diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml new file mode 100644 index 00000000..eecf0d13 --- /dev/null +++ b/.github/workflows/draft-pdf.yml @@ -0,0 +1,23 @@ +on: [push] + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v4 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + # This should be the path to the paper within your repo. + paper-path: paper/paper.md + - name: Upload + uses: actions/upload-artifact@v1 + with: + name: paper + # This is the output path where Pandoc will write the compiled + # PDF. Note, this should be the same directory as the input + # paper.md + path: paper/paper.pdf diff --git a/paper/Makefile b/paper/Makefile new file mode 100644 index 00000000..735dae45 --- /dev/null +++ b/paper/Makefile @@ -0,0 +1,9 @@ +CMDbib = biber --tool --output_align --output_indent=2 --output_fieldcase=lower --output-legacy-dates --output-field-replace=journaltitle:journal + +final: + ${CMDbib} literature_final.bib + mv literature_final_bibertool.bib literature_final.bib + +bib: + ${CMDbib} paper_tdep_joss.bib + mv paper_tdep_joss_bibertool.bib literature.bib diff --git a/paper/literature.bib b/paper/literature.bib new file mode 100644 index 00000000..710a0d92 --- /dev/null +++ b/paper/literature.bib @@ -0,0 +1,795 @@ +@misc{tdeptools, + author = {Knoop, F.}, + publisher = {GitHub}, + url = {https://github.com/flokno/tools.tdep}, + title = {{tdeptools: tools for TDEP}}, + year = {2023}, +} + +@article{Castellano.2023, + abstract = {{The dynamical properties of nuclei, carried by the concept of phonon quasiparticles, are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics.}}, + author = {Castellano, Aloïs and Batista, José and Verstraete, Matthieu J}, + doi = {10.48550/arxiv.2303.10621}, + eprint = {2303.10621}, + journal = {arXiv}, + title = {{Mode-coupling theory of lattice dynamics for classical and quantum crystals}}, + year = {2023}, +} + +@article{Reig.2022, + abstract = {{Understanding heat flow in layered transition metal dichalcogenide (TMD) crystals is crucial for applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood, in particular how transport is affected by material thickness and the material's environment. This combined experimental–theoretical study establishes a unifying physical picture of the intrinsic lattice thermal conductivity of the representative TMD MoSe2. Thermal conductivity measurements using Raman thermometry on a large set of clean, crystalline, suspended crystals with systematically varied thickness are combined with ab initio simulations with phonons at finite temperature. The results show that phonon dispersions and lifetimes change strongly with thickness, yet the thinnest TMD films exhibit an in‐plane thermal conductivity that is only marginally smaller than that of bulk crystals. This is the result of compensating phonon contributions, in particular heat‐carrying modes around ≈0.1 THz in (sub)nanometer thin films, with a surprisingly long mean free path of several micrometers. This behavior arises directly from the layered nature of the material. Furthermore, out‐of‐plane heat dissipation to air molecules is remarkably efficient, in particular for the thinnest crystals, increasing the apparent thermal conductivity of monolayer MoSe2 by an order of magnitude. These results are crucial for the design of (flexible) TMD‐based (opto‐)electronic applications. Combined experimental–theoretical study using Raman thermometry and ab initio simulations to unravel the heat transport properties of suspended MoSe2 crystals with systematic thickness variation down to the monolayer. Monolayer films have almost the same in‐plane thermal conductivity as bulk material thanks to an additional heat‐carrying low‐frequency mode. Out‐of‐plane heat dissipation to air is extremely efficient for the thinnest flakes.}}, + author = {Reig, David Saleta and Varghese, Sebin and Farris, Roberta and Block, Alexander and Mehew, Jake D. and Hellman, Olle and Woźniak, Paweł and Sledzinska, Marianna and Sachat, Alexandros El and Chávez‐Ángel, Emigdio and Valenzuela, Sergio O. and Hulst, Niek F. van and Ordejón, Pablo and Zanolli, Zeila and Torres, Clivia M. Sotomayor and Verstraete, Matthieu J. and Tielrooij, Klaas‐Jan}, + doi = {10.1002/adma.202108352}, + issn = {0935-9648}, + journal = {Advanced Materials}, + number = {10}, + pages = {2108352}, + title = {{Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer}}, + volume = {34}, + year = {2022}, +} + +@article{Menahem.2022, + abstract = {{The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.}}, + author = {Menahem, Matan and Benshalom, Nimrod and Asher, Maor and Aharon, Sigalit and Korobko, Roman and Safran, Sam and Hellman, Olle and Yaffe, Omer}, + eprint = {2208.05563}, + journal = {arXiv}, + title = {{The Disorder Origin of Raman Scattering In Perovskites Single Crystals}}, + year = {2022}, +} + +@article{Benshalom.2022v0s, + abstract = {{We have found that the polarization dependence of the Raman signal in organic crystals can only be described by a fourth-rank formalism. The generalization from the traditional second-rank Raman tensor \$\textbackslashmathcal\{R\}\$ is physically motivated by consideration of the light scattering mechanism of anharmonic crystals at finite temperatures, and explained in terms of off-diagonal components of the crystal self-energy. We thus establish a novel manifestation of anharmonicity in inelastic light scattering, markedly separate from the better known phonon lifetime.}}, + author = {Benshalom, Nimrod and Asher, Maor and Jouclas, Rémy and Korobko, Roman and Schweicher, Guillaume and Liu, Jie and Geerts, Yves and Hellman, Olle and Yaffe, Omer}, + eprint = {2204.12528}, + journal = {arXiv}, + title = {{Phonon-phonon interactions in the polarizarion dependence of Raman scattering}}, + year = {2022}, +} + +@article{Laniel.2022, + abstract = {{The lanthanum-hydrogen system has attracted significant attention following the report of superconductivity in LaH10 at near-ambient temperatures and high pressures. Phases other than LaH10 are suspected to be synthesized based on both powder X-ray diffraction and resistivity data, although they have not yet been identified. Here, we present the results of our single-crystal X-ray diffraction studies on this system, supported by density functional theory calculations, which reveal an unexpected chemical and structural diversity of lanthanum hydrides synthesized in the range of 50 to 180 GPa. Seven lanthanum hydrides were produced, LaH3, LaH\textbackslashtextasciitilde4, LaH4+δ, La4H23, LaH6+δ, LaH9+δ, and LaH10+δ, and the atomic coordinates of lanthanum in their structures determined. The regularities in rare-earth element hydrides unveiled here provide clues to guide the search for other synthesizable hydrides and candidate high-temperature superconductors. The hydrogen content variability in lanthanum hydrides and the samples’ phase heterogeneity underline the challenges related to assessing potentially superconducting phases and the nature of electronic transitions in high-pressure hydrides. The lanthanum-hydrogen system has attracted attention following the observation of superconductivity in LaH10 at near-ambient temperatures and high pressures. Here authors describe the high-pressure syntheses of seven La-H phases; they report crystal structures and remarkable regularities in rare-earth element hydrides.}}, + author = {Laniel, Dominique and Trybel, Florian and Winkler, Bjoern and Knoop, Florian and Fedotenko, Timofey and Khandarkhaeva, Saiana and Aslandukova, Alena and Meier, Thomas and Chariton, Stella and Glazyrin, Konstantin and Milman, Victor and Prakapenka, Vitali and Abrikosov, Igor A. and Dubrovinsky, Leonid and Dubrovinskaia, Natalia}, + doi = {10.1038/s41467-022-34755-y}, + eprint = {2208.10418}, + journal = {Nature Communications}, + keywords = {me}, + number = {1}, + pages = {6987}, + title = {{High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content}}, + volume = {13}, + year = {2022}, +} + +@article{Lin.2022, + abstract = {{The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.}}, + author = {Lin, Changpeng and Poncé, Samuel and Marzari, Nicola}, + doi = {10.1038/s41524-022-00920-6}, + eprint = {2209.09520}, + journal = {npj Computational Materials}, + number = {1}, + pages = {236}, + title = {{General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials}}, + volume = {8}, + year = {2022}, +} + +@article{Cohen.2022, + abstract = {{Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K. Raman spectroscopy is used to compare the anharmonic expressions in the structural dynamics of two halide perovskites. In Cs2AgBiBr6, clear normal modes are observed in all measured temperatures. Contrary to this, the Raman spectrum of CsPbBr3 exhibits a breakdown of the normal‐mode picture above 200 K. Implications of these diverging behaviors on the electronic properties of the crystals is discussed.}}, + author = {Cohen, Adi and Brenner, Thomas M. and Klarbring, Johan and Sharma, Rituraj and Fabini, Douglas H. and Korobko, Roman and Nayak, Pabitra K. and Hellman, Olle and Yaffe, Omer}, + doi = {10.1002/adma.202107932}, + issn = {0935-9648}, + journal = {Advanced Materials}, + pages = {2107932}, + title = {{Diverging Expressions of Anharmonicity in Halide Perovskites}}, + year = {2022}, +} + +@article{Benshalom.2022, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature-dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasiharmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + doi = {10.1103/physrevmaterials.6.033607}, + journal = {Physical Review Materials}, + number = {3}, + pages = {033607}, + title = {{Dielectric response of rock-salt crystals at finite temperatures from first principles}}, + volume = {6}, + year = {2022}, +} + +@article{Reig.2021, + abstract = {{Understanding thermal transport in layered transition metal dichalcogenide (TMD) crystals is crucial for a myriad of applications exploiting these materials. Despite significant efforts, several basic thermal transport properties of TMDs are currently not well understood. Here, we present a combined experimental-theoretical study of the intrinsic lattice thermal conductivity of the representative TMD MoSe\$\_2\$, focusing on the effect of material thickness and the material's environment. We use Raman thermometry measurements on suspended crystals, where we identify and eliminate crucial artefacts, and perform \$ab\$ \$initio\$ simulations with phonons at finite, rather than zero, temperature. We find that phonon dispersions and lifetimes change strongly with thickness, yet (sub)nanometer thin TMD films exhibit a similar in-plane thermal conductivity (\$\textbackslashsim\$20\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$) as bulk crystals (\$\textbackslashsim\$40\textbackslashtextasciitildeWm\$\textasciicircum\{-1\}\$K\$\textasciicircum\{-1\}\$). This is the result of compensating phonon contributions, in particular low-frequency modes with a surprisingly long mean free path of several micrometers that contribute significantly to thermal transport for monolayers. We furthermore demonstrate that out-of-plane heat dissipation to air is remarkably efficient, in particular for the thinnest crystals. These results are crucial for the design of TMD-based applications in thermal management, thermoelectrics and (opto)electronics.