arXiv subjects

Kristian Berland

Publications and source records attributed to Kristian Berland.

At least 37 records · Page 2Linked to original sources

arXiv2021

Lattice thermal conductivity of half-Heuslers with density functional theory and machine learning: Enhancing predictivity by active sampling with principal component analysis

Low lattice thermal conductivity is essential for high thermoelectric performance of a material. Lattice thermal conductivity is often computed using density functional theory (DFT), typically at a high computational cost. Training machine learning models to predict lattice thermal conductivity could offer an effective procedure to identify low lattice thermal conductivity compounds. However, in doing so, we must face the fact that such compounds can be quite rare and distinct from those in a typical training set. This distinctness can be problematic as standard machine learning methods are inaccurate when predicting properties of compounds with features differing significantly from those in the training set. By computing the lattice thermal conductivity of 122 half-Heusler compounds, using the temperature-dependent effective potential method, we generate a data set to explore this issue. We first show how random forest regression can fail to identify low lattice thermal conductivity compounds with random selection of training data. Next, we show how active selection of training data using feature and principal component analysis can be used to improve model performance and the ability to identify low lattice thermal conductivity compounds. Lastly, we find that active learning without the use of DFT-based features can be viable as a quicker way of selecting samples.

cond-mat.mtrl-sci↗

arXiv2021

Discarded gems: Thermoelectric performance of materials with band gap emerging at the hybrid-functional level

A finite electronic band gap is a standard filter in high-throughput screening of materials using density functional theory (DFT). However, because of the systematic underestimation of band gaps in standard DFT approximations, a number of compounds may incorrectly be predicted metallic. In a more accurate treatment, such materials may instead appear as low band gap materials and could e.g. have good thermoelectric properties if suitable doping is feasible. To explore this possibility, we performed hybrid functional calculations on 1093 cubic materials listed in the MaterialsProjects database with four atoms in the primitive unit cell, spin-neutral ground state, and a formation energy within 0.3 eV of the convex hull. Out of these materials, we identified eight compounds for which a finite band gap emerges. Evaluating electronic and thermal transport properties of these compounds, we found the compositions MgSc2 Hg and Li2 CaSi to exhibit promising thermoelectric properties. These findings underline the potential of reassessing band gaps and band structures of compounds to indentify additional potential thermoelectric materials.

cond-mat.mtrl-sci↗

arXiv2020

Next-generation non-local van der Waals density functional

The fundamental ideas for a non-local density functional theory -- capable of reliably capturing van der Waals interaction -- were already conceived in the 1990's. In 2004, a seminal paper introduced the first practical non-local exchange-correlation functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost two decades of development and testing, we present the next-generation non-local correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semi-empirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for non-local van der Waals density functional theory.

cond-mat.mtrl-sci↗

arXiv2020

Non-trivial retardation effects in dispersion forces: From anomalous distance dependence to novel traps

In the study of dispersion forces, nonretarded, retarded and thermal asymptotes with their distinct scaling laws are regarded as cornerstone results governing interactions at different separations. Here, we show that when particles interact in a medium, the influence of retardation is qualitatively different, making it necessary to consider the non-monotonous potential in full. We discuss different regimes for several cases and find an anomalous behaviour of the retarded asymptote. It can change sign, and lead to a trapping potential.

