Home
Search
Collections
Journals
About
Contact us
My IOPscience
Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 015005 (http://iopscience.iop.org/0953-8984/27/1/015005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.197.26.12 This content was downloaded on 15/06/2017 at 10:06 Please note that terms and conditions apply.
You may also be interested in: Effect of cation dopants in zirconia on interfacial properties in nickel/zirconia systems: an atomistic modeling study Albert M Iskandarov, Yingna Ding and Yoshitaka Umeno Ab initio kinetic Monte Carlo model of ionic conduction in bulk yttria-stabilized zirconia Eunseok Lee, Friedrich B Prinz and Wei Cai A charge optimized many-body (comb) potential for titanium and titania Yu-Ting Cheng, Tzu-Ray Shan, Tao Liang et al. First-principles study of hydrogen configurations at the core of a high-angle grain boundary in cubic yttria-stabilized zirconia A G Marinopoulos Molecular dynamics simulation of yttria-stabilized zirconia (YSZ) crystalline andamorphous solids Kah Chun Lau and Brett I Dunlap Bulk, surface and point defect properties in UO2 from a tight-binding variable-charge model G Sattonnay and R Tétot Many-body central force potentials for tungsten G Bonny, D Terentyev, A Bakaev et al. A modified embedded atom method potential for the titanium–oxygen system W J Joost, S Ankem and M M Kuklja Convergence of an analytic bond-order potential for collinear magnetism in Fe Michael E Ford, Ralf Drautz, Thomas Hammerschmidt et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 015005 (9pp)
doi:10.1088/0953-8984/27/1/015005
Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface Albert M Iskandarov1,2,3 , Atsushi Kubo1 and Yoshitaka Umeno1,2 1 Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan 2 CREST, Japan Science and Technology Agency, K’s Gobancho, 7, Chiyoda-ku, Tokyo 102-0076, Japan 3 Institute for Metals Superplasticity Problems, Russian Academy of Science, Khalturin St. 39, Ufa 450001, Russia
E-mail: [email protected] Received 22 July 2014, revised 13 October 2014 Accepted for publication 31 October 2014 Published 24 November 2014 Abstract
We developed a new interatomic potential for yttria-stabilized zirconia (YSZ) based on the dipole model initially proposed by Tangney and Scandolo. It is demonstrated that the potential can successfully reproduce not only basic bulk properties, including interaction between point defects, but also energies and structures of clean (1 1 0) and (1 1 1) surfaces. We confirmed that the highly perturbed structure of (1 1 0) surface doped by yttria is in a good agreement with results of DFT calculations. Yttrium segregation at (1 1 1) surface was predicted and discussed by comparison with results of DFT simulations. Keywords: yttria-stabilized zirconia, surface, dipole model (Some figures may appear in colour only in the online journal)
due to temperature cycling during SOFC operation. This may eventually trigger mechanical failure because of induced local stress fields. Therefore, stabilization of the cubic phase at operating temperatures of SOFC helps to avoid this problem. Due to the aforementioned prominent unique properties c-YSZ is still the most widely used electrolyte in SOFC. Computer simulations have been extensively used to investigate some aspects of YSZ properties, which are often inaccessible directly in experiments. First principles calculations were successively used to describe bulk properties of different phases of YSZ [7, 8], properties of defects and their interactions [7], surface structures and properties [9–12], etc. However, because of high computational cost, first principles calculations can be efficiently used neither for large systems nor for evaluation of YSZ structure at operating conditions. Therefore, for instance, to study oxygen ion conductivity or Ni sintering, classical molecular dynamics (MD) and MonteCarlo (MC) methods with empirical potentials are employed [13–16]. Though being able to treat larger systems, these methods must use adequate interatomic potentials to describe correctly properties of interest to obtain reliable results.