}}, + author = {Reig, D Saleta and Varghese, S and Farris, R and Block, A and Mehew, J D and Hellman, O and Woźniak, P and Sledzinska, M and Sachat, A El and Chávez-Ángel, E and Valenzuela, S O and Hulst, N F Van and Ordejón, P and Zanolli, Z and Torres, C M Sotomayor and Verstraete, M J and Tielrooij, K J}, + eprint = {2109.09225}, + journal = {arXiv}, + title = {{Unraveling heat transport and dissipation in suspended MoSe\$\_2\$ crystals from bulk to monolayer}}, + year = {2021}, +} + +@article{Monacelli.2021, + abstract = {{The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This technique rigorously describes the full thermodynamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the SSCHA and its dynamical extension, making particular emphasis on the physical inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-density-wave materials, and thermoelectric compounds are also reviewed.}}, + author = {Monacelli, Lorenzo and Bianco, Raffaello and Cherubini, Marco and Calandra, Matteo and Errea, Ion and Mauri, Francesco}, + doi = {10.1088/1361-648x/ac066b}, + eprint = {2103.03973}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {36}, + pages = {363001}, + title = {{The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects}}, + volume = {33}, + year = {2021}, +} + +@article{Dangic.2021, + abstract = {{The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.}}, + author = {Dangić, Đorđe and Hellman, Olle and Fahy, Stephen and Savić, Ivana}, + doi = {10.1038/s41524-021-00523-7}, + journal = {npj Computational Materials}, + number = {1}, + pages = {57}, + title = {{The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe}}, + volume = {7}, + year = {2021}, +} + +@article{Benshalom.2021, + abstract = {{We combine ab initio simulations and Raman scattering measurements to demonstrate explicit anharmonic effects in the temperature dependent dielectric response of a NaCl single crystal. We measure the temperature evolution of its Raman spectrum and compare it to both a quasi-harmonic and anharmonic model. Results demonstrate the necessity of including anharmonic lattice dynamics to explain the dielectric response of NaCl, as it is manifested in Raman scattering. Our model fully captures the linear dielectric response of a crystal at finite temperatures and may therefore be used to calculate the temperature dependence of other material properties governed by it.}}, + author = {Benshalom, Nimrod and Reuveni, Guy and Korobko, Roman and Yaffe, Omer and Hellman, Olle}, + eprint = {2108.04589}, + journal = {arXiv}, + title = {{The dielectric response of rock-salt crystals at finite temperatures from first principles}}, + year = {2021}, +} + +@article{Heine.2021, + abstract = {{We put forth an ab initio framework to calculate local moment magnetic interaction parameters, renormalized to treat both the lattice and magnetic systems as a function of temperature T. For bcc Fe, magnetic and lattice thermal disorders act in opposition, the former strengthening the Heisenberg-like interactions, while the latter decreasing them. Below TC, J stays nearly independent of T, while around and above TC, it exhibits a sharp decrease. This remarkable behavior reflects an intricate spin-lattice coupling and its evolution with T, in which magnetic interactions and interatomic bonds are each renormalized by the other. This finding is consistent with magnetization data and with the observed softening of magnon and phonon modes at high temperatures. Magnetization as well as magnon and phonon mode softening are discussed.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.103.184409}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {18}, + pages = {184409}, + title = {{Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles}}, + volume = {103}, + year = {2021}, +} + +@article{Roekeghem.2021, + abstract = {{The Quantum Self-Consistent Ab-Initio Lattice Dynamics package (QSCAILD) is a python library that computes temperature-dependent effective 2nd and 3rd order interatomic force constants in crystals, including anharmonic effects. QSCAILD’s approach is based on the quantum statistics of a harmonic model. The program requires the forces acting on displaced atoms of a solid as an input, which can be obtained from an external code based on density functional theory, or any other calculator. This article describes QSCAILD’s implementation, clarifies its connections to other methods, and illustrates its use in the case of the SrTiO3 cubic perovskite structure. Program Program Title: QSCAILD CPC Library link to program files: https://doi.org/10.17632/y4c922fwtf.1 Licensing provisions: GNU General Public License version 3.0 Programming language: Python External routines/libraries: MPI, NumPy, SciPy, spglib, phonopy, sklearn Nature of problem: Calculation of effective interatomic force constants at finite temperature Solution method: Regression analysis of forces from density functional theory coupled with a harmonic model of the quantum canonical ensemble, performed in an iterative way to achieve self-consistency of the phonon spectrum}}, + author = {Roekeghem, Ambroise van and Carrete, Jesús and Mingo, Natalio}, + doi = {10.1016/j.cpc.2021.107945}, + eprint = {2006.12867}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + pages = {107945}, + title = {{Quantum Self-Consistent Ab-Initio Lattice Dynamics}}, + volume = {263}, + year = {2021}, +} + +@article{Cai.2021, + abstract = {{Phonon chirality has attracted intensive attention since it breaks the traditional cognition that phonons are linear propagating bosons. This new quasiparticle property has been extensively studied theoretically and experimentally. However, characterization of the phonon chirality throughout the full Brillouin zone is still not possible due to the lack of available experimental tools. In this work, phonon dispersion and chirality of tungsten carbide were investigated by millielectronvolt energy-resolution inelastic X-ray scattering. The atomistic calculation indicates that in-plane longitudinal and transverse acoustic phonons near K and K\$\textasciicircum\textbackslashprime\$ points are circularly polarized due to the broken inversion symmetry. Anomalous inelastic X-ray scattering by these circularly polarized phonons was observed and attributed to their chirality. Our results show that inelastic X-ray scattering can be utilized to characterize phonon chirality in materials and suggest that a revision to the phonon scattering function is necessary.}}, + author = {Cai, Qingan and Hellman, Olle and Wei, Bin and Sun, Qiyang and Said, Ayman H and Gog, Thomas and Winn, Barry and Li, Chen}, + eprint = {2108.06631}, + journal = {arXiv}, + title = {{Direct Observation of Chiral Phonons by Inelastic X-ray Scattering}}, + year = {2021}, +} + +@article{Klarbring.2020vk, + abstract = {{The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs2AgBiBr6, the prototypical compound in this class and show that the lattice dynamics of Cs2AgBiBr6 is highly anharmonic, largely in regards to tilting of AgBr6 and BiBr6 octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs2AgBiBr6 yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.}}, + author = {Klarbring, Johan and Hellman, Olle and Abrikosov, Igor A. and Simak, Sergei I.}, + doi = {10.1103/physrevlett.125.045701}, + eprint = {1912.05351}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {4}, + pages = {045701}, + title = {{Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites}}, + volume = {125}, + year = {2020}, +} + +@article{Bottin.2020rn5, + abstract = {{In this paper, we present the a-TDEP post-process code implemented in the Abinit package. This one is able to capture the explicit thermal effects in solid state physics and to produce a large number of temperature dependent thermodynamic quantities, including the so-called anharmonic effects. Its use is straightforward and require only a single ab initio molecular dynamic (AIMD) trajectory. A Graphical User Interface (GUI) is also available, making the use even easier. We detail our home made implementation of the original “Temperature Dependent Effective Potential” method proposed by Hellman et al. (2011). In particular, we present the various algorithms and schemes used in a-TDEP which enable to obtain the effective Interatomic Force Constants (IFC). The 2nd and 3rd order effective IFC are produced self-consistently using a least-square method, fitting the AIMD forces on a model Hamiltonian function of the displacements. In addition, we stress that we face to a constrained least-square problem since all the effective IFC have to fulfill the several symmetry rules imposed by the space group, by the translation or rotation invariances of the system and by others. Numerous thermodynamic quantities can be computed starting from the 2nd order effective IFC. The first one is the phonon spectrum, from which a large number of other quantities flow : internal energy, entropy, free energy, specific heat... The elastic constants and other usual elastic moduli (the bulk, shear and Young moduli) can also be produced at this level. Using the 3rd order effective IFC, we show how to extract the thermodynamic Grüneisen parameter, the thermal expansion, the sound velocities... and in particular, how to take into account the anisotropy of the system within. As representative applications of a-TDEP capabilities, we show the thermal evolution of the soft phonon mode of α -U, the thermal stabilization of the bcc phase of Zr and the thermal expansion of diamond Si. All these features highlight the strong anharmonicity included in these systems.}}, + author = {Bottin, François and Bieder, Jordan and Bouchet, Johann}, + doi = {10.1016/j.cpc.2020.107301}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + pages = {107301}, + title = {{a-TDEP: Temperature Dependent Effective Potential for Abinit – Lattice dynamic properties including anharmonicity}}, + volume = {254}, + year = {2020}, +} + +@article{Eriksson.2019, + abstract = {{The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely extend beyond third order when input data is obtained from first‐principles calculations. Methods based on parameter fitting in the spirit of interatomic potentials, on the other hand, can extract FC parameters from semi‐random configurations of high information density and advanced regularized regression methods can recover physical solutions from a limited amount of data. Here, the hiphive Python package, that enables the construction of force constant models up to arbitrary order is presented. hiphive exploits crystal symmetries to reduce the number of free parameters and then employs advanced machine learning algorithms to extract the force constants. Depending on the problem at hand, both over and underdetermined systems are handled efficiently. The FCs can be subsequently analyzed directly and or be used to carry out, for example, molecular dynamics simulations. The utility of this approach is demonstrated via several examples including ideal and defective monolayers of MoS2 as well as bulk nickel. The hiphive package is a powerful tool for the efficient extraction of high‐order force constants. It thereby enables modeling the thermodynamic and vibrational properties of, for example, large, low‐symmetry systems and strongly anharmonic materials. This ultimately includes, for example, temperature‐dependent phonon dispersions, life times, and the thermal conductivity.