Relaxed Surface Energies Research Articles

Surface Energies of LaMnO3 High-Index Surfaces Obtained from Density-Functional Theory

The first six cubic LaMnO3 high-index surfaces, (210), (211), (221), (310), (311), and (320), are examined for the first time. The unrelaxed and relaxed surface energies of the surfaces are computed as a function of surface model thickness using unrelaxed and relaxed surface models, respectively. The (210), (320), (211), and (221) surfaces are found to be more stable than the low-index (011) and (111) surfaces. Helping to explain this result, the surface terminations of the (210), (320), (211), or (221) surface are seen to exhibit a rotational relaxation of the MnO6 or oxygen octahedra extending from the surface into the bulk. By contrast, the relaxed surface energies of the (310) and (311) surfaces are concluded to be difficult to determine due to a structural transformation or phase change in the surface models of the surfaces away from cubic LaMnO3. The finding of a phase change is important. It indicates that a phase change in the surface models of a surface for another material could occur if the surface is relatively open and a different phase of the material is stable at low temperature. When modeling such a surface, two steps are suggested to be taken.

WhereWulff: A Semiautonomous Workflow for Systematic Catalyst Surface Reactivity under Reaction Conditions.

This paper introduces WhereWulff, a semiautonomous workflow for modeling the reactivity of catalyst surfaces. The workflow begins with a bulk optimization task that takes an initial bulk structure and returns the optimized bulk geometry and magnetic state, including stability under reaction conditions. The stable bulk structure is the input to a surface chemistry task that enumerates surfaces up to a user-specified maximum Miller index, computes relaxed surface energies for those surfaces, and then prioritizes those for subsequent adsorption energy calculations based on their contribution to the Wulff construction shape. The workflow handles computational resource constraints such as limited wall-time as well as automated job submission and analysis. We illustrate the workflow for oxygen evolution reaction (OER) intermediates on two double perovskites. WhereWulff nearly halved the number of Density Functional Theory (DFT) calculations from ∼240 to ∼132 by prioritizing terminations, up to a maximum Miller index of 1, based on surface stability. Additionally, it automatically handled the 180 additional resubmission jobs required to successfully converge 120+ atoms systems under a 48-h wall-time cluster constraint. There are four main use cases that we envision for WhereWulff: (1) as a first-principles source of truth to validate and update a closed-loop self-sustaining materials discovery pipeline, (2) as a data generation tool, (3) as an educational tool, allowing users (e.g., experimentalists) unfamiliar with OER modeling to probe materials they might be interested in before doing further in-domain analyses, (4) and finally, as a starting point for users to extend with reactions other than the OER, as part of a collaborative software community.

Insights into the structures, energies and electronic properties of nesquehonite surfaces by first-principles calculations

By using the first-principles calculations, the structure, energies and electronic properties of four commonly exposed surfaces for the nesquehonite crystal were investigated. The needle-like nesquehonite whisker is well developed with smooth side faces and irregular hexagonal end faces. Surface energy results indicate that the (101) surface is the most stable surface and corresponds to the side face. The density of dangling bond has a positive relationship with surface energy and the (101) surface has the least dangling bonds. In terms of relaxed surface energy, the order of relaxed surfaces is (101) < (200)-H < (301) < (200)-M < (004). During surface relaxation, the changes in the length of Mg-O bonds and hydrogen bonds contribute to generating a more stable surface with a lower surface energy. The PDOS (partial density of states) of these surfaces are mainly dominated by Mg and O atoms. A small peak value is found in the PDOS of (101) and (301) surfaces, which have less exposed Mg-O bonds. Electron transfer causes changes in the length of Mg-O bonds. A more active surface will obtain a larger value of transferred electrons during surface relaxation.

New LaMnO3 surface energy results obtained from density-functional theory

The surface energies of cubic LaMnO3 (001), (011), and (111) surfaces are computed as a function of surface model thickness using both asymmetric and symmetric surface models. A new procedure is used to avoid the divergence of the surface energy with increasing model thickness. In the literature, certain relaxed surface energies have been reported for the (001) surface that are significantly different and for the (011) surface that are significantly different. Using the results of this work, these different surface energies for the (001) and (011) surfaces can be explained.

