arXiv subjects

Michiel Sprik

Publications and source records attributed to Michiel Sprik.

15 recordsLinked to original sources

arXiv2026

Chemical pressure and vacancies in crystals under nonhydrostatic stress

Inhomogeneous stress is a driving force for diffusion of vacancies in crystals. The other way around a non-uniform distribution of vacancies induces stress. The accepted theory of composition-stress coupling in crystals is Larch\'{e}-Cahn (LC) theory. Composition is defined in terms of the population of lattice sites with a limit of one-particle per site. Coupling is modelled by adding a compositional strain term to the elastic strain in the constitutive relation for stress. An alternative mechanism, proposed here, is letting the site binding energy vary with spatial (deformed) density. This generates a chemical pressure adding to the elastic stress. The governing equations for this model are derived using non-equilibrium continuum thermodynamic methods. The gradient of the chemical pressure has a dual function acting both as the drift force for migration and as an effective internal one body force in the Cauchy equation for the elastic stress. The practical evaluation presented in the paper is restricted to equilibrium properties. We examine the effect of externally applied non-hydrostatic stress, either in the form of surface tractions or a one-body force density (gravitation). The model system is a one component crystal with a fixed number of lattice sites. The number of particles can be variable but is always smaller than the number of lattice sites. The linear elastic response is modelled by the standard Lam\'{e} stress tensor. The results for systems deformed by surface tractions are in qualitative agreement with LC theory allowing for differences in the expression for the elastic moduli. Deviations are more serious for the crystal deformed by gravitation.

cond-mat.mtrl-sci↗

arXiv2025

Thermodynamics of a compressible lattice gas crystal: Generalized Gibbs-Duhem equation and adsorption

Compressible lattice gas models are used in material science to understand the coupling between composition and strain in alloys. The seminal work in this field is the 1973 Larché-Cahn paper (Acta Metall. 21, 1051-1063). Single-phase crystals in Larché-Cahn theory are stable under open constant pressure, constant temperature conditions. The Gibbs free energy does not have to match the product $μN$ of the number of particles $N$ and their chemical potential $μ$. Similarly, the grand potential and the product $pV$ of pressure and volume $V$ may not add up to zero. Discrepancies already arise under hydrostatic stress. The elastic energy is not proportional to volume and the Gibbs-Duhem relation valid for liquids is violated. Extensivity is recovered by treating the number of lattice sites $M$ as an additional thermodynamic variable. The difference $ G-μN $ can be identified with $νM$ where $ν$ is the thermodynamic force conjugate to $M$. The reinstated Gibbs-Duhem equation can be cast in the form of an adsorption equation and applied to quantify the tendency to vacancy creation under isothermal isobaric conditions. We have worked this out for a uniform one-component compressible lattice gas crystal. Shear stress is omitted. The coupling between composition and strain is implemented by decomposing pressure in a mechanical component depending on deformed density $N/V$ and an elastic term linear in the volume strain as determined by $V/M$. Various $\left( μ, p, T \right) $ response functions are compared to the $\left( μ, V, T \right) $ counterparts.

cond-mat.mtrl-sci↗

arXiv2024

On the chemical potential and grand potential density of solids under non-hydrostatic stress

Non-hydrostatic stress has a peculiar effect on the phase equilibrium between solids and liquids. This was already pointed out by Gibbs. Gibbs derived his formulation of the condition for liquid-solid coexistence applying a surface accretion process without imposing chemical equilibrium between liquid and solid. Adding particles to the bulk of a solid was not possible in his view at the time. Chemical potentials for solids were later introduced by material scientists. This required extending chemical and mechanical equilibrium with a third condition involving a relation between grand potential densities controlling the migration of the interface. These issues are investigated using a non-linear elastic continuum model (technically an open compressible neo-Hookean material) developed in a previous publication (M. Sprik, J. Chem. Phys. 155, (2021) 244701). In common with a liquid, the grand potential density of the model is equal to minus the mean pressure even if the stress is non-hydrostatic. Applying isothermal compression normal to a liquid-solid interface initially in hydrostatic equilibrium drives the system away from coexistence. We derive the Gibbs-Thomson correction to the pressure of the liquid required to restore phase equilibrium. We find that the coupling between chemical potential of the solid and shear stress is a purely non-linear effect.