}}, + author = {Eriksson, Fredrik and Fransson, Erik and Erhart, Paul}, + doi = {10.1002/adts.201800184}, + eprint = {1811.09267}, + issn = {2513-0390}, + journal = {Advanced Theory and Simulations}, + number = {5}, + pages = {1800184}, + title = {{The Hiphive Package for the Extraction of High‐Order Force Constants by Machine Learning}}, + volume = {2}, + year = {2019}, +} + +@article{Manley.2019, + abstract = {{Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties. To optimize the performance of lead chalcogenides for thermoelectric applications, strategies to further reduce the crystal’s thermal conductivity is required. Here, the authors discover anharmonic localized vibrations in PbSe crystals for optimizing the crystal’s vibrational transport properties.}}, + author = {Manley, M. E. and Hellman, O. and Shulumba, N. and May, A. F. and Stonaha, P. J. and Lynn, J. W. and Garlea, V. O. and Alatas, A. and Hermann, R. P. and Budai, J. D. and Wang, H. and Sales, B. C. and Minnich, A. J.}, + doi = {10.1038/s41467-019-09921-4}, + journal = {Nature Communications}, + number = {1}, + pages = {1928}, + title = {{Intrinsic anharmonic localization in thermoelectric PbSe}}, + volume = {10}, + year = {2019}, +} + +@article{Heine.2019, + abstract = {{We present a first-principles theoretical approach to calculate temperature dependent phonon dispersions in bcc Fe, which captures finite temperature spin-lattice coupling by treating thermal disorder in both the spin and lattice systems simultaneously. With increasing temperature, thermal atomic displacements are found to induce increasingly large fluctuations in local magnetic moment magnitudes. The calculated phonon dispersions of bcc Fe show excellent agreement with measured data over a wide range of temperatures both above and below the magnetic and structural transition temperatures, suggesting the applicability of the developed approach to other magnetic materials.}}, + author = {Heine, Matthew and Hellman, Olle and Broido, David}, + doi = {10.1103/physrevb.100.104304}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {10}, + pages = {104304}, + title = {{Effect of thermal lattice and magnetic disorder on phonons in bcc Fe: A first-principles study}}, + volume = {100}, + year = {2019}, +} + +@article{Ravichandran.2018, + abstract = {{The conventional first-principles theory for the thermal and thermodynamic properties of insulators is based on the perturbative treatment of the anharmonicity of crystal bonds. While this theory has been a successful predictive tool for strongly bonded solids such as diamond and silicon, here we show that it fails dramatically for strongly anharmonic (weakly bonded) materials, and that the conventional quasiparticle picture breaks down at relatively low temperatures. To address this failure, we present a unified first-principles theory of the thermodynamic and thermal properties of insulators that captures multiple thermal properties within the same framework across the full range of anharmonicity from strongly bonded to weakly bonded insulators. This theory features a new phonon renormalization approach derived from many-body physics that creates well-defined quasiparticles even at relatively high temperatures, and it accurately captures the effects of strongly anharmonic bonds on phonons and thermal transport. Using a prototypical strongly anharmonic material, sodium chloride (NaCl), as an example, we demonstrate that our new first-principles framework simultaneously captures the apparently contradictory experimental observations of large thermal expansion and low thermal conductivity of NaCl on the one hand, and anomalously weak temperature dependence of phonon modes on the other, while the conventional theory fails in all three cases. We demonstrate that four-phonon scattering due to higher-order anharmonicity significantly lowers the thermal conductivity of NaCl and is required for a proper comparison to experiment. Furthermore, we show that our renormalization framework, along with four-phonon scattering, also successfully predicts the measured phonon frequencies and thermal properties of a weakly anharmonic material, diamond, indicating universal applicability for thermal properties of insulators. Our work gives new insights into the physics of heat flow in solids, and presents a computationally efficient and rigorous framework that captures the thermal and thermodynamic properties of both weakly and strongly bonded insulators simultaneously.}}, + author = {Ravichandran, Navaneetha K. and Broido, David}, + doi = {10.1103/physrevb.98.085205}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {8}, + pages = {085205}, + title = {{Unified first-principles theory of thermal properties of insulators}}, + volume = {98}, + year = {2018}, +} + +@article{Kim.2018, + abstract = {{Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.}}, + author = {Kim, D. S. and Hellman, O. and Herriman, J. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B.}, + doi = {10.1073/pnas.1707745115}, + eprint = {1610.08737}, + issn = {0027-8424}, + journal = {Proceedings of the National Academy of Sciences}, + number = {9}, + pages = {201707745}, + title = {{Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon}}, + volume = {115}, + year = {2018}, +} + +@article{Zhou.2018, + abstract = {{Structural phase transitions and soft phonon modes pose a long-standing challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO3 is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200 K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO3 between 150–300 K, and reveal the microscopic origin of its roughly T-3 trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.}}, + author = {Zhou, Jin-Jian and Hellman, Olle and Bernardi, Marco}, + doi = {10.1103/physrevlett.121.226603}, + eprint = {1806.05775}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {22}, + pages = {226603}, + title = {{Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO3 Perovskite from First Principles}}, + volume = {121}, + year = {2018}, +} + +@article{Larsen.2017, + abstract = {{The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.}}, + author = {Larsen, Ask Hjorth and Mortensen, Jens Jørgen and Blomqvist, Jakob and Castelli, Ivano E and Christensen, Rune and Dułak, Marcin and Friis, Jesper and Groves, Michael N and Hammer, Bjørk and Hargus, Cory and Hermes, Eric D and Jennings, Paul C and Jensen, Peter Bjerre and Kermode, James and Kitchin, John R and Kolsbjerg, Esben Leonhard and Kubal, Joseph and Kaasbjerg, Kristen and Lysgaard, Steen and Maronsson, Jón Bergmann and Maxson, Tristan and Olsen, Thomas and Pastewka, Lars and Peterson, Andrew and Rostgaard, Carsten and Schiøtz, Jakob and Schütt, Ole and Strange, Mikkel and Thygesen, Kristian S and Vegge, Tejs and Vilhelmsen, Lasse and Walter, Michael and Zeng, Zhenhua and Jacobsen, Karsten W}, + doi = {10.1088/1361-648x/aa680e}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {27}, + pages = {273002}, + title = {{The atomic simulation environment—a Python library for working with atoms}}, + volume = {29}, + year = {2017}, +} + +@article{Shulumba.20179s8e, + abstract = {{Molecular crystals such as polyethylene are of intense interest as flexible thermal conductors, yet their intrinsic upper limits of thermal conductivity remain unknown. Here, we report a study of the vibrational properties and lattice thermal conductivity of a polyethylene molecular crystal using an ab initio approach that rigorously incorporates nuclear quantum motion and finite temperature effects. We obtain a thermal conductivity along the chain direction of around 160 W m−1 K−1 at room temperature, providing a firm upper bound for the thermal conductivity of this molecular crystal. Furthermore, we show that the inclusion of quantum nuclear effects significantly impacts the thermal conductivity by altering the phase space for three-phonon scattering. Our computational approach paves the way for ab initio studies and computational material discovery of molecular solids free of any adjustable parameters.}}, + author = {Shulumba, Nina and Hellman, Olle and Minnich, Austin J.}, + doi = {10.1103/physrevlett.119.185901}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {18}, + pages = {185901}, + title = {{Lattice Thermal Conductivity of Polyethylene Molecular Crystals from First-Principles Including Nuclear Quantum Effects}}, + volume = {119}, + year = {2017}, +} + +@article{Shulumba.2017, + abstract = {{Lead chalcogenides such as PbS, PbSe, and PbTe are of interest for their exceptional thermoelectric properties and strongly anharmonic lattice dynamics. Although PbTe has received the most attention, PbSe has a lower thermal conductivity and a nonlinear temperature dependence of thermal resistivity despite being stiffer, trends that prior first-principles calculations have not fully reproduced. Here, we use ab initio calculations that explicitly account for strong anharmonicity and a computationally efficient stochastic phase-space sampling scheme to identify the origin of this low thermal conductivity as an anomalously large anharmonic interaction, exceeding in strength that in PbTe, between the transverse optic and longitudinal acoustic branches. The strong anharmonicity is reflected in the striking observation of an intrinsic localized mode that forms in the acoustic frequencies. Our work shows the deep insights into thermal phonons that can be obtained from ab initio calculations that do not rely on perturbations from the ground-state phonon dispersion.}}, + author = {Shulumba, Nina and Hellman, Olle and Minnich, Austin J.}, + doi = {10.1103/physrevb.95.014302}, + eprint = {1609.08254}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {1}, + pages = {014302}, + title = {{Intrinsic localized mode and low thermal conductivity of PbSe}}, + volume = {95}, + year = {2017}, +} + +@article{Dewandre.2016, + abstract = {{The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.