Lattice dynamics of Ge and Si using the Born-von Karman model

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728 · see citing works

Data Reduction and Error Analysis for the Physical Sciences.

C., E. L., & Bevington, P. R. (1972) · Journal of the American Statistical Association · doi:10.2307/2284752 · Cited by 3,586 · see citing works

Theory of lattice dynamics in the harmonic approximation

Ipatova, I. P., Maradudin, A. A., Montroll, E. W., & Weiss, G. H. (1971) · Academic Press eBooks · Cited by 1,727 · see citing works

Accurate Numerical Method for Calculating Frequency-Distribution Functions in Solids

Gilat, G., & Raubenheimer, L. J. (1966) · Physical Review · doi:10.1103/physrev.144.390 · Cited by 806 · see citing works

Measurement of Elastic Constants at Low Temperatures by Means of Ultrasonic Waves–Data for Silicon and Germanium Single Crystals, and for Fused Silica

McSkimin, H. J. (1953) · Journal of Applied Physics · doi:10.1063/1.1721449 · Cited by 778 · see citing works

Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α−Sn

Weber, W. (1977) · Physical review. B, Solid state · doi:10.1103/physrevb.15.4789 · Cited by 703 · see citing works

Multiphonon Raman Spectrum of Silicon

Temple, P. A., & Hathaway, C. E. (1973) · Physical review. B, Solid state · doi:10.1103/physrevb.7.3685 · Cited by 689 · see citing works

Symmetry Principles in Solid State and Molecular Physics

Barton, G. (1975) · Physics Bulletin · doi:10.1088/0031-9112/26/7/031 · Cited by 391 · see citing works

The heat capacity of pure silicon and germanium and properties of their vibrational frequency spectra

Flubacher, P., Leadbetter, A. J., & Morrison, J. A. (1959) · Philosophical magazine · doi:10.1080/14786435908233340 · Cited by 360 · see citing works

The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide

Dolling, G., & Cowley, R. A. (1966) · Proceedings of the Physical Society · doi:10.1088/0370-1328/88/2/318 · Cited by 346 · see citing works

Lattice Dynamics and Spectroscopic Properties by a Valence Force Potential of Diamondlike Crystals: C, Si, Ge, and Sn

TUBINO, R., Piseri, L., & Zerbi, G. (1972) · The Journal of Chemical Physics · doi:10.1063/1.1677264 · Cited by 332 · see citing works

Normal Modes of Germanium by Neutron Spectrometry

Brockhouse, B. N., & Iyengar, P. K. (1958) · Physical Review · doi:10.1103/physrev.111.747 · Cited by 303 · see citing works

Phonon Dispersion Relations in Ge at 80 °K

Nilsson, G., & Nelin, G. (1971) · Physical review. B, Solid state · doi:10.1103/physrevb.3.364 · Cited by 289 · see citing works

Crystal Dynamics and Electronic Specific Heats of Palladium and Copper

Miiller, A. P., & Brockhouse, B. N. (1971) · Canadian Journal of Physics · doi:10.1139/p71-087 · Cited by 242 · see citing works

Lattice vibrational spectrum of germanium

Herman, F. (1959) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(59)90376-2 · Cited by 229 · see citing works

The theory of the vibrations and the Raman spectrum of the diamond lattice

Smith, H. M. J. (1948) · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · doi:10.1098/rsta.1948.0010 · Cited by 203 · see citing works

New Bond-Charge Model for the Lattice Dynamics of Diamond-Type Semiconductors

Weber, W. (1974) · Physical Review Letters · doi:10.1103/physrevlett.33.371 · Cited by 198 · see citing works

Phonon Density of States in Germanium at 80 K Measured by Neutron Spectrometry

Nelin, G., & Nilsson, G. (1972) · Physical review. B, Solid state · doi:10.1103/physrevb.5.3151 · Cited by 146 · see citing works

Second-Order Raman Spectrum of Germanium

Weinstein, B. A., & Cardona, M. (1973) · Physical review. B, Solid state · doi:10.1103/physrevb.7.2545 · Cited by 123 · see citing works

Zur Raumgittertheorie des Diamanten

Born, M. (1914) · Annalen der Physik · doi:10.1002/andp.19143491209 · Cited by 116 · see citing works

Thermal scattering of X-rays by crystals - I. Dynamical foundation

Begbie, G. H., & Born, M. (1947) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1947.0003 · Cited by 93 · see citing works

Critical-point analysis of the two-phonon Raman spectrum of silicon

Uchinokura, K., Sekine, T., & Matsuura, E. (1974) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(74)90031-6 · Cited by 89 · see citing works