The dynamic cleavage energy of brittle single crystals

Crack initiation in brittle materials is usually dictated by the energy required to create two new surfaces. This energy is known as Griffith barrier and equals twice the free and relaxed surface energy, 2γs. This value is usually taken as the cleavage energy for crack propagation as well. We investigated, experimentally, the fundamentals of cracks dynamics in brittle single crystals, with emphasis on the cleavage energy at initiation and during propagation. Silicon single crystal, which has a diamond cubic symmetry, served as a model material. The experiments were performed using the Coefficient of Thermal Expansion Mismatch method (CTEM), developed in our laboratory in recent years. The CTEM method possesses the advantage of controlling the quasi-static energy release rate (ERR) gradient to the crack front, dG0/da, denoted here Θ.The cleavage energies at initiation and propagation of dynamic cracks on two Low-Energy Cleavage Systems (LECSs) of brittle silicon crystal, (110)[11¯0] and (111)[112¯], were evaluated by comparing the experimental energy–speed relationship with the theoretical one, manifested by Freund theory for cracks dynamics, known as Freund equation of motion. The ERR, G0, was evaluated using quasi-static, anisotropic Finite Element Analysis (FEA), and the crack speed was measured using Potential Drop Technique (PDT).The experiments revealed that the energy required to initiate and propagate a crack is governed by Θ. When Θ > 0.7 J/m2mm, the cleavage energy at initiation is higher than 2γs and linearly increase with increasing Θ for both LECSs of silicon. Surprisingly, the cleavage energy for initiation and propagation remain constant during the event of fracture for a prescribed Θ, meaning, it is not crack speed dependent. Moreover, we show that all the variables participating dynamic cleavage are linearly dependent on Θ, which provides the evidences that the ERR gradient is the controlling variable governs cracks dynamics.Finally, we suggest that the physics of the above fundamental behavior is laying on the way crack initiate and propagate at the atomistic scale, i.e., the bond breaking mechanisms in form of kinks.

Rutile (β-)MnO2 Surfaces and Vacancy Formation for High Electrochemical and Catalytic Performance

MnO2 is a technologically important material for energy storage and catalysis. Recent investigations have demonstrated the success of nanostructuring for improving the performance of rutile MnO2 in Li-ion batteries and supercapacitors and as a catalyst. Motivated by this we have investigated the stability and electronic structure of rutile (β-)MnO2 surfaces using density functional theory. A Wulff construction from relaxed surface energies indicates a rod-like equilibrium morphology that is elongated along the c-axis, and is consistent with the large number of nanowire-type structures that are obtainable experimentally. The (110) surface dominates the crystallite surface area. Moreover, higher index surfaces than considered in previous work, for instance the (211) and (311) surfaces, are also expressed to cap the rod-like morphology. Broken coordinations at the surface result in enhanced magnetic moments at Mn sites that may play a role in catalytic activity. The calculated formation energies of oxygen vacancy defects and Mn reduction at key surfaces indicate facile formation at surfaces expressed in the equilibrium morphology. The formation energies are considerably lower than for comparable structures such as rutile TiO2 and are likely to be important to the high catalytic activity of rutile MnO2.

Morphology and surface structure of cubic BaTiO&lt;sub&gt;3&lt;/sub&gt; using first-principles density functional theory

First-priciples density functional theory (DFT) techniques are used to provide atomic-scale insight into the surface structures and crystal morphologies of cubic barium titanate, BaTiO3. Relaxed surface structures and energies are calculated for 3 low index planes and resulting equilibrium morphology based on Wulff’s theorem with {001} and {011} faces were constructed. The calculated surface energies are strongly dependent on the coordination loss of TiO6 octahedra at the surface. The optimized structure at the low-energy surfaces shows that only atoms at 1st perovskite layer are displaced from ideal position, while no significant displacements are indicated. On the other hand, the Bader charge analysis shows that the ionicity of whole the cations in the slab (7 perovskite layers) is larger than that in the bulk. Therefore, change of electric property is expected at the surface region, which is not due to the surface reconstruction, but to the change of electronic structure.