cond-mat.mtrl-sci↗

arXiv2021

Computational Amperometry of Nanoscale Capacitors in Molecular Simulations

In recent years, constant applied potential molecular dynamics has allowed to study the structure and dynamics of the electrochemical double-layer of a large variety of nanoscale capacitors. Nevertheless it remained impossible to simulate polarized electrodes at fixed total charge. Here we show that combining a constant potential electrode with a finite electric displacement fills this gap by allowing to simulate open circuit conditions. The method can be extended by applying an electric displacement ramp to perform computational amperometry experiments at different current intensities. As in experiments, the full capacitance of the system is obtained at low intensity, but this quantity decreases when the applied ramp becomes too fast with respect to the microscopic dynamics of the liquid.

cond-mat.mtrl-sci↗

arXiv2020

Electric field based Poisson-Boltzmann: Treating mobile charge as polarization

Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform dielectric body. Writing the electrostatic interactions as an integral over electric field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua (Arch. Rational Mech. Anal. 2007, 183, 299-313). The Maxwell field equations are enforced by extending the set of variational parameters by a vector potential representing the dielectric displacement which is fully transverse in a dielectric system without embedded external charge. The electric field energy density in this representation is a function of the vector potential and the sum of ionic and solvent polarization making the mutual screening explicit.

cond-mat.soft↗

arXiv2020

Continuum model of the simple dielectric fluid: Consistency between density based and continuum mechanics methods

The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: The coupling of polarization to an external field, the electrostatic energy of the induced electric field interacting with itself and the stored polarization energy quadratic in the polarization. A local function of density accounts for the mechanical state of the fluid. Viewed as a non-equilibrium free energy functional of number density and polarization, minimization in these two densities under constraints of the Maxwell field equations should lead the correct equilibrium state. The alternative is a continuum mechanics approach in which the mechanical degree of freedom is extended to full deformation. We show that the continuum electromechanics method leads to a force balance equation which is consistent with the density functional equilibrium equation. The continuum mechanics procedure is significantly more demanding. The gain is a well defined pressure tensor derived from deformation of total energy. This resolves the issue of the uncertainty in the pressure tensor obtained from integration of the force density, which is the conventional method in density based thermomechanics. Our derivation is based on the variational electrostatics approach developed by Ericksen (Arch. Rational Mech. Anal. {\bf 183} 299 (2007)).

cond-mat.soft↗

arXiv2020

Finite field formalism for bulk electrolyte solutions

The manner in which electrolyte solutions respond to electric fields is crucial to understanding the behavior of these systems both at, and away from, equilibrium. The present formulation of linear response theory for such systems is inconsistent with common molecular dynamics (MD) implementations. Using the finite field formalism, suitably adapted for finite temperature MD, we investigate the response of bulk aqueous NaCl solutions to both finite Maxwell ($\mathbf{E}$) and electric displacement ($\mathbf{D}$) fields. The constant $\mathbf{E}$ Hamiltonian allows us to derive the linear response relation for the ionic conductivity in a simple manner that is consistent with the forces used in conventional MD simulations. Simulations of a simple point charge model of an electrolyte solution at constant $\mathbf{E}$ yield conductivities at infinite dilution within 15% of experimental values. The finite field approach also allows us to measure the solvent's dielectric constant from its polarization response, which is seen to decrease with increasing ionic strength. Comparison of the dielectric constant measured from polarization response versus polarization fluctuations enables direct evaluation of the dynamic contribution to this dielectric decrement, which we find to be small but not insignificant. Using the constant $\mathbf{D}$ formulation, we also rederive the Stillinger-Lovett conditions, which place strict constraints on the coupling between solvent and ionic polarization fluctuations.

cond-mat.stat-mech↗

arXiv2019

Electromechanics of the liquid water vapour interface

Two collective properties distinguishing the thin liquid water vapour interface from the bulk liquid are the anisotropy of the pressure tensor giving rise to surface tension and the orientational alignment of the molecules leading to a finite dipolar surface potential. Both properties can be regarded as capillary phenomena and are likely to be coupled. We have investigated this coupling by determining the response of the tangential component of the surface tension to the application of an electric field normal to the surface using finite field molecular dynamics simulations. We find an upside down parabola with a maximum shifted away from zero field. Comparing the molecular dynamics results to an elementary electromechanical continuum model we relate the zero field derivative of the tangential part of the surface tension to the electrostatic potential generated by the spontaneous dipole alignment. The calculations show that these quantities have similar values but are not and in fact need not be identical. The electromechanical model also allows us to convert the absolute curvature of the quadratic field dependence to an effective dielectric constant of the water interface which is found to be much lower compared to the bulk value as expected.

