effects. It is applied to highly anharmonic materials such as NaCl and AgI as well as weakly anharmonic ones like cBN and 3C-SiC to examine phonon dispersion, linewidth, scattering, and temperature-dependent lattice thermal conductivity.

Core claim

The self-consistent phonon renormalization method reveals phonons as quasiparticles, diverging from their conventional characterization as bare normal modes of lattice vibration. The extension of the renormalization impact to interatomic force constants (IFCs) of third and fourth orders is also integrated and demonstrated. An iterative solution of the Peierls-Boltzmann transport equation determines thermal conductivity, and Helmholtz free energy calculations encompass anharmonicity effects up to the fourth order.

What carries the argument

Self-consistent phonon renormalization applied to interatomic force constants of third and fourth orders, which updates the phonon properties at finite temperature to account for anharmonicity.

If this is right

  • More accurate phonon dispersion and linewidths at elevated temperatures for anharmonic materials.
  • Improved predictions of lattice thermal conductivity using the PBTE with renormalized quantities.
  • Helmholtz free energy calculations that include fourth-order anharmonicity effects.
  • Applicability demonstrated for both strongly anharmonic and weakly anharmonic crystalline materials.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such a framework could enable more reliable design of thermoelectric devices through better thermal property predictions.
  • Future extensions might check whether fifth-order terms become necessary in some materials.
  • Direct comparisons with molecular dynamics results could further validate the quasiparticle picture.

Load-bearing premise

That the self-consistent renormalization procedure extended to third- and fourth-order interatomic force constants is numerically stable and physically sufficient.

What would settle it

Experimental measurements of thermal conductivity in NaCl or AgI at high temperatures that deviate substantially from the framework's predictions would challenge the method's accuracy.

Figures

Figures reproduced from arXiv: 2402.02787 by Manish Jain, Prabal K. Maiti, Soham Mandal.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Phonon dispersion of cBN along the high symmetry path calculated from QHA and renormalized IFCs at 300K. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Phonon dispersion of 3C-SiC along the high symmetry path calculated from QHA and renormalized IFCs at 300K. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Phonon dispersion of NaCl along the high-symmetry path at 300K. The renormalization leads to an upward shift in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Thermal conductivity of NaCl calculated using the QHA and renormalization. Notably, renormalization consistently [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Phonon dispersion of AgI along the high symmetry path calculated from QHA and renormalized IFCs at 300K. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Variation of harmonic and fourth-order free energy with unit cell volume at 300K. Observe the overlap between [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

The occurrence of thermal transport phenomena is widespread, exerting a pivotal influence on the functionality of diverse electronic and thermo-electric energy-conversion devices. The traditional first-principles theory governing the thermal and thermodynamic characteristics of insulators relies on the perturbative treatment of interatomic potential and ad-hoc displacement of atoms within supercells. However, the limitations of these approaches for highly anharmonic and weakly bonded materials, along with discrepancies arising from not considering explicit finite temperature effects, highlight the necessity for a well-defined quasiparticle approach to the lattice vibrations. To address these limitations, we present a comprehensive numerical framework in this study, designed to compute the thermal and thermodynamic characteristics of crystalline semiconductors and insulators. The self-consistent phonon renormalization method we have devised reveals phonons as quasiparticles, diverging from their conventional characterization as bare normal modes of lattice vibration. The extension of the renormalization impact to interatomic force constants (IFCs) of third and fourth orders is also integrated and demonstrated. For the comprehensive physical insights, we employed an iterative solution of the Peierls-Boltzmann transport equation (PBTE) to determine thermal conductivity and carry out Helmholtz free energy calculations, encompassing anharmonicity effects up to the fourth order. In this study, we utilize our numerical framework to showcase its applicability through an examination of phonon dispersion, phonon linewidth, anharmonic phonon scattering, and temperature-dependent lattice thermal conductivity in both highly anharmonic materials (NaCl and AgI) and weakly anharmonic materials (cBN and 3C-SiC).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript presents a numerical framework for computing thermal and thermodynamic properties of crystalline insulators based on self-consistent phonon renormalization, which treats phonons as quasiparticles and extends renormalization effects to third- and fourth-order interatomic force constants. The approach is demonstrated on NaCl and AgI (highly anharmonic) as well as cBN and 3C-SiC (weakly anharmonic), with thermal conductivity obtained from iterative solution of the Peierls-Boltzmann transport equation and Helmholtz free energy calculations that incorporate anharmonicity up to fourth order.

