Strong Isotopic Effect in Phase II of Dense Solid Hydrogen and Deuterium

Quantum nuclear zero-point motions in solid H$_2$ and D$_2$ under pressure are investigated at 80 K up to 160 GPa by first-principles path-integral molecular dynamics calculations. Molecular orientations are well-defined in phase II of D$_2$, while solid H$_2$ exhibits large and very asymmetric angular quantum fluctuations in this phase, with possible rotation in the (bc) plane, making it difficult to associate a well-identified single classical structure. The mechanism for the transition to phase III is also described. Existing structural data support this microscopic interpretation.Comment: 5 pages, 3 figure

Photostriction in Ferroelectrics from Density Functional Theory

International audienceAn ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed n e concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of n e. This method is applied to bulk multiferroic BiFeO 3 and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect. The coupling of ferroelectric or multiferroic materials with light is currently attracting a lot of attention [1], as, e.g., demonstrated by the above-band-gap photovoltages found in BiFeO 3 (BFO) thin films [2], the search of low band gap materials for photovoltaic applications [3], or the recent development in the so-called hybrid perovskite solar cells [4]. Beyond the photovoltaic effect, there is another coupling between light and properties of ferroelectrics or multiferroics that is of current interest, namely, the so-called photostriction effect, a deformation of the material under illumination [5]. The photostriction phenomenon opens new perspectives for combining several functionalities in future generations of remote switchable devices and is promising for the realization of light-induced actuators [5]. It has been recently observed in BFO under visible light [6,7]. A giant shear strain generated by femtosecond laser pulses was also reported [8,9], and time-resolved synchrotron diffraction reported a shift of the Bragg peak on a picosecond time scale in both bismuth ferrite [10] and lead titanate [11]. However, the microscopic mechanism responsible for photostriction is poorly understood [8,9]. Obviously, having accurate numerical techniques able to tackle photostriction will allow us to " shed some light " on this effect. However, to the best of our knowledge, such numerical tools allowing a systematic study of the photostriction phenomenon and its atomistic origin are not available yet, despite recent attempts to use Density Functional Theory (DFT) as a tool to fit x-ray absorption spectra in pump-probe photostriction experiments [12]. Here, we report the development of an ab initio procedure to compute photostriction from first principles. This procedure not only reproduces the order of magnitude of the observed change of lattice constant in BFO [6], but also reveals that photostriction mostly originates from the combination of the screening of the polarization by the electrons photoejected in the conduction band and the inverse piezoelectric effect. It is also found that photo-striction depends on the precise conduction state the electron is excited into, and on the crystallographic direction along which the effect is studied. In order to realize the difficulty in mimicking photo-striction, let us start by recalling that the Kohn-Sham (KS) implementation of DFT [13] reformulates the many-body problem of interacting electrons into many single-body problems, and " only " guarantees that the model noninter-acting KS Hamiltonian yields the same ground state density and energy as the real interacting Hamiltonian. Such a fact, therefore, leaves the description of unoccupied states within traditional DFT an unanswered question, and the determination of excitation energies remains the privilege of rather costly techniques, such as time-dependent DFT [14] or the GW approximation [15]. However, an alternative formulation of DFT that treats ground and excited states on the same footing has been proposed [16]. In particular, Ref. [16] connected each eigenstate of a real interacting Hamiltonian with the eigenstate of a model noninteracting Hamiltonian through a generalized adiabatic connection (GAC) scheme. The so-called ΔSCF method [17] takes advantage of this GAC scheme, and assumes an one-to-one correspondence between the excited states of a single Kohn-Sham system and the real system [16]. This ΔSCF scheme has proved successful and computationall

Two-lattice-vibration theory for proton transfer in cubic perovskites: Barium zirconate versus potassium tantalate

