We present an ab-initio-based effective interaction model (EIM) for the study of magnetism, thermodynamics, and their interplay in body-centered cubic Fe-Co alloys, with Co content from 0 to 70%. The model includes explicitly both spin and chemical variables. For the former, a Heisenberg formalism is adopted. But, the spin magnitude of each Fe atom varies according to its local chemical environment, following a simple rule determined by density functional theory (DFT) calculations. The proposed model is able to describe precisely the ground-state magneto-energetic landscape of both chemically ordered and disordered Fe-Co systems, as given by DFT and experiments. In combination with on-lattice Monte Carlo simulations, it enables an accurate prediction at finite temperatures. In particular, the Curie point and the chemical order-disorder (B2-A2) transition temperature are accurately predicted, for all the concentrations considered. A strong dependency of the chemical transition temperature on the magnetic configuration is evidenced and analyzed. We also suggest a more important effect of magnetic rather than vibrational entropy on the chemical transition. However, this transition is not affected by a commonly accessible external magnetic field.
We investigate the contributions of finite-temperature magnetic fluctuations to the thermodynamic properties of bcc Fe as a function of pressure. First, we apply a tight-binding total-energy model parameterized to first-principles linearized augmented planewave computations to examine various ferromagnetic, anti-ferromagnetic, and noncollinear spin spiral states at zero temperature. The tight-binding data are fit to a generalized Heisenberg Hamiltonian to describe the magnetic energy functional based on local moments. We then use Monte Carlo simulations to compute the magnetic susceptibility, …
We here study electronic structure and magnetic properties of bcc Co$_{x}$Fe$_{1-x}$, Cr$_{x}$Fe$_{1-x}$ and Mn$_{x}$Fe$_{1-x}$ in their ferromagnetic phases using Augmented Space Recursion technique coupled with tight-binding linearized muffin tin orbital (TB-LMTO) method. We make a systematic study of magnetic properties like magnetic moment and Curie temperature and try to draw some conclusions on their variation across the row of 3-{\it d} transition metal series in periodic table using arguments based on effects like charge transfer, exchange splitting and hybridization.
The pressure induced bcc to hcp transition in Fe has been investigated via ab-initio electronic structure calculations. It is found by the disordered local moment (DLM) calculations that the temperature induced spin fluctuations result in the decrease of the energy of Burgers type lattice distortions and softening of the transverse $N$-point $TA_1$ phonon mode with $[\bar{1}10]$ polarization. As a consequence, spin disorder in an system leads to the increase of the amplitude of atomic displacements. On the other hand, the exchange coupling parameters obtained in our calculations strongly decre…
Co-rich Co$_{1-x}$Mn$_x$ alloys have hcp or fcc disordered phases and those ferromagnetic orderings are significantly deteriorated with increasing Mn concentration $x$ in bulk. On the other hand, those metastable bcc phases show properties attractive to spintronics, e.g., high tunnel magnetoresistance (TMR) ratio of more than 200% (600%) at 300 K (10 K) in magnetic tunnel junctions (MTJs) with the $x$ = 0.25 bcc alloy electrodes [Kunimatsu et al., Appl. Phys. Express 13, 083007 (2020)]. Here, we report systematic study of structure and magnetism for epitaxial thin films as well as the TMR effe…
Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1$_0$ and L1$_2$ orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phase…
The magnetic and electronic structures of $3d$ impurity atoms from Sc to Zn in ferromagnetic body-centered cubic iron are investigated using the all-electron full-potential linearized augmented plane-wave method based on the generalized gradient approximation (GGA). We found that in general, the GGA results are closer to the experimental values than those of the local spin density approximation. The calculated formation enthalpy data indicate the importance of a systematic study on the ternary Fe-C-$X$ systems rather than the binary Fe-$X$ systems, in steel design. The lattice parameters are o…
