Predicted Surface Energy Research Articles

Calculating the surface energies of crystals on a face-specific and whole particle basis: Case study of the α- and β-polymorphic forms of L-glutamic acid

Molecular-scale modelling for predicting surface energies on a face-specific and whole particle basis is applied to all the crystallographically-independent surfaces of L-glutamic acid forms. The predicted data is found to be in good general agreement with measured surface energies using inverse gas chromatography and Washburn capillary rise techniques with the former revealing higher values compared to the prediction, perhaps consistent with the polar (zwitterionic) nature of this material. This fusion of experimental and computational data provides a high-fidelity definition of the face-by-face breakdown of the energetic anisotropy of the crystals. There is increasing industrial interest in defining the potential impact of whole particle properties on the performance of formulated drug product and their manufacturability especially as the community accelerates the molecule to medicine journey. The overall molecular modelling approach highlights its application in designing ingredients for optimising face-specific particle surface energies for product formulatability particularly in early phase process development.

Surface energy calculation of brookite TiO2 using Inverse Wulff Construction

The Wulff construction methodology proves to be a highly useful approach in predicting the morphologies of nanoparticles. However, this approach requires the precise determination of surface energies for all orientations, which can be a challenging task due to the inherent complexity of measuring surface-free energies. In this work, the inverse Wulff construction is employed to effectively predicted surface energies from brookite TiO2 particle morphologies. This method can provide guidance for researchers to understand how to control the brookite TiO2 crystal morphology according to the synthetic method used.

Machine learning on properties of multiscale multisource hydroxyapatite nanoparticles datasets with different morphologies and sizes

Machine learning models for exploring structure-property relation for hydroxyapatite nanoparticles (HANPs) are still lacking. A multiscale multisource dataset is presented, including both experimental data (TEM/SEM, XRD/crystallinity, ROS, anti-tumor effects, and zeta potential) and computation results (containing 41,976 data samples with up to 9768 atoms) of nanoparticles with different sizes and morphologies at density functional theory (DFT), semi-empirical DFTB, and force field, respectively. Three geometric descriptors are set for the explainable machine learning methods to predict surface energies and surface stress of HANPs with satisfactory performance. To avoid the pre-determination of features, we also developed a predictive deep learning model within the framework of graph convolution neural network with good generalizability. Energies with DFT accuracy are achievable for large-sized nanoparticles from the learned correlations and scale functions for mapping different theoretical levels and particle sizes. The simulated XRD spectra and crystallinity values are in good agreement with experiments.

Role of brine composition on rock surface energy and its implications for subcritical crack growth in calcite

Subcritical crack growth in calcite-bearing reservoirs plays a vital role in rock deformation. Published experimental results show that fluid-rock interaction likely affects rock surface energy and triggers fracture propagation. However, much of research up to now has been only descriptive in nature, impairing a substantial interpretation to predict subcritical crack growth. In this study, we developed a physicochemical model to relate fluid-calcite interaction in particular surface potential to surface energy in light of capacitance theory. To test the model, we calculated calcite surface chemical species and surface potential as a function of pH, ion type and fluid salinity using surface complexation modeling. Moreover, we compared the predicted surface energy with Bergsaker et al.'s experimental measurements.Our results confirm that fluid chemistry would affect calcite surface species distribution and surface energy. At high acidic condition, lowering salinity increases surface potential of brine-calcite. At alkaline condition, lowering salinity decreases surface potential in the presence of MgSO4 and MgCl2 but increases that of Na2SO4. Furthermore, pH would affect the level of bonding-capable divalent such as Ca2+ through the equilibrium of calcite dissolution-precipitation, and thus indirectly influence surface energy. Our results unveil the importance of fluid-rock interaction on subcritical crack growth and shed light on hydrocarbon exploitation and CO2 capture and storage in carbonate reservoirs. These findings also delineate the inner connection between geochemical and geo-mechanical properties at subsurface.

