Dr Lucy Whalley Northumbria University, Newcastle upon Tyne, United Kingdom A lecture for TDEP2023 

“Northern Research Powerhouse” Northumbria University, Newcastle upon Tyne Hello!! 👋 • Computational materials science: solid state physics + quantum chemistry + high-performance-computing + • Energy materials: halide and chalcogenide perovskites • Software sustainability (better software, better research) documentation + testing + maintenance + Our Research Prakriti Kayastha 

single-point DFT or force field calculations Self consistent phonons Temperature dependent effective potential Raman scattering First—principles lattice dynamics Pre-requisite This lecture This summer school Lecture Aims: To better understand “every-day” phonon calculations To better connect theory and practice (Quantum) thermodynamics Note: Interrupt, question and tell me how things can be improved – feedback welcome Thermal transport Wigner thermal transport 

Schematics of octahedral tilting phonon mode in perovskite • Born Oppenheimer approximation – solve electronic Schrödinger equation for fixed ions • However atoms in a material vibrate around their (T-dependent) equilibrium position • This impacts on the behaviour of a material e.g. band gap, e- mobility, thermodynamics, IR absorption… • In a crystal the vibrations are periodic and can be described as a collective excitation (quasi-particle): phonon 

To predict atom motion we need to model the potential within which the atoms move Potential Energy Surfaces Harmonic Anharmonic (single well) Anharmonic (double well) Potential energy (collective) displacement Anharmonicity * * * * = equilibrium position * Low T High T 

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Perturbative Taylor expansion Ab initio molecular dynamics (Most often) less computationally intensive Computationally intensive: phase space sampling & frequency resolution Treating anharmonic effects as a perturbation– validity? Anharmonicity at all orders Limited to smaller amplitude displacements (not suitable at high-T or near a phase transition) Suitable for large amplitude displacements Equilibrium position fixed Equilibrium position can change with temperature 

Model validity depends on the shape of the PES and the mode occupation ! 𝑛! 𝑇 from Bose-Einstein statistics Harmonic approximation valid Harmonic approximation invalid Low temperature, low energy eigenstates dominate High temperature, higher energy eigenstates contribute PES as potential in 1D Schrodinger equation à solve to give vibrational eigenstates See e.g. Whalley et al (2016) Phys. Rev. B 94, 220301(R) 

Restorative force proportional to distance Harmonic approximation valid * * Non-restorative force proportional to distance Harmonic approximation invalid Low temperature High temperature Quantifying anharmonicity Anharmonicity measure for materials Knoop et al 2020 Phys. Rev. Materials 4, 083809 Model validity depends on the shape of the PES and the mode occupation ! 𝑛! 𝑇 from Bose-Einstein statistics See e.g. Whalley et al (2016) Phys. Rev. B 94, 220301(R) 

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Restorative force – real positive phonon frequency Harmonic approximation valid * * Non-restorative force – imaginary phonon frequency Harmonic approximation invalid Low temperature High temperature Harmonic energy is expressed as a function of displacement amplitude Q AAACEnicbVDLSsNAFJ34rPUVdelmsAgtQkmqqMuimy5bsA9o0jCZTtqhk0yYmYgl5Bvc+CtuXCji1pU7/8bpY6GtBy4czrmXe+/xY0alsqxvY2V1bX1jM7eV397Z3ds3Dw5bkicCkybmjIuOjyRhNCJNRRUjnVgQFPqMtP3R7cRv3xMhKY/u1DgmbogGEQ0oRkpLnlmqFRsl6KA4FvwB1jwLnkEnEAindpZWMoeHZIB6lUav4pkFq2xNAZeJPScFMEfdM7+cPsdJSCKFGZKya1uxclMkFMWMZHknkSRGeIQGpKtphEIi3XT6UgZPtdKHARe6IgWn6u+JFIVSjkNfd4ZIDeWiNxH/87qJCq7dlEZxokiEZ4uChEHF4SQf2KeCYMXGmiAsqL4V4iHSgSidYl6HYC++vExalbJ9WT5vXBSqN/M4cuAYnIAisMEVqIIaqIMmwOARPINX8GY8GS/Gu/Exa10x5jNH4A+Mzx/2jpvQ H(Q) ⇡ H0 + 1 2! 2 Q 2 Phonon mode frequency Pallikara et al 2022 Electron. Struct. 4 033002 