cond-mat.mes-hall↗

arXiv2019

Shallow impurity band in ZrNiSn

ZrNiSn and related half Heusler compounds are candidate materials for efficient thermoelectric energy conversion with a reported thermoelectric figure-of-merit of n-type ZrNiSn exceeding unity. Progress on p-type materials has been more limited, which has been attributed to the presence of an impurity band, possibly related to the presence of Ni interstitials in nominally vacant 4d position. The specific energetic position of this band, however, has not been resolved. Here, we report results of a concerted theory-experiment investigation for a nominally undoped ZrNiSn, based on measurements of electrical resistivity, Hall coefficient, Seebeck coefficient and Nernst coefficient, measured in a temperature range from 80 to 420 K. The results are analyzed with a semi-analytical model combining a density functional theory (DFT) description for ideal ZrNiSn, with a simple analytical correction for the impurity band. The model provides a good quantitative agreement with experiment, describing all salient features in the full temperature span for the Hall, conductivity, and Seebeck measurements, while also reproducing key trends in the Nernst results. This comparison pinpoints the impurity band edge to 40 meV below the conduction band edge, which agrees well with a separate DFT study of a supercell containing Ni interstitials. Moreover, we corroborate our result with a separate study of ZrNiSn0.9Pb0.1 sample showing similar agreement with an impurity band edge shifted to 32 meV below the conduction band.

cond-mat.mtrl-sci↗

arXiv2019

Thermoelectric transport trends in group 4 half-Heusler alloys

The thermoelectric properties of 54 different group 4 half-Heusler (HH) alloys have been studied from first principles. Electronic transport was studied with density functional theory using hybrid functionals facilitated by the $\mathbf{k} \cdot \mathbf{p}$ method, while the temperature dependent effective potential method was used for the phonon contributions to the figure of merit $ZT$. The phonon thermal conductivity was calculated including anharmonic phonon-phonon, isotope, alloy and grain-boundary scattering. HH alloys have an ${\it XYZ}$ composition and those studied here are in the group 4-9-15 (Ti,Zr,Hf)(Co,Rh,Ir)(As,Sb,Bi) and group 4-10-14 (Ti,Zr,Hf)(Ni,Pd,Pt)(Ge,Sn,Pb). The electronic part of the thermal conductivity was found to significantly impact $ZT$ and thus the optimal doping level. Furthermore, the choice of functional was found to significantly affect thermoelectric properties, particularly for structures exhibiting band alignment features. The intrinsic thermal conductivity was significantly reduced when alloy and grain boundary scattering were accounted for, which also reduced the spread in thermal conductivity. It was found that sub-lattice disorder on the ${\it Z}$-site, i.e. the site occupied by group 14 or 15 elements, was more effective than ${\it X}$-site substitution, occupied by group 4 elements. The calculations confirmed that ZrNiSn, ZrCoSb and ZrCoBi based alloys display promising thermoelectric properties. A few other n-type and p-type compounds were also predicted to be potentially excellent thermoelectric materials, given that sufficiently high charge carrier concentrations can be achieved. This study provides insight into the thermoelectric potential of HH alloys and casts light on strategies to optimize thermoelectric performance of multicomponent alloys.

cond-mat.mtrl-sci↗

arXiv2018

Optical properties of Cu2ZnSn(SxSe1-x)4 by first-principles calculations

Structural, electronic and optical properties of Cu2ZnSn(SxSe1-x)4 semiconductors are studied theoretically for different concentration of S and Se anions. The optical properties are calculated at three levels of theory, in the generalized gradient approximation (GGA), meta-GGA, and with a hybrid functional. The GGA and meta-GGA calculations are corrected with an on-site Coulomb Ud term. Lattice constants, dielectric constants, and band-gaps are found to vary almost linearly with the concentration of S. We also show that a dense sampling of the Brillouin zone is required to accurately account for the shape of the dielectric function, which is hard to attain with hybrid functionals. This issue is resolved with a recently developed k dot p based interpolation scheme, which allows us to compare results of the hybrid functional calculations on an equal footing with the GGA and meta-GGA results. We find that the hybrid functionals provide the overall best agreement with the experimental dielectric function.

cond-mat.mtrl-sci↗

arXiv2018

Thermoelectric transport of GaAs, InP, and PbTe: Hybrid functional with ${\bf \it k \cdot p}$ interpolation versus scissor-corrected generalized gradient approximation