Theory of the Lattice Vibrations of Germanium

Cochran, W. G. (1959) · Physical Review Letters · doi:10.1103/physrevlett.2.495 · Cited by 58 · see citing works

Second order Raman spectrum and phonon density of states of silicon

Wang, C. S., Chen, J. M., Becker, R., & Zdetsis, A. D. (1973) · Physics Letters A · doi:10.1016/0375-9601(73)91001-3 · Cited by 31 · see citing works

Harmonic lattice dynamics of germanium

Nelin, G. (1974) · Physical review. B, Solid state · doi:10.1103/physrevb.10.4331 · Cited by 15 · see citing works

Lattice dynamics of germanium by the C.G.W. type of angular force model

Pandey, B. P., & Dayal, B. (1972) · Solid State Communications · doi:10.1016/0038-1098(72)90268-2 · Cited by 14 · see citing works

Angular forces in the lattice dynamics of diamond crystal lattices

Bose, G., Tripathi, B. B., & Gupta, H. (1973) · Journal of Physics and Chemistry of Solids · doi:10.1016/s0022-3697(73)80107-6 · Cited by 13 · see citing works

Lattice dynamics of silicon and diamond

Pandey, B. P., & Dayal, B. (1973) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/6/20/007 · Cited by 13 · see citing works

Isotope scattering of dispersive phonons in Ge

Tamura, S.-I. (1983) · Physical review. B, Condensed matter · doi:10.1103/physrevb.27.858 · Cited by 567 · see citing works

The optical properties of luminescence centres in silicon

Davies, G. (1989) · Physics Reports · doi:10.1016/0370-1573(89)90064-1 · Cited by 558 · see citing works

Two-channel model for nonequilibrium thermal transport in pump-probe experiments

Wilson, R. B., Feser, J. P., Hohensee, G. T., & Cahill, D. G. (2013) · Physical Review B · doi:10.1103/physrevb.88.144305 · Cited by 112 · see citing works

Optimized interatomic potential for silicon and its application to thermal stability of silicene

Pun, G. P. P., & Mishin, Y. M. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.224103 · Cited by 65 · see citing works

Lattice dynamical Debye-Waller factor for silicon

Flensburg, C., & Stewart, R. F. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.60.284 · Cited by 61 · see citing works

Electronic charge distribution in silicon

Deutsch, M., & Hart, M. (1985) · Physical review. B, Condensed matter · doi:10.1103/physrevb.31.3846 · Cited by 60 · see citing works

Specific heat of amorphous silicon at low temperatures

Mertig, M., Pompe, G., & Hegenbarth, E. (1984) · Solid State Communications · doi:10.1016/0038-1098(84)90589-1 · Cited by 55 · see citing works

Phonon spectroscopy

Wybourne, M. N., & Wigmore, J. K. (1988) · Reports on Progress in Physics · doi:10.1088/0034-4885/51/7/001 · Cited by 51 · see citing works

Phonon Focusing of Large- k→ Acoustic Phonons in Germanium

Dietsche, W., Northrop, G. A., & Wolfe, J. P. (1981) · Physical Review Letters · doi:10.1103/physrevlett.47.660 · Cited by 43 · see citing works

Ternary thermoelectric AB2C2 Zintls

Zheng, L., Li, W., Sun, C. H., Shi, X., Zhang, X., & Pei, Y. (2019) · Journal of Alloys and Compounds · doi:10.1016/j.jallcom.2019.153497 · Cited by 40 · see citing works

Phonon Imaging: Theory and Applications

Northrop, G. A., & Wolfe, J. P. (1985) · Springer eBooks · doi:10.1007/978-1-4613-2501-7_5 · Cited by 39 · see citing works

Large-wave-vector phonons in highly dispersive crystals: Phonon-focusing effects

Tamura, S.-I. (1983) · Physical review. B, Condensed matter · doi:10.1103/physrevb.28.897 · Cited by 32 · see citing works

Raman scattering study of H2 in Si

Hiller, M. M., Lavrov, E. V., & Weber, J. (2006) · Physical Review B · doi:10.1103/physrevb.74.235214 · Cited by 30 · see citing works

Möbius inversion transform for diamond-type materials and phonon dispersions

Li, M., & Chen, N. X. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.997 · Cited by 27 · see citing works

Effects of impurities on the lattice dynamics of nanocrystalline silicon for thermoelectric application

Claudio, T., Schierning, G., Theissmann, R., Wiggers, H., Schober, H., Koza, M. M., & Hermann, R. P. (2012) · Journal of Materials Science · doi:10.1007/s10853-012-6827-y · Cited by 26 · see citing works

