Non-adiabatic vibrational spectra from first principles

Final Report – Return Phase

PIIFR-GA-2014-911070

Main Researchers: Prof. Dr. Aldo Humberto RomeroMaterials Department, CINVESTAV Queretaro

Prof. Dr. Eberhard K. U. GrossMax-Planck-Institut fuer Mikrostrukturphysik, Halle, Germany

1. Executive Summary

The main goals of the return phase PIIFR-GA-2011-911070, Non adiabatic phonon project were the following:

1) To transfer the experiences obtained during the initial year at the Max Planck Institute to the research group lead by Prof Aldo Humberto Romero.

2) To continue the research on thermal properties and in particular on anharmonic effects.

3) To establish long-term collaborations with European institutions and creation of coherent joint research projects.

4) To enhance mobility, international presence and research interaction with members of the group of Prof Aldo Romero.

5) To increase the join collaboration research with European groups further than the one involved in the initial IFF project.

After a year of intense research and development activities, the majority of the goals proposed in the return phase have been reached. In particular, target (1) was a success. The experiences obtained during the first year of the IFF support have been shared with the group and in particular with students, who are those who can benefit the most. In relation with targets (2) and (3), we demonstrate that we have increased the number of publications in the field of thermal properties and thanks to the established collaborations, we can now predict that those will continue increasing. We have now further our intentions of collaborations with a larger network of European scientists from Belgium (M. Verstraete, E. Bousquet, F. Renner), Germany (S. Botti and M. Marques), Sweden (O. Hellman), Spain (A. Cantarero) and Switzerland (S. Goedecker and M. Amsler). This takes us to targets (4) and (5), where thanks to the obtained support it has allowed students to have international experience and to strength out the networking with groups throughout the world. Additionally, we have been able to increase our collaboration starting from theoretical groups and now including two experimental groups, one in spain (Cantarero) and one in Belgium (Renner). The started project with those groups will be discussed below. On the other hand, in relation with the group of Prof. E.K.U. Gross, we are in the

process of finishing a paper on PbTe, based on the performed calculations that we plan to submit to Nature Materials in the next few weeks. One task that was pending from the proposed original project, it is based on the implementation of the Maximally Localized Wannier functions within the software ELK, that will allow us to extrapolate energies and wave functions into a much larger grid based on a coarse grid. At this point, the Wannier functions interface has been partially finished with the software Wannier90 (www.wannier.org). Even though, due to the different development of the research projects started with other groups in Europe, we have not find the time to finish this implementation. We will try to due this before the end of the year.

At his stage this project was not only focused on the technical aspects of the problem of non-adiabatic phonons but also to establish a collaboration network with different institutions in Europe that were originally set during the first year of the IIF award. This has been attained thanks to the initial exchange of information provided during the first year. Now, we see a more steady collaboration and we expect to keep for long.

In general, we have gained a great deal of understanding of non-adiabatic phenomena, in particular, to valuate materials where this effect has important consequences. For those, we have considered InSe and PbTe as examples, while we are also including Bi and SnSe as new prototypes. The performed implementations will also impact general users of the code ELK. Where the analysis of Maximally localized Wannier functions will be useful to understand the chemistry of a given material.

In the first part of this report, we describe the most technical aspects of the research performed during the recent year. Technical issues as well as the encountered problems will be discussed. In the second part of the report, we focused more on the dissemination, productivity and planned activities derived from this project.

2. Introduction.

An adiabatic transformation in a quantum systems relate to slow adjustments in the system due to gradual changes in some external parameters, such that the system rapidly adapt to the performed changes. In the context of materials, this relates to the ion dynamics, where the electrons will adapt rather fast to the change in the atomic positions. Even though, this is in the root of the Born-Oppenheimer approximation, recent experiments have been able to clearly show that for many systems, this approximation is violated. This leads to dependences of physical parameters with respect to temperature that are not lineal and go beyond the second order response. The interest has been raised and it becomes the core of this research project, where we develop and/or use existing methods to identify those cases where the adiabatic approximation breaks down and an observable can be detected, providing novel properties in the specific material. In the following projects, we have use different implementations to study the thermodynamic behavior of several materials and predict those where the anharmonicity plays an important role. At the same time, we have been developing and using different implementations to perform

throughput materials design and using thermal calculations to help in the prediction of the thermal stability.