Significance. If the extension to higher-order IFCs proves numerically stable and convergent, the framework would offer a systematic quasiparticle treatment of finite-temperature anharmonicity that goes beyond standard perturbative expansions, potentially improving predictive accuracy for thermal transport in strongly anharmonic and weakly bonded materials.

major comments (1)
  1. The central methodological step—extension of the self-consistent renormalization procedure to third- and fourth-order IFCs—is presented as both numerically stable and physically sufficient for the reported PBTE results. However, no iteration counts to convergence, supercell-size sensitivity tests, or estimates of truncation error from omitted fifth-order terms are supplied for the higher-order IFCs. This verification is load-bearing for the claims on NaCl/AgI and for the quasiparticle picture itself.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address the major comment point by point below and have prepared revisions to enhance the manuscript accordingly.

read point-by-point responses

  1. Referee: The central methodological step—extension of the self-consistent renormalization procedure to third- and fourth-order IFCs—is presented as both numerically stable and convergent. However, no iteration counts to convergence, supercell-size sensitivity tests, or estimates of truncation error from omitted fifth-order terms are supplied for the higher-order IFCs. This verification is load-bearing for the claims on NaCl/AgI and for the quasiparticle picture itself.

    Authors: We agree that explicit verification of numerical stability and convergence for the renormalization of third- and fourth-order IFCs is important to support the claims, particularly for NaCl and AgI. In the revised manuscript we will add the iteration counts to convergence for the self-consistent procedure applied to the higher-order force constants. We will also include supercell-size sensitivity tests showing that the computed phonon dispersions, linewidths, and thermal conductivities remain stable across the supercell sizes employed. For truncation error from omitted fifth-order terms, we will add a discussion based on the observed convergence of the fourth-order results with temperature and direct comparison to experimental thermal conductivity data, which indicates that the truncation is sufficient within the temperature range considered. These additions will be incorporated to strengthen the quasiparticle treatment. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents a numerical framework extending self-consistent phonon renormalization to third- and fourth-order IFCs, then solving the Peierls-Boltzmann transport equation iteratively for thermal conductivity and free energy. No load-bearing step reduces by construction to fitted inputs, self-citations, or renamed known results; the approach builds on standard perturbative and renormalization methods without self-definitional loops or uniqueness theorems imported from the authors' prior work. The central claims remain independent of the target outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; standard phonon and Boltzmann-transport concepts are invoked without additional detail.

pith-pipeline@v0.9.0 · 5822 in / 1098 out tokens · 19816 ms · 2026-05-24T04:14:17.362518+00:00 · methodology

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Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    Alf` e, Phon: A program to calculate phonons using the small displacement method, Computer Physics Commu- nications 180, 2622 (2009)

    D. Alf` e, Phon: A program to calculate phonons using the small displacement method, Computer Physics Commu- nications 180, 2622 (2009)

    work page 2009

  2. [2]

    Togo and I

    A. Togo and I. Tanaka, First principles phonon calcu- lations in materials science, Scripta Materialia 108, 1 (2015)

    work page 2015

  3. [3]

    A. Togo, L. Chaput, and I. Tanaka, Distributions of phonon lifetimes in brillouin zones, Phys. Rev. B 91, 094306 (2015)

    work page 2015

  4. [4]

    W. Li, J. Carrete, N. A. Katcho, and N. Mingo, Sheng- BTE: a solver of the Boltzmann transport equation for phonons, Comp. Phys. Commun. 185, 1747–1758 (2014)

    work page 2014

  5. [5]

    Mounet and N

    N. Mounet and N. Marzari, First-principles determina- tion of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives, Phys. Rev. B 71, 205214 (2005)

    work page 2005

  6. [6]