}}, + author = {Dewandre, Antoine and Hellman, Olle and Bhattacharya, Sandip and Romero, Aldo H. and Madsen, Georg K. H. and Verstraete, Matthieu J.}, + doi = {10.1103/physrevlett.117.276601}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {27}, + pages = {276601}, + title = {{Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles}}, + volume = {117}, + year = {2016}, +} + +@article{Feng.2016, + abstract = {{Recently, first principle-based predictions of lattice thermal conductivity κ from perturbation theory have achieved significant success. However, it only includes three-phonon scattering due to the assumption that four-phonon and higher-order processes are generally unimportant. Also, directly evaluating the scattering rates of four-phonon and higher-order processes has been a long-standing challenge. In this work, however, we have developed a formalism to explicitly determine quantum mechanical scattering probability matrices for four-phonon scattering in the full Brillouin zone, and by mitigating the computational challenge we have directly calculated four-phonon scattering rates. We find that four-phonon scattering rates are comparable to three-phonon scattering rates at medium and high temperatures, and they increase quadratically with temperature. As a consequence, κ of Lennard-Jones argon is reduced by more than 60\% at 80 K when four-phonon scattering is included. Also, in less anharmonic materials—diamond, silicon, and germanium—κ is still reduced considerably at high temperature by four-phonon scattering by using the classical Tersoff potentials. Also, the thermal conductivity of optical phonons is dominated by the fourth- and higher-orders phonon scattering even at low temperature.}}, + author = {Feng, Tianli and Ruan, Xiulin}, + doi = {10.1103/physrevb.93.045202}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {4}, + pages = {045202}, + title = {{Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids}}, + volume = {93}, + year = {2016}, +} + +@article{Shulumba.2016, + abstract = {{We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti1-xAlxN alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti1-xAlxN alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti0.5Al0.5N alloys agree with the calculated phase diagram.}}, + author = {Shulumba, Nina and Hellman, Olle and Raza, Zamaan and Alling, Björn and Barrirero, Jenifer and Mücklich, Frank and Abrikosov, Igor A. and Odén, Magnus}, + doi = {10.1103/physrevlett.117.205502}, + eprint = {1503.02459}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {20}, + pages = {205502}, + title = {{Lattice Vibrations Change the Solid Solubility of an Alloy at High Temperatures}}, + volume = {117}, + year = {2016}, +} + +@article{Romero.2015, + abstract = {{We investigate the harmonic and anharmonic contributions to the phonon spectrum of lead telluride and perform a complete characterization of how thermal properties of PbTe evolve as temperature increases. We analyze the thermal resistivity's variation with temperature and clarify misconceptions about existing experimental literature. The resistivity initially increases sublinearly because of phase space effects and ultra strong anharmonic renormalizations of specific bands. This effect is the strongest factor in the favorable thermoelectric properties of PbTe, and it explains its limitations at higher T. This quantitative prediction opens the prospect of phonon phase space engineering to tailor the lifetimes of crucial heat carrying phonons by considering different structure or nanostructure geometries. We analyze the available scattering volume between TO and LA phonons as a function of temperature and correlate its changes to features in the thermal conductivity.}}, + author = {Romero, A. H. and Gross, E. K. U. and Verstraete, M. J. and Hellman, Olle}, + doi = {10.1103/physrevb.91.214310}, + eprint = {1402.5535}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {21}, + pages = {214310}, + title = {{Thermal conductivity in PbTe from first principles}}, + volume = {91}, + year = {2015}, +} + +@article{Tadano.2015, + abstract = {{We present an ab initio framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO3 and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistortive mode depends significantly on the system size near the critical temperature of the cubic-to-tetragonal phase transition. By applying perturbation theory to the SCPH result, phonon lifetimes are calculated for cubic SrTiO3, which are then employed to predict lattice thermal conductivity using the Boltzmann transport equation within the relaxation-time approximation. The presented methodology is efficient and accurate, paving the way toward a reliable description of thermodynamic, dynamic, and transport properties of systems with severe anharmonicity, including thermoelectric, ferroelectric, and superconducting materials.}}, + author = {Tadano, Terumasa and Tsuneyuki, Shinji}, + doi = {10.1103/physrevb.92.054301}, + eprint = {1506.01781}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {5}, + pages = {054301}, + title = {{Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO3 with first-principles anharmonic force constants}}, + volume = {92}, + year = {2015}, +} + +@article{Mei.2015, + abstract = {{Structural phase transitions in epitaxial stoichiometric VN/MgO(011) thin films are investigated using temperature-dependent synchrotron x-ray diffraction (XRD), selected-area electron diffraction (SAED), resistivity measurements, high-resolution cross-sectional transmission electron microscopy, and ab initio molecular dynamics (AIMD). At room temperature, VN has the B1 NaCl structure. However, below Tc=250K, XRD and SAED results reveal forbidden (00l) reflections of mixed parity associated with a noncentrosymmetric tetragonal structure. The intensities of the forbidden reflections increase with decreasing temperature following the scaling behavior I∝(Tc−T)1/2. Resistivity measurements between 300 and 4 K consist of two linear regimes resulting from different electron/phonon coupling strengths in the cubic and tetragonal-VN phases. The VN transport Eliashberg spectral function αtr2F(ℏω), the product of the phonon density of states F(ℏω) and the transport electron/phonon coupling strength αtr2(ℏω), is determined and used in combination with AIMD renormalized phonon dispersion relations to show that anharmonic vibrations stabilize the NaCl structure at T>Tc. Free-energy contributions due to vibrational entropy, often neglected in theoretical modeling, are essential for understanding the room-temperature stability of NaCl-structure VN, and of strongly anharmonic systems in general.}}, + author = {Mei, A. B. and Hellman, O. and Wireklint, N. and Schlepütz, C. M. and Sangiovanni, D. G. and Alling, B. and Rockett, A. and Hultman, L. and Petrov, I. and Greene, J. E.}, + doi = {10.1103/physrevb.91.054101}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {5}, + pages = {054101}, + title = {{Dynamic and structural stability of cubic vanadium nitride}}, + volume = {91}, + year = {2015}, +} + +@article{Zhang.2014up, + abstract = {{We use a hybrid strategy to obtain anharmonic frequency shifts and lifetimes of phonon quasiparticles from first principles molecular dynamics simulations in modest size supercells. This approach is effective irrespective of crystal structure complexity and facilitates calculation of full anharmonic phonon dispersions, as long as phonon quasiparticles are well defined. We validate this approach to obtain anharmonic effects with calculations in MgSiO3 perovskite, the major Earth forming mineral phase. First, we reproduce irregular thermal frequency shifts of well characterized Raman modes. Second, we combine the phonon gas model (PGM) with quasiparticle frequencies and reproduce free energies obtained using thermodynamic integration. Combining thoroughly sampled quasiparticle dispersions with the PGM we then obtain first-principles anharmonic free energy in the thermodynamic limit (N→∞).}}, + author = {Zhang, Dong-Bo and Sun, Tao and Wentzcovitch, Renata M.}, + doi = {10.1103/physrevlett.112.058501}, + eprint = {1312.7490}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {5}, + pages = {058501}, + title = {{Phonon Quasiparticles and Anharmonic Free Energy in Complex Systems}}, + volume = {112}, + year = {2014}, +} + +@article{Tadano.2014, + abstract = {{A systematic method to calculate anharmonic force constants of crystals is presented. The method employs the direct-method approach, where anharmonic force constants are extracted from the trajectory of first-principles molecular dynamics simulations at high temperature. The method is applied to Si where accurate cubic and quartic force constants are obtained. We observe that higher-order correction is crucial to obtain accurate force constants from the trajectory with large atomic displacements. The calculated harmonic and anharmonic force constants are, then, combined with the Boltzmann transport equation (BTE) and non-equilibrium molecular dynamics (NEMD) methods in calculating the thermal conductivity. The BTE approach successfully predicts the lattice thermal conductivity of bulk Si, whereas NEMD shows considerable underestimates. To evaluate the linear extrapolation method employed in NEMD to estimate bulk values, we analyze the size dependence in NEMD based on BTE calculations. We observe strong nonlinearity in the size dependence of NEMD in Si, which can be ascribed to acoustic phonons having long mean-free-paths and carrying considerable heat. Subsequently, we also apply the whole method to a thermoelectric material Mg2Si and demonstrate the reliability of the NEMD method for systems with low thermal conductivities.}}, + author = {Tadano, T and Gohda, Y and Tsuneyuki, S}, + doi = {10.1088/0953-8984/26/22/225402}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {22}, + pages = {225402}, + title = {{Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations}}, + volume = {26}, + year = {2014}, +} + +@article{Hellman.2013oi5, + abstract = {{The temperature-dependent effective potential (TDEP) method is generalized beyond pair interactions. The second- and third-order force constants are determined consistently from ab initio molecular dynamics simulations at finite temperature. The reliability of the approach is demonstrated by calculations of the mode Grüneisen parameters for Si. We show that the extension of TDEP to a higher order allows for an efficient calculation of the phonon life time, in Si as well as in ε-FeSi; a system that exhibits anomalous softening with temperature.}}, + author = {Hellman, Olle and Abrikosov, I. A.