AAACEnicbVDLSsNAFJ34rPUVdelmsAgtQkmqqMuimy5bsA9o0jCZTtqhk0yYmYgl5Bvc+CtuXCji1pU7/8bpY6GtBy4czrmXe+/xY0alsqxvY2V1bX1jM7eV397Z3ds3Dw5bkicCkybmjIuOjyRhNCJNRRUjnVgQFPqMtP3R7cRv3xMhKY/u1DgmbogGEQ0oRkpLnlmqFRsl6KA4FvwB1jwLnkEnEAindpZWMoeHZIB6lUav4pkFq2xNAZeJPScFMEfdM7+cPsdJSCKFGZKya1uxclMkFMWMZHknkSRGeIQGpKtphEIi3XT6UgZPtdKHARe6IgWn6u+JFIVSjkNfd4ZIDeWiNxH/87qJCq7dlEZxokiEZ4uChEHF4SQf2KeCYMXGmiAsqL4V4iHSgSidYl6HYC++vExalbJ9WT5vXBSqN/M4cuAYnIAisMEVqIIaqIMmwOARPINX8GY8GS/Gu/Exa10x5jNH4A+Mzx/2jpvQ H(Q) ⇡ H0 + 1 2! 2 Q 2 Frequency Pallikara et al 2022 Electron. Struct. 4 033002 `Mode-mapping’: distort the crystal structure along a particular phonon eigenvector(s) to map out the Potential Energy Surface Low-T Pnma phase geometry 

Crystal Potential Static model Anharmonicity Phonon scattering Required for e.g. thermal conductivity Harmonic Phonons Non-interacting phonons “Infinite lifetimes” Ionic Forces = 0 at equilibrium Taylor expansion of the potential energy surface 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 H = H0 + ↵ i u ↵ i + 1 2 ↵ ij u ↵ i uj + 1 6 ↵ ijk u ↵ i uj uk + . . . 

Anharmonicity Phonon scattering Required for e.g. thermal conductivity In Out Example 3-phonon process high energy phonon low energy phonons 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 H = H0 + ↵ i u ↵ i + 1 2 ↵ ij u ↵ i uj + 1 6 ↵ ijk u ↵ i uj uk + . . . “But it was also known that [….] the so-called anharmonic terms, were important. These terms cause a coupling between the otherwise independent waves of different length and direction. They are responsible for the absorption of sound waves, which, in the linear approximation, could travel indefinite distances without damping, and for the heat conductivity." -- Rudolf Peierls, Bird of Passage (or see “Recollections of early solid state physics”) 

Crystal Potential Static model Anharmonicity Phonon scattering Required for e.g. thermal conductivity Harmonic Phonons Non-interacting phonons “Infinite lifetimes” Ionic Forces = 0 at equilibrium Force constant tensors describe the PES 2nd order 3rd order 

• Force constants are the essential ingredient for phonon calculations • Calculating force constants is often the most computationally intensive part of a lattice dynamics calculation • Computational cost is determined by: • Rank of tensor (2nd/3rd/4th order) • Number of atoms in system (supercell expansion) • Crystal symmetry From TDEP Code documentation 

Real space finite displacement (AKA Direct, Supercell) Density Functional Perturbation Theory Intuitive approach to understand Less intuitive theoretical approach Flexible: can be combined with a variety of functionals, and levels of theory Requires implementation for a particular level of theory Can be split into many smaller jobs: can “game” the computer queues Consists of one larger job which requires significant memory Can only calculate perturbations at the gamma point: supercells commensurate with q are required Perturbation of of any wave vector q possible (note: not available in VASP) Scales poorly with system size Improved scaling with system size; for larger jobs can be computationally cheaper 

• phonondb • Materials Project • NOMAD Phonon databases 

Build supercell and generate displacements (optional) calculate born effective charges & dielectric tensor Post-process e.g. dispersion, heat capacity Relax unit cell Extract forces, build and diagonalise dynamical matrix Calculate forces + codes that can stitch it all together, e.g. fhivibes TASKS CODES Knoop et al., (2020) Journal of Open Source Software, 5(56), 2671 

Build supercell and generate displacements calculate born effective charges & dielectric tensor Post-process e.g. dispersion, heat capacity Relax unit cell Extract forces, build & diagonalise dynamical matrix Calculate Forces Files available here: http://github.com/nu-CEM/phonons_tutorial/ 

Atomic Simulation Environment The sum over the unit cells in the dynamical matrix requires supercells that adequately capture all pairwise interactions • For this reason you may want a cell that is fairly cubic • For this reason you need to do convergence testing 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 D(q)↵ ij = 1 p mimj X l ↵ i0jl exp{iq · [rjl rj0]} Atom-atom interaction 