International audienceProton transfer (PT) in proton-conducting oxides is an intrinsically quantum phenomenon, due to the very strong quantization of the OH stretching vibration (ℏω~ 0.4 eV). Up to high temperatures, the proton is frozen in the ground state associated with the OH stretching motion, and thus does not undergo the thermal agitation for this vibration. Therefore, these are the thermal fluctuations of the (heavier) lattice atoms which make PT possible, at least above ~ half the Debye temperature of the lattice. These fluctuations may occasionally and randomly produce specific lattice configurations in which the quantum protonic ground levels in the two wells are equalized (coincidence), making PT possible, however with a certain probability. An analytical expression of this transfer probability may be obtained as the solution of a curve-crossing quantum-mechanical problem, and thus described by the Landau-Zener (LZ) formula. Two lattice vibrations play a fundamental role in intra-octahedral PT: (i) a reorganization of the lattice, that sends the protonated system from its initial self-trapped configuration up to the coincidence manifold, and (ii) a reduction of the (donor) oxygen - (acceptor) oxygen distance Q, which facilitates PT by leading the system to coincidence configurations with smaller proton barrier, and thus larger LZ probability. In cubic perovskites, the set of the coincidence configurations plays the role of the transition state for PT. The implementation of this theory of proton transfer [G. Geneste, Solid State Ionics 323, 172 (2018)] is here strongly improved on several points: description of the coincidence configurations, proton zero-point energies and proton potential at coincidence. It is then re-applied to barium zirconate (BZO), and also to potassium tantalate (KTO), with parameters derived from density-functional theory (DFT) calculations. The theory confirms the adiabatic PT regime in BZO, common to most proton conductors, with a negligible contribution of non-adiabatic tunneling transfers to the transfer rate. In KTO, by contrast, the relative contribution of non-adiabatic tunneling transfers is larger than in BZO, especially below ~ 250–300 K. The present work helps to characterize intrinsic features common to most proton conductors, at least from the point of view of proton mobility within the lattice. The activations energies for proton transfer at high temperature are predicted at 0.11 eV (BZO) and 0.25 eV (KTO)

Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

International audienceThe radio-frequency dielectric response of the lead-free BaðZr 0.5 Ti 0.5 ÞO 3 relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio–based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors. Relaxors with a perovskite structure form an important family of functional materials that exhibit intriguing dielectric properties [1,2]: the real part of the frequency-dependent dielectric permittivity has a maximum with temperature, at T max , while the system remains macro-scopically paraelectric down to the lowest temperature, and T max depends on the frequency of the applied electric field, a phenomenon called dielectric relaxation. Different suggestions have been proposed to explain these macroscopic properties, such as nonlocal (electric or elastic) random fields (RFs) (electric or elastic fields on site i depending on the chemical disorder surrounding i) [3], and the possible existence and interplay of polar nanoregions (PNRs), i.e., polar instabilities that correlate the elementary dipoles on a few lattice constants. The location and properties of these PNRs would be dependent on the local chemical disorder that relaxors can exhibit on one of their sublattices [4]. The dynamics of the electric dipoles of such structures is believed to be associated with characteristic times much larger than typical atomic times, and being temperature dependent (as a result of thermal activation). These large time scales are responsible for the frequency dependence of the dielectric permittivity in the radio-frequency domain (from kHz up to several tens of MHz). Recently, microscopic description of relaxors, based on model Hamiltonians derived from first principles coupled to Monte Carlo (MC) or molecular dynamics (MD) simulations , have provided precious information about the effect of RFs on relaxor properties and the nature of these PNRs [5–12]. In heterovalent relaxors such as PbMg 1=3 Nb 2=3 O 3 (PMN) [13–16], the PNRs are suggested to arise from complex phenomena including strong nonlocal electric RFs [17,18]. In contrast, in homovalent relaxors such as BaðZr; TiÞO 3 (BZT), Ref. [9] numerically found that PNRs appear in regions where the chemical species driving the polar instability (Ti) is more abundant; i.e., it is the local RFs arising from the difference in polarizability between Ti and Zr ions that induce relaxor behavior, while nonlocal electric and elastic RFs have a rather negligible effect. Note that local RFs can lead to very long relaxation times in disordered magnets [19], which may also be the case for relaxors [15]. In order to gain a deeper understanding of relaxor ferroelectrics, it is highly desired to have numerical schemes that are able to simulate the most striking characteristics of relaxors, i.e., the radio-frequency dielec-tric relaxation. However, to the best of our knowledge, such schemes do not exist. One reason behind this paucity is that MD simulations are limited to a few nanoseconds, and thus cannot give access to the time scales required to mimic the radio-frequency dielectric response of relaxors. However, the kinetic Monte Carlo (KMC) method, which we recently applied to simulate the radio-frequency dielectric response of Li-doped KTaO 3 (KLT) [20], is able to reproduce such time scales. Nevertheless, in KLT, the elementary processes driving the dielectric response involve few degrees of freedom (hoppings of individual Li impurities), with rather temperature-independent energy barriers [20], two assumptions clearly not obeyed in relaxor ferroelectrics; this is evidenced, e.g., by the fact that PNRs do not exist above the Burns temperature and that the processes responsible for the dielectric response involve the collective motion of several microscopic degrees of freedom, since a PNR should extend over several unit cells