Figure 1: Phonon dispersion relation of the Rocksalt PbTe at the ground state, PbTe Neutron scattering cross section. Notice the double peaks close to and the lifting of the optical branches above the acoustic captured within the TDEP method as compared to experiment. The quasiharmonic are included only for reference.. 2.1 Thermoelectrics

Normal electric power is generated around the world with efficiencies limited to about 40 percent. This provides a vast amount of thermal loss that can potentially be recovered by the use of thermoelectrics, materials that use the non linear dependence of the thermal response to create electrical conductance. The thermoelectric efficiency of a material is captured by the figure of merit, ZT=T S2 / , where T is the temperature, S is the Seebeck coefficient, and and are the electrical and thermal conductivities. Most materials have a direct dependence between the main two parameters in this quantity, when increases increases. Here, we are interest it in a material where there is a counter relation, such that when one growths, the other will be depleted. Therefore, the search for good thermoelectrics is centered on finding materials with a high figure of merit, which implies large electric and small thermal conductivities. Properties that could be self-defeating and up to now a relatively small number compounds are shown such a coupling. Since the 1990s, many new materials and paradigms have appeared, and a large number of energy harvesting applications has been proposed [1-4]. Many materials have been proposed and tested but only few of them have been optimized, most recently SnSe [5] which has a spectacular ZT of 2.6 along one axis in bulk single crystalline form. Therefore, in order to quest this search, we need to find

out the main reason, why in those materials, the optimal relation between the two dependent transport quantities is obtained. In order to understand the behavior of composite nanostructured or alloyed materials based on PbTe or SnSe, it is important to be able to explain the thermoelectric properties of pristine PbTe, and, in particular, its low thermal conductivity between 450 and 800K, which is the basis for its high efficiency at ambient conditions and makes it such a good starting point for nanostructuring and doping. For the crystalline system, the low thermal conductivity has been correlated to the presence of large anharmonic effects at the point and zone boundary, and a very low speed of sound [6, 7, 8]. It is also important to note that the recently found high thermoelectric material, SnSe, is related to PbTe and it is expected that are encompassed by the same strong anharmonicity.

Experimentally, in most thermoelectrics, the phonon spectrum shows a strong dependence on temperature. One of the most important features reported in PbTe is the longitudinal/optical crossing which occurs around 1/3 along the path from to X. The coupling between the acoustic and transverse optical (TO) modes has been identified to correlate strongly with the thermal conductivity, and there is a very strong anharmonic coupling between the transverse mode, which is ferroelectric, and the longitudinal acoustic mode, which carries most of the heat. The crossing reduces the group velocity of the acoustic branch, and hence the thermal conductivity. A large difference was found between calculations by using the quasiharmonic approximation (QHA) and experimental values, as it can be observed in Figure 1. Delaire et al. concluded that the anharmonicity comes mostly from higher order terms in the inter-atomic force constants [6]. They report inelastic neutron scattering data, where the temperature effects are shown to affect strongly the zone boundary by hardening the TO modes, such that the crossing between LA and TO is lifted as a function of temperature. This anomalous hardening of the TO frequency with temperature is the central factor which limits the performance of PbTe at higher temperatures. Such effects can be obtained by including all high order corrections to the inter-atomic force constants.

Figure 2: Calculations are based on force constants from an abinitio molecular dynamics at T=300 K. (a) Calculated linear thermal expansion coefficient for InSb as a function of temperature, compared to experimental data (red circles[9] and triangles[10]). Results are from a supercell 3x3x3 with different exchange correlation functionals: PBEsol and AM05 and different thermostat: Berendsen and Langevin. Effect of volumetric expansion is considered by changing the volume by +1% and -1%. (b) Calculated and measured [11] thermal resistivity as a function of temperature. Theoretical results include PS-B, PS-L, AM05-B

and AM05-L with a0, a0 +1%, and a0 -1%.