The effects of magnetism on the Bain transformation of $α$-phase FeNi systems are investigated by using the full potential linearized augmented plane wave (FLAPW) method based on the generalized gradient approximation (GGA). We found that Ni impurity in bcc Fe increases the lattice constant in ferromagnetic (FM) states, but not in the nonmagnetic (NM) states. The shear modulus $G$ and Young's modulus $E$ of bcc Fe are also increased by raising the concentration of nickel. All the compositions considered show high shear anisotropy and the ratio of the bulk to shear modulus is greater than 1.75 …
Refractory high entropy alloys containing elements from the Ti, V and Cr columns of the periodic table form body centered cubic (BCC) structures. Elements from the Ti column are noteworthy because they take the BCC structure at high temperature but undergo a shear instability and transform to the hexagonal (HCP) structure at low temperature. We show that the instability of these elements impacts the properties of the HEAs that contain them. In particular, the shear moduli are greatly reduced, causing increased dynamic contributions to lattice distortion. Relatively large size differences betwe…
Using a first principles based, magnetic tight-binding total energy model, the magnetization energy and moments are computed for various ordered spin configurations in the high pressure polymorphs of iron (fcc, or $γ$-Fe, and hcp, or $ε$-Fe), as well ferromagnetic bcc iron ($α$-Fe). For hcp, a non-collinear, antiferromagnetic, spin configuration that minimizes unfavorable ferromagnetic nearest neighbor ordering is the lowest energy state and is more stable than non-magnetic $ε$ iron up to about 75 GPa. Accounting for non-collinear magnetism yields better agreement with the experimental equatio…
The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, Cr-Ni alloys and ternary Fe-Cr-Ni alloys is investigated using a combination of density functional theory (DFT), Cluster Expansion (CE) and Magnetic Cluster Expansion (MCE). Energies, magnetic moments, and volumes of more than 500 alloy structures are evaluated using DFT, and the most stable magnetic configurations are compared with experimental data. Deviations from the Vegard law in fcc Fe-Cr-Ni alloys, associated with non-linear variation of atomic magnetic moments as functions of alloy composition, are observed. Accuracy of t…
Beryllium (Be) is an important material with wide applications ranging from aerospace components to X-ray equipments. Yet a precise understanding of its phase diagram remains elusive. We have investigated the phase stability of Be using a recently developed hybrid free energy computation method that accounts for anharmonic effects by invoking phonon quasiparticles. We find that the hcp to bcc transition occurs near the melting curve at 0<P<11 GPa with a positive Clapeyron slope of 41 K/GPa. The bcc phase exists in a narrow temperature range that shrinks with increasing pressure, explaining the…
A first-principles study of bcc chromium beyond the generalized gradient approximation (GGA)
Institute of Physics, Nicolaus Copernicus University（尼古拉·哥白尼大学物理研究所）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文学系）；Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（韩国基础科学研究院复杂系统理论物理中心）
We employ state-of-the-art ab initio simulations within the dynamical mean-field theory to study three likely phases of iron (hexogonal close-packed, hcp, face centered cubic, fcc, and body centered cubic, bcc) at the Earth's core conditions. We demonstrate that the correction to the electronic free energy due to correlations can be significant for the relative stability of the phases. The strongest effect is observed in bcc Fe, which shows a non-Fermi liquid behaviour, and where a Curie-Weiss behaviour of the uniform susceptbility hints at a local magnetic moment still existing at 5800 K and …
The effects of magnetism on high pressure properties of transition metals and transition metal compounds can be quite important. In the case of Fe, magnetism is responsible for stability of the body-centered cubic (bcc) phase at ambient conditions, and the large thermal expansivity in face-centered cubic (fcc) iron, and also has large effects on the equation of state and elasticity of hexagonal close-packed (hcp) iron. In transition metal oxides, local magnetic moments are responsible for their insulating behavior. LDA+U results are presented for CoO and FeO, and predictions are made for high …