}, + doi = {10.1103/physrevb.88.144301}, + eprint = {1308.5436}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144301}, + title = {{Temperature-dependent effective third-order interatomic force constants from first principles}}, + volume = {88}, + year = {2013}, +} + +@article{Hellman.2013, + abstract = {{We have developed a thorough and accurate method of determining anharmonic free energies, the temperature dependent effective potential technique (TDEP). It is based on ab initio molecular dynamics followed by a mapping onto a model Hamiltonian that describes the lattice dynamics. The formalism and the numerical aspects of the technique are described in detail. A number of practical examples are given, and results are presented, which confirm the usefulness of TDEP within ab initio and classical molecular dynamics frameworks. In particular, we examine from first principles the behavior of force constants upon the dynamical stabilization of the body centered phase of Zr, and show that they become more localized. We also calculate the phase diagram for 4He modeled with the Aziz et al. potential and obtain results which are in favorable agreement both with respect to experiment and established techniques.}}, + author = {Hellman, Olle and Steneteg, Peter and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.87.104111}, + eprint = {1303.1145}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {10}, + pages = {104111}, + title = {{Temperature dependent effective potential method for accurate free energy calculations of solids}}, + volume = {87}, + year = {2013}, +} + +@article{Errea.2013, + abstract = {{Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.}}, + author = {Errea, Ion and Calandra, Matteo and Mauri, Francesco}, + doi = {10.1103/physrevlett.111.177002}, + eprint = {1305.7123}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {17}, + pages = {177002}, + title = {{First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds}}, + volume = {111}, + year = {2013}, +} + +@thesis{Hellman.2012, + author = {Hellman, Olle}, + title = {{Thermal properties of materials from first principles}}, + type = {phdthesis}, + year = {2012}, +} + +@article{Hellman.2011, + abstract = {{An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic—or higher order—potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.}}, + author = {Hellman, O. and Abrikosov, I. A. and Simak, S. I.}, + doi = {10.1103/physrevb.84.180301}, + eprint = {1103.5590}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {18}, + pages = {180301}, + title = {{Lattice dynamics of anharmonic solids from first principles}}, + volume = {84}, + year = {2011}, +} + +@article{Hooton.2010, + abstract = {{The thermodynamical formulae of the previous paper are worked out with the help of an adaptation of Debye's continuum approximation ; in particular, the specific heat at constant volume is put into a form suitable for numerical calculation. This formula contains, however, a factor which expresses the (possibly strong) volume dependence of the relation between the new frequency spectrum and that of the customary lattice dynamics : the factor appears in addition to the Debye characteristic temperature θ and must be estimated in any particular application—for example, in the following consideration of solid helium it will be approximated from a linear chain model. The meaning of a Debye characteristic temperature in the anharnionic theory is discussed, and the place of an empirical Debye temperature, determined by fitting specific heat measurements to a theoretical specific heat formula, is also considered. A discussion of this fitted Debye temperature (due to Domb and Salter) is adapted to the anharmonic theory in order to give later a correct application to solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520576}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {433--442}, + title = {{LII. A new treatment of anharmonicity in lattice thermodynamics: II}}, + volume = {46}, + year = {2010}, +} + +@article{Hooton.2010mfn, + abstract = {{Born has given a method by which the anharmonic vibrational motion of the atoms in a crystal can be approximated in terms of an adapted set of harmonic oscillations, these differing from the usualmodes of vibration of harmonic lattice dynamics ; this method is here redeveloped from another standpoint and extended to give explicit results. The thermodynamical formulae of the anharmonic crystal can be given a simple form: they consist of the customary formulae for a set of harmonic oscillators, but now expressed in terms of new frequencies denned essentially from the quadratic and quartic terms in an expansion of the potential energy, plus correction terms which express the difference between the actual anharmonic motion and the harmonic approximation. For small anharmonicity the formulae reduce to thoseof the usual perturbation procedure (allowance for thermal expansion) with some extensions, but they also give a solution in the case of strong anharmonicity. This latter solution will later be used in a discussion of solid helium.}}, + author = {Hooton, D.J.}, + doi = {10.1080/14786440408520575}, + issn = {1941-5982}, + journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + number = {375}, + pages = {422--432}, + title = {{LI. A new treatment of anharmonicity in lattice thermodynamics: I}}, + volume = {46}, + year = {2010}, +} + +@article{Esfarjani.2008, + abstract = {{A method for extracting force constants (FCs) from first principles is introduced. In principle, provided that forces are accurate enough, it can extract harmonic as well as anharmonic FCs up to any neighbor shell. Symmetries of the FCs as well as those of the lattice are used to reduce the number of parameters to be calculated. The results are illustrated for the case of the Lennard-Jones potential, wherein forces are exact and FCs can be analytically calculated, and Si in the diamond structure. The latter are compared to the previously calculated harmonic FCs.}}, + author = {Esfarjani, Keivan and Stokes, Harold T.}, + doi = {10.1103/physrevb.77.144112}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {14}, + pages = {144112}, + title = {{Method to extract anharmonic force constants from first principles calculations}}, + volume = {77}, + year = {2008}, +} + +@article{Souvatzis.2008, + abstract = {{Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born’s interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.}}, + author = {Souvatzis, P. and Eriksson, O. and Katsnelson, M. I. and Rudin, S. P.}, + doi = {10.1103/physrevlett.100.095901}, + eprint = {0803.1325}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {9}, + pages = {095901}, + title = {{Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory}}, + volume = {100}, + year = {2008}, +} + +@article{Broido.2007, + abstract = {{We present an ab initio theoretical approach to accurately describe phonon thermal transport in semiconductors and insulators free of adjustable parameters. This technique combines a Boltzmann formalism with density functional calculations of harmonic and anharmonic interatomic force constants. Without any fitting parameters, we obtain excellent agreement (<5\% difference at room temperature) between the calculated and measured intrinsic lattice thermal conductivities of silicon and germanium. As such, this method may provide predictive theoretical guidance to experimental thermal transport studies of bulk and nanomaterials as well as facilitating the design of new materials.}}, + author = {Broido, D. A. and Malorny, M. and Birner, G. and Mingo, Natalio and Stewart, D. A.}, + doi = {10.1063/1.2822891}, + issn = {0003-6951}, + journal = {Applied Physics Letters}, + number = {23}, + pages = {231922}, + title = {{Intrinsic lattice thermal conductivity of semiconductors from first principles}}, + volume = {91}, + year = {2007}, +} + +@article{West.2006, + abstract = {{The vibrational lifetimes and decay channels of local vibrational modes are calculated from first principles at various temperatures. Our method can be used to predict the temperature dependence of the lifetime of any normal mode in any crystal. We focus here on the stretch modes of H2*, HBC+, and VH·HV in Si. The frequencies are almost identical, but the lifetimes vary from 4 to 295 ps. The calculations correctly predict the lifetimes for T>50 K and illustrate the critical importance of pseudolocal modes in the decay processes of high-frequency local vibrational modes.}}, + author = {West, D. and Estreicher, S. K.}, + doi = {10.1103/physrevlett.96.115504}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {11}, + pages = {115504}, + title = {{First-Principles Calculations of Vibrational Lifetimes and Decay Channels: Hydrogen-Related Modes in Si}}, + volume = {96}, + year = {2006}, +} + +@article{Dove.1986, + abstract = {{As a contribution to the understanding of the incommensurate phase transitions in thiourea, we present a theoretical study of the crystallographic details of the parael ectric phase. A model intermolecular potential is developed, which includes a reasonable distribution of electrostatic multipole interactions as well as the standard dispersive and repulsive interactions. The model gives a satisfactory prediction of the structure of the para electric phase, and in particular explains the occurrence of the hydrogen-bond network. Calculations of phonon-dispersion curves predict a soft-phonon branch in the b direction with the same symmetry as that observed experimentally. Computer simulations predict reasonable values for the vibrational amplitudes, and show the existence of large-amplitude fluctuations of an harmonic quantities at incommensurate wave vectors. However, although the model displays a strong tendency towards incommensurate and lock-in ordering, it does not in fact give a phase transition at a finite temperature. This failure is attributed to the neglect of molecular polarizability, and it is concluded that this feature provides the mechanism that stabilizes the low-temperature phases.For the interested reader, full details of the molecular dynamics simulation technique using parallel processing are presented here. In particular, a method of extracting normal-mode eigenvectors from the results of the simulations is described.}}, + author = {Dove, Martin T. and Lynden-bell, Ruth M.}, + doi = {10.1080/13642818608236861}, + issn = {1364-2812}, + journal = {Philosophical Magazine Part B}, + number = {6}, + pages = {443--463}, + title = {{A model of the paraelectric phase of thiourea}}, + volume = {54}, + year = {1986}, +} + +@article{Levy.1984, + abstract = {{A quasi‐harmonic approximation is described for studying very low frequency vibrations and flexible paths in proteins. The force constants of the empirical potential function are quadratic approximations to the potentials of mean force; they are evaluated from a molecular dynamics simulation of a protein based on a detailed anharmonic potential. The method is used to identify very low frequency (∼1 cm−1) normal modes for the protein pancreatic trypsin inhibitor. A simplified model for the protein is used, for which each residue is represented by a single interaction center. The quasi‐harmonic force constants of the virtual internal coordinates are evaluated and the normal‐mode frequencies and eigenvectors are obtained. Conformations corresponding to distortions along selected low‐frequency modes are analyzed.