After the learning process for this compound, we have decided to extend our analysis to other materials where similar effects have been experimentally detected. In that respect, we have finished a calculation for the case of InSb, as it is summarized in Figure 2. A combination of DFT-based molecular dynamics and the TDEP method has been used in order to the harmonic and anharmonic lattice vibrational properties of InSb. In particular, we focus on the calculated temperature dependent second and third order force constants. The calculated lattice thermal resistivity is in fair agreement with experimental data, whereas our prediction underestimates TEC at high temperature. This disagreement needs to be checked by considering other effects such as thermal expansion or different pseudopotentials. In general, we also provide quantitative evaluations of the effects of the xc-functional, thermostat, volume and size of the supercell.

The reported calculations have been obtained by performing an ab initio molecular dynamics and fitting the inter-atomic force constants from the trajectory, where those have been constrained to the original symmetry point group. The agreement between our calculated spectra and the obtained experimental measurement is quite amazing and quantifies the reason for the appereance of the small thermal conductivity. Likewise, the thermal conductivity is found to be in very good agreement with published experimental data. This analysis is quite important because it really nails down the dependence of the different physical parameters with temperature and how they affect the thermoelectric response. The analysis and conclusion has been already spelled out and a paper has been recently accepted. It is also important to note that one of the students of Prof. Romero was visiting Belgium for almost 10 months, which help to strength the interaction with the European group and to offer the student the experience of being in an excellent research environment.

Extensions of this calculation are also on the way to compute the response of SnSe, which recently has been also proposed as a very good thermoelectric.

2.2 Thermal characterization of low dimensional materials.

As low dimensional materials we understand those, which at least one of the three dimensions is intermediate between those characteristic of atoms/molecules and those of the bulk material. There are many different realizations for 2-dimensional such as nanowires, nanotubes, layered materials, etc. One of the most important characteristics is the very high surface area to volume ratio. Due to that, the surface or edge states become important and even dominant. In this joint research effort we have focused on two and three- dimensional materials and in particular we would like to investigate the effect of confinement and weak interactions between layers to the vibrational properties. As it has been already reported, we expect to have important quantum size effects, which can significantly change the energy spectrum of electrons and their behavior, leading to novel thermal properties. Therefore, as a result, some properties of such systems are very different from those of their bulk counterparts.

In collaboration with Prof. Cantarero from Valencia University in Spain and Prof. D. Karaiskaj from Florida State University, we have started to look into some specific problems involving InSe and GaSe, both layered materials. On both groups, synthesis and characterization are part of the research projects and thanks to the experience obtained from the IFF support, we got in contact with both groups and we have started to perform calculations that help to understand and support the experimental results. For example, in Figure 3, we report the optimized hexagonal layer of GaSe and the corresponding vibrational spectra. Those can now be related to specific measured properties as for example excitons measurements or Raman scattering. In this project, we expect to offer a light on how excitations propagate in this type of two- dimensional systems. We want to pursuit the design of two-dimensional materials based the compounds study in this project.

Figure 3: Right hand side: Relaxed GaSe monolayer with a hexagonal set up. Left hand side: vibrational spectra of the GaSe Monolayer. Notice that all phonons are positive, reassuring the thermal stability of the material. Such behavior has been also extended to bulk materials as well as for a small number of layers.

