Free-energy landscape and nucleation pathway of polymorphic minerals from solution in a Potts lattice-gas model

Okamoto, Atsushi; Kuwatani, Tatsu; Omori, Toshiaki; Hukushima, Koji

doi:10.1103/physreve.92.042130

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…Becoming trapped in a local minimum is a common problem for traditional nonlinear optimization algorithms [24,25], preventing determination of the parameters. In this study, the EMC method [26][27][28]35,36], which is also called parallel tempering [37], is used as an iterative minimization routine to overcome this problem.…”

Section: General Frameworkmentioning

confidence: 99%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

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Water-rock interaction in surface and subsurface environments occurs in complex multicomponent systems and involves several reactions, including element transfer. Such kinetic information is obtained by fitting a forward model into the temporal evolution of solution chemistry or the spatial pattern recorded in the rock samples, although geochemical and petrological data are essentially sparse and noisy. Therefore, the optimization of kinetic parameters sometimes fails to converge toward the global minimum due to being trapped in a local minimum. In this study, we simultaneously present a novel framework to estimate multiple reaction-rate constants and the diffusivity of aqueous species from the mineral distribution pattern in a rock by using the reactive transport model coupled with the exchange Monte Carlo method. Our approach can estimate both the maximum likelihood and error of each parameter. We applied the method to the synthetic data, which were produced using a model for silica metasomatism and hydration in the olivine-quartz-H 2 O system. We tested the robustness and accuracy of our method over a wide range of noise intensities. This methodology can be widely applied to kinetic analyses of various kinds of water-rock interactions.2 of 15 happen simultaneously. Even for monomineralic systems, such as feldspar-water or olivine-water systems in batch experiments, coupled reactions could occur, marked by the dissolution of the primary mineral and the formation of a secondary mineral [9,[20][21][22][23]. Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors. Such errors on rate constants are typically ignored to avoid the complex computations required to handle error propagation. Therefore, it would be ideal to develop a versatile method that can extract multiple kinetic parameters and associated errors from noisy laboratory datasets without becoming trapped in local minima.In this study, we present a novel method to estimate not only multiple reaction-rate constants, but also the diffusivity of aqueous species using only the dataset of spatial mineral distribution, and by combining the reactive transport model and the exchange Monte Carlo (EMC) method [26][27][28]. The latter is well-known as an improvement on Markov chain Monte Carlo (MCMC) ...

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Section: General Frameworkmentioning

confidence: 99%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

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“…The dissolution and precipitation process can be regarded as one of the most fundamental and substantial surface heterogeneous reactions for solid-liquid interactions. For example, dissolutionprecipitation processes of minerals play important roles in geoscientific and environmental phenomena in the earth's crust [2][3][4][5][26][27][28]. In laboratory experiments investigating solid-liquid interactions, it is often the case that only concentrations of intermediate products dissolved in liquid phase are quantitatively observable, and the observed time-series data are generally sparse and noisy [3][4][5].…”

Section: Estimation Algorithmmentioning

confidence: 99%

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions

et al. 2016

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It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

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“…Lattice models remain a useful tool in nucleation theory, yielding insights into nonclassical phenomena, [15][16][17] multistep pathways, 18,19 heterogeneous nucleation, 20,21 and limitations of calculation methodology. 22,23 In the following contribution, we present a lattice model of nucleation from solution, where the solute may form disordered, ordered, or semi-ordered solids.…”

Section: Introductionmentioning

confidence: 99%

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

Lifanov

Vorselaars

Quigley

2016

The Journal of Chemical Physics

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We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO 3 ). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force ∆µ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Free-energy landscape and nucleation pathway of polymorphic minerals from solution in a Potts lattice-gas model

Cited by 6 publications

References 20 publications

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

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