openmaterials.ai / codes / D3Q
A Quantum ESPRESSO extension: three-phonon matrix elements for arbitrary wave vectors by the 2n+1 theorem, and the phonon Boltzmann equation solved exactly by conjugate gradients.
The 2n+1 theorem of density functional perturbation theory gives the third derivative of the energy from first-order wave functions, for three arbitrary wave vectors and for metals as well as insulators (Paulatto 2013).
An extension of the D3 code computes the anharmonic coefficients on a coarse q grid, 4x4x4 for diamond, then Fourier interpolates them to the dense mesh (Fugallo 2013).
The exact BTE solution minimizes a quadratic functional. Preconditioned conjugate gradients converge in four iterations where plain iteration fails at 77 (Fugallo 2013).
Three-phonon normal and Umklapp collisions, elastic isotope scattering from mass variance, and border scattering through a Casimir length and shape factor (Fugallo 2013).
Anharmonic broadening of each branch at finite T, with steps and spikes along the optical branches of graphene and nonzero TA and LA widths at small q (Paulatto 2013).
The exact solution holds collective phonon excitations, the heat carriers in graphite and graphene, where the SMA is ten times too low (Fugallo 2014).
The exact BTE gives the 2000 W/m/K measured in graphite. The SMA gives a tenth. Graphene reaches intrinsic kappa only near 1 mm, with mean free paths of hundreds of um (Fugallo 2014). Fugallo 2014
In graphene, BN, MoS2, graphane and fluorographene normal scattering dominates above cryogenic T: Poiseuille and Ziman regimes, second sound over about 1 mm in graphene (Cepellotti 2015). Cepellotti 2015
At 100 K the exact BTE follows measurements for 98.9%, 99.9% and 99.93% C12 samples, and predicts up to three times higher kappa for fully enriched diamond (Fugallo 2013). Fugallo 2013
Quantum ESPRESSO ground state and DFPT phonons on a coarse q grid. d3_q2r.x writes mat2R.
The 2n+1 matrix elements on the coarse grid. d3_qq2rr.x writes the real-space mat3R.
d3_asr3.x imposes acoustic sum rules and d3_sparse.x prunes small elements.
d3_lw.x with calculation='lw imag' on a dense q mesh and a smearing in cm-1.
d3_tk.x with calculation='sma' for RTA or 'cgp' for the exact variational solution.