First‐principles study of the atomic structures, electronic properties, and surface stability of BaTiO3 (001) and (011) surfaces

The atomic structures, electronic properties, and surface stability of (001) and (011) surfaces of BaTiO3 are studied by first‐principles calculations. Four differently terminated BaTiO3 surfaces are considered in this study, including (001)‐BaO, (001)‐TiO2, (011)‐BaTiO, and (011)‐O2 terminations. The relaxations and rumplings are calculated and discussed, finding that the first layer relaxes inwards, while the second layer relaxes outwards for (001) and (110) surfaces. The data obtained for electronic properties show that O2p states in (001)‐BaO/(001)‐TiO2 termination shift to the lower/higher energy region, leading to a wide/narrow band gap. And the new produced surface states are observed in (011) surface terminations, which is mainly attributed to the supplied electrons from outermost surface atoms, even O atoms are oxidized. Furthermore, the (001) surface of BaTiO3 is found to be more stable than the (011) surface according to the predicted surface energy which is 0.86 and 2.92 J/m2 for (001) and (011) surfaces, respectively. Of which, BaO termination is predicted to be more likely to cleavage from the (001) direction than the TiO2 termination is.

Predicting Surface Energies and Particle Morphologies of Boehmite (γ-AlOOH) from Density Functional Theory

Particle morphology is an important property affecting the reactivity of solid phases. The aluminum oxyhydroxide boehmite (γ-AlOOH) is one example for which particle morphology has relevance to geochemistry, environmental management, and catalysis. Accurate predictions of the morphology of boehmite particles are currently missing, and the dependence of these predictions on the level of theory and complexity of the physics involved is not known. Density functional theory calculations were therefore performed for a wide range of exchange-correlation (XC) functionals, including a hybrid functional, to calculate the energetics of the four main low-index surfaces of boehmite ((100), (010), (001), and (101)) in aqueous conditions and predict equilibrium and growth morphologies. The results highlight the critical need for converged plane-wave basis sets to obtain accurate surface energies as well as the strong influence the XC functional can have on surface energies and water adsorption energies. The predicted m...

Molecule-decorated rutile-type ZnF2(110): A periodic DFT study

Weak binding of small molecules onto surfaces is a powerful tool whereby interfacial phenomena are studied in atomistic level. It is well-recognized that physisorption is a precursor to chemisorption and the subsequent heterogeneous catalysis. Although at least in part overlooked, vdW-driven sorption of particles on rutile-like substrates is of potential value due to the wide variety of the applications it serves. Probing the acidity of rutile-structured adsorbents by means of molecular adsorption is the quintessential case of long-range-dominated adsorption on such materials. Monomer, half-layer and monolayer physisorption of gaseous CO and N2 at (110) facet of rutile-like ZnF2 was investigated through dispersion free and dispersion-corrected DFT. The PBE and optB88-vdW calculated stretching frequencies for freestanding and adsorbed CO and N2 were in excellent agreement with their experimentally observed counterparts, when available. Traditional vdW-DF, its successor, vdW-DF2, and RPBE-D3 predict surface energies that match well with B3LYP result. As well, outstanding consistency was found between the vdW-DF and vdW-DF2 computed binding energies and their highly accurate LMP2 equivalent. Whilst being computationally far more efficient, vdW-DF and vdW-DF2 attained interaction energies were closer to the LMP2 benchmark data than the previously reported B3LYP adsorption energy.

Modeling the formation of TiO2 ultra-small nanoparticles.

The structures of TiO2 ultra-small nanoparticles (USNPs) at the atomistic level have been predicted because of their potential importance in catalytic, environmental, biological and energy applications. Low energy (TiO2)n clusters and USNPs (n up to 80 at the B3LYP/DZVP2 level, and up to 384 at the PM6 level) were found using a novel bottom-up global optimization approach that is based on all-atom real-space calculations. These structures include USNPs that belong to 1-D, 2-D and 3-D USNP series where all the members share the same fragment types and local translational symmetries. Most of the metastable 2-D and 3-D USNPs contain tubular building blocks similar to the 1-D USNPs. The 3-D USNPs that resemble the bulk anatase are predicted to be energetically favorable structures for 64 ≤ n ≤ 384. A fragment-based model was developed to relate the energy with geometry for the 1-D, 2-D and 3-D USNPs. Surface energy densities were predicted for surface fragments at the different positions of the USNPs using this new model. Based on the predicted surface energy densities and the partial density of states, the most catalytically active sites for the anatase-like 3-D USNPs were predicted to be the kink sites on Face-x surfaces consisting of an octahedral-Ti, the step (edge) sites between the Face-x and Face-y surfaces consisting of a square pyramidal-Ti (on Face-x), and the step sites consisting of a trigonal bipyramidal Ti on the Face-y surfaces.