Mécanismes élémentaires de la croissance oxyde sur oxyde (étude ab initio et semi-empirique de MgO/MgO(001))

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF

Surface polarization, rumpling, and domain ordering of strained ultrathin BaTiO 3 (001) films with in-plane and out-of-plane polarization

International audienceBaTiO 3 ultrathin films (thickness ≈ 1.6 nm) with in-and out-of-plane polarization are studied by first-principles calculations. Out-of-plane polarization is simulated using the method proposed by Shimada et al. [Phys. Rev. B 81, 144116 (2010)], which consists in building a supercell containing small domains with alternating up and down polarization. This allows one to investigate the properties of defect free BaTiO 3 ultrathin films with polarization perpendicular to the surface, as a function of in-plane lattice constant, i.e., epitaxial strain. The configurations with polarization perpendicular to the surface (c phase) are found stable under compressive strain, while under tensile strain, the polarization tends to lie in-plane (aa phase), along [110]. In the c phase, the most stable domain width is predicted to be 1 to 2 lattice constants, and the magnitude of the surface rumpling varies according to the direction of the polarization (upwards versus downwards), though its sign is unchanged, the oxygen anions pointing in all cases outwards. Finally, all the surfaces studied are found to be insulating. Analysis of the atom-projected electronic density of states gives insight into the surface contributions to the electronic structure. An important reduction of the Kohn-Sham band gap is predicted at TiO 2 terminations in the c phase (≈ 1 eV with respect to the aa phase). The Madelung potential at the surface plays the dominant role in modifications of the surface electronic structure

Competition between elastic and chemical effects in the doping, defect association, and hydration of barium stannate

International audienceDensity-functional theory calculations are performed to examine how two characteristics of a trivalent dopant (the one, physical – the ionic radius, the other, chemical – the electronegativity) impact the thermodynamics of doping, the defect association energy and the hydration energy in barium stannate, a perovskite oxide candidate as an electrolyte for Solid Oxide or Protonic Ceramic Fuel Cells. The formation energies of several trivalent dopants currently used in experimental works are computed in different external conditions and on the two possible sites (Ba, Sn), in their ionized state. These dopants cover a wide range of ionic radii (from 0.62 to 1.03 Å) and can be divided in two families according to their electronegativity: elements of group IIIA (Ga, In), versus IIIB transitions metals and Rare Earths (Sc, Lu, Y, Gd, Sm, La). The oxygen vacancy and the protonic defect are also studied, either isolated or in the vicinity of the dopant substituted on Sn site (1st & 2nd neighbors). The association energy between the dopant and both the oxygen vacancy and the proton, as well as the formation energy of the dopant on the Ba site, are mainly governed by the ionic radius of the dopant, with the exception that electronegative dopants stabilize more the oxygen vacancy in their vicinity. Therefore, a subtle interplay between elastic effects and chemistry is found to control the hydration energy/enthalpy, the more electronegative dopants – indium particularly – producing, at given radius, a less stable hydrated state. We provide with general trends likely to help experimentalists in the design of new materials, regarding the choice of dopant

