Ab initio studies of defect concentrations and diffusion in metal oxides
Author(s)
Frensch, Kilian
Type
Thesis
Abstract
This work presents a methodology for determining the concentrations and diffusion
coefficients of point defects in metal oxides using ab initio calculations of defect formation
energies and diffusion barriers, and the binding energies of defect-impurity
clusters. The methodology is applied to analyse the long-standing mysteries surrounding
the mechanism of self-diffusion in α-Al2O3.
Al2O3 is a prototypical large band gap ceramic with extensive applications, many
of which depend on its defect chemistry. In particular, point defect concentrations,
that vary with temperature and impurity doping, govern diffusion properties such
as creep, sintering, or the oxidation rate of Al-containing alloys. Experimental
measurements of the self-diffusion coefficients in bulk alumina reveal three important
truths that theory cannot reconcile, collectively termed the ’corundum conundrum’.
First, large experimental activation energies for oxygen and aluminum diffusion
and low theoretical formation energies imply unreasonably high diffusion barriers
of ∼ 5eV. Second, aluminum diffusion is orders of magnitude faster than oxygen
diffusion. Third, the oxygen diffusion coefficient is relatively insensitive to aliovalent
doping, increasing by a factor of 100 on heavy Mg2+-doping, and decreasing by a
similar amount on Ti4+-doping.
We attempt to resolve this conundrum by calculating the formation energies and
binding energies of a raft of native point defects and defect-impurity clusters as functions
of temperature T and oxygen partial pressure pO2 , and the diffusion barriers of
the native defects, using density functional theory. We then use a thermodynamic
mass action approach to determine the concentrations of the defects and clusters,
and the diffusion coefficients of the defects, as functions of T, pO2 , and the concentrations
of aliovalent dopants, [Mg2+] and [Ti4+]. In the process, we discover
new ground-state defect structures for the aluminum vacancy and oxygen interstitial,
and demonstrate that diffusion of aluminum vacancies and interstitials occurs
by extended vacancy and interstitialcy mechanisms, and oxygen interstitials by a
dumbbell interstitialcy mechanism, all of which yield much lower migration barriers
than previous theory.
Unfortunately, the results do not demonstrate the experimentally-found insensitivity
of the oxygen diffusivity to aliovalent doping. This could be an artefact of approximations
within density functional theory and our methodology, and we show that
modest changes in the calculated binding energies lead to significant defect clustering.
This defect clustering could result in a buffering mechanism that can explain
the insensitivity of the diffusivity to aliovalent doping, and may occur in other ionic
materials. More accurate calculations, employing hybrid functionals or quantum
Monte Carlo methods, may be necessary to elucidate this effect, but are currently
computationally intractable for our purposes.
coefficients of point defects in metal oxides using ab initio calculations of defect formation
energies and diffusion barriers, and the binding energies of defect-impurity
clusters. The methodology is applied to analyse the long-standing mysteries surrounding
the mechanism of self-diffusion in α-Al2O3.
Al2O3 is a prototypical large band gap ceramic with extensive applications, many
of which depend on its defect chemistry. In particular, point defect concentrations,
that vary with temperature and impurity doping, govern diffusion properties such
as creep, sintering, or the oxidation rate of Al-containing alloys. Experimental
measurements of the self-diffusion coefficients in bulk alumina reveal three important
truths that theory cannot reconcile, collectively termed the ’corundum conundrum’.
First, large experimental activation energies for oxygen and aluminum diffusion
and low theoretical formation energies imply unreasonably high diffusion barriers
of ∼ 5eV. Second, aluminum diffusion is orders of magnitude faster than oxygen
diffusion. Third, the oxygen diffusion coefficient is relatively insensitive to aliovalent
doping, increasing by a factor of 100 on heavy Mg2+-doping, and decreasing by a
similar amount on Ti4+-doping.
We attempt to resolve this conundrum by calculating the formation energies and
binding energies of a raft of native point defects and defect-impurity clusters as functions
of temperature T and oxygen partial pressure pO2 , and the diffusion barriers of
the native defects, using density functional theory. We then use a thermodynamic
mass action approach to determine the concentrations of the defects and clusters,
and the diffusion coefficients of the defects, as functions of T, pO2 , and the concentrations
of aliovalent dopants, [Mg2+] and [Ti4+]. In the process, we discover
new ground-state defect structures for the aluminum vacancy and oxygen interstitial,
and demonstrate that diffusion of aluminum vacancies and interstitials occurs
by extended vacancy and interstitialcy mechanisms, and oxygen interstitials by a
dumbbell interstitialcy mechanism, all of which yield much lower migration barriers
than previous theory.
Unfortunately, the results do not demonstrate the experimentally-found insensitivity
of the oxygen diffusivity to aliovalent doping. This could be an artefact of approximations
within density functional theory and our methodology, and we show that
modest changes in the calculated binding energies lead to significant defect clustering.
This defect clustering could result in a buffering mechanism that can explain
the insensitivity of the diffusivity to aliovalent doping, and may occur in other ionic
materials. More accurate calculations, employing hybrid functionals or quantum
Monte Carlo methods, may be necessary to elucidate this effect, but are currently
computationally intractable for our purposes.
Date Issued
2011
Date Awarded
2011-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Finnis, Mike
Foulkes, Matthews
Creator
Frensch, Kilian
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)