Boltzmann transport calculations based on band structures generated with density functional theory (DFT) are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense ${\it k}$-point sampling of the Brillouin zone and are therefore typically limited to the generalized gradient approximation (GGA), whereas more accurate methods such as hybrid functionals would have been preferable. GGA variants, however, generally underestimate the band gap. While premature onset of minority carriers can be avoided with scissor corrections, the band gap also affects the band curvature. In this study, we resolved the ${\it k}$-point sampling issue in hybrid-functional based calculations by extending our recently developed ${\it k}\cdot\tilde{\it p}$ interpolation scheme [Comput. Mater. Sci. 134, 17 (2017)] to non-local one-electron potentials and spin-orbit coupling. The Seebeck coefficient generated based on hybrid functionals were found to agree better than GGA with experimental data for GaAs, InP, and PbTe. For PbTe, even the choice of hybrid functional has bearing on the interpretation of experimental data, which we attribute to the description of valley convergence of the valence band.

cond-mat.mtrl-sci↗

arXiv2017

The role of grain boundary scattering in reducing the thermal conductivity of polycrystalline XNiSn (X = Hf, Zr, Ti) half-Heusler alloys

Thermoelectric application of half-Heusler compounds suffers from their fairly high thermal conductivities. Insight into how effective various scattering mechanisms are in reducing the thermal conductivity of fabricated XNiSn compounds (X = Hf, Zr, Ti, and mixtures thereof) is therefore crucial. Here, we show that such insight can be obtained through a concerted theory-experiment comparison of how the lattice thermal conductivity kLat(T) depends on temperature and crystallite size. Comparing theory and experiment for a range of Hf0.5Zr0.5NiSn and ZrNiSn samples reported in the literature and in the present paper revealed that grain boundary scattering plays the most important role in bringing down kLat, in particular so for unmixed compounds. Our concerted analysis approach was corroborated by a good qualitative agreement between the measured and calculated kLat of polycrystalline samples, where the experimental average crystallite size was used as an input parameter for the calculations. The calculations were based on the Boltzmann transport equation and ab initio density functional theory. Our analysis explains the significant variation of reported kLat of nominally identical XNiSn samples and is expected to provide valuable insights into the dominant scattering mechanisms even for other materials.

cond-mat.mtrl-sci↗

arXiv2017

Enabling accurate first-principle calculations of electronic properties with a corrected k.p scheme

A computationally inexpensive k.p-based interpolation scheme is developed that can extend the eigenvalues and momentum matrix elements of a sparsely sampled k-point grid into a densely sampled one. Dense sampling, often required to accurately describe transport and optical properties of bulk materials, can be demanding to compute, for instance, in combination with hybrid functionals in density functional theory (DFT) or with perturbative expansions beyond DFT such as the $GW$ method. The scheme is based on solving the k.p method and extrapolating from multiple reference k-points. It includes a correction term that reduces the number of empty bands needed and ameliorates band discontinuities. We show how the scheme can be used to generate accurate band structures, density of states, and dielectric functions. Several examples are given, using traditional and hybrid functionals, with Si, TiNiSn, and Cu as model materials. We illustrate that d-electron and semi-core states, which are particular challenging for the k.p method, can be handled with the correction scheme if the sparse grid is not too sparse.

cond-mat.mtrl-sci↗

arXiv2017

Assessment of two hybrid van der Waals density functionals for covalent and non-covalent binding of molecules