The half-metallic properties of the (110) and (001) surfaces of rocksalt VPo: A first-principles study

In this paper, we conduct a theoretical study of the half-metallic properties of the bulk and the (110) and (001) surfaces of rocksalt VPo with an equilibrium lattice constant of 0.59nm. The calculations are done using the first-principles full-potential linearized augmented plane–wave method based on the density functional theory. We show that both the (110) and (001) surfaces of rocksalt VPo preserve the bulk half-metallicity, and the atomic magnetic moments at both the (110) and (001) surfaces are increased compared to those in bulk VPo. Moreover, by calculating the relaxed surface energies, we assess the surface stability, and find that both (110) and (001) surfaces are not stable in equilibrium conditions, and non-equilibrium growth techniques are required for the realization of rocksalt VPo thin films.

Tunable magnetism and half-metallicity in bulk and (1 0 0) surface of quaternary Co2MnGe1−xGax Heusler alloy

The structural, magnetic and half-metallic properties of the bulk and (1 0 0) surface of quaternary Heusler alloy Co2MnGe1−xGax are investigated from the first-principles calculations. For the bulk, the lattice constant and total magnetic moment follow the Vegard law and Slater–Pauling rule well, respectively. Except for Co2MnGa, the Co2MnGe1−xGax series are half-metallic. Because the Fermi level of Co2MnGe0.5Ga0.5 is just located at the middle of the minority-spin gap, we predict that it bears the most robust half-metallicity as against remnant doped alloys. As for the Co2MnGe1−xGax(1 0 0) surface, the analyses on relaxed atomic positions and surface energies reveal that Co–Ge and Co–Ga bonding are more favourable than Co–Mn bonding and the terminations involving surface Mn atoms are more stable than CoCo terminations. By comparing with the bulk values, the surface Co and Mn magnetic moments are enhanced obviously. The calculated PDOS of all accessible ‘ideal’ surfaces show that the half-metallicity observed in bulk has been destroyed by the surface states, which is a possible reason why the tunnel magnetoresistence steeply drops as temperature increases. However, in the pure atomic terminations the surface properties can be slightly adjusted by the Ga-doped concentrations in bulk through the dipolar interaction. As a result, in the MnMn termination of Co2MnGe0.5Ga0.5(1 0 0) the spin polarization of 1 0 0% is detected, indicating that in the pure Mn atomic termination the half-metallicity of the (1 0 0) surface can remain if the corresponding bulk presents excellent half-metallic stability. Thus we predict that this thin film will present a higher potential for applications in ferromagnetic electrodes.

Theoretical Equilibrium Shape of Calcite. 2. [4̅41] Zone and Its Role in Biomineralization

The Hartman–Perdok analysis on the ⟨441⟩ zone of calcite was carried out, and the calculation of the surface and attachment athermal energies was performed on both unrelaxed and relaxed surfaces by using the interatomic Rohl potential and the GULP simulation code. The flat (F) character of the {1014} and {1120} forms and the stepped (S) character of the {0118} and {2134} forms contradict the observed occurrence frequency of natural crystals: {2134} > {0118} > {1014} > {1120}. A minor reduction of the relaxed surface energy values of both {0118} and {2134} forms could be sufficient to make the theoretical equilibrium shape of the crystal composed by the {1014}, {0112}, {1010}, {0001}, {0118}, and {2134} forms, which can explain the richness of the growth morphology of calcite, even if water adsorption is not considered. The theoretical analysis is focused on the {2134} scalenohedron to understand the adsorption of the enantiomers of some amino acids. Epitaxy models are described: (i) betwe...

Molecular dynamics simulation study on surface structure and surface energy of anatase

Molecular dynamics simulations were performed to investigate the relaxed structures and surface energies of perfect and pit anatase TiO2 surfaces. It is shown that the slab containing more than two unit-cell layers away from the fixed layer expresses the surface characteristics of perfect anatase TiO2 (1 0 1) and (1 0 0) surfaces well, while the slab containing more than one unit-cell layer away from the fixed layer expresses the surface characteristics of the (0 0 1) surface well. Their surface energies follow the sequence (0 0 1) < (1 0 1) < (1 0 0). Simulation results also indicate that the pit edges expose many undercoordinated atoms, and the more highly undercoordinated atoms exhibit the larger displacement vectors. Moreover, the surface energy of the pit surface is higher than that of the perfect surface. The surface energies of pit anatase (1 0 1) surfaces are linearly related to the pit sizes along the [] and [0 1 0] directions, and the changes in their surface energies are less than 0.05 J m−2, while the surface energies increase sharply with the increase in pit depth within 1 nm. Therefore, for anatase (1 0 1) surface, in order to obtain a higher surface energy, one may increase the pit sizes, particularly along the [1 0 1] direction.

