A. Tröster

Numerical approaches to determine the interface tension of curved interfaces from free energy calculations

A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).

Beyond the Van Der Waals loop: What can be learned from simulating Lennard-Jones fluids inside the region of phase coexistence

As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρl yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ=μcoex for ρυ<ρ<ρl yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of t...

Ordering and elasticity associated with low-temperature phase transitions in lawsonite

Abstract The two low-temperature phase transitions of lawsonite have been studied using single-crystal X-ray diffraction from 86 to 318 K and a single-crystal high-frequency continuous-wave resonance technique from 323 to 102 K. While recently published data of the variations of strains, birefringence, and IR line widths are consistent with the (271 K) Cmcm-Pmcn transition being simply tricritical, our investigation of critical X-ray reflections and the six diagonal elastic constants of lawsonite reveals, consistently, a more complex crossover pattern in the temperature range of 205.225 K. Below 205 K the overall pattern is again in good agreement with a tricritical solution of the Cmcm-Pmcn transition and a second-order behavior of the (120 K) Pmcn-P21cn transition. The structure determination from single-crystal X-ray data at 215 K reveals a possible orientational disorder of some of the hydroxyl groups in the Pmcn phase. From this and a recent strain analysis of deuterated and hydrogenated lawsonite we conclude that down to 205 K the Cmcm-Pmcn transition is driven by a displacive component, as observed in strain and birefringence data, plus an order/disorder component or dynamical effects associated with proton ordering. Below 205 K only the displacive component plays a role, and the (120 K) Pmcn-P21cn transition is driven by a single order parameter. The remarkable elastic softening of C66 ahead of the Cmcm-Pmcn transition indicates another orthorhombic-monoclinic transition, which is suppressed on cooling through the low-temperature phase sequence Cmcm-Pmcn-P21cn, but can be observed on applying pressure to the mineral.

Finite strain Landau theory of high pressure phase transformations

The properties of materials near structural phase transitions are often successfully described in the framework of Landau theory. While the focus is usually on phase transitions, which are induced by temperature changes approaching a critical temperature Tc, here we will discuss structural phase transformations driven by high hydrostatic pressure, as they are of major importance for understanding processes in the interior of the earth. Since at very high pressures the deformations of a material are generally very large, one needs to apply a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) into account. In particular it is necessary to retune

Coarse Graining the φ4 Model: Landau-Ginzburg Potentials from Computer Simulations

We discuss the problem of how to calculate Landau and Landau-Ginzburg free energies for lattice spin models from computer simulations. In setting up a proper simulation algorithm, emphasis is placed on the coarse grained nature of these potentials, which must be take into account by any suitable simulation approach. The development of theory and simulation results is reviewed and the results of a novel Monte Carlo algorithm using Fourier amplitudes are presented, which partly confirm and sharpen the assumptions on the temperature behavior of the Landau-Ginzburg coefficients made in the literature.

The noise of many needles: Jerky domain wall propagation in PbZrO3 and LaAlO3

Measurements of the sample length of PbZrO3 and LaAlO3 under slowly increasing force (3-30 mN/min) yield a superposition of a continuous decrease interrupted by discontinuous drops. This strain intermittency is induced by the jerky movement of ferroelastic domain walls through avalanches near the depinning threshold. At temperatures close to the domain freezing regime, the distributions of the calculated squared drop velocity maxima N(υm2) follow a power law behaviour with exponents e=1.6±0.2. This is in good agreement with the energy exponent e=1.8±0.2 recently found for the movement of a single needle tip in LaAlO3 [R. J. Harrison and E. K. H. Salje, Appl. Phys. Lett. 97, 021907 (2010)]. With increasing temperature, N(υm2) changes from a power law at low temperatures to an exponential law at elevated temperatures, indicating that thermal fluctuations increasingly enable domain wall segments to unpin even when the driving force is smaller than the corresponding barrier.

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

Landaus thermodynamic approach to structural phase transitions is typically only applicable at ambient pressures. New results reveal how this powerful theory can be extended to the high-pressure environments ubiquitously found in planet interiors.

Interplay of fast and slow dynamics in rare transition pathways: The disk-to-slab transition in the 2d Ising model

Rare transitions between long-lived stable states are often analyzed in terms of free energy landscapes computed as functions of a few collective variables. Here, using transitions between geometric phases as example, we demonstrate that the effective dynamics of a system along these variables are an essential ingredient in the description of rare events and that the static perspective provided by the free energy alone may be misleading. In particular, we investigate the disk-to-slab transition in the two-dimensional Ising model starting with a calculation of a two-dimensional free energy landscape and the distribution of committor probabilities. While at first sight it appears that the committor is incompatible with the free energy, they can be reconciled with each other using a two-dimensional Smoluchowski equation that combines the free energy landscape with state dependent diffusion coefficients. These results illustrate that dynamical information is not only required to calculate rate constants but that neglecting dynamics may also lead to an inaccurate understanding of the mechanism of a given process.

Wilsonʼs momentum shell renormalization group from Fourier Monte Carlo simulations

Abstract Previous attempts to accurately compute critical exponents from Wilsonʼs momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model, we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants ( u 0 , r 0 ) for different values of the momentum shell thickness parameter b by simulation using our recently developed Fourier Monte Carlo algorithm. We report strong anomalies in the b -dependence of the fixed point couplings and the resulting exponents y τ and ω in the vicinity of a shell parameter b ⁎ 1 characterizing a thin but finite momentum shell. Evaluation of the exponents for this value of b yields a dramatic improvement of their numerical accuracy, indicating a strong damping of the influence of irrelevant couplings for b = b ⁎ .

Monte Carlo simulation in Fourier space

In the context of solving the long-standing problem of computing Landau–Ginzburg free energies including gradient corrections for the φ 4 model, we recently introduced a new Monte Carlo algorithm for lattice spin systems based exclusively on Fourier amplitudes of the underlying spin configurations [A. Troster, Phys. Rev. B 76 (2007) 012402]. In the present paper we shall provide additional information on the motivation, main ideas and constructions underlying the algorithm. Also we discuss important details of its construction with emphasis on an analysis of its scaling behavior with system size.