Hole polarons in LaFeO 3 and La1−x_{1−x}Srx_xFeO3−δ_{3−δ} : Stability, trapping, mobility, effect of Sr concentration, and oxygen vacancies

International audienceThe stability, trapping and mobility of electron holes are investigated in lanthanum ferrite LaFeO$_3$ , and in La$_{1−x}$Sr$_x$FeO$_{3−δ}$ ($x$ ≈ 0.1, 0.4 and 0.6) by hybrid-density-functional and densityfunctional-theory $+ U$ calculations. In pure LaFeO$_3$ , the electron hole is more stable under a localized (polaronic) form than under a delocalized form, the energy difference (self-trapping energy) lie between ≈-0.3 and-0.4 eV. This self-trapped hole polaron is not strictly localized on a single Fe atom: instead, it occupies a quantum state made of a 3d orbital of a Fe atom, strongly hybridized with 2$p$ orbitals of four neighboring oxygens. The hole polaron is thus localized on five atoms (among which one single Fe), which can be described as the Fe$^{3+}$ oxidation into Fe$^{4+}$. Electron hole transport results from the combination of onsite reorientations and hoppings, with energy barriers estimated at ≈0.01–0.20 eV and 0.3–0.4 eV, respectively. The aliovalent substitution of lanthanum by strontium in LaFeO$_3$ induces the presence of localized electron holes, preserving the insulating character of La$_{1−x}$Sr$_x$FeO$_3$, regardless of the studied Sr concentration. The formation energy of the oxygen vacancy in La$_{1−x}$Sr$_x$FeO$_3$ (x ≈ 0.1 and 0.4) is estimated at ≈ +0.8 eV. This value is here successfully use to quantify the evolution of defect concentration as a function of the oxygen partial pressur

Reply to the ‘Comment on “Proton transport in barium stannate: classical, semi-classical and quantum regime”’

International audienceWe respond to the erroneous criticisms about our modeling of proton transport in barium stannate [G. Geneste et al., Phys. Chem. Chem. Phys., 2015, 17, 19104]. In this previous work, we described, on the basis of density-functional calculations, proton transport in the classical and semi-classical regimes, and provided arguments in favor of an adiabatic picture for proton transfer at low temperature. We re-explain here our article (with more detail and precision), the content of which has been distorted in the Comment, and reiterate our arguments in this reply. We refute all criticisms. They are completely wrong in the context of our article. Even though a few of them are based on considerations probably true in some metals, they make no sense here since they do not correspond to the content of our work. It has not been understood in the Comment that two competitive configurations, associated with radically different transfer mechanisms, have been studied in our work. It has also not been understood in the Comment that the adiabatic regime described for transfer occurs in the protonic ground state, in a very-low barrier configuration with the protonic ground state energy larger than the barrier. Serious confusion has been made in the Comment with the case of H in metals like Nb or Ta, leading to the introduction of the notion of (protonic) “excited-state proton transfer”, relevant for H in some metals, but (i) that does not correspond to the (ground state) adiabatic transfers here described, and (ii) that does not correspond to what is commonly described as the “adiabatic limit for proton transfer” in the scientific literature. We emphasize, accordingly, the large differences between proton transfer in the present oxide and hydrogen jumps in metals like Nb or Ta, and the similarities between proton transfer in the present oxide and in acid–base solutions. We finally describe a scenario for proton transfer in the present oxide regardless of the temperature regime