    D. C. Wallace, Thermodynamics of Crystals (John Wiley & Sons, Inc., New York, 1972)

    work page 1972

  7. [7]

    Baroni, S

    S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Gi- annozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001)

    work page 2001

  8. [8]

    A. H. Romero, D. C. Allan, B. Amadon, G. An- tonius, T. Applencourt, L. Baguet, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, F. Bruneval, G. Brunin, D. Caliste, M. Cˆ ot´ e, J. Denier, C. Dreyer, P. Ghosez, M. Giantomassi, Y. Gillet, O. Gingras, D. R. Hamann, G. Hautier, F. Jollet, G. Jomard, A. Martin, H. P. C. Miranda, F. Naccarato, G. Petretto, N. A....

    work page doi:10.1063/1.5144261/16711978/124102 2020

  9. [9]

    W. Li, L. Lindsay, D. A. Broido, D. A. Stewart, and N. Mingo, Thermal conductivity of bulk and nanowire mg2sixsn1−x alloys from first principles, Phys. Rev. B 86, 174307 (2012)

    work page 2012

  10. [10]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, J. Phys. Condens. Matter 35, 353001 (2023)

    work page 2023

  11. [11]

    Togo, First-principles phonon calculations with phonopy and phono3py, J

    A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023)

    work page 2023

  12. [12]

    Paulatto, F

    L. Paulatto, F. Mauri, and M. Lazzeri, Anharmonic prop- erties from a generalized third-order ab initio approach: Theory and applications to graphite and graphene, Phys. Rev. B 87, 214303 (2013)

    work page 2013

  13. [13]

    Z. Han, X. Yang, W. Li, T. Feng, and X. Ruan, Four- phonon: An extension module to shengbte for computing four-phonon scattering rates and thermal conductivity, Computer Physics Communications 270, 108179 (2022)

    work page 2022

  14. [14]

    Feng and X

    T. Feng and X. Ruan, Quantum mechanical prediction of four-phonon scattering rates and reduced thermal con- ductivity of solids, Phys. Rev. B 93, 045202 (2016)

    work page 2016

  15. [15]

    T. Feng, L. Lindsay, and X. Ruan, Four-phonon scatter- ing significantly reduces intrinsic thermal conductivity of solids, Phys. Rev. B 96, 161201 (2017)

    work page 2017

  16. [16]

    Han and X

    Z. Han and X. Ruan, Thermal conductivity of monolayer graphene: Convergent and lower than diamond, Phys. Rev. B 108, L121412 (2023)

    work page 2023

  17. [17]

    Y. Xia, V. I. Hegde, K. Pal, X. Hua, D. Gaines, S. Pa- tel, J. He, M. Aykol, and C. Wolverton, High-throughput study of lattice thermal conductivity in binary rocksalt and zinc blende compounds including higher-order an- harmonicity, Phys. Rev. X 10, 041029 (2020)

    work page 2020

  18. [18]

    Knoop, T

    F. Knoop, T. A. R. Purcell, M. Scheffler, and C. Car- bogno, Anharmonicity in thermal insulators: An anal- ysis from first principles, Phys. Rev. Lett. 130, 236301 (2023)

    work page 2023

  19. [19]

    Knoop, M

    F. Knoop, M. Scheffler, and C. Carbogno, Ab ini- tio green-kubo simulations of heat transport in solids: Method and implementation, Phys. Rev. B 107, 224304 (2023)

    work page 2023

  20. [20]

    Mandal, I

    S. Mandal, I. Maity, A. Das, M. Jain, and P. K. Maiti, Tunable lattice thermal conductivity of twisted bilayer mos2, Phys. Chem. Chem. Phys. 24, 13860 (2022)

    work page 2022

  21. [21]

    Hellman, I

    O. Hellman, I. A. Abrikosov, and S. I. Simak, Lattice dynamics of anharmonic solids from first principles, Phys. Rev. B 84, 180301 (2011)

    work page 2011

  22. [22]

    Hellman and I

    O. Hellman and I. A. Abrikosov, Temperature-dependent effective third-order interatomic force constants from first principles, Phys. Rev. B 88, 144301 (2013)

    work page 2013

  23. [23]