A canonical band theory of non-collinear magnetism is developed and applied to the close packed fcc and bcc crystal structures. Several examples of non-collinear magnetism in the periodic table are seen to be canonical in origin. This is a parameter free theory where the crystal and magnetic symmetry, and exchange splitting, uniquely determine the electronic bands. The only contribution to the determination of magnetic stability is the change in band energy due to hybridisation resulting from spin mixing, and on this basis we are able to analyse the origin of the stability of non-collinear mag…
The effect of the film thickness and temperature on structural phase transformations in infinite films of bcc zirconium with (001) crystallographic orientation is studied by the molecular dynamics method with a many-body potential of interatomic interaction obtained within the embedded atom model. It is shown that the mechanism, sequence and final structures of phase transitions in bcc Zr films essentially depend on the film thickness. The films with (001) surface up to 6.1 nm thick experience an orientational transition into the bcc (110) phase through an intermediate metastable fcc phase, an…
The occurrence of bcc-fcc ($α$-$γ$) and fcc-bcc ($γ$-$δ$) phase transitions in magnetic iron stems from the interplay between magnetic excitations and lattice vibrations. However, this fact has never been proven by a direct dynamic simulation, treating non-collinear magnetic fluctuations and dynamics of atoms, and their coupling at a finite temperature. Starting from a large set of data generated by ab initio simulations, we derive non-collinear magnetic many-body potentials for bcc and fcc iron describing fluctuations in the vicinity of near perfect lattice positions. We then use spin-lattice…
We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc-Zr. In particular, we compute the isothermal elastic constants in the temperature range 1200K < T < 2000K by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with C'. However, the temperature decrease of…
We compute lattice dynamical properties of iron at the bcc-fcc phase transition using dynamical mean-field theory implemented with the frozen-phonon method. Electronic correlations are found to have a strong effect on the lattice stability of paramagnetic iron in the bcc phase. Our results for the structural phase stability and lattice dynamical properties of iron are in good agreement with experiment.
We critically discuss the stability of edge states and edge magnetism in zigzag edge graphene nanoribbons (ZGNRs). We point out that magnetic edge states might not exist in real systems, and show that there are at least three very natural mechanisms - edge reconstruction, edge passivation, and edge closure - which dramatically reduce the effect of edge states in ZGNRs or even totally eliminate them. Even if systems with magnetic edge states could be made, the intrinsic magnetism would not be stable at room temperature. Charge doping and the presence of edge defects further destabilize the intr…
We develop a self-consistent relativistic disordered local moment (RDLM) scheme aimed at describing finite temperature magnetism of itinerant metals from first principles. Our implementation in terms of the Korringa--Kohn--Rostoker multiple scattering theory and the coherent potential approximation allows to relate the orientational distribution of the spins to the electronic structure, thus a self-consistent treatment of the distribution is possible. We present applications for bulk bcc Fe, L1$_0$-FePt and FeRh ordered in the CsCl structure. The calculations for Fe show significant variation …
It is well known that conventional harmonic lattice dynamics cannot be applied to energetically unstable crystals at 0 K, such as high temperature body centered cubic (BCC) phase of crystalline Zr. Predicting phonon spectra at finite temperature requires the calculation of force constants to the third, fourth and even higher orders, however, it remains challenging to determine to which order the Taylor expansion of the potential energy surface for different materials should be cut off. Molecular dynamics, on the other hand, intrinsically includes arbitrary orders of phonon anharmonicity, howev…
We present theoretical results on the high-temperature phase stability and phonon spectra of paramagnetic bcc iron which explicitly take into account many-body effects. Several peculiarities, including a pronounced softening of the [110] transverse (T$_1$) mode and a dynamical instability of the bcc lattice in harmonic approximation are identified. We relate these features to the $α$-to-$γ$ and $γ$-to-$δ$ phase transformations in iron. The high-temperature bcc phase is found to be highly anharmonic and appears to be stabilized by the lattice entropy.
Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transi…
The phase stability of the various crystalline structures of the super-heavy element Copernicium was determined based on the first-principles calculations with different levels of the relativistic effects. We utilized the Darwin term, mass-velocity, and spin-orbit interaction with the single electron framework of the density functional theory while treating the exchange and correlation effects using local density approximations. It is found that the spin-orbit coupling is the key component to stabilize the body-centered cubic ($bcc$) structure over the hexagonal closed packed ($hcp$) structure…
Ab initio calculation results for the electronic structure of disordered bcc Fe(x)Al(1-x) (0.4<x<0.75), Co(x)Al(1-x) and Ni(x)Al(1-x) (x=0.4; 0.5; 0.6) alloys near the 1:1 stoichiometry, as well as of the ordered B2 (FeAl, CoAl, NiAl) phases with point defects are presented. The calculations were performed using the coherent potential approximation within the Korringa-Kohn-Rostoker method (KKR-CPA) for the disordered case and the tight-binding linear muffin-tin orbital (TB-LMTO) method for the intermetallic compounds. We studied in particular the onset of magnetism in Fe-Al and Co-Al systems a…
High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEA's exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr-Mo-Nb-V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-pri…
We report a correlation between structural phase stability and magnetic properties of Co2FeO4 spinel oxide. We employed mechanical alloying and subsequent annealing to obtain the desired samples. The particle size of the samples changes from 25 nm to 45 nm. The structural phase separation of samples, except sample annealed at 9000C, into Co rich and Fe rich spinel phase has been examined from XRD spectrum, SEM picture, along with EDAX spectrum, and magnetic measurements. The present study indicated the ferrimagnetic character of Co2FeO4, irrespective of structural phase stability. The observat…
Recently synthesized NdFe12N has excellent magnetic properties, while it is thermodynamically unstable. Using first-principles method, we study the effect of substitutional 3d transition metal elements to the mother compound NdFe12. We find that Co has positive effect on the stability of the ThMn12 structure. In contrast with Ti substitution, Co substitution does not reduce the magnetization significantly. The crystal field parameter <r^{2}>A_{0}^{2} is nearly unchanged by Co substitution, and nitrogenation to NdFe11Co greatly enhances <r^{2}>A_{0}^{2}. This suggests that Co is a good candidat…
The equation of state, structural behavior and phase stability of α-uranium have been investigated up to 1.3 TPa using density functional theory, adopting a simple description of electronic structure that neglects the spin-orbit coupling and strong electronic correlations. The comparison of the enthalpies of Cmcm (alpha-U), bcc, hcp, fcc, and bct predicts that the aplpha-U phase is stable up to a pressure of ~285 GPa, above which it transforms to a bct-U phase. The enthalpy differences between the bct and bcc phase decrease with pressure, but bcc is energetically unfavorable at least up to 1.3…
First-principles based on density functional theory is used to study the phase stability, elastic, magnetic, and electronic properties of cubic (c)-Fe$_4$C. Our results show that c-Fe$_{4}$C has a ferromagnetic (FM) ground state structure compared with antiferromagnetic (AFM) and nonmagnetic (NM)states. To study the phase stability of c-Fe$_4$C, BCC Fe$_4$C, FCC Fe$_4$C, and BCC Fe$_{16}$C, where C is considered at tetrahedral and octahedral interstitial sites, are also considered. Although, the formation energy of c-Fe$_4$C is smaller than BCC Fe$_4$C, but the shear moduli of c-Fe$_4$C is neg…
First-principles density functional theory (DFT) study of embedding V and Nb atom in monovacant and divacant graphene is reported. Complete/almost complete spin polarization is verified for V/Nb embedding in MV/DV graphene. The origin of magnetism has been identified via interaction of 3d-states of embedded trnasition metal atom with p-states of inequivalent C atoms present in the vicinity of embedding site. Band structure analysis has been performed to address the semiconducting behavior of graphene in minority spin channel on embedding V/Nb atom. The isosurface plots also confirm the magneti…