The finite displacement method requires a supercell to capture off-Γ phonons Maurya et al Physical Review B 96, 134114 (2017) If you want to access a off-Γ wave vector q, you need to map that wave vector q to the Γ-point by using a commensurate supercell Bi4 Ti3 O12 (½, 0, 0) 

Imaginary modes can be formed from interpolation at q-points incommensurate with the supercell Rahim et al, Chem. Sci., 2020,11, 7904-7909 Bi2 Sn2 O7 (0, 0, ½) 

Some supercell expansions can suppress distortions and lead to incorrect results (bigger isn’t always better) CsPbI3 tilting distortion to tetragonal phase 2x2 3x2 

Most studies use diagonal supercells, but non-diagonal supercells can be used to reduce computational cost Lloyd-Williams and Monserrat, Phys. Rev. B 92, 184301 Diagonal elements. Supercell is S11 x S22 x S33 primitive cells. e.g. “2x3x1 supercell” is 6 primitive cells diagonal supercell 4 primitive cells non-diagonal supercell 2 primitive cells (½ , ½) 

“Phonons & Phonopy: Pro Tips” from J.M. Skelton (available on SlideShare) To fix this either increase size of the FFT grid (plane wave basis) or integration grid (atom-centred basis), or apply a post-hoc correction Numerical approaches can lead to broken translational symmetry and small imaginary frequencies around the gamma point. FC_SYMMETRY = .TRUE. FC_SYMMETRY = .FALSE. 

LO/TO splitting results from the macroscopic electric field associated with a separation of ions (Coloumb interaction) For TO mode: - E ⊥ q ⇒ E.q = 0 Transverse Optic Longitudinal Optic For LO mode: - E.q is non-zero - E-field adds restoring force. - Frequency is upshifted. 

Togo et al J. Phys. Condens. Matter 35 (2023) 353001 Post-hoc correction using Born effective charge and high-frequency (optical, ion- clamped) dielectric tensors 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 D↵ (jj0, q ! 0) = D↵ (jj0, q = 0) + 1 p mjmj0 4⇡ ⌦0 hP q Z⇤ j, ↵ i hP 0 q 0 Z⇤ j0, 0 i P ↵ q↵✏1 ↵ q . D↵ (jj0, q = 0) + 1 p mjmj0 4⇡ ⌦0 hP q Z⇤ j, ↵ i hP 0 q 0 Z⇤ j0, 0 i P ↵ q↵✏1 ↵ q . LO/TO splitting results from the macroscopic electric field associated with a separation of ions (Coloumb interaction) 

“Phonons are fussy little buggers” - Dr Adam Jackson, STFC UK See Pallikara et al 2022 Electron. Struct. 4 033002 • A very well relaxed structure is a pre-requisite • tighten force convergence criteria for structure relaxation (e.g. to < 0.01 eV Å−1) • Accurate forces are essential • converge forces with respect to the basis set, k-point sampling density and SCF criteria • plane-wave basis: increase cut-off energy by at least 25% above default, up to 2× may be required. • numerical atom-centered basis: the default cut-offs tightened by an order of magnitude. • Avoid interpolation artefacts (imaginary frequencies or flat bands) • use supercell (finite displacement) or q-point grid (DFPT) commensurate with wavevector • Make use of the short (or free queue) • Finite difference consists of several small jobs – possible to be done “for free” 