Two hybrid van der Waals density functionals (vdW-DFs) are constructed using 25%, Fock exchange with i) the consistent-exchange vdW-DF-cx functional and ii) with the vdW-DF2 functional. The ability to describe covalent and non-covalent binding properties of molecules are assessed. For properties related to covalent binding, atomization energies (G2-1 set), molecular reaction energies (G2RC set), as well as ionization energies (G21IP set) are benchmarked against experimental reference values. We find that hybrid-vdW-DF-cx yields results that are rather similar to those of the standard non-empirical hybrid PBE0 [JCP 110, 6158 (1996)]. Hybrid vdW-DF2 follows somewhat different trends, showing on average significantly larger deviations from the reference energies, with a MAD of 14.5 kcal/mol for the G2-1 set. Non-covalent binding properties of molecules are assessed using the S22 benchmark set of non-covalently bonded dimers and the X40 set of dimers of small halogenated molecules, using wavefunction-based quantum chemistry results for references. For the S22 set, hybrid-vdW-DF-cx performs better than standard vdW-DF-cx for the mostly hydrogen-bonded systems. Hybrid-vdW-DF2 offers a slight improvement over standard vdW-DF2. Similar trends are found for the X40 set, with hybrid-vdW-DF-cx performing particularly well for binding involving the strongly polar hydrogen halides, but poorly for systems with tiny binding energies. Our study of the X40 set reveals both the potential of mixing Fock exchange with vdW-DF, but also highlights shortcomings of the hybrids constructed here. The solid performance of hybrid-vdW-DF-cx for covalent-bonded systems, as well as the strengths and issues uncovered for non-covalently bonded systems, makes this study a good starting point for developing even more precise hybrid vdW-DFs.

physics.chem-ph↗

arXiv2017

Lattice thermal conductivity of Ti$_x$Zr$_y$Hf$_{1-x-y}$NiSn half-Heusler alloys calculated from first principles: Key role of nature of phonon modes

In spite of their relatively high lattice thermal conductivity $κ_{\ell}$, the XNiSn (X=Ti, Zr or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that $κ_{\ell}$ can be reduced by sublattice-alloying on the X-site. To cast light on how the alloy composition affects $κ_\ell$, we study this system using the phonon Boltzmann-transport equation within the relaxation time approximation in conjunction with density functional theory.The effect of alloying through mass-disorder scattering is explored using the virtual crystal approximation to screen the entire ternary Ti$_x$Zr$_{y}$Hf$_{1-x-y}$NiSn phase diagram. The lowest lattice thermal conductivity is found for the Ti$_x$Hf$_{1-x}$NiSn compositions; in particular, there is a shallow minimum centered at Ti$_{0.5}$Hf$_{0.5}$NiSn with $κ_l$ taking values between 3.2 and 4.1 W/mK when the Ti content varies between 20 and 80\%. Interestingly, the overall behavior of mass-disorder scattering in this system can only be understood from a combination of the nature of the phonon modes and the magnitude of the mass variance. Mass-disorder scattering is not effective at scattering acoustic phonons of low energy. By using a simple model of grain boundary scattering, we find that nanostructuring these compounds can scatter such phonons effectively and thus further reduce the lattice thermal conductivity; for instance, Ti$_{0.5}$Hf$_{0.5}$NiSn with a grain size of $L= 100$ nm experiences a 42\% reduction of $κ_{\ell}$ compared to that of the single crystal.

cond-mat.mtrl-sci↗

arXiv2016

Structural and excited-state properties of oligoacene crystals from first principles

Molecular crystals are a prototypical class of van der Waals (vdW) bound organic materials with excited state properties relevant for optoelectronics applications. Predicting the structure and excited state properties of molecular crystals presents a challenge for electronic structure theory, as standard approximations to density functional theory (DFT) do not capture long range vdW dispersion interactions and do not yield excited state properties. In this work, we use a combination of DFT including vdW forces) using both non local correlation functionals and pair wise correction methods (together with many body perturbation theory (MBPT) to study the geometry and excited states, respectively, of the entire series of oligoacene crystals, from benzene to hexacene. We find that vdW methods can predict lattice constants within 1 percent of the experimental measurements, on par with the previously reported accuracy of pairwise approximations for the same systems. We further find that excitation energies are sensitive to geometry, but if optimized geometries are used MBPT can yield excited state properties within a few tenths of an eV from experiment. We elucidate trends in MBPT computed charged and neutral excitation energies across the acene series and discuss the role of common approximations used in MBPT.

cond-mat.mtrl-sci↗

arXiv2016

Enhancement of thermoelectric properties by energy filtering: Theoretical potential and experimental reality in nanostructured ZnSb