2.3 Ferroelectrics.

Since the discovery of ferroelectricy in BaTiO3, a typical perovskite-structure oxide, the field has attracted tremendous interest, ranging from fundamental studies to technological applications [12]. Indeed, the transition-metal/oxygen bond, with its large polarizability, is particularly favourable for promoting the transition-metal off-centering that can result in a ferroelectric ground state [13,14]. Ferroelectrics also exist, of course, in many compounds that do not contain oxygen, with a particularly extensive range of fluorine-based examples, including both polymers and ceramics in many crystal classes (for a review see Ref. [15]). Perhaps not surprisingly given the low polarizability of bonds with fluorine, the mechanisms for ferroelectricity in fluorine-based ferroelectrics are distinct from those in oxides, ranging from molecular reorientation in polymers, to geometric reconstructions in ceramics. These alternative mechanisms are of particular interest because, again unlike the oxides, they are not contra-indicated by transition metal d electrons, and so allow simultaneous ferroelectricity and magnetic ordering (multiferroism). Interestingly, however, almost none of the known perovskite fluorides is reported to be ferroelectric and no explanation has been addressed in the literature about the absence of ferroelectricity in these crystals. Therefore, in order to address this issue, we can commited with a group of researches in Belgium to perform a series of

density functional calculations in order to offer some light into the potential ferroelectric behavior of Fluorides.

For example, we have already perform a series of calculation for many compouds with the chemical formulae AMnF3. For many of them, we have been able to identify unstable phonon modes that could lead to ferroelectricity as it happens for the oxides (see the case of NaMnF3 in Figure 4).

Figure 4: (Color online) Calculated phonon dispersion curves of cubic NaMnF3 with a G-type AFM order. Unstable modes are depicted as negative numbers. The branch colors are assigned according to the contribution of each atom to the dynamical matrix eigenvector: red for Na, green for Mn, and blue for F. In the botton panel, the lower eigendisplacements at M, X and R for the modes that contribute most to the fully relaxed ground state are shown.

By the time we have analyze the different atomic contributions to the eigen-phonon vector of the ferroelectric mode, we have observed that the origin of the FE instability in fluoro-perovskites is very different than in the case of oxides. We found that the FE instability in these ionic systems originates from the softness of the A -site displacements which in turn is caused by a simple geometric ionic size effect. Due to its geometric origin, the fluoride FE instability is rather insensitive to pressure or epitaxial strain and most fluorides remain non-ferroelectric at all reasonable strain values. An exception is Pnma

NaMnF3, in which the FE mode is particularly soft, so that it becomes ferroelectric and indeed multiferroic through coherent heteroepitaxy even at zero strain. We hope that our results will motivate experimentalists to revisit the FE behavior of perovskite-structure fluorides. We are now continuing our understanding for these compounds and we are considering their properties as function of pressure or strain. Lastly, we have also started a new set of theoretical calculations in order to see the properties of interfaces with oxides, where we predict un-compensation of the electronic charge due to the dissimilarity between Oxygen and Fluor. Such endeavor has just started and it will be conducted in the next few months. We should also point out that one of the students involved in this project has been partially supported from this project to visits to USA and Europe in order to exchange experiences and write papers based in the analysis. He will also be awarded the PhD diploma from the Belgium and the Mexican institutions, which point out how the efforts are recognized on both sides.

2.4 Crystal Structure Search

As we know, modern materials science is based on a structure-property paradigm related to materials hierarchical nature, which yields a connection of macroscopic properties over multiple length and time scales. The smallest and most basic scale is related to the atoms, where the electrons and ions configure the materials properties, becoming then the most important ingredient for the chemical bonding, the glue for the materials formation. The strategies we discuss here basically rely on electronic structure calculations that provide a basic understanding of the materials properties at the atomic scale. Therefore, if we now approach the problem of predicting the structure of a given material, we need to rely on the correct atomic description, which is provided from Quantum Mechanics. In the recent years, many different methodologies have been developed to design new materials with tailored properties before actually casting them. This is the field of high-throughput materials design, which purpose is to help in the discovery, development and design of materials, having a direct impact in many different applications. This has been accompanied by the efforts in creating a more manageable theory and stable/general software that is able to predict the properties of materials before the experiment is performed.