1. Introduction
Yttria-stabilized zirconia (YSZ) is a ceramic material that plays an important role in many technological applications. Besides thermal barrier coatings in a gas-turbine engines [1], oxygen sensors [2], etc solid oxide fuel cells (SOFC) [3] is a major application of YSZ. In particular, high oxygen vacancy concentration makes YSZ a fast solid-state oxygen ion conductor, which is attractive for using it in oxygen sensors [4] and as an electrolyte in SOFCs. High anion conductivity of YSZ in anode facilitates oxygen ion movement towards triple phase boundaries (TPB), the only place where fuel oxidation can take place. In addition, YSZ is used very commonly as a part of porous Ni/YSZ anode. Another effect of doping zironia with yttria is stabilization of the cubic (c-) phase at low temperatures, while pure zirconia is in the cubic phase only above 2650 K. Zirconia undergoes phase transition to tetragonal (t-) (below 2650 K) or, at even lower temperatures (below 1450 K) to (m-) monoclinic phase [5, 6]. Such phase transitions are highly undesirable because they are inevitably accompanied by volume changes 0953-8984/15/015005+09$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 015005
A M Iskandarov et al
Since the spectrum of properties of interest is very wide for YSZ and it turned out to be impossible to study all of them using a single potential, there are many interatomic potentials that have been designed for particular problems. For instance, for c ↔ t phase transition problem, Schelling et al [17] modified parameters of the Zacate potential [18] for c-YSZ. The calculated values of the phase transition temperature and the c/a ratio are underestimated compared with experimental data [19–22]. Lau and Dunlap [14] combined slightly modified parameters of Zacate [18], Lewis [23], Minervini [24] potentials and incorporated the shell-model [25] to study anion and cation diffusion in crystalline and amorphous YSZ. Ion diffusion in c-YSZ has also been widely studied with the pairwise potential developed by Dwivedi and Cormack [26] and obtained results [16, 27–29] agree with experimental data. However, the abovementioned potentials were fitted to the properties of bulk YSZ crystals, and their validity for studying complex YSZ structures was only assumed. For instance, under this assumption Lee et al performed an analysis of Y segregation at free (1 0 0) surface [16]. Therefore, the necessity to perform MD and MC studies of more complicated structures, e.g. free surfaces, interfaces, triple phase boundaries [16, 30], and processes, such as fuel oxidation, urges to develop more sophisticated and transferable models. The ReaxFF method is probably the most complicated, and was originally developed to account for chemical reactions [31]. For YSZ a ReaxFF potential was first parameterized by van Duin et al [32]. However, even this rather complicated potential model was reparameterized to perform accurate simulations of a free (1 1 1)YSZ surface [33]. In this study we develop, to the best of our knowledge, the first interatomic potential for YSZ based on the dipole model originally proposed by Tangney and Scandolo (TS) [34]. The distinct feature of the TS model is incorporation of electric polarization of ions, which is especially large for oxygen ions in oxides. Tangney and Scandolo demonstrated that introducing the polarizability effect for liquid silica leads to better reproduction of the equation of state and the Si–O–Si angle distribution [34], as compared to the pairwise potential proposed by Beest, Kramer, and van Santen (BKS) [35]. Besides being applicable for liquid silica, developed interatomic potentials were reported to be highly transferable. Indeed, though not included in fitting, silica polymorphs, such as quartz, cristobalite, and coesite, were better described by the TS model than by the BKS potential. Recently, the TS model was also successfully implemented for liquid magnesia [36]. High transferability of the TS model makes it attractive for parameterizing for YSZ, because of its numerous properties of interest. In this paper, we illustrate that with the TS model one can achieve improvement in a wider spectrum of properties compared with pairwise potentials, while the TS model is simpler and less expensive than the ReaxFF approach. The developed potential was designed to be able to reproduce bulk properties, such as the lattice constant and the cohesive energy, and energies of (1 1 1) and (1 1 0) surfaces. Details of the model and the procedure of its parameter determination are described in the next section (section 2). Validation of the potential is performed in