Energy filtering has been suggested by many authors as a means to improve thermoelectric properties. The idea is to filter away low-energy charge carriers in order to increase Seebeck coefficient without compromising electronic conductivity. This concept was investigated in the present paper for a specific material (ZnSb) by a combination of first-principles atomic-scale calculations, Boltzmann transport theory, and experimental studies of the same system. The potential of filtering in this material was first quantified, and it was as an example found that the power factor could be enhanced by an order of magnitude when the filter barrier height was 0.5~eV. Measured values of the Hall carrier concentration in bulk ZnSb were then used to calibrate the transport calculations, and nanostructured ZnSb with average grain size around 70~nm was processed to achieve filtering as suggested previously in the literature. Various scattering mechanisms were employed in the transport calculations and compared with the measured transport properties in nanostructured ZnSb as a function of temperature. Reasonable correspondence between theory and experiment could be achieved when a combination of constant lifetime scattering and energy filtering with a 0.25~eV barrier was employed. However, the difference between bulk and nanostructured samples was not sufficient to justify the introduction of an energy filtering mechanism. The reasons for this and possibilities to achieve filtering were discussed in the paper.

cond-mat.mtrl-sci↗

arXiv2014

van der Waals forces in density functional theory: The vdW-DF method

A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals Density Functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasising more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only for dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.

cond-mat.mtrl-sci↗

arXiv2014

Interpretation of van der Waals density functionals

The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method [Phys. Rev. Lett. 92, 246401 (2004); Phys. Rev. B 76, 125112 (2007); Phys. Rev. B 89, 035412 (2014)] can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method [Phys. Rev. B 82, 081101(2010)]. We explore the internal xc hole components, showing that they share properties with those of the generalized-gradient approximation. We use these results to illustrate the nonlocality in the vdW-DF description and analyze the vdW-DF formulation of nonlocal correlation.

physics.chem-ph↗

arXiv2014

van der Waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions

The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory (DFT). One proposed approach, the van der Waals density functional (vdW-DF) method, rests on strong physical foundations and offers simple yet accurate and robust functionals. A very recent functional within this method called vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412] stands out in its attempt to use an exchange energy derived from the same plasmon-based theory from which the nonlocal correlation energy was derived. Encouraged by its good performance for solids, layered materials, and aromatic molecules, we apply it to several systems that are characterized by competing interactions. These include the ferroelectric response in PbTiO$_3$, the adsorption of small molecules within metal-organic frameworks (MOFs), the graphite/diamond phase transition, and the adsorption of an aromatic-molecule on the Ag(111) surface. Our results indicate that vdW-DF-cx is overall well suited to tackle these challenging systems. In addition to being a competitive density functional for sparse matter, the vdW-DF-cx construction presents a more robust general purpose functional that could be applied to a range of materials problems with a variety of competing interactions.

cond-mat.mtrl-sci↗

arXiv2013

An exchange functional that tests the robustness of the plasmon description of the van der Waals density functional

Is the plasmon description within the non-local correlation of the van der Waals density functional by Dion and coworkers (vdW-DF1) robust enough to describe all exchange-correlation components? To address this question, we design an exchange functional, termed LV-PW86r based on this plasmon description as well as recent analysis on exchange in the large $s$-regime. In the regime with reduced gradients $s=|\nabla n|/2n k_{\rm F}(n)$ smaller than $\approx 2.5$, dominating the non-local correlation part of the binding energy, the enhancement factor $F_x(s)$ closely resembles the Langreth-Vosko screened exchange. In the $s$-regime beyond, dominated by exchange, $F_x(s)$ passes smoothly over to the revised Perdew-Wang-86 form. Our tests indicate that vdW-DF1(LV-PW86r) produces accurate separations and binding energies of the S22 data set of molecular dimers as well as accurate lattice constants of layered materials and tightly-bound solids. These results suggest that vdW-DF1 has a good plasmon description in the low-to-moderate $s$-regime.

cond-mat.mtrl-sci↗