In this direction, we did start collaborating with the group of Prof. M.A.L Marques and S. Botti in France (now in Germany) in the previous year of this proposal. The used technique, the so-called Minima Hopping Method (MHM), is able to search quickly the configurational space, as well as been able to compare and screen different structures become in need. This method is based on molecular dynamics, where the system is allowed to jump from minima to minima by allowing changes in the ionic temperature [15,16]. This variable is set according with a criterion based on visited minima and sufficient energy to jump over local minima. In order to guide the molecular dynamics in a smart way, the driven force is assisted at every initial search for another minima along the direction of the minima Hessian eigenvalue, this guarantee that the system will search along low energy barriers. We perform calculations for a chemical

composition of a compound of interest. The lower energy structures are marked for re-convergence with a tighten criteria to be used for posterior analysis.

The first expressed interest in this research project did focus on light materials, basically those with a large presence of lithium, the third element in the periodic table. Due to the importance of this element in batteries and structural components, we have considered two types of alloys, LiAl and LiSi. Both have been reported as potential materials in battery applications due to the large amount of lithium uptake. For example, Figure 5 shows the calculated convex hull from the method herein discussed.

Figure 5. Convex hull of the LiAl binary system. Black line: convex hull constructed from the ab initio MHM calculations. Red line: convex hull constructed from the experimentally known structures and calculated from first principles. Crosses indicate different metastable phases identified in the MHM runs. The thermodynamically stable compositions are indicated by circles: red filled: experimental structures; black: novel structures.

The agreement between the predicted theoretical convex hull and the obtained by optimizing the predicted experimental structure is quite encouraging. The obvious conclusion is that MHM is able to reproduce experimental structures but also it is able to provide novel structures for compositions not experimentally considered. Additionally to the structures, we cannot perform a complete theoretical characterization, which provide an insight into the chemical, elastic and thermal behavior of the material. For example, Figure 6 shows some representative structures for the Li-rich case. In summary, we have discovered several unknown ordered phases of the Al-Li binary system that are thermodynamically stable. Phonon band structure indicates that these new Li–

Al structures are also dynamically stable. Analysis of the elastic constants indicate that the stiffness of LiAl alloys with up to 60% of Li remains essentially equal to the one of Al, with a marked maximum at LiAl3. This can be understood by the stabilization of these compounds (due to a transfer from Li atoms to Al bonds) that increases the atomic number density and therefore the stiffness. These results expand greatly our knowledge of the Li–Al phase diagram and can have profound influence in the understanding and design of new Li–Al alloys for lightweight engineering.

Figure 6: Minimal energy crystal structures of the Li-rich phases of Li–Al: (a) Li (rhombohedral, R-3m); (b) Li7Al2 (rhombohedral, R-3m); (c) Li5Al2 (monoclinic,

C2/m); (d) Li2Al (monoclinic, P21/m); (e) Li3Al2 (rhombohedral, R-3m); (f) Li5Al4 (trigonal, -3m1). Li atoms are green while Al atoms are blue.

Similar calculations are now being performed but for the LiAu alloy, which become of interest to the experimental group of Prof. Renner in Belgium. This alloy corresponds to a very rich system with a very large number of observed phases depending on the lithium concentration. The experimental group has developed a novel technique to synthetize this alloy but they have a large difficulty in understanding the X-ray diffraction due to the lack of precise knowledge of the lithium concentration. That is where our theoretical predictions can be of help, basically because after deriving the lowest energy structure, we can now simulate the X-ray diffraction pattern and compare directly to the experimental observations. This is an on-going investigation but we can see the potential of the joint experiment-theory effort.

Figure 7. Convex hull of the LiAu binary system. Black line: convex hull constructed from the ab initio MHM calculations. Crosses indicate different metastable phases identified in the MHM runs. The thermodynamically stable compositions are indicated by black circles.