Gruneisen Entropy Heat capacity • In the harmonic approximation, the lattice parameters are temperature independent, so cannot predict (the effects of) thermal expansion • At finite temperature, the system will minimise its free energy rather than its lattice internal energy Quasi-harmonic approximation can be used to model the effects of thermal lattice expansion • The fit provides equilibrium volume V(T) and the bulk modulus B(T). From this a number of other properties can be derived: AAACAXicbVDLSsNAFJ3UV62vqBvBTbAIFaQk4mtZdOOyQl+QhDCZTtqhM5MwMxFKqBt/xY0LRdz6F+78GydtFtp64MLhnHu5954woUQq2/42SkvLK6tr5fXKxubW9o65u9eRcSoQbqOYxqIXQokp4bitiKK4lwgMWUhxNxzd5n73AQtJYt5S4wT7DA44iQiCSkuBeeAxqIaCZYzwieuxNCC11mnzxA/Mql23p7AWiVOQKijQDMwvrx+jlGGuEIVSuo6dKD+DQhFE8aTipRInEI3gALuacsiw9LPpBxPrWCt9K4qFLq6sqfp7IoNMyjELdWd+r5z3cvE/z01VdO1nhCepwhzNFkUptVRs5XFYfSIwUnSsCUSC6FstNIQCIqVDq+gQnPmXF0nnrO5c1i/uz6uNmyKOMjgER6AGHHAFGuAONEEbIPAInsEreDOejBfj3fiYtZaMYmYf/IHx+QMUPpal min[µi(T, P)] AAACAXicbVDLSsNAFJ3UV62vqBvBTbAIFaQk4mtZdOOyQl+QhDCZTtqhM5MwMxFKqBt/xY0LRdz6F+78GydtFtp64MLhnHu5954woUQq2/42SkvLK6tr5fXKxubW9o65u9eRcSoQbqOYxqIXQokp4bitiKK4lwgMWUhxNxzd5n73AQtJYt5S4wT7DA44iQiCSkuBeeAxqIaCZYzwieuxNCC11mnzxA/Mql23p7AWiVOQKijQDMwvrx+jlGGuEIVSuo6dKD+DQhFE8aTipRInEI3gALuacsiw9LPpBxPrWCt9K4qFLq6sqfp7IoNMyjELdWd+r5z3cvE/z01VdO1nhCepwhzNFkUptVRs5XFYfSIwUnSsCUSC6FstNIQCIqVDq+gQnPmXF0nnrO5c1i/uz6uNmyKOMjgER6AGHHAFGuAONEEbIPAInsEreDOejBfj3fiYtZaMYmYf/IHx+QMUPpal min[µi(T, P)] 

Quasi-harmonic approximation can be used to model the effects of thermal lattice expansion Expand and contract structures Run phonopy-qha for post- processing Relax unit cell For each structure calculate thermal properties with harmonic phonons For each structure calculate AAAB+3icbVDLSgMxFM3UV62vsS7dBIvgqsyIr2XxhcsKfUE7Dpk004YmmSHJiGWYX3HjQhG3/og7/8ZM24W2HggczrmXe3KCmFGlHefbKiwtr6yuFddLG5tb2zv2brmlokRi0sQRi2QnQIowKkhTU81IJ5YE8YCRdjC6yv32I5GKRqKhxzHxOBoIGlKMtJF8u3zj04e0x5EeSp5e3zayzLcrTtWZAC4Sd0YqYIa6b3/1+hFOOBEaM6RU13Vi7aVIaooZyUq9RJEY4REakK6hAnGivHSSPYOHRunDMJLmCQ0n6u+NFHGlxjwwk3lINe/l4n9eN9HhhZdSESeaCDw9FCYM6gjmRcA+lQRrNjYEYUlNVoiHSCKsTV0lU4I7/+VF0jquumfV0/uTSu1yVkcR7IMDcARccA5q4A7UQRNg8ASewSt4szLrxXq3PqajBWu2swf+wPr8ASVvlIc= EDFT i e-v.dat thermal_properties.yaml Also see fhi-vibes 

Pallikara et al., Phys. Chem. Chem. Phys., 2021,23, 19219-19236 

Phonons can now interact with one another. Rough idea and workflow. 3-phonon interactions give a finite phonon lifetime which can be used to calculate thermal conductivity Single mode relaxation time approximation to the Boltzmann transport equation In Out Example 3-phonon process high energy phonon low energy phonons Heat capacity Group velocity unit cell volume Num. of q in sum Note: This approach ignores higher order terms (e.g. 4-phonon interactions), volume expansion, and scattering from other sources (e.g. impurities or crystal boundaries). Togo et al., Phys. Rev. B 91, 094306 

3-phonon interactions give a finite phonon lifetime which can be used to calculate thermal conductivity Now calculating: Similar to the harmonic calc BUT • Many more displacements • New parameter “cutpair” • Computationally demanding post-processing Build supercell Build force constant tensor(s) Post-process to extract properties per- mode Relax unit cell Calculate Forces Generate displacements Converge w.r.t. pair cutoff distance Togo et al., Phys. Rev. B 91, 094306 