Surface reconstructions and relaxation effects in a centre-symmetrical crystal: the {00.1} form of calcite (CaCO3)

Reconstructing polar surfaces of crystals represents the pathway needed to obtain both surface stability and minimum of surface free energy. Knowing these equilibrium conditions is, in turn, necessary to interpret surface kinetics, especially when foreign adsorption or epitaxial phenomena are involved. Here we reconstructed the {00.1} dipolar surfaces of a centre-symmetrical crystal, calcite (CaCO3), either by removing one half of the ions in the outermost layer of the face, or by applying calcite to the octopolar Lacmann's model, already proposed for NaCl-like lattices. This second way respects the bulk symmetry of the crystal and was carried out by removing ¾ of the ions in the outermost layer and ¼ in the second to last one, respectively. Relaxed and athermal surface energies were determined at the empirical level and the octopolar CO3 terminated {00.1} form was the most stable. Moreover, calculation shows that the {00.1} form, along with the {10.4} and {01.2} rhombohedra, can enter the athermal equilibrium morphology of the calcite crystal. Finally, when recollecting our results on the reconstructed {01.2} form of calcite and {111} NaCl octahedron, it can be stressed that the bulk crystal symmetry has to be considered if one aims to achieve the self consistency of the surface reconstruction (Curie's principle).

Surface sp half-metallicity of zinc-blende calcium monocarbide

Recent studies by Gao et al. [Phys. Rev. B 75, 174442 (2007)] indicate zinc-blende CaC, SrC, and BaC exhibit robust sp half-metallic ferromagnetism with Curie temperatures higher than room temperature. Here we further investigate the surface electronic and magnetic properties of CaC by using the first-principles full-potential linearized augmented plane-wave method. The (001) surfaces terminated with Ca and C, respectively, and the (110) surface terminated with both Ca and C are considered. We discuss the surface stabilities from the calculated relaxed surface energies. Electronic structure calculations indicate that the half-metallicity is destroyed for both the Ca- and C-terminated (001) surfaces; however, the (110) surface preserves the half-metallic characteristic of the bulk CaC. We further reveal that the atomic magnetic moments of the (001) surfaces are greatly different from the bulk values, but the difference of atomic magnetic moments between the (110) surface and the bulk CaC is very small.

Atomistic simulation of the surface structure of electrolytic manganese dioxide

Atomistic simulation methods were used to investigate the surface structures and stability of pyrolusite and ramsdellite polymorphs of electrolytic manganese dioxide (EMD). The interactions between the atoms were described using the Born model of Solids. This model was used to calculate the structures and energies of the low index surfaces {0 0 1}, {0 1 0}, {0 1 1}, {1 0 0}, {1 0 1} and {1 1 0} for both pyrolusite and ramsdellite. Pyrolusite is isostructural with rutile and similar to rutile the {1 1 0} surface is found to be the most stable with the relaxed surface energy 2.07 J m −2. In contrast, for ramsdellite the {1 0 1} surface is the most stable with a surface energy of 1.52 J m −2. Pyrolusite {1 0 0} and ramsdellite {1 0 0} b surfaces have equivalent energies of 2.43 J m −2 and 2.45 J m −2, respectively and similar surface areas and hence are the likely source for the intergrowths. Finally, comparison of the energies of reduction suggests that the more stable surfaces of pyrolusite are more easily reduced.

