Non-adiabatic vibrational spectra from first principles
Final Report – Return Phase
PIIFR-GA-2014-911070
Main Researchers: Prof. Dr. Aldo Humberto Romero
Materials Department, CINVESTAV Queretaro
Prof. Dr. Eberhard K. U. Gross
Max-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 BornOppenheimer 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
re, S is the Seebeck
the electrical and thermal conductivities. Most
materials have a direct dependence between the main two parameters in this
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
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 threedimensional 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 twodimensional 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 contraindicated 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 eigenphonon 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.
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Outreach
Talks.
March, 2014
Systematic Phase Diagram of LiSi and LiAl compounds from Minimal Hopping
Method, Denver, USA.
June, 2014
Introduction 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. ArancibiaMiranda, 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-onedimensional 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 phasetransition 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, 4954.
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 FirstPrinciples, 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.