The evaluation of phase stabilities of unstable elemental phases is a long-standing problem in the computational assessment of phase diagrams. Here we tackle this problem by explicitly calculating phase diagrams of intermetallic systems where its effect should be most conspicuous, binary systems of titanium with bcc transition metals (Mo, Nb, Ta and V). Two types of phase diagrams are constructed: one based on the lattice stabilities extracted from empirical data, and the other using the lattice stabilities computed from first principles. It is shown that the phase diagrams obtained using the …
For (CoCrFeMn)$_{100-x}$Al$_{x}$ high-entropy alloys, we investigate the phase evolution with increasing Al-content (0 $\le$ x $\le$ 20 at.%). From first-principles theory, the Al-doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. We highlight the effect of Al-doping on the formation enthalpy and electronic structure of (CoCrFeMn)$_{100-x}$Al$_{x}$ alloys. As chemical short-range order (SRO) in multicomponent alloys indicates the nascent local order (and entropy changes), as well as expected low-tem…
Prediction of the Curie temperature is of significant importance for the design of ferromagnetic materials. Even though the Curie temperature has been estimated using the Heisenberg model, magnetic exchange coupling parameters widely used is thus far based on first-principles calculations at zero temperature. In the explicit consideration of temperature effects, it is important to minimise the total free energy, because the magnetic and phonon free energies correlate with each other. Here, we propose a first-principles thermodynamic approach to minimise the total free energy considering both t…
We use first principles molecular dynamics simulations coupled to the thermodynamic integration method to study the hcp-bcc transition and melting of beryllium up to a pressure of 1600~GPa. We derive the melting line by equating solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit $T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good agreement with previous two-phase simulations below 6000~K. We also derive the hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation underestimates the stability of the hcp structure, predicting…
We investigate the interplay between the structural reconstruction and the magnetic properties of Fe doublelayers on Ir (111)-substrate using first-principles calculations based on density functional theory and mapping of the total energies on an atomistic spin model. We show that, if a second Fe monolayer is deposited on Fe/Ir (111), the stacking may change from hexagonal close-packed to bcc (110)-like accompanied by a reduction of symmetry from trigonal to centered rectangular. Although the bcc-like surface has a lower coordination, we find that this is the structural ground state. This reco…
This work is focused in the stability and magnetic properties of complex graphene multivacancy systems, studied by Density Functional Theory calculations. The removal of a sequence of carbon atoms -i.e. the complementary figure- leads to these multivacancy systems. We show evidence that dendritic-like complementary figures yield to very stable defected graphene structures. If this dendritic complementary figure is aliphatic, the stress of the defected graphene system is enough to decrease the symmetry of such a system. In the cases that the complementary figure is based in phenyl- or pyrenyl-l…
Chromium trihalides, CrX$_3$ (with X = Cl, Br, I), are a family of layered magnetic materials that can be easily exfoliated to provide ferromagnetic monolayers. When two layers are stacked together to form a bilayer the interlayer exchange coupling can be either ferromagnetic or antiferromagnetic depending on the stacking sequence. Here we combine crystallographic arguments based on the close-packing condition with first-principles simulations to enumerate all possible stacking patterns in CrX$_3$ bilayers that preserve the spatial periodicity of each layer. We recover all configurations obser…
In spintronics, one of the long standing questions is why the MgO-based magnetic tunnel junction (MTJ) is almost the only option to achieve a large tunnelling magnetoresistance (TMR) ratio at room temperature (RT) but not as large as the theoretical prediction. This study focuses on the development of an almost strain-free MTJ using metastable bcc CoxMn100-x ferromagnetic films. We have investigated the degree of crystallisation in MTJ consisting of CoxMn100-x/MgO/CoxMn100-x (x = 66, 75, 83 and 86) in relation to their TMR ratios. Cross-sectional high resolution transmission electron microscop…