Bibliography

[1] Zebarjadi, M, Esfarjani, K, Dresselhaus, M. S, Ren, Z. F, & Chen, G. (2012) Energy & Environmental Science 5, 5147.[2] LaLonde, A. D, Pei, Y, Wang, H, Jeffrey Snyder, G. (2011) Materials Today

14, 526-532.[3] Minnich, A. J, Dresselhaus, M. S, Ren, Z. F, Chen, G. (2009) Energy & Environmental Science 2, 466.[4] Dresselhaus, M. S, Chen, G, Ren, Z, Dresselhaus, G, Henry, A, Fleurial, J. P. (2009) JOM 61, 86-90.[5] Zhao, L.-D., Lo, S.-H., Zhang, Y., Sun, H., Tan, G., Uher, C., Wolverton, C., Dravid, V. P., and Kanatzidis, M. G. (2014) Nature 508, 373.[6] Delaire, O, Ma, J, Marty, K, May, A. F, McGuire, M. A, Du, M.-H, Singh, D. J, Podlesnyak, A, Ehlers, G, Lumsden, M. D, Sales, B. C. (2011) Nature Materials 10, 614-9.[7] LaLonde, A. D, Pei, Y, Snyder, G. J. (2011) Energy & Environmental Science 4, 2090.[8] An, J, Subedi, A, Singh, D. J. (2008) Solid State Communications 148, 417-419.[9] Sparks P W and Swenson C A Nov 1967 Phys. Rev. 163 779.[10] Gibbons D F Oct 1958 Phys. Rev. 112 136.[11] Holland M G Apr 1964 Phys. Rev. 134 A471.[12] M. E. Lines and A. M. Glass, book "Principles and applications of ferroelectrics and related materials", Ed. Clarendon Press, Oxford, 1977.[13] G. Sághi-Szabó and Ronald E. Cohen and Henry Krakauer, Phys. Rev. Lett. 80 (19), 4321-4324 (1998).[14] N.A. Hill, J. Phys. Chem. B, 104 (29), 6694-6709 (2000).[15] J. F. Scott and R Blinc, J. Phys. Condens. Matter 23(11), 113202 (2011).[16] S. Goedecker, J. Chem. Phys. 120 9911 (2004).[17] M. Amsler, S. Goedecker. J. Chem. Phys. 133 224104 (2010).

Outreach

Talks.

March, 2014Systematic Phase Diagram of LiSi and LiAl compounds from Minimal Hopping Method, Denver, USA.

June, 2014Introduction to ab initio molecular dynamics, Universidad del Norte, Colombia (a full week, 20 hrs).

Articles.

Published

1) A.C. Garcia-Castro, N.A. Spaldin, A.H. Romero and E. Bousquet, (2014). Geometric ferroelectricity in fluoroperovskites. Physical Review B, 89(10), 104107.

2) S.E. Baltazar, A. García, A.H. Romero, M.A. Rubio, N. Arancibia-Miranda, and D. Altbir, (2014). Surface rearrangement of nanoscale

zerovalent iron: the role of pH and its implications in the kinetics of arsenate sorption. Environmental Technology, (ahead-of-print), 1-8.

3) P. Dey, J. Paul, N. Glikin, Z.D. Kovalyuk, Z.R. Kudrynskyi, A.H. Romero, D. Karaiskaj, D. (2014). Mechanism of excitonic dephasing in layered InSe crystals. Physical Review B, 89(12), 125128.

4) J. Mejía-López, J. Mazo-Zuluaga, S. López-Moreno, F. Muñoz, L.F. Duque and A.H. Romero, (2014). Physical properties of quasi-one-dimensional MgO and Fe3O4-based nanostructures, Physical Review B, 90, 035411.

5) R. Lauck, M. Cardona, R.K. Kremer, G. Siegle, J.S. Bhosale, A.K. Ramdas, A. Burger, A. (2014). Chemical vapor transport of chalcopyrite semiconductors: CuGaS2 and AgGaS2. Journal of Crystal Growth.

6) R. Sarmiento-Pérez, T.F.T. Cerqueira, I. Valencia-Jaime, M. Amsler, S. Goedecker, S. Botti, M.A.L. Marques and A.H. Romero (2013). Sodium–gold binaries: novel structures for ionic compounds from an ab initio structural search. New Journal of Physics, 15(11), 115007.

7) Bautista-Hernández, A., Rangel, T., Romero, A. H., Rignanese, G. M., Salazar-Villanueva, M., & Chigo-Anota, E. (2013). Structural and vibrational stability of M and Z phases of silicon and germanium from first principles. Journal of Applied Physics, 113(19), 193504.