}}, + author = {Levy, R. M. and Srinivasan, A. R. and Olson, W. K. and McCammon, J. A.}, + doi = {10.1002/bip.360230610}, + issn = {0006-3525}, + journal = {Biopolymers}, + number = {6}, + pages = {1099--1112}, + title = {{Quasi‐harmonic method for studying very low frequency modes in proteins}}, + volume = {23}, + year = {1984}, +} + +@book{Wallace.1972, + author = {Wallace, Duane C.}, + location = {New York}, + publisher = {John Wiley \& Sons, Inc.}, + note = {Read up on operator-renormalization method - pressure: p. 74, 154, 192, 193}, + title = {{Thermodynamics of Crystals}}, + year = {1972}, +} + +@article{Klein.1972, + author = {Klein, M. L. and Horton, G. K.}, + doi = {10.1007/bf00654839}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {3-4}, + pages = {151--166}, + title = {{The rise of self-consistent phonon theory}}, + volume = {9}, + year = {1972}, +} + +@article{Horner.1972, + abstract = {{Numerical calculations of phonon spectra, including damping, are reported for bcc3He and4He and for fcc4He. Strong damping is found for the longitudinal branches near the boundary of the Brillouin zone. In the bcc phase anomalous dispersion occurs for several directions at long wavelengths, which is most pronounced in the lowest transverse branch in (110) direction. This leads to an anomaly in the specific heat at low temperatures. In this calculation anharmonicities and short-range correlations are treated in a self-consistent way.}}, + author = {Horner, Heinz}, + doi = {10.1007/bf00653877}, + issn = {0022-2291}, + journal = {Journal of Low Temperature Physics}, + number = {5-6}, + pages = {511--529}, + title = {{Phonons and thermal properties of bcc and fcc helium from a self-consistent anharmonic theory}}, + volume = {8}, + year = {1972}, +} + +@article{Koehler.1971, + abstract = {{A theory is presented of the damping and frequency shift of phonons and of the ground-state energy corrections due to interactions between phonons in quantum crystals with singular forces. The technique begins with the adoption of a trial ground-state wave function of the Jastrow form, together with trial excited-state wave functions constructed to represent one-, two-, and three-phonon excitations. The Hamiltonian matrix in this restricted basis is diagonalized, and the basis is optimized by minimizing the lowest eigenvalue with respect to variational phonon parameters. Using a lowest-order cluster expansion, the unambiguous prescription is obtained that a specific effective potential, softened by the Jastrow correlation function, replaces everywhere the true potential in the existing self-consistent theory of phonon damping applicable to nonsingular forces. Close analogies are drawn with the correlated basis function treatment, of superfluid liquid helium.}}, + author = {Koehler, T. R. and Werthamer, N. R.}, + doi = {10.1103/physreva.3.2074}, + issn = {1050-2947}, + journal = {Physical Review A}, + number = {6}, + pages = {2074--2083}, + title = {{Phonon Spectral Functions and Ground-State Energy of Quantum Crystals in Perturbation Theory with a Variationally Optimum Correlated Basis Set}}, + volume = {3}, + year = {1971}, +} + +@article{Werthamer.1970kr, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics is derived via a stationary functional formulation. The crystal dynamics is approximated by a set of damped oscillators, and these are used to construct a trial action, analytically continued into the complex time-temperature plane. Using the action, a free-energy functional is required to be stationary with respect to the trial oscillators. The resulting phonon modes are undamped at the first order of approximation, whereas to second order the phonon spectral function is determined self-consistently. Expressions are obtained in first order for various thermodynamic derivatives, such as pressure, elastic constants, specific heats, and thermal expansion.}}, + author = {Werthamer, N. R.}, + doi = {10.1103/physrevb.1.572}, + issn = {1098-0121}, + journal = {Physical Review B}, + number = {2}, + pages = {572--581}, + title = {{Self-Consistent Phonon Formulation of Anharmonic Lattice Dynamics}}, + volume = {1}, + year = {1970}, +} + +@book{Choquard.1967, + author = {Choquard, Philippe F.}, + publisher = {W.A. Benjamin, Inc.}, + title = {{The Anharmonic Crystal}}, + year = {1967}, +} + +@article{Gillis.1967, + abstract = {{The self-consistent phonon theory of anharmonic lattice dynamics, devised independently by several authors using varying techniques and implemented computationally by Koehler, is here applied to the crystals of neon and argon. A Lennard-Jones 6-12 interatomic potential is assumed. The quantities calculated are the phonon spectrum and the bulk thermodynamic properties of thermal expansion, compressibility, and specific heat, all as a function of temperature at zero pressure. Although the computations are intended primarily to explore in detail the content of the self-consistent phonon approximation preparatory to incorporating the more elaborate expressions of the next higher approximation, comparison is made with the existing experimental data.}}, + author = {Gillis, N. S. and Werthamer, N. R. and Koehler, T. R.}, + doi = {10.1103/physrev.165.951}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3}, + pages = {951--959}, + title = {{Properties of Crystalline Argon and Neon in the Self-Consistent Phonon Approximation}}, + volume = {165}, + year = {1967}, +} + +@article{Koehler.1966, + author = {Koehler, Thomas R.}, + doi = {10.1103/physrevlett.17.89}, + issn = {0031-9007}, + journal = {Physical Review Letters}, + number = {2}, + pages = {89--91}, + title = {{Theory of the Self-Consistent Harmonic Approximation with Application to Solid Neon}}, + volume = {17}, + year = {1966}, +} + +@article{Kohn.1965, + abstract = {{From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 23.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.}}, + author = {Kohn, W. and Sham, L. J.}, + doi = {10.1103/physrev.140.a1133}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {4A}, + pages = {A1133--A1138}, + title = {{Self-Consistent Equations Including Exchange and Correlation Effects}}, + volume = {140}, + year = {1965}, +} + +@article{Hohenberg.1964, + abstract = {{This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, F[n(r)], independent of v(r), such that the expression E≡∫v(r)n(r)dr+F[n(r)] has as its minimum value the correct ground-state energy associated with v(r). The functional F[n(r)] is then discussed for two situations: (1) n(r)=n0+ñ(r), ñn0≪1, and (2) n(r)=ϕ(rr0) with ϕ arbitrary and r0→∞. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.}}, + author = {Hohenberg, P. and Kohn, W.}, + doi = {10.1103/physrev.136.b864}, + issn = {0031-899X}, + journal = {Physical Review}, + number = {3B}, + pages = {B864--B871}, + title = {{Inhomogeneous Electron Gas}}, + volume = {136}, + year = {1964}, +} + +@article{Cowley.1963, + abstract = {{The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.}}, + author = {Cowley, R.A.}, + doi = {10.1080/00018736300101333}, + issn = {0001-8732}, + journal = {Advances in Physics}, + number = {48}, + pages = {421--480}, + title = {{The lattice dynamics of an anharmonic crystal}}, + volume = {12}, + year = {1963}, +} + +@article{Hooton.1958, + abstract = {{Skyrme has recently discussed the use of a model in quantum mechanics. His method is applied to the case of the anharmonic vibrations of a crystal lattice, and compared with a previous treatment by the present author. Some remarks are added which give a new and more physical interpretation of the results of this earlier work.}}, + author = {Hooton, D. J.}, + doi = {10.1080/14786435808243224}, + issn = {0031-8086}, + journal = {Philosophical Magazine}, + number = {25}, + pages = {49--54}, + title = {{The use of a model in anharmonic lattice dynamics}}, + volume = {3}, + year = {1958}, +} + +@article{Hooton.1955, + abstract = {{Eine neue Methode zur Beschreibung anharmonischer Gitterschwingungen, die aufMax Born zurückgeht, wird hier von einem anderen Gesichtspunkt aus betrachtet und weiterentwickelt. Es werden effektive harmonische Schwingungen definiert, durch welche sich die freie Energie darstellen läßt; es werden die Fälle schwacher und starker Anharmonizität betrachtet. Die Formeln werden für das Beispiel einer linearen Kette explizit gelöst und an Hand von Werten des festen Heliums numerisch illustriert.}}, + author = {Hooton, D. J.}, + doi = {10.1007/bf01330055}, + issn = {0044-3328}, + journal = {Zeitschrift für Physik}, + number = {1}, + pages = {42--57}, + title = {{Anharmonische Gitterschwingungen und die lineare Kette}}, + volume = {142}, + year = {1955}, +} + +@book{Born.1954, + author = {Born, Max and Huang, Kun}, + location = {Oxford}, + publisher = {Clarendon Press}, + note = {Grilnoisc11,E., 21, 49, 50, 52, 60, 187, 188.}, + title = {{Dynamical theory of crystal lattices}}, + year = {1954}, +} + +@article{Born.1951, + author = {Born, Max and Brix, Peter and Kopfermann, Hans and Heisenberg, W. and Staudinger, Hermann and Stille, Hans and Weizsäcker, Carl Friedrich v. and Euler, Hans von and Hedvall, J. Arvid and Siegel, Carl Ludwig and Rellich, Franz and Nevanlinna, Rolf}, + doi = {10.1007/978-3-642-86703-3}, + title = {{Festschrift zur Feier des Zweihundertjährigen Bestehens der Akademie der Wissenschaften in Göttingen, I. Mathematisch-Physikalische Klasse}}, + year = {1951}, +} + +@article{Boer.1948, + abstract = {{It is shown in a quite general way, that the equation of states of the noble gases, H2, D2 and N2 can be written in a reduced form, in which the thermodynamic quantities T, P, V, etc. are expressed in “molecular units”, i.e. units obtained from the characteristics parameters of the intermolecular field. In general the reduced equation of states contains a parameter A∗, containing also h and the mass of the molecules, which measures essentially the influence of quantum mechanics on the phenomenon considered. Only when classical statistics can be applied and A∗ = 0, the reduced equation of states implies the law of corresponding states in its classical form.The reduction with molecular units is applied to the condensed phase of the substances mentioned above to study experimentally the thermodynamical properties as a function of A∗ and to obtain in this way information on the influence of quantum theory on these phenomena.}}, + author = {Boer, J De}, + doi = {10.1016/0031-8914(48)90032-9}, + issn = {0031-8914}, + journal = {Physica}, + number = {2-3}, + pages = {139--148}, + title = {{Quantum theory of condensed permanent gases I the law of corresponding states}}, + volume = {14}, + year = {1948}, +} + +@article{Born.1912, + author = {Born, M. and Karman, T. von}, + journal = {Physikalische Zeitschrift}, + pages = {297--309}, + title = {{Über Schwingungen in Raumgittern}}, + volume = {13}, + year = {1912}, +} + diff --git a/paper/literature_final.bib b/paper/literature_final.bib new file mode 100644 index 00000000..226017b5 --- /dev/null +++ b/paper/literature_final.bib @@ -0,0 +1,743 @@ +@misc{tdeptools, + author = {Knoop, F.