    Bottin, J

    F. Bottin, J. Bieder, and J. Bouchet, a-tdep: Temper- ature dependent effective potential for abinit – lattice dynamic properties including anharmonicity, Computer Physics Communications 254, 107301 (2020)

    work page 2020

  24. [24]

    Jain, Multichannel thermal transport in crystalline tl3vse4, Phys

    A. Jain, Multichannel thermal transport in crystalline tl3vse4, Phys. Rev. B 102, 201201 (2020)

    work page 2020

  25. [25]

    Tadano, Y

    T. Tadano, Y. Gohda, and S. Tsuneyuki, Anharmonic force constants extracted from first-principles molecu- lar dynamics: applications to heat transfer simulations, Journal of Physics: Condensed Matter 26, 225402 (2014)

    work page 2014

  26. [26]

    G. D. Mahan, Many-Particle Physics (Springer New York, NY, 2000)

    work page 2000

  27. [27]

    Anderson, Z

    E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide , 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999)

    work page 1999

  28. [28]

    Togo and I

    A. Togo and I. Tanaka, Spglib: a software library for crystal symmetry search 10.48550/arXiv.1808.01590 (2018), arXiv:1808.01590 [cond-mat.mtrl-sci]

    work page doi:10.48550/arxiv.1808.01590 2018

  29. [29]

    Y. Wang, J. J. Wang, W. Y. Wang, Z. G. Mei, S. L. Shang, L. Q. Chen, and Z. K. Liu, A mixed-space ap- proach to first-principles calculations of phonon frequen- cies for polar materials, Journal of Physics: Condensed Matter 22, 202201 (2010)

    work page 2010

  30. [30]

    Gonze, J.-C

    X. Gonze, J.-C. Charlier, D. Allan, and M. Teter, Inter- atomic force constants from first principles: The case of α-quartz, Phys. Rev. B 50, 13035 (1994)

    work page 1994

  31. [31]

    Gonze and C

    X. Gonze and C. Lee, Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation the- ory, Phys. Rev. B 55, 10355 (1997)

    work page 1997

  32. [32]

    West and S

    D. West and S. K. Estreicher, First-principles cal- culations of vibrational lifetimes and decay channels: Hydrogen-related modes in si, Phys. Rev. Lett. 96, 115504 (2006)

    work page 2006

  33. [33]

    Shulumba, O

    N. Shulumba, O. Hellman, and A. J. Minnich, Intrin- sic localized mode and low thermal conductivity of pbse, Phys. Rev. B 95, 014302 (2017)

    work page 2017

  34. [34]

    N. K. Ravichandran and D. Broido, Unified first- principles theory of thermal properties of insulators, Phys. Rev. B 98, 085205 (2018)

    work page 2018

  35. [35]

    J. M. Soler, E. Artacho, J. D. Gale, A. Garc´ ıa, J. Jun- quera, P. Ordej´ on, and D. S´ anchez-Portal, The siesta method for ab initio order-n materials simulation, Jour- nal of Physics: Condensed Matter 14, 2745 (2002)

    work page 2002

  36. [36]

    K. Pal, Y. Xia, and C. Wolverton, Microscopic mecha- nism of unusual lattice thermal transport in tlinte2, npj Computational Materials 7, 5 (2021)

    work page 2021

  37. [37]

    Tamura, Isotope scattering of dispersive phonons in ge, Phys

    S.-i. Tamura, Isotope scattering of dispersive phonons in ge, Phys. Rev. B 27, 858 (1983)

    work page 1983

  38. [38]

    Ziman, Electrons and Phonons: The Theory of Trans- port Phenomena in Solids (Oxford University Press, 2001)

    J. Ziman, Electrons and Phonons: The Theory of Trans- port Phenomena in Solids (Oxford University Press, 2001)

    work page 2001

  39. [39]

    D. A. Broido, A. Ward, and N. Mingo, Lattice thermal conductivity of silicon from empirical interatomic poten- tials, Phys. Rev. B 72, 014308 (2005)

    work page 2005

  40. [40]