Prediction of the surface tension of cesium in the whole liquid range

ABSTRACTSurface tension is an important quantity, both as physical and technological features. We applied the general form of Lennard-Jones potential model, LJ (m-n), and some thermodynamic arguments in the Kirkwood and Buff equation to calculate the surface tension of liquid cesium. To find out the surface tension in a wide temperature range, only pVT data are required. By this method, we investigated the influence of the potential model on the surface tension. For two selected potential models [LJ (6–3) and LJ (8.5–4)], the values of the calculated surface tension and the predicted surface energy agree with the experimental values.

The surface and structural properties of graphite fluoride

The structural properties of graphite fluoride are not well characterized despite many experimental and theoretical studies. Computational investigations have indicated the existence of several possible stacking sequences for this material, but the methods used were incapable of adequately describing the dispersive interactions between graphite-like layers. We studied the structural and surface properties of graphite fluoride using the random phase approximation method, which provides dispersive (van der Waals) interactions with the correct asymptotic decay. The chair conformation with the AA stacking sequence is predicted to be the most stable structure, having lattice parameters of a=2.58Å, and c=5.75Å. The energetic difference between AB and ABC stacking is small, so a statistical ensemble of several stacking arrangements can be expected in graphite fluoride samples. The energy needed for the exfoliation of graphite fluoride into individual CF layers is 190mJ/m2, which is lower than the corresponding energy for graphite. The predicted surface energy of graphite fluoride is 100mJ/m2. We also measured the surface energy of graphite fluoride powder experimentally using inverse gas chromatography, yielding a value of 79±7mJ/m2 that agreed well with the computational result.

Accurate surface energies from first principles

The absolute values of solids’ surface energies are among the least well-known physical quantities, despite their fundamental importance. Experimental values obtained by various methods often differ by over 100%, mostly because the measurements are indirect and complicated. Reliable computational methods for predicting surface energies would therefore be extremely valuable. Here we assess the utility of using exact exchange (EXX) in conjunction with the many-electron perturbation theory extension of density functional theory, i.e., the random phase approximation (RPA), when predicting surface energies. The EXX + RPA approach was used to calculate the surface energies and cleavage properties of LiH, Mg, Pb, MgO, and NiAl, materials for which reliable experimental surface energies are available. The calculated values agreed well with the experimental data in all cases, suggesting that the longstanding problem of reliably predicting surface energies has been solved. DOI: 10.1103/PhysRevB.91.115402

Integrated experimental and theoretical approach for corrosion and wear evaluation of laser surface nitrided, Ti–6Al–4V biomaterial in physiological solution

A laser based surface nitriding process was adopted to further enhance the osseo-integration, corrosion resistance, and tribological properties of the commonly used bioimplant alloy, Ti–6Al–4V. Earlier preliminary osteoblast, electrochemical, and corrosive wear studies of laser nitrided titanium in simulated body fluid clearly revealed improvement of cell adhesion as well as enhancement in corrosion and wear resistance but mostly lacked the in-depth fundamental understanding behind these improvements. Therefore, a novel integrated experimental and theoretical approach were implemented to understand the physical phenomena behind the improvements and establish the property–structure–processing correlation of nitrided surface. The first principle and thermodynamic calculations were employed to understand the thermodynamic, electronic, and elastic properties of TiN for enthalpy of formation, Gibbs free energy, density of states, and elastic properties of TiN were investigated. Additionally, open circuit potential and cyclic potentio-dynamic polarization tests were carried out in simulated body fluid to evaluate the corrosion resistance that in turn linked with the experimentally measured and computationally predicted surface energies of TiN. From these results, it is concluded that the enhancement in the corrosion resistance after laser nitriding is mainly attributed to the presence of covalent bonding via hybridization among Ti (p) and N (d) orbitals. Furthermore, mechanical properties, such as, Poisson׳s ratio, stiffness, Pugh׳s ductility criteria, and Vicker׳s hardness, predicted from first principle calculations were also correlated to the increase in wear resistance of TiN. All the above factors together seem to have contributed to significant improvement in both wear and corrosion performance of nitride surface compared to the bare Ti–6Al–4V in physiological environment indicating its suitability for bioimplant applications.