}, + publisher = {GitHub}, + url = {https://github.com/flokno/tools.tdep}, + title = {{tdeptools: tools for TDEP}}, + year = {2023}, +} + +@article{Castellano.2023, + author = {Castellano, Aloïs and Batista, J. P. Alvarinhas and Verstraete, Matthieu J.}, + title = "{Mode-coupling theory of lattice dynamics for classical and quantum crystals}", + journal = {The Journal of Chemical Physics}, + volume = {159}, + number = {23}, + pages = {234501}, + year = {2023}, + month = {12}, + issn = {0021-9606}, + doi = {10.1063/5.0174255}, + url = {https://doi.org/10.1063/5.0174255}, +} + +@article{Reig.2022, + author = {Reig, D. S. and Varghese, S. and Farris, R. and Block, A. and Mehew, J. D. and Hellman, O. and Woźniak, P. and Sledzinska, M. and Sachat, A. E. and Chávez‐Ángel, E. and Valenzuela, S. O. and Hulst, N. F. van and Ordejón, P. and Zanolli, Z. and Torres, C. M. S. and Verstraete, M. J. and Tielrooij, K.‐J.}, + doi = {10.1002/adma.202108352}, + issn = {0935-9648}, + journal = {Advanced Materials}, + number = {10}, + pages = {2108352}, + title = {{Unraveling Heat Transport and Dissipation in Suspended MoSe2 from Bulk to Monolayer}}, + volume = {34}, + year = {2022}, +} + +@article{Menahem.2022, + author = {Menahem, M. and Benshalom, N. and Asher, M. and Aharon, S. and Korobko, R. and Safran, S. and Hellman, O. and Yaffe, O.}, + eprint = {2208.05563}, + journal = {arXiv}, + title = {{The Disorder Origin of Raman Scattering In Perovskites Single Crystals}}, + year = {2022}, +} + +@article{Benshalom.2022v0s, + author = {Benshalom, N. and Asher, M. and Jouclas, R. and Korobko, R. and Schweicher, G. and Liu, J. and Geerts, Y. and Hellman, O. and Yaffe, O.}, + eprint = {2204.12528}, + journal = {arXiv}, + title = {{Phonon-phonon interactions in the polarization dependence of Raman scattering}}, + year = {2022}, +} + +@article{Laniel.2022, + author = {Laniel, D. and Trybel, F. and Winkler, B. and Knoop, F. and Fedotenko, T. and Khandarkhaeva, S. and Aslandukova, A. and Meier, T. and Chariton, S. and Glazyrin, K. and Milman, V. and Prakapenka, V. and Abrikosov, I. A. and Dubrovinsky, L. and Dubrovinskaia, N.}, + doi = {10.1038/s41467-022-34755-y}, + eprint = {2208.10418}, + journal = {Nature Communications}, + keywords = {me}, + number = {1}, + pages = {6987}, + title = {{High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content}}, + volume = {13}, + year = {2022}, +} + +@article{Lin.2022, + author = {Lin, C. and Poncé, S. and Marzari, N.}, + doi = {10.1038/s41524-022-00920-6}, + eprint = {2209.09520}, + journal = {npj Computational Materials}, + number = {1}, + pages = {236}, + title = {{General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials}}, + volume = {8}, + year = {2022}, +} + +@article{Cohen.2022, + author = {Cohen, A. and Brenner, T. M. and Klarbring, J. and Sharma, R. and Fabini, D. H. and Korobko, R. and Nayak, P. K. and Hellman, O. and Yaffe, O.}, + doi = {10.1002/adma.202107932}, + issn = {0935-9648}, + journal = {Advanced Materials}, + pages = {2107932}, + title = {{Diverging Expressions of Anharmonicity in Halide Perovskites}}, + year = {2022}, +} + +@article{Benshalom.2022, + author = {Benshalom, N. and Reuveni, G. and Korobko, R. and Yaffe, O. and Hellman, O.}, + doi = {10.1103/physrevmaterials.6.033607}, + journal = {Physical Review Materials}, + number = {3}, + pages = {033607}, + title = {{Dielectric response of rock-salt crystals at finite temperatures from first principles}}, + volume = {6}, + year = {2022}, +} + +@article{Reig.2021, + author = {Reig, D. S. and Varghese, S. and Farris, R. and Block, A. and Mehew, J. D. and Hellman, O. and Woźniak, P. and Sledzinska, M. and Sachat, A. E. and Chávez-Ángel, E. and Valenzuela, S. O. and Hulst, N. F. Van and Ordejón, P. and Zanolli, Z. and Torres, C. M. Sotomayor and Verstraete, M. J. and Tielrooij, K. J.}, + eprint = {2109.09225}, + journal = {arXiv}, + title = {{Unraveling heat transport and dissipation in suspended MoSe\$\_2\$ crystals from bulk to monolayer}}, + year = {2021}, +} + +@article{Monacelli.2021, + author = {Monacelli, L. and Bianco, R. and Cherubini, M. and Calandra, M. and Errea, I. and Mauri, F.}, + doi = {10.1088/1361-648x/ac066b}, + eprint = {2103.03973}, + issn = {0953-8984}, + journal = {Journal of Physics: Condensed Matter}, + number = {36}, + pages = {363001}, + title = {{The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects}}, + volume = {33}, + year = {2021}, +} + +@article{Dangic.2021, + author = {Dangić, Đ. and Hellman, O. and Fahy, S. and Savić, I.}, + doi = {10.1038/s41524-021-00523-7}, + journal = {npj Computational Materials}, + number = {1}, + pages = {57}, + title = {{The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe}}, + volume = {7}, + year = {2021}, +} + +@article{Benshalom.2021, + author = {Benshalom, N. and Reuveni, G. and Korobko, R. and Yaffe, O. and Hellman, O.}, + eprint = {2108.04589}, + journal = {arXiv}, + title = {{The dielectric response of rock-salt crystals at finite temperatures from first principles}}, + year = {2021}, +} + +@article{Heine.2021, + author = {Heine, M. and Hellman, O. and Broido, D.}, + doi = {10.1103/physrevb.103.184409}, + issn = {2469-9950}, + journal = {Physical Review B}, + number = {18}, + pages = {184409}, + title = {{Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles}}, + volume = {103}, + year = {2021}, +} + +@article{Roekeghem.2021, + author = {Roekeghem, A. van and Carrete, J. and Mingo, N.}, + doi = {10.1016/j.cpc.2021.107945}, + eprint = {2006.12867}, + issn = {0010-4655}, + journal = {Computer Physics Communications}, + pages = {107945}, + title = {{Quantum Self-Consistent Ab-Initio Lattice Dynamics}}, + volume = {263}, + year = {2021}, +} + +@article{Cai.2021, + author = {Cai, Q. and Hellman, O. and Wei, B. and Sun, Q. and Said, A. H. and Gog, T. and Winn, B. and Li, C.}, + eprint = {2108.06631}, + journal = {arXiv}, + title = {{Direct Observation of Chiral Phonons by Inelastic X-ray Scattering}}, + year = {2021}, +} + +@article{Klarbring.2020vk, + author = {Klarbring, J. and Hellman, O. and Abrikosov, I. A. and Simak, S. 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Mathematisch-Physikalische Klasse}}, + year = {1951}, +} + +@article{Boer.1948, + author = {{de Boer}, J.}, + doi = {10.1016/0031-8914(48)90032-9}, + issn = {0031-8914}, + journal = {Physica}, + number = {2-3}, + pages = {139--148}, + title = {{Quantum theory of condensed permanent gases I: the law of corresponding states}}, + volume = {14}, + year = {1948}, +} + +@article{Born.1912, + author = {Born, M. and {von Karman}, T.}, + journal = {Physikalische Zeitschrift}, + pages = {297--309}, + title = {{Über Schwingungen in Raumgittern}}, + volume = {13}, + year = {1912}, +} + diff --git a/paper/paper.md b/paper/paper.md new file mode 100644 index 00000000..3cf62c18 --- /dev/null +++ b/paper/paper.md @@ -0,0 +1,127 @@ +--- +title: "TDEP: Temperature Dependent Effective Potentials" +tags: + - Fortran + - Physics + - Phonons + - Temperature + - Anharmonicity + - Thermal transport + - Neutron spectroscopy + - Raman spectroscopy +authors: + - name: Florian Knoop + orcid: 0000-0002-7132-039X + affiliation: 1 + - name: Nina Shulumba + orcid: 0000-0002-2374-7487 + affiliation: 1 + - name: Aloïs Castellano + orcid: 0000-0002-8783-490X + affiliation: 3 + - name: J. P. Alvarinhas Batista + orcid: 0000-0002-3314-249X + affiliation: 3 + - name: Roberta Farris + orcid: 0000-0001-6710-0100 + affiliation: 7 + - name: Matthieu J. Verstraete + orcid: 0000-0001-6921-5163 + affiliation: 3, 8 + - name: Matthew Heine + orcid: 0000-0002-4882-6712 + affiliation: 5 + - name: David Broido + orcid: 0000-0003-0182-4450 + affiliation: 5 + - name: Dennis S. Kim + orcid: 0000-0002-5707-2609 + affiliation: 6 + - name: Johan Klarbring + orcid: 0000-0002-6223-5812 + affiliation: 1, 4 + - name: Igor A. Abrikosov + orcid: 0000-0001-7551-4717 + affiliation: 1 + - name: Sergei I. Simak + orcid: 0000-0002-1320-389X + affiliation: 1, 9 + - name: Olle Hellman + orcid: 0000-0002-3453-2975 + affiliation: 2 +affiliations: + - name: Theoretical Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden + index: 1 + - name: Weizmann Institute of Science, Rehovot, Israel + index: 2 + - name: Nanomat group, QMAT center, CESAM research unit and European Theoretical Spectroscopy Facility, Université de Liège, allée du 6 août, 19, B-4000 Liège, Belgium + index: 3 + - name: Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK + index: 4 + - name: Department of Physics, Boston College, Chestnut Hill, MA 02467, USA + index: 5 + - name: College of Letters and Science, Department of Chemistry and Biochemistry, University of California, Los Angeles (UCLA), California 90025, USA + index: 6 + - name: Catalan Institute of Nanoscience and Nanotechnology - ICN2 (BIST and CSIC), Campus UAB, 08193 Bellaterra (Barcelona), Spain + index: 7 + - name: ITP, Physics Department, University of Utrecht, 3584 CC Utrecht, the Netherlands + index: 8 + - name: Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden + index: 9 +date: 2023 +bibliography: literature_final.bib +--- + +# Summary + +The Temperature Dependent Effective Potential (TDEP) method is a versatile and efficient approach to include temperature in _ab initio_ materials simulations based on phonon theory. TDEP can be used to describe thermodynamic properties in classical and quantum ensembles, and several response properties ranging from thermal transport to Neutron and Raman spectroscopy. A stable and fast reference implementation is given in the software package of the same name described here. The underlying theoretical framework and foundation is briefly sketched with an emphasis on discerning the conceptual difference between bare and effective phonon theory, in both self-consistent and non-self-consistent formulations. References to numerous applications and more in-depth discussions of the theory are given. + +# Introduction + +The properties of materials change both qualitatively and quantitatively with temperature, i.e., the macroscopic manifestation of the microscopic vibrational motion of electrons and nuclei. In thermal equilibrium, temperature influences the structural phase, the density, and many mechanical properties. Out of thermal equilibrium, for instance, when applying a thermal gradient or an external spectroscopic probe such as a light or neutron beam, temperature influences the response of the material to the perturbation, for example its ability to conduct heat, or the lineshape of the spectroscopic signal. Temperature is therefore at the core of both applied and fundamental materials science. + +In _ab initio_ materials modeling, the contribution of electronic temperature is straightforward to include through appropriate occupation of the electronic states, whereas the nuclear contribution needs to be accounted for explicitly. This can be done by performing molecular dynamics (MD) simulations which aim at _numerically_ reproducing the thermal nuclear motion in an atomistic simulation, and obtaining temperature-dependent observables either in equilibrium, through averaging, or out of equilibrium from time-dependent correlation functions or by directly observing the relaxation dynamics. + +An alternative strategy is to construct approximate model Hamiltonians for the nuclear subsystem, which enables an _analytic_ description of the nuclear motion by leveraging perturbation theory starting from an exactly solvable lowest-order model. In this approach, the starting point is given in terms of _phonons_ which are eigensolutions of a Hamiltonian of harmonic form, i.e., quadratic in the nuclear displacements. Anharmonic contributions can be included via established perturbative techniques, in practice up to quartic terms. Higher-order contributions are elusive because the complexity and number of terms in the perturbative expansion grows very quickly with system size and perturbation order. The lattice-dynamics approach is therefore not formally exact. However, the phonon picture is useful for describing a wide range of materials properties in practice, and often reaches excellent accuracy in comparison to experiment while providing precise microscopic insight into the underlying physical phenomena. + +The chemical bonding in the lattice dynamics Hamiltonian is represented through force constants. These can be obtained in a purely perturbative, temperature-independent way by constructing a Taylor expansion of the interatomic potential energy about the periodically-arranged atom positions in the crystal. This idea is more than a century old and traces back to Born and von Karman [@Born.1912]. Alternatively, temperature-dependent, _effective_ model Hamiltonians are used in situations where the quadratic term in a bare Taylor expansion is not positive definite, i.e., the average atomic position does _not_ coincide with a minimum of the potential. The classic example is the $^4$He problem, in which a Taylor expansion led to imaginary phonon frequencies in the dense solid phase [@Boer.1948]. Born and coworkers solved this problem in the 1950's by developing a _self-consistent phonon theory_ in which an effective, positive-definite Hamiltonian yielding well-defined phonons is obtained self-consistently using a variational principle [@Born.1951; @Hooton.2010mfn; @Hooton.2010]. An excellent historical review of this development is given in [@Klein.1972]. + +While the theoretical foundation of (self-consistent) phonon theory has been well-established for decades, more recent developments are concerned with implementing this theory in computer simulations, typically based on density functional theory (DFT) [@Hohenberg.1964; @Kohn.1965]. This has led to a variety of approaches that tackle the self-consistent phonon problem for anharmonic and dynamically stabilized systems [@Souvatzis.2008; @Errea.2013; @Tadano.2015; @Roekeghem.2021; @Monacelli.2021]. Another development was the _non_-self-consistent construction of effective Hamiltonians by optimizing the force constants to the fully anharmonic dynamics observed during MD simulations [@Levy.1984; @Dove.1986]. This idea was extended in the TDEP method to describe phonons in systems like Zirconium in the high-temperature body-centered cubic (bcc) phase, which is dynamically unstable at low temperatures [@Hellman.2011; @Hellman.2013]. While the initial TDEP method was based on _ab initio_ MD, a self-consistent extension was later proposed in the form of _stochastic_ TDEP (sTDEP), where thermal samples are created from the model Hamiltonian itself and the force constants are optimized iteratively until self-consistency is achieved [@Shulumba.2017; @Benshalom.2022]. sTDEP furthermore allows to include nuclear quantum effects in materials with light elements in a straightforward way [@Shulumba.20179s8e; @Laniel.2022]. + +Effective phonons capture anharmonic frequency renormalization, but they are still non-interacting quasiparticles with infinite lifetime, or equivalently infinitesimal linewidth. The effect of linewidth broadening due to anharmonic phonon-phonon interactions can be included by using higher-order force constants up to third or fourth order [@Cowley.1963; @Hellman.2013oi5; @Feng.2016]. These can be used to get better approximations to the free energy [@Wallace.1972], describe thermal transport [@Broido.2007; @Romero.2015; @Klarbring.2020vk; @Dangic.2021; @Reig.2022], and linewidth broadening in spectroscopic experiments [@Romero.2015; @Kim.2018; @Benshalom.2022]. In practice, it was noted that the renormalized phonon quasiparticles interact more weakly than bare phonons. This means that the effective approach remains applicable in systems with strong anharmonicity where the bare phonon quasiparticle picture becomes invalid [@Ravichandran.2018]. A formal justification in terms of mode-coupling theory, as well as a detailed comparison between bare perturbation theory with force constants from a Taylor expansion, self-consistent effective, and non-self-consistent effective approaches was recently given by some of us in [@Castellano.2023]. Explicitly incorporating dielectric response properties for light-scattering experiments such as infrared and Raman was recently proposed [@Benshalom.2022]. + + +# Statement of need +The TDEP open-source code is the reference implementation for the TDEP method introduced above. It delivers a clean and fast Fortran implementation with Message Passing Interface (MPI) parallelism both for constructing and solving effective lattice-dynamics Hamiltonians. This allows for materials simulations of simple elemental solids up to complex compounds with reduced symmetry under realistic conditions. + +To extract force constants from thermal snapshots efficiently, TDEP employs the permutation and spacegroup symmetries of a given system to reduce the free parameters in the model to an irreducible set before fitting them [@Esfarjani.2008]. For example, this reduces the number of harmonic force constants of a 4x4x4 supercell of a bcc lattice (128 atoms) from 147456 to only 11 unknowns. This can speed up the convergence by several orders of magnitude when comparing to a _post hoc_ symmetrization of the force constants [@Hellman.2013]. Further lattice dynamics sum rules are enforced after fitting, i.e., acoustic (translational) and rotational invariances, as well as the Huang invariances, which ensure the correct number of independent elastic constants in the long-wavelength limit [@Born.1954]. While TDEP was one of the first numerical approaches exploiting all these constraints in a general way for arbitrary systems, other codes have adopted this practice by now [@Eriksson.2019; @Lin.2022]. + +Another distinctive feature of TDEP is the use of plain input and output files which are code-agnostic and easy to create and parse. These are either plain-text formats, established human-readable formats like CSV, or self-documented HDF5 files for larger datasets. Thanks to the exploitation of the force constant symmetries, the respective output files are very compact, even for anharmonic force constants. + +Additionally, TDEP provides tools to prepare and organize _ab initio_ supercell simulations, e.g., analyzing the crystal symmetry, finding good simulation (super)cells, visualizing the pair distribution functions from MD simulations, and creating thermal snapshots for accelerated and self-consistent sampling. Each program is fully documented with background information, and an extensive set of realistic research workflow tutorials is available as well. A list of the most important available features and respective programs is given below. + +## Features + +Here we list the most important codes that are shipped with the TDEP package, explain their purpose, and list the respective references in the literature. A more detailed explanation of all features can be found in the online documentation. + +- `generate_structure`: Generate supercells of target size, with options to make them as cubic as possible to maximize the real-space cutoff for the force constants [@Hellman.2011]. + +- `canonical_configuration`: Create supercells with thermal displacements from an initial guess or existing force constants, using Monte Carlo sampling from a classical or quantum canonical distribution [@West.2006; @Shulumba.2017]. Self-consistent sampling with sTDEP is explained in detail in [@Benshalom.2022]. + +- `extract_forceconstants`: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces [@Hellman.2013]. Optionally, fit higher-order force constants [@Hellman.2013oi5], or dielectric tensor properties [@Benshalom.2022]. + +- `phonon_dispersion_relations`: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants [@Hellman.2013], including Grüneisen parameters from third-order force constants [@Hellman.2013oi5]. + +- `thermal_conductivity`: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity [@Broido.2007; @Romero.2015]. + +- `lineshape`: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone [@Romero.2015; @Shulumba.2017]. The grid mode computes _spectral_ thermal transport properties [@Dangic.2021]. + +A separate python library for interfacing with different DFT and force field codes through the Atomic Simulation Environment (ASE) [@Larsen.2017], as well as processing and further analysis of TDEP output files is available as well [@tdeptools]. + +We note that parts of the TDEP method have been implemented in other code packages as well [@Bottin.2020rn5]. + +# Acknowledgements + +F.K. and O.H. acknowledge support from the Swedish Research Council (VR) program 2020-04630, and the Swedish e-Science Research Centre (SeRC). Work at Boston College was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award #DE-SC0021071. M.J.V., A.C., and J.P.B. acknowledge funding by ARC project DREAMS (G.A. 21/25-11) funded by Federation Wallonie Bruxelles and ULiege, and by Excellence of Science project CONNECT number 40007563 funded by FWO and FNRS. R.F. acknowledges financial support by the Spanish State Research Agency under grant number PID2022-139776NB-C62 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe. J. K. acknowledges support from the Swedish Research Council (VR) program 2021-00486. I.A.A. and S.I.S. acknowledge support by the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). I.A.A. is a Wallenberg Scholar (grant no. KAW-2018.0194). S.I.S. acknowledges the support from Swedish Research Council (VR) (Project No. 2023-05247) and the ERC (synergy grant FASTCORR project 854843). F.K. thanks Christian Carbogno for introducing him to Olle. + +# References