cond-mat.soft↗

arXiv2019

Simulating electrochemical systems by combining the finite field method with a constant potential electrode

A better understanding of interfacial mechanisms is needed to improve the performances of electrochemical devices. Yet, simulating an electrode surface at fixed electrolyte composition remains a challenge. Here we apply a finite electric field to a single electrode held at constant potential and in contact with an aqueous ionic solution, using classical molecular dynamics. The polarization yields two electrochemical interfaces on opposite sides of the same metal slab. While the net charge on one electrode surface is the opposite of the net charge on the other, maintaining overall charge neutrality of the metal. The electrode surface charges fluctuations are compensated by the adsorption of ions from the electrolyte, forming a pair of electric double layers with aligned dipoles. This opens the way towards the efficient simulation of electrochemical interfaces using any flavor of molecular dynamics, from classical to first principles-based methods.

cond-mat.mtrl-sci↗

arXiv2019

Coupling of surface chemistry and electric double layer at TiO$_2$ electrochemical interfaces

Surfaces of metal oxides at working conditions are usually electrified due to the acid-base chemistry. The charged interface compensated with counterions forms the so-called electric double layer. The coupling of surface chemistry and electric double layer is considered to be crucial but poorly understood because of lacking the information at the atomistic scale. Here, we used the latest development in density functional theory based finite-field molecular dynamics simulation to investigate pH-dependence of the Helmholtz capacitance at electrified rutile TiO$_2$ (110)-NaCl electrolyte interfaces. It is found that, due to competing forces from surface adsorption and from electric double layer, water molecules have a stronger structural fluctuation at high pH and this leads to a much larger capacitance. It is also seen that, interfacial proton transfers at low pH increase significantly the capacitance value. These findings elucidate the microscopic origin for the same trend observed in titration experiments.

cond-mat.soft↗

arXiv2018

Charge compensation at the interface between the polar NaCl(111) surface and a NaCl aqueous solution

Periodic supercell models of electric double layers formed at the interface between a charged surface and an electrolyte are subject to serious finite size errors and require certain adjustments in the treatment of the long-range electrostatic interactions. In a previous publication (C. Zhang, M. Sprik, Phys. Rev. B 94, 245309 (2016)) we have shown how this can be achieved using finite field methods. The test system was the familiar simple point charge model of a NaCl aqueous solution confined between two oppositely charged walls. Here this method is extended to the interface between the (111) polar surface of a NaCl crystal and a high concentration NaCl aqueous solution. The crystal is kept completely rigid and the compensating charge screening the polarization can only be provided by the electrolyte. We verify that the excess electrolyte ionic charge at the interface conforms to the Tasker 1/2 rule for compensating charge in the theory of polar rocksalt (111) surfaces. The interface can be viewed as an electric double layer with a net charge. We define a generalized Helmholtz capacitance $C_\text{H}$ which can be computed by varying the applied electric field. We find $C_\text{H} = 8.23 \, μ\mathrm{Fcm}^{-2}$, which should be compared to the $4.23 \, μ\mathrm{Fcm}^{-2}$ for the (100) non-polar surface of the same NaCl crystal. This is rationalized by the observation that compensating ions shed their first solvation shell adsorbing as contact ions pairs on the polar surface.

physics.chem-ph↗

arXiv2018

Finite electric displacement simulations of polar ionic solid-electrolyte interfaces: Application to NaCl(111)/aqueous NaCl solution

