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Statistical error in simulations of Poisson processes: Example of diffusion in solids
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0001-6083-091X
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0002-3933-9066
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2016 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 94, no 8, 085206Article in journal (Refereed) Published
Abstract [en]

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations. 

Place, publisher, year, edition, pages
American Physical Society , 2016. Vol. 94, no 8, 085206
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-192485DOI: 10.1103/PhysRevB.94.085206OAI: oai:DiVA.org:kth-192485DiVA: diva2:968929
Funder
Swedish Energy Agency, 355151Carl Tryggers foundation , CTS 14:433Swedish Research Council, 2014-5993Swedish Research Council, 2011-42-59
Note

QC 20160913

Available from: 2016-09-13 Created: 2016-09-13 Last updated: 2016-09-13Bibliographically approved
In thesis
1. First-principles studies of kinetic effects in energy-related materials
Open this publication in new window or tab >>First-principles studies of kinetic effects in energy-related materials
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantum mechanical calculations based on first-principles (lat. ab initio) methods have over the past decades proved very successful for the study of many materials properties. Based solely on the fundamental constants of physics, the strength of these methods lies not only in describing existing materials, but also in predicting completely new ones. This thesis contains work both related to the quest for improved materials, and to the development of new methods.

Equilibrium ab initio molecular dynamics methods are powerful for simulating diffusion in solids but are accompanied with high computational costs. This is related to the inherent slowness of the diffusion process in solids. To tackle this problem, we implement the color-diffusion algorithm into the Vienna ab initio simulation package to perform non-equilibrium ab initio molecular dynamics (NEMD) simulations. Ion diffusion in ceria doped with Gd and Sm is studied, and the calculated conductivities is found to agree well with experiment. However, although the NEMD method significantly lowers the computational cost, statistical quality in the calculated conductivity still comes expensive. Knowing the error resulting from limited statistics is therefore important.

We derive an analytical expression for the error in calculated ion conductivity, which is verified numerically using the Kinetic Monte Carlo (KMC) method. Being developed particularly for the simulation of slow events, the great advantage of the KMC method over the NEMD method is that it is much less computationally expensive. This allows for long simulation times and large system sizes. The effect of dopant type and dopant distribution on the oxygen ion diffusivity is investigated with KMC simulations of rare-earth doped ceria. The full set of diffusion barriers in the simulation cell is calculated from first-principles within a density functional theory (DFT) framework.

This Thesis also includes a study of processes involving water on a rutile TiO2(110) surface. The basic processes are: diffusion, dissociation, recombination, and clustering of water molecules. The barriers for these processes are calculated with DFT employing different exchange-correlation (XC) functionals. Using the barriers calculated from two XC functionals, we perform KMC simulations and find that the choice of XC functional radically alters the dynamics of the simulated water-titania system.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 68 p.
National Category
Materials Engineering
Research subject
Materials Science and Engineering
Identifiers
urn:nbn:se:kth:diva-192343 (URN)9789177291022 (ISBN)
External cooperation:
Public defence
2016-10-07, F3, Lindstedsvägen 26, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20160913

Available from: 2016-09-13 Created: 2016-09-09 Last updated: 2016-09-13Bibliographically approved

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Publisher's full texthttp://link.aps.org/doi/10.1103/PhysRevB.94.085206

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