Relative stability of low-index V2O5 surfaces: a density functional investigation

Ab initio density functional calculations of the structural and electronic properties ofV2O5 bulk and its low-index surfaces are presented. For the bulk oxide and the (010) surface (thenatural cleavage plane) a good agreement with experiment and with earlier ab initiocalculations is found. For the first time, the investigations are extended to otherlow-index surfaces: (001) and (100). On both surfaces, termination conserving abulk-like stoichiometry is preferred, but—in contrast to the (010) surface—a strongstructural relaxation takes place. Relaxation reduces the surface energy from 1.16 to0.48 J m−2 for the (001) andfrom 0.61 to 0.55 J m−2 for the (100) surface. Although the relaxed surface energies are stillone order of magnitude higher than calculated for the (010) surface(0.047 J m−2), theWulff construction demonstrates that (001) and (100) surfaces contribute about 15% of the total surfacearea of a V2O5 crystallite, indicating a non-negligible role in the catalytic activity ofV2O5.

Molecular dynamics study on surface structure and surface energy of rutile TiO 2 (1 1 0)

The formula for surface energy was modified in accordance with the slab model of molecular dynamics (MDs) simulations, and MD simulations were performed to investigate the relaxed structure and surface energy of perfect and pit rutile TiO 2(1 1 0). Simulation results indicate that the slab with a surface more than four layers away from the fixed layer expresses well the surface characteristics of rutile TiO 2 (1 1 0) surface; and the surface energy of perfect rutile TiO 2 (1 1 0) surface converges to 1.801 ± 0.001 J m −2. The study on perfect and pit slab models proves the effectiveness of the modified formula for surface energy. Moreover, the surface energy of pit surface is higher than that of perfect surface and exhibits an upper-concave parabolic increase and a step-like increase with increasing the number of units deleted along [0 0 1] and [1 1 0], respectively. Therefore, in order to obtain a higher surface energy, the direction along which atoms are cut out should be chosen in accordance with the pit sizes: [ 1 ¯ 1 0 ] direction for a small pit size and [0 0 1] direction for a big pit size; or alternatively the odd units of atoms along [1 1 0] direction are removed.

Density Functional Theory Study on the Structural and Electronic Properties of Low Index Rutile Surfaces for TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 Composite Systems

The present study is concerned with the structural and electronic properties of the TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 composite systems. Periodic quantum mechanical method with density functional theory at the B3LYP level has been carried out. Relaxed surface energies, structural characteristics and electronic properties of the (110), (010), (101) and (00) low-index rutile surfaces for TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 models are studied. For comparison purposes, the bare rutile TiO2 and SnO2 structures are also analyzed and compared with previous theoretical and experimental data. The calculated surface energy for both rutile TiO2 and SnO2 surfaces follows the sequence (110) < (010) < (101) < (001) and the energy increases as (010) < (101) < (110) < (001) and (010) approximately = (110) < (101) < (001) for SnO2/TiO2/SnO2 and TiO2/SnO2/TiO2 composite systems, respectively. SnO2/TiO2/SnO2 presents larger values of surface energy than the individual SnO2 and TiO2 metal oxides and the TiO2/SnO2/TiO2 system renders surface energy values of the same order that the TiO2 and lower than the SnO2. An analysis of the electronic structure of the TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 systems shows that the main characteristics of the upper part of the valence bands for all the studied surfaces are dominated by the external layers, i.e., by the TiO2 and the SnO2, respectively, and the topology of the lower part of the conduction bands looks like the core layers. There is an energy stabilization of both valence band top and conduction band bottom for (110) and (010) surfaces of the SnO2/TiO2/SnO2 composite system in relation to their core TiO2, whereas an opposite trend is found for the same surfaces of the TiO2/SnO2/TiO2 composite system in relation to the bare SnO2. The present theoretical results may explain the growth of TiO2@SnO2 bimorph composite nanotape.

Theoretical structure and surface energy of the reconstructed {01.2} form of calcite (CaCO 3) crystal