    Lindsay and D

    L. Lindsay and D. A. Broido, Three-phonon phase space and lattice thermal conductivity in semiconductors, Jour- nal of Physics: Condensed Matter 20, 165209 (2008)

    work page 2008

  41. [41]

    Omini and A

    M. Omini and A. Sparavigna, An iterative approach to the phonon boltzmann equation in the theory of ther- mal conductivity, Physica B: Condensed Matter212, 101 (1995)

    work page 1995

  42. [42]

    A. H. MacDonald, S. H. Vosko, and P. T. Coleridge, Ex- tensions of the tetrahedron method for evaluating spec- tral properties of solids, Journal of Physics C: Solid State Physics 12, 2991 (1979)

    work page 1979

  43. [43]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996). 17

    work page 1996

  44. [44]

    J. A. Sanjurjo, E. L´ opez-Cruz, P. Vogl, and M. Cardona, Dependence on volume of the phonon frequencies and the ir effective charges of several iii-v semiconductors, Phys. Rev. B 28, 4579 (1983)

    work page 1983

  45. [45]

    Reich, A

    S. Reich, A. C. Ferrari, R. Arenal, A. Loiseau, I. Bello, and J. Robertson, Resonant raman scattering in cubic and hexagonal boron nitride, Phys. Rev. B 71, 205201 (2005)

    work page 2005

  46. [46]

    Kikkawa, T

    J. Kikkawa, T. Taniguchi, and K. Kimoto, Nanometric phonon spectroscopy for diamond and cubic boron ni- tride, Phys. Rev. B 104, L201402 (2021)

    work page 2021

  47. [47]

    K. Chen, B. Song, N. K. Ravichandran, Q. Zheng, X. Chen, H. Lee, H. Sun, S. Li, G. A. G. U. Gam- age, F. Tian, Z. Ding, Q. Song, A. Rai, H. Wu, P. Koirala, A. J. Schmidt, K. Watanabe, B. Lv, Z. Ren, L. Shi, D. G. Cahill, T. Taniguchi, D. Broido, and G. Chen, Ultrahigh thermal conductivity in isotope- enriched cubic boron nitride, Science 367, 555 (2020), ...

    work page doi:10.1126/science.aaz6149 2020

  48. [48]

    J. S. Kang, M. Li, H. Wu, H. Nguyen, and Y. Hu, Experimental observation of high thermal conduc- tivity in boron arsenide, Science 361, 575 (2018), https://www.science.org/doi/pdf/10.1126/science.aat5522

    work page doi:10.1126/science.aat5522 2018

  49. [49]

    Serrano, J

    J. Serrano, J. Strempfer, M. Cardona, M. Schwoerer- B¨ ohning, H. Requardt, M. Lorenzen, B. Stojetz, P. Pavone, and W. J. Choyke, Determination of the phonon dispersion of zinc blende (3C) silicon carbide by inelastic x-ray scattering, Applied Physics Letters 80, 4360 (2002), https://pubs.aip.org/aip/apl/article- pdf/80/23/4360/10192323/4360 1 online.pdf

    work page 2002

  50. [50]

    D. T. Morelli, J. P. Heremans, and G. A. Slack, Estima- tion of the isotope effect on the lattice thermal conduc- tivity of group iv and group iii-v semiconductors, Phys. Rev. B 66, 195304 (2002)

    work page 2002

  51. [51]

    L. M. Ivanova, P. A. Aleksandrov, and K. D. Demakov, Thermoelectric properties of vapor-grown polycrystalline cubic sic, Inorganic Materials 42, 1205 (2006)

    work page 2006

  52. [52]

    Raunio, L

    G. Raunio, L. Almqvist, and R. Stedman, Phonon dis- persion relations in nacl, Phys. Rev. 178, 1496 (1969)

    work page 1969

  53. [53]

    E. R. Cowley, S. Satija, and R. Youngblood, Line shapes of longitudinal-optic phonons in sodium chloride at 300 and 600 k, Phys. Rev. B 28, 993 (1983)

    work page 1983

  54. [54]