Harmonic phonons also give key insights into thermal transport properties AAACFnicbVDLSsNAFJ3UV62vqEs3g0VwY0nE17LoQpcV7AOaUm6mk3boTBJmJkIJ+Qo3/oobF4q4FXf+jdM2grYeGDiccy93zvFjzpR2nC+rsLC4tLxSXC2trW9sbtnbOw0VJZLQOol4JFs+KMpZSOuaaU5bsaQgfE6b/vBq7DfvqVQsCu/0KKYdAf2QBYyANlLXPvI0JF2Pm40eYC+WUawj7AUSSOpmqXcNQsCPn3XtslNxJsDzxM1JGeWode1PrxeRRNBQEw5KtV0n1p0UpGaE06zkJYrGQIbQp21DQxBUddJJrAwfGKWHg0iaF2o8UX9vpCCUGgnfTArQAzXrjcX/vHaig4tOysI40TQk00NBwrFJPu4I95ikRPORIUAkM3/FZACmEm2aLJkS3NnI86RxXHHPKqe3J+XqZV5HEe2hfXSIXHSOqugG1VAdEfSAntALerUerWfrzXqfjhasfGcX/YH18Q0EOZ/t ⌧ / 1 2nd order calculation 3rd order calculation conservation of energy and momentum; are there available states to scatter into? coupling between states Togo et al., Phys. Rev. B 91, 094306 

AAACFnicbVDLSsNAFJ3UV62vqEs3g0VwY0nE17LoQpcV7AOaUm6mk3boTBJmJkIJ+Qo3/oobF4q4FXf+jdM2grYeGDiccy93zvFjzpR2nC+rsLC4tLxSXC2trW9sbtnbOw0VJZLQOol4JFs+KMpZSOuaaU5bsaQgfE6b/vBq7DfvqVQsCu/0KKYdAf2QBYyANlLXPvI0JF2Pm40eYC+WUawj7AUSSOpmqXcNQsCPn3XtslNxJsDzxM1JGeWode1PrxeRRNBQEw5KtV0n1p0UpGaE06zkJYrGQIbQp21DQxBUddJJrAwfGKWHg0iaF2o8UX9vpCCUGgnfTArQAzXrjcX/vHaig4tOysI40TQk00NBwrFJPu4I95ikRPORIUAkM3/FZACmEm2aLJkS3NnI86RxXHHPKqe3J+XqZV5HEe2hfXSIXHSOqugG1VAdEfSAntALerUerWfrzXqfjhasfGcX/YH18Q0EOZ/t ⌧ / 1 Calculate interaction strengths for perfect bulk only Calculate harmonic phonons for defect systems Moxon et al, J. Mater. Chem. A, 2022, 10, 1861 … 

Various physical observables can be gotten from phonon modes and frequencies Vibrational spectra Free Energies Crystal structure prediction Rahim et al. Chem. Sci., 2020,11, 7904-7909 Ruan et al J. Phys. Chem. C 2020, 124, 4, 2265–2272 Jackson et al, Chem. Sci., 2016,7, 1082-1092 

1) Vibrational spectra 2) Free Energies BaZrS3 (target) Ba4 Zr3 S10 (RP phase) Harmonic phonon spectra à Case Study: High temperature equilibrium of 3D and Ruddlesden-Popper (Ban+1 Zrn S3n+1 ) chalcogenide perovskites Kayastha et al, Solar RRL (2023) 7: 2201078 Primary challenge for chalcogenide perovskites: phase control “The synthesis is pretty damn hard” - Jonathan Scragg, MRS Fall 2022 Dr Giulia Longo 

BaZrS3 (target) Ba4 Zr3 S10 Kayastha et al, Solar RRL (2023) 7: 2201078 There is a characteristic peak in the Raman spectra for layered RP phases 

Prakriti Kayastha Poster presentation + github.com/skelton-group/Phonopy-Spectroscopy • Calculate infrared (IR) intensities • Calculate Raman-activity tensors • Output simulated spectra • Include first-principles mode linewidths / 

github.com/skelton-group/Phonopy-Spectroscopy 1) Identify Raman active modes 2) Generate displaced structures along each mode 3) Calculate dielectric constants for each structure Polarisability tensor Mode eigenvector High-frequency dielectric constant ----> database of Raman spectra for all competing phases in Ba-Zr-S system Prakriti Kayastha Poster presentation Kayastha et al, Solar RRL (2023) 7: 2201078 

Three degradation processes to RP phases: <50meV [1] [2] [3] Ba3 Zr2 S7 and Ba4 Zr3 S10 are energetically accessible during synthesis at high T See Jackson and Walsh Phys. Rev. B 2013 88, 165201 Available online: NU-CEM/ThermoPot phonon calcs 

Dr Lucy Whalley Northumbria University, Newcastle upon Tyne, United Kingdom Presentation and example files available here: http://github.com/nu-CEM/phonons_tutorial/ Dr Giulia Longo Northumbria Experimental characterization BaZrS3 Prakriti Kayastha Ab-initio calcs BaZrS3 Poster presentation Dr Jonathan Skelton Uni. Manchester Phonopy- spectroscopy Dr Adam Jackson STFC Ab-initio Thermodyna- mics