8) J.A. Barreda-Argüeso, S. López-Moreno, M.N. Sanz-Ortiz, F. Aguado, R. Valiente, J. González and F. Baudelet, (2013). Pressure-induced phase-transition sequence in CoF2: An experimental and first-principles study on the crystal, vibrational, and electronic properties. Physical Review B, 88(21), 214108.

9) P. Dey, J. Paul, J. Bylsma, D. Karaiskaj, J.M. Luther, M.C. Beard, A.H. Romero (2013). Origin of the temperature dependence of the band gap of PbS and PbSe quantum dots. Solid State Communications, 165, 49-54.

10)C. Espejo, T. Rangel, A.H. Romero, X. Gonze and G.M. Rignanese, G. M. (2013). Band structure tunability in MoS2 under interlayer compression: A DFT and GW study. Physical Review B, 87(24), 245114.

11)M.J. Duarte, J. Klemm, S.O. Klemm, K.J.J. Mayrhofer, M. Stratmann, S. Borodin, A.H. Romero, M. Madinehei, D. Crespo, J. Serrano, S.S.A. Gerstl, P.P. Choi, D. Daabe and Renner, F. U. (2013). Element-Resolved Corrosion Analysis of Stainless-Type Glass-Forming Steels. Science, 341(6144), 372-376.

Submitted and Accepted

1) Romero, A. H., Gross, E. K. U., Verstraete, M. J., & Hellman, O. (2014). Thermal Anharmonic Effects in PbTe from First Principles. arXiv preprint arXiv:1402.5535.

2) A.L. Miranda, B. Xu, O. Hellman, A.H. Romero and M. Verstraete, Ab initio calculation of the thermal conductivity of InSb, accepted in Semiconductor, Science adn Techology (2014).

3) A.C. Garcia-Castro, A.H. Romero and E. Bousquet, Strong Noncollinear Magnetism in predicted NaMnF$_3$ Post-perovskite from First-Principles, submitted to Phys. Rev. B (2014).

4) R. Sarmiento-Pérez, T.F.T. Cerqueira, I. Valencia-Jaime, M. Amsler, S. Goedecker, A.H. Romero, S. Botti, M.A.L. Marques (2013). Novel phases of lithium-aluminum binaries from first-principles structural search. Submitted to J. Phys. Chem. C(2014).

Summay and impact of the project.

We have been able to investigate and characterize a large set of crystalline materials and in particular focusing on the thermal properties of those. We have studied materials where large anharmonic effects are important and mostly they are responsible for the low thermal conductivity. Such property becomes relevant when a thermoelectric material is search for. We have generalized those effects to materials with different chemical composition as well as different crystal structure. This should enhance our experience to design materials with thermal properties out of normal and to understand the basic physics behind such phenomena. Up to know, most of our calculations have refer to three-dimensional crystalline structures, we know plan to continue using the same approach but now for two-dimensional materials, where the confinement and localization of states is going to be important. We will also plan to finish the implementation of Wannier functions on top of ELK, allowing users to make use of such approach. This will allow us to go back and revise some of the specific objectives proposed in the original research work and approach again but now with a denser grid in reciprocal space.

In general the number of publications during the last year was outstanding (more than 12 publications, with one in Science). Those publications are the conclusion of many different new projects generated with European groups, where the main purpose is to identify novel properties in crystal materials. Different fields were study, even though with the common ground to be investigated by using theoretically thermal properties. One very interesting outcome of the support obtained from this award has been to strength out a lot of collaborations with European scientists, which we expect to formalize in the next few months by reporting our research and looking for additional support to help out with the networking. Even though, the number of publications obtained during the course of this project is rather good, we need to improve the quality of those. At least one paper has been published in Science and one in Physical Review letter but we expect to have a more continuous presence in those journals.

We have to acknowledge the support received from the IIF Marie Curie actions, without it, we would not be able to engage with so many different European scientists. The results obtained up to now are very encouraging and we hope the impact of the network can be evaluated in the years to come.