    H˚ akansson and P

    B. H˚ akansson and P. Andersson, Thermal conductiv- ity and heat capacity of solid nacl and nai under pres- sure, Journal of Physics and Chemistry of Solids 47, 355 (1986)

    work page 1986

  55. [55]

    M. V. Klein and R. F. Caldwell, Low Temper- ature System for Thermal Conductivity Mea- surements, Review of Scientific Instruments 37, 1291 (2004), https://pubs.aip.org/aip/rsi/article- pdf/37/10/1291/8352456/1291 1 online.pdf

    work page 2004

  56. [56]

    K. A. McCarthy and S. S. Ballard, Thermal Con- ductivity of Eight Halide Crystals in the Temperature Range 220 °K to 390 °K, Journal of Applied Physics 31, 1410 (2004), https://pubs.aip.org/aip/jap/article- pdf/31/8/1410/7928241/1410 1 online.pdf

    work page 2004

  57. [57]

    Goetz and J

    M. Goetz and J. Cowen, The thermal conductivity of silver iodide, Solid State Communications41, 293 (1982)

    work page 1982

  58. [58]

    Y. Wang, Q. Gan, M. Hu, J. Li, L. Xie, and J. He, An- harmonic lattice dynamics and the origin of intrinsic ul- tralow thermal conductivity in agi materials, Phys. Rev. B 107, 064308 (2023)

    work page 2023

  59. [59]

    Acharyya, T

    P. Acharyya, T. Ghosh, K. Pal, K. S. Rana, M. Dutta, D. Swain, M. Etter, A. Soni, U. V. Waghmare, and K. Biswas, Glassy thermal conductivity in cs3bi2i6cl3 single crystal, Nature Communications 13, 5053 (2022)

    work page 2022

  60. [60]

    Acharyya, K

    P. Acharyya, K. Pal, A. Ahad, D. Sarkar, K. S. Rana, M. Dutta, A. Soni, U. V. Waghmare, and K. Biswas, Extended antibonding states and phonon localization induce ultralow thermal con- ductivity in low dimensional metal halide, Ad- vanced Functional Materials 33, 2304607 (2023), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adfm.202304607

    work page doi:10.1002/adfm.202304607 2023

  61. [61]

    Ouyang, Z

    N. Ouyang, Z. Zeng, C. Wang, Q. Wang, and Y. Chen, Role of high-order lattice anharmonicity in the phonon thermal transport of silver halide Ag x(x = Cl , Br, I), Phys. Rev. B 108, 174302 (2023)

    work page 2023

  62. [62]

    Hsieh, High-pressure thermal conductivity and compressional velocity of nacl in b1 and b2 phase, Scien- tific Reports 11, 21321 (2021)

    W.-P. Hsieh, High-pressure thermal conductivity and compressional velocity of nacl in b1 and b2 phase, Scien- tific Reports 11, 21321 (2021)

    work page 2021

  63. [63]

    Srivastava and H

    K. Srivastava and H. Merchant, Thermal expansion of alkali halides above 300°k, Journal of Physics and Chem- istry of Solids 34, 2069 (1973)

    work page 2069

  64. [64]

    N. K. Ravichandran and D. Broido, Non-monotonic pres- sure dependence of the thermal conductivity of boron ar- senide, Nature Communications 10, 827 (2019)

    work page 2019

  65. [65]

    Lindsay, D

    L. Lindsay, D. A. Broido, and T. L. Reinecke, First- principles determination of ultrahigh thermal conductiv- ity of boron arsenide: A competitor for diamond?, Phys. Rev. Lett. 111, 025901 (2013)

    work page 2013

  66. [66]

    N. K. Ravichandran and D. Broido, Phonon-phonon in- teractions in strongly bonded solids: Selection rules and higher-order processes, Phys. Rev. X 10, 021063 (2020)

    work page 2020

  67. [67]

    N. H. Protik, C. Li, M. Pruneda, D. Broido, and P. Ordej´ on, The elphbolt ab initio solver for the cou- pled electron-phonon boltzmann transport equations, npj Computational Materials 8, 28 (2022)

    work page 2022