Tasker type III polar terminations of ionic crystals carry a net surface charge as well as a dipole moment and are fundamentally unstable. In contact with electrolytes, such polar surfaces can be stabilized by adsorption of counter ions from solution to form electric double layers (EDLs). In a previous work (J. Chem. Phys 147, 104702 (2017)) we reported on a classical force field based molecular dynamics study of a prototype model system namely a NaCl(111) slab interfaced with an aqueous NaCl solution on both sides. A serious hurdle in the simulation is that the finite width of the slab admits an electric field in the solid perturbing the theoretical charge balance at the interface of semi-infinite systems (half the surface charge density for NaCl(111)). It was demonstrated that the application of a finite macroscopic field $E$ cancelling the internal electric field can recover the correct charge compensation at the interface. In the present work, we expand this method by applying a conjugate electric displacement field $D$. The benefits of using $D$ instead of $E$ as the control variable are two fold: it does not only speed up the convergence of the polarization in the simulation but also leads to a succinct expression for the biasing displacement field involving only structural parameters which are known in advance. This makes it feasible to study the charge compensating phenomenon of this prototype system with density functional theory based molecular dynamics (DFTMD), as shown in this work.

physics.chem-ph↗

arXiv2017

Water adsorption on the P-rich GaP(100) surface: Optical spectroscopy from first principles

The contact of water with semiconductors typically changes its surface electronic structure by oxidation or corrosion processes. A detailed knowledge - or even control of - the surface structure is highly desirable, as it impacts the performance of opto-electronic devices from gas-sensing to energy conversion applications. It is also a prerequisite for density functional theory-based modelling of the electronic structure in contact with an electrolyte. The P-rich GaP(100) surface is extraordinary with respect to its contact with gas-phase water, as it undergoes a surface reordering, but does not oxidise. We investigate the underlying changes of the surface in contact with water by means of theoretically derived reflection anisotropy spectroscopy (RAS). A comparison of our results with experiment reveals that a water-induced hydrogen-rich phase on the surface is compatible with the boundary conditions from experiment, reproducing the optical spectra. We discuss potential reaction paths that comprise a water-enhanced hydrogen mobility on the surface. Our results also show that computational RAS - required for the interpretation of experimental signatures - is feasible for GaP in contact with water double layers. Here, RAS is sensitive to surface electric fields, which are an important ingredient of the Helmholtz-layer. This paves the way for future investigations of RAS at the semiconductor-electrolyte interface.

cond-mat.mtrl-sci↗

arXiv2016

Finite Field Methods for the Supercell Modelling of Charged Insulator-Electrolyte Interfaces

Surfaces of ionic solids interacting with an ionic solution can build up charge by exchange of ions. The surface charge is compensated by a strip of excess charge at the border of the electrolyte forming an electric double layer. These electric double layers are very hard to model using the supercells methods of computational condensed phase science. The problem arises when the solid is an electric insulator (as most ionic solids are) permitting a finite interior electric field over the width of the slab representing the solid in the supercell. The slab acts as a capacitor. The stored charge is a deficit in the solution failing to compensate fully for the solid surface charge. Here we show how these problems can be overcome using the finite field methods developed by Stengel, Spaldin and Vanderbilt [Nat. Phys. {\bf 5}, 304, (2009)]. We also show how the capacitance of the double layer can be computed once overall electric neutrality of the double layer is restored by application of a finite macroscopic field $\mathbf{E}$ or alternatively by zero electric displacement $\mathbf{D}$. The method is validated for a classical model of a solid-electrolyte interface using the finite temperature molecular dynamics adaptation of the constant field method presented previously [Phys. Rev. B, 2016, 93, 144201]. Because ions in electrolytes can diffuse across supercell boundaries, this application turns out to be a critical illustration of the multivaluedness of polarization in periodic systems.

physics.chem-ph↗

arXiv2016

Computing the dielectric constant of liquid water at constant dielectric displacement

The static dielectric constant of liquid water is computed using classical force field based molecular dynamics simulation at fixed electric displacement D. The method to constrain the electric displacement is the finite temperature classical variant of the constant-D method developed by Stengel, Spaldin and Vanderbilt (Nat. Phys. 2009, 5: 304). There is also a modification of this scheme imposing fixed values of the macroscopic field E. The method is applied to the popular SPC/E model of liquid water. We compare four different estimates of the dielectric constant, two obtained from fluctuations of the polarization at D = 0 and E = 0 and two from the variation of polarization with finite D and E. It is found that all four estimates agree when properly converged. The computational effort to achieve convergence varies however, with constant D calculations being substantially more efficient. We attribute this difference to the much shorter relaxation time of longitudinal polarization compared to transverse polarization accelerating constant D calculations.

physics.chem-ph↗