Precise control of crystallography and magnetism in focused-ion-beam transformed iron-nickel thin films
CEITEC BUT, Brno University of Technology（布尔诺理工大学欧洲技术与创新卓越中心）；Institute of Applied Physics, TU Wien（维也纳工业大学应用物理研究所）；Institute of Physical Engineering, Brno University of Technology（布尔诺理工大学物理工程学院）
We present a coarse molecular-dynamics (CMD) approach for the study of stress-induced structural transformations in crystals at finite temperatures. The method relies on proper choice of a coarse variable (order parameter, observable), which parameterizes the changes in effective free energy during the transformation. Results are reported for bcc-to-hcp lattice transitions under pressure. We explore coarse-variable space to reconstruct an effective free-energy landscape quantifying the relative stability of different metastable basins and locate the onset, at a critical pressure, of the bcc-to…
Temperature-dependent magnetic experiments like pump-probe measurements generated by a pulsed laser have become a crucial technique for switching the magnetization in the picosecond time scale. Apart from having practical implications on the magnetic storage technology, the research field of ultrafast magnetization poses also fundamental physical questions. To correctly describe the time evolution of the atomic magnetic moments under the influence of a temperature-dependent laser pulse, it remains crucial to know if the magnetic material under investigation has magnetic excitation spectrum tha…
The magnetic properties of iron (spin and orbital magnetic moments, magnetocrystalline anisotropy energy) in various geometries and dimensionalities are investigated by using a parametrized tight-binding model in an $s$, $p$ and $d$ atomic orbital basis set including spin polarization and the effect of spin-orbit coupling. The validity of this model is well established by comparing the results with those obtained by using an ab-initio code. This model is applied to the study of iron in bulk bcc and fcc phases, $(110)$ and $(001)$ surfaces and to the monatomic wire, at several interatomic dista…
In the framework of density functional theory (DFT), the structural and magnetic properties of FeN mono nitride have been investigated using the all electrons augmented spherical wave method (ASW) with a generalized gradient GGA functional for treating the effects of exchange and correlation. Calculation of the energy versus volume in hypothetic rocksalt (RS), zinc-blende (ZB) and wurtzite (W) types structures shows that the RS-type structure is more stable than the others. Spin polarized calculation results at equilibrium volume indicate that the ground state of RS-FeN is ferromagnetic with a…
The stability of Cr, V, Al carbide MAX phases, materials of interest for a variety of magnetic as well as high temperature applications, has been studied using density-functional-theory first-principles calculations. The enthalpy of mixing predicts these alloys to be unstable towards unmixing at 0 K. The calculations also predict, however, that these phases would be thermally stabilised by configurational entropy at temperatures well below the values used for synthesis. The temperature Ts below which they become unstable is found to be quite sensitive to the presence of magnetic moments on Cr …
The modern quantum theory of magnetism in solids is getting commonly derived using Green's functions formalism. The popularity draws itself from remarkable opportunities to capture the microscopic landscape of exchange interactions, starting from a tight-binding representation of the electronic structure. Indeed, the conventional method of infinitesimal spin rotations, considered in terms of local force theorem, opens vast prospects of investigations regarding the magnetic environment, as well as pairwise atomic couplings. However, this theoretical concept practically does not devoid of intrin…
From Entropy to Compression: Competing Thermodynamic Drivers of Structural Transitions in Transition Metals
University of Manchester（曼彻斯特大学）；University of Oxford（牛津大学）；Center for Advanced Systems Understanding（高级系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；TU Dresden（德累斯顿工业大学）
First-Principles Study of Two-Dimensional CeN: Interplay between Structural Stability, Electronic Structure, and Magnetism
Instituto de Física “Ing. Luis Rivera Terrazas”, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学路易斯·里韦拉·特拉亚斯物理研究所）；Facultad de Ingeniería, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学工程学院）