Two different reconstructions of the (01.2) face (Ca or CO 3 terminated) of calcite (CaCO 3) were studied: (i) R1 reconstruction: the outermost layer is based on the [0 1 0] × 1/3[2 1 1] rectangular mesh, which is symmetrical with respect to the c glide plane of the crystal, thus fulfilling the 2D symmetry of the face and (ii) R2 reconstruction: the outermost layer is based on a 1 / 6 [ 4 2 1 ¯ ] × 1 / 6 [ 2 2 ¯ 1 ] lozenge shaped mesh that does not respect the 2D symmetry of the face. The ( 01.2 ) R 1 Ca , ( 01.2 ) R 1 CO 3 , ( 01.2 ) R 2 Ca and ( 01.2 ) R 2 CO 3 slabs geometry optimizations of calcite (CaCO 3) were performed either at DFT level or by using empirical potentials; the results obtained with these two different calculation methodologies are in good agreement. With respect to their arrangement in the bulk, the CO 3 groups of the outermost layer are significantly rotated about the crystallographic a-axis and about the normal to the 01.2 plane; further, the thickness of the outermost layer is significantly lower than that of the underneath ones. The surfaces energies ( γ) at 0 K, for relaxed and unrelaxed ( 01.2 ) R 1 Ca , ( 01.2 ) R 1 CO 3 , ( 01.2 ) R 2 Ca and ( 01.2 ) R 2 CO 3 faces, were determined either at DFT level or by using empirical potentials. Independently of the method of calculation employed, the stability order of the relaxed faces is ( 01.2 ) R 1 CO 3 < ( 01.2 ) R 2 Ca < ( 01.2 ) R 2 CO 3 < ( 01.2 ) R 1 Ca . Concerning the unrelaxed faces, whose energies were evaluated by using empirical potentials only, the stability order is instead ( 01.2 ) R 1 Ca < ( 01.2 ) R 2 Ca < ( 01.2 ) R 1 CO 3 < ( 01.2 ) R 2 CO 3 ; such different ordering shows the importance of geometry relaxation in the calculation of the surface energy. The values of the relaxed surface energies are γ ( 01.2 ) R 1 CO 3 ≈ 750 , γ ( 01.2 ) R 2 Ca ≈ 950 , γ ( 01.2 ) R 2 CO 3 ≈ 980 and γ ( 01.2 ) R 1 Ca ≈ 1050 erg/cm 2.

Structures and Surface Energies of (100) and Octopolar (111) Faces of Halite (NaCl): an Ab initio Quantum-Mechanical and Thermodynamical Study

The structures of the (100), octopolar (111) Na-terminated [(111)Na], and (111) Cl-terminated [(111)Cl] surfaces of halite (NaCl) were determined by means of ab initio quantum mechanical calculations (density functional theory, DFT). The (111) surfaces show higher surface relaxation with respect to the (100) surface. The surface energies (γ) at T = 0 K for relaxed and unrelaxed (100) and (111) faces were determined at DFT level. The values of the surface energy for the relaxed faces are γ(100) = 160, γ(111)Cl = 390 and γ(111)Na = 405 erg/cm2; therefore, the stability order of relaxed surfaces reads: (100) < (111)Cl < (111)Na. For the unrelaxed faces, the surface energies are higher: γ(100) = 161, γ(111)Cl = 552 and γ(111)Na = 551 erg/cm2.To check if the octopolar (111) faces can belong to the equilibrium morphology of the crystal/vapor system, the relaxed surface energies at T > 0 K were calculated by considering both the vibrational motion of atoms and the surface configurational entropy. From these calculations it resulted that the octopolar (111)Na and (111)Cl faces cannot belong to the equilibrium morphology. Octopolar reconstruction and both surface vibrational and configurational entropy then allow us to explain why the {111} NaCl form cannot enter the equilibrium shape of the crystal.

Surface structures and crystal morphologies of LiFePO4: relevance to electrochemical behaviour

Advanced simulation techniques are used to provide atomic-scale insight into the surface structures and crystal morphologies of the lithium battery cathode material LiFePO4. Relaxed surface structures and energies are reported for 19 low index planes. The calculated equilibrium morphology takes on a rounded, isometric appearance, with {010}, {201}, {011}, and {100} faces prominent. Almost all of the low energy surfaces are lithium-deficient relative to the bulk lattice, requiring Li vacancies at the surface. The calculated growth morphology exhibits the {010}, {100} and {101} faces, with an elongated hexagonal prism-like shape; this morphology is more consistent with experimentally observed LiFePO4 particles. The exposure of the (010) surface in our calculated equilibrium and growth morphologies is significant since it is normal to the most facile pathway for lithium ion conduction (along the [010] channel), and hence important for the reversible insertion/de-insertion of lithium ions. SEM images of plate-like crystallites from hydrothermal synthesis are also simulated by our methods, and exhibit large (010) faces.