First-Principles Study on the Surface Energies of Rutile TiO<sub>2</sub>(110) vs (011)-2×1 Surfaces

First-principles calculations based on density functional theory have been used to study the surface energies of the rutile TiO2(110) and (011)-2×1 surfaces. We investigate the effect of the slab thickness on the predicted surface energy and find that slab thicknesses of at least 5 layers are necessary to converge the surface energy to within 0.01 J/m2for both rutile TiO2(110) and (011)-2×1 surfaces. For the rutile TiO2(110) surface, it should be noted that the surface energy oscillates with the number of layers (odd-even oscillations). However, the calculated surface energies of the rutile TiO2(011)-2×1 surface are closer to the linear relationship for the number of layers larger than 4. Finally, our calculated results indicate that the rutile TiO2(011)-2×1 surface has a significantly higher surface energy than the rutile TiO2(110) surface.

DFT Studies of Pristine Hexagonal Ge1Sb2Te4(0001), Ge2Sb2Te5(0001), and Ge1Sb4Te7(0001) Surfaces

Ternary alloys of germanium, antimony, and tellurium (GexSbyTez) are not only prominent phase-change data-storage materials with intriguing properties; they also form precisely ordered crystal structures if one allows them to do so. Here, we study atomically pristine surfaces of representative GexSbyTez alloys using density functional theory (DFT) and suitable plane-wave-based slab models. In particular, we look at the hexagonal (0001) surfaces of Ge1Sb2Te4, Ge2Sb2Te5, and Ge1Sb4Te7 but with the intent to draw some general conclusions beyond those explicit compositions. The conditions for thermodynamic stability of the ternary surfaces (i.e., the space of permissible chemical potentials) are delineated, and a simple general expression to estimate the latter is given. Because of weak van der Waals-type interactions between Te atomic layers, we assess how surface energy computations are affected by the choice of exchange–correlation functional and also by the use of dispersion corrections (here, Grimme’s DFT+D2 scheme). LDA and PBE+D2 predicted surface energies are similar to a degree that is rather unexpected; generally, Te terminations are lowest in surface energy regardless of the compound and methodology. Implications for further surface studies of “less ideal’’ GexSbyTez surfaces are discussed.

Construction of embedded-atom-method interatomic potentials for alkaline metals (Li, Na, and K) by lattice inversion

The lattice-inversion embedded-atom-method interatomic potential developed previously by us is extended to alkaline metals including Li, Na, and K. It is found that considering interatomic interactions between neighboring atoms of an appropriate distance is a matter of great significance in constructing accurate embedded-atom-method interatomic potentials, especially for the prediction of surface energy. The lattice-inversion embedded-atom-method interatomic potentials for Li, Na, and K are successfully constructed by taking the fourth-neighbor atoms into consideration. These angular-independent potentials markedly promote the accuracy of predicted surface energies, which agree well with experimental results. In addition, the predicted structural stability, elastic constants, formation and migration energies of vacancy, and activation energy of vacancy diffusion are in good agreement with available experimental data and first-principles calculations, and the equilibrium condition is satisfied.

Lattice-Inversion Embedded-Atom-Method Interatomic Potentials for Group-VA Transition Metals

The lattice-inversion embedded-atom-method (LI-EAM) interatomic potential we developed previously [J. Phys.: Condens. Matter 22 (2010) 375503] is extended to group-VA transition metals (V, Nb and Ta). It is found that considering interatomic interactions up to appropriate-distance-neighbor atoms is crucial to constructing accurate EAM potentials, especially for the prediction of surface energy. The LI-EAM interatomic potentials for group-VA transition metals are successfully built by considering interatomic interactions up to the fifth neighbor atoms. These angular-independent potentials drastically promote the accuracy of the predicted surface energies, which match the experimental results well.