Phonon focusing of dispersive phonons in Ge

Northrop, G. A. (1982) · Physical review. B, Condensed matter · doi:10.1103/physrevb.26.903 · Cited by 25 · see citing works

Lattice constant and coefficient of linear thermal expansion of the silicon crystal. Influence of isotopic composition

Zhernov, A. P. (2000) · Low Temperature Physics · doi:10.1063/1.1334443 · Cited by 14 · see citing works

Isotope effect for the thermal expansion coefficient of germanium

Ozhogin, V. I., Babushkina, N. A., Belova, L. M., Zhernov, A. P., Häller, E. E., & Itoh, K. M. (1999) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.558775 · Cited by 10 · see citing works

A Frequency Sum Rule and Spectral Moments in Lattice Dynamics

Frei, V., & Deus, P. (1984) · physica status solidi (b) · doi:10.1002/pssb.2221250113 · Cited by 9 · see citing works

Lattice Dynamics and Thermal Properties of SiGe Solid Solution

Soma, T., Kitani, Y., & Kagaya, H. ‐. (1984) · physica status solidi (b) · doi:10.1002/pssb.2221210208 · Cited by 8 · see citing works

Atomistic origin of the entropy of melting from inelastic neutron scattering and machine learned molecular dynamics

Bernal-Choban, C. M., Ladygin, V. V., Granroth, G. E., Saunders, C. N., Lohaus, S. H., Abernathy, D. L., Lin, J., & Fultz, B. T. (2024) · Communications Materials · doi:10.1038/s43246-024-00695-x · Cited by 7 · see citing works

Comparison of Peridynamics and Lattice Dynamics Wave Dispersion Relationships

Oterkus, S., & Oterkus, E. (2022) · Journal of Peridynamics and Nonlocal Modeling · doi:10.1007/s42102-022-00087-0 · Cited by 7 · see citing works

Phonons in highly-crystalline mesoporous silicon: The absence of phonon-softening upon structuring silicon on sub-10 nanometer length scales

Hofmann, T., Kojda, D., Haseeb, H., Wallacher, D., Sobolev, O., & Habicht, K. (2020) · Microporous and Mesoporous Materials · doi:10.1016/j.micromeso.2020.110814 · Cited by 6 · see citing works

Measurement of Phonon Energies in Silicon under Uniaxial Stress

Estel, J., Kalus, J., & Pintschovius, L. (1984) · physica status solidi (b) · doi:10.1002/pssb.2221260115 · Cited by 6 · see citing works

Chain character of vacancy-type defects in silicon

Sieverts, E. G., Sprenger, M., & Ammerlaan, C. A. J. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.41.8630 · Cited by 6 · see citing works

A hybrid methodology based on first-principles calculations and Calphad to predict the Ni-Co phase diagram incorporating configurational, vibrational and magnetic contributions

Shi, C., Shao, W., & LLorca, J. (2025) · Acta Materialia · doi:10.1016/j.actamat.2025.121476 · Cited by 5 · see citing works

First-principles prediction of the Co–Al phase diagram including configurational, vibrational and magnetic contributions

Shao, W., Hou, H., Liu, S., & LLorca, J. (2024) · Journal of Materials Research and Technology · doi:10.1016/j.jmrt.2024.06.143 · Cited by 5 · see citing works

Local and Band Mode Frequencies of Si1−xGex Solid Solution

Soma, T., Kitani, Y., & Kagaya, H. ‐. (1984) · physica status solidi (b) · doi:10.1002/pssb.2221220250 · Cited by 5 · see citing works

Investigation of defect structure of neutron-irradiated crystalline silicon by low-temperature thermal conductivity

Pompe, G., el Rehim, N. A., & Mertig, M. (1989) · Journal of Low Temperature Physics · doi:10.1007/bf00682670 · Cited by 5 · see citing works

Boundary conditions dictate frequency dependence of thermal conductivity in silicon

Liu, Y., Li, Q., Liu, F., Wang, X., & Sun, B. (2025) · Applied Physics Reviews · doi:10.1063/5.0254248 · Cited by 4 · see citing works

The effect of porosity on the vibrational and low temperature equilibrium thermodynamic properties of amorphous silicon via computer simulation

Noyola-Pineda, J. C., & Valladares, A. (2016) · Journal of Non-Crystalline Solids · doi:10.1016/j.jnoncrysol.2016.10.017 · Cited by 4 · see citing works

Temperature dependence of the interface energy in Al-Cu alloys from first-principles and phonon calculations