Thermodynamic properties of Au–Pd nanostructured surfaces studied by atomic scale modelling

AbstractWe address the question of the sensitivity of the segregation and ordering properties to the surface energy of Au‐Pd alloys and nanoalloys. To this purpose, the parameterization of an EAM potential fitted to the vacancy formation energy was modified in order to predict surface energies closer to the experimentally measured ones. Metropolis Monte Carlo sampling was used to predict segregation and ordering. We show in the detail that modifying the surface energies of Au and Pd by up to 50 percent and, their surface energy difference by about 35 percent is of no major importance for the ordering and segregation properties of nanostructured Au‐Pd alloy surfaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Embedded-atom-method interatomic potentials from lattice inversion

The present work develops a physically reliable procedure for building theembedded-atom-method (EAM) interatomic potentials for the metals with fcc, bcc andhcp structures. This is mainly based on Chen–Möbius lattice inversion (Chen et al 1997 Phys. Rev. E 55 R5) and first-principles calculations. Following Baskes (Baskes et al 2007 Phys. Rev. B 75 094113), this new version of the EAM eliminates all of theprior arbitrary choices in the determination of the atomic electron density andpair potential functions. Parameterizing the universal form deduced from thecalculations within the density-functional scheme for homogeneous electron gas as theembedding function, the new-type EAM potentials for Cu, Fe and Ti metals havesuccessfully been constructed by considering interatomic interactions up to the fifthneighbor, the third neighbor and the seventh neighbor, respectively. The predictionsof elastic constants, structural energy difference, vacancy formation energy andmigration energy, activation energy of vacancy diffusion, latent heat of melting andrelative volume change on melting all satisfactorily agree with the experimentalresults available or first-principles calculations. The predicted surface energies forlow-index crystal faces and the melting point are in agreement with the experimentaldata to the same extent as those calculated by other EAM-type potentials suchas the FBD-EAM, 2NN MEAM and MS-EAM. In addition, the order amongthe predicted low-index surface energies is also consistent with the experimentalinformation.

Comment on ‘Modelling of surface energies of elemental crystals’

Jiang et al (2004 J. Phys.: Condens. Matter 16 521) present a model based on thetraditional broken-bond model for predicting surface energies of elemental crystals. It isfound that bias errors can be produced in calculating the coordination numbers ofsurface atoms, especially in the prediction of high-Miller-index surface energies.

First-principles study of surface properties ofLiFePO4: Surface energy, structure, Wulff shape, and surface redox potential

Using first-principles calculations within the generalized gradient approximation $(\mathrm{GGA})+U$ framework, we investigate several surface properties of olivine structure $\mathrm{Li}\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$. Calculated surface energies and surface redox potentials are found to be very anisotropic. Low-energy surfaces are in the [1 0 0], [0 1 0], [0 1 1], [1 0 1], and [2 0 1] orientations of the orthorhombic structure. We find that the coordination loss of Fe atoms on the surface is energetically more unfavorable than for Li, and generally a low-energy surface has fewer Fe-O bonds affected by the surface cut. Conversely, undercoordinated Li on the surface are somehow beneficial to reduce the energy of a surface except for the twofold coordinated Li. With the calculated surface energies, we provide the thermodynamic equilibrium shape of the $\mathrm{Li}\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$ crystal through a Wulff construction. The two low-energy surfaces (0 1 0) and (2 0 1) dominate in the Wulff shape and make up almost 85% of the surface area. Similar calculations for $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$ indicate a very low energy for the (0 1 0) surface of $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$. This result suggests that surface chemistry can induce a change in the aspect ratio of the Wulff shape. Surface redox potentials for the extraction and insertion of Li from various surfaces are also investigated in this work. The Li redox potential for the (0 1 0) surface is calculated to be $2.95\phantom{\rule{0.3em}{0ex}}\mathrm{V}$, which is significantly lower than the bulk value of $3.55\phantom{\rule{0.3em}{0ex}}\mathrm{V}$. For several other surfaces the Li extraction potential is above the bulk potential. We also develop a simple model that can be used to predict surface energies based on the change in the coordination of Fe and Li.