Shao, W., Yang, Y., Wróbel, J. S., & LLorca, J. (2026) · Acta Materialia · doi:10.1016/j.actamat.2026.121925 · Cited by 3 · see citing works

Thermal expansion of crystal lattices of germanium with different isotopic compositions

Zhernov, A. P. (1998) · Physics of the Solid State · doi:10.1134/1.1130628 · Cited by 3 · see citing works

Abinitiophonon quantities of simple metals from Hartree-Fock cluster techniques

Zdetsis, A. D. (1987) · Physical review. B, Condensed matter · doi:10.1103/physrevb.35.5868 · Cited by 3 · see citing works

Boundary conditions dictate frequency dependence of thermal conductivity in silicon

Liu, Y., Li, Q., Liu, F., Wang, X., & Sun, B. (2024) · arXiv · doi:10.48550/arxiv.2412.02227 · Cited by 2 · see citing works

Characteristic features of the low-temperature thermal conductivity of highly-enriched and natural germanium

Zhernov, A. P., & Zhernov, D. A. (1998) · Physics of the Solid State · doi:10.1134/1.1130613 · Cited by 1 · see citing works

Estimation of inter-atomic force constants and phonon dispersion using correlation effects among thermal displacement of atoms in Ge

Sakuma, T., Mohapatra, S. R., Isozaki, N., Uehara, H., Xianglian, X., Basar, K., Takahashi, H., Kamishima, O., & Igawa, N. (2010) · Journal of Non-Crystalline Solids · doi:10.1016/j.jnoncrysol.2010.06.054 · Cited by 1 · see citing works

Effect of isotopic disorder on the thermal conductivity of germanium in the region of the maximum

Zhernov, A. P. (1999) · Physics of the Solid State · doi:10.1134/1.1130940 · Cited by 1 · see citing works

A method to calculate thermal conductivity of a nonperiodic system, bamboo Si1−xGex nanowire with axially degraded components

Xia, M., Han, J., Cheng, Z., Zhang, S., & Li, B. (2017) · The European Physical Journal B · doi:10.1140/epjb/e2017-80211-8 · Cited by 1 · see citing works

Low-temperature thermal conductivity of highly enriched and natural germanium

Zhernov, A. P., & Zhernov, D. A. (1998) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.558744 · Cited by 1 · see citing works

Effect of isotopic composition on the linear thermal expansion coefficient of a germanium crystal lattice

Zhernov, A. P. (1998) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.558667 · Cited by 1 · see citing works

Lattice dynamics of Si/Ge (001) superlattices

Mu, Y.-M., & Tao, R. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.42.5875 · Cited by 1 · see citing works

A microscopic calculation of force constants in crystals

Rakel, H., Falter, C., & Ludwig, W. (1989) · The European Physical Journal B · doi:10.1007/bf01307998 · Cited by 1 · see citing works

Materials informatics approach for design of Si/Ge layered nanostructures with low thermal conductivity

Takahashi, N., Liu, Y., & Kaneta, C. (2020) · Japanese Journal of Applied Physics · doi:10.35848/1347-4065/ab8700

Silicon (Si) phonon dispersion relations

(2005) · Springer eBooks · doi:10.1007/10551045_200

Bayesian Estimation of Phonon Dispersion Relation from Thermal Diffuse Scattering

Yui, K., Ueda, H., Katakami, S., Christiansen‐Salameh, J., Tian, Z., Shiomi, J., & Okada, M. (2025) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.94.083601

Thermodynamic stability of Al/MgZn2 interfaces including vibrational entropy and thermal expansion contributions

Shao, W., Yang, Y., Wróbel, J. S., & LLorca, J. (2026) · Acta Materialia · doi:10.1016/j.actamat.2026.122830

Lattice vibrational spectrum of germanium

Herman, F. (1959) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(59)90376-2 · Cited by 229 · see citing works

Lattice dynamics of diamond

Aggarwal, K. G. (1967) · Proceedings of the Physical Society · doi:10.1088/0370-1328/91/2/316 · Cited by 191 · see citing works

A parallel Born-von Karman study of diamond and the diamond type crystals

Zdetsis, A. D. (1979) · Chemical Physics · doi:10.1016/0301-0104(79)85147-2 · Cited by 25 · see citing works

Lattice dynamics of silicon and diamond

Pandey, B. P., & Dayal, B. (1973) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/6/20/007 · Cited by 13 · see citing works

Valence force potential calculations of the lattice dynamics of diamond-type crystals

Bell, M. I. (1975) · The Journal of Chemical Physics · doi:10.1063/1.430918 · Cited by 2 · see citing works