section 3 by comparison of reproduced properties with those obtained from first principles calculations and experimental data. Among examined properties are the energy of defect interactions, surface energies and structures and yttrium surface segregation. We also examine how results derived with our potential compare with those obtained by widely used the Dwivedi and Cormack interatomic potential [26]. For this purpose in section 3 we present and discuss properties calculated using both potentials if corresponding data for the Dwivedi and Cormack potential is available in literature. 2. Potential fitting 2.1. Dipole potential model
Total potential energy, Etot , of a condensed ionic system, according to the TS model, is calculated as a sum of two contributions: energy of short-range pairwise interactions sr , and energy of long-range electrostatic between ions, Etot el interactions, Etot . The short range interactions are described by the Buckingham potential, which for a pair of atoms i and j can be written as 6 bij Eijsr (rij ) = aij e−rij /bij − cij , (1) rij where rij is the distance between the atoms, aij , bij , and cij are parameters of the Buckingham potential that depend only sr is calculated as a on types of atoms i and j . The value of Etot sr sum of Eij (rij ) for all pairs of atoms i and j located within a cut-off radius, Rcsr = 10 Å, from each other, i.e. sr Etot =
N
N
i=1
j >i,rij Rcsr
Eijsr ,
(2)
where N is the number of atoms in the system. A distinctive feature of theTSmodel is incorporation of electrostatic dipole moments, pi , induced on ions. This allows to account for charge polarization of the ions. Thus, el , consists not total energy of electrostatic interactions, Etot only of energies ofelectrostatic interactions, E qq , between ions’ point charges, qj , but includes two more energy terms, namely el = E qq + E pq + E pp , (3) Etot where E pq is energy of electrostatic interactions between point charges and dipoles, and E pp —between dipoles. In order to calculate the two latter terms in equation (3), one has to determine dipole moments, {pi }, which are formed by two contributions. first contribution to pi comes from The the point charges qj of surrounding ions within cut-off radius, Rcel = 14 Å, and can be written as j =N
pPi = αi
j =1,j =i,rij
Search
Collections
Journals
About
Contact us
My IOPscience
Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 015005 (http://iopscience.iop.org/0953-8984/27/1/015005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.197.26.12 This content was downloaded on 15/06/2017 at 10:06 Please note that terms and conditions apply.
You may also be interested in: Effect of cation dopants in zirconia on interfacial properties in nickel/zirconia systems: an atomistic modeling study Albert M Iskandarov, Yingna Ding and Yoshitaka Umeno Ab initio kinetic Monte Carlo model of ionic conduction in bulk yttria-stabilized zirconia Eunseok Lee, Friedrich B Prinz and Wei Cai A charge optimized many-body (comb) potential for titanium and titania Yu-Ting Cheng, Tzu-Ray Shan, Tao Liang et al. First-principles study of hydrogen configurations at the core of a high-angle grain boundary in cubic yttria-stabilized zirconia A G Marinopoulos Molecular dynamics simulation of yttria-stabilized zirconia (YSZ) crystalline andamorphous solids Kah Chun Lau and Brett I Dunlap Bulk, surface and point defect properties in UO2 from a tight-binding variable-charge model G Sattonnay and R Tétot Many-body central force potentials for tungsten G Bonny, D Terentyev, A Bakaev et al. A modified embedded atom method potential for the titanium–oxygen system W J Joost, S Ankem and M M Kuklja Convergence of an analytic bond-order potential for collinear magnetism in Fe Michael E Ford, Ralf Drautz, Thomas Hammerschmidt et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 015005 (9pp)
doi:10.1088/0953-8984/27/1/015005
Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface Albert M Iskandarov1,2,3 , Atsushi Kubo1 and Yoshitaka Umeno1,2 1 Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan 2 CREST, Japan Science and Technology Agency, K’s Gobancho, 7, Chiyoda-ku, Tokyo 102-0076, Japan 3 Institute for Metals Superplasticity Problems, Russian Academy of Science, Khalturin St. 39, Ufa 450001, Russia
E-mail: [email protected] Received 22 July 2014, revised 13 October 2014 Accepted for publication 31 October 2014 Published 24 November 2014 Abstract
We developed a new interatomic potential for yttria-stabilized zirconia (YSZ) based on the dipole model initially proposed by Tangney and Scandolo. It is demonstrated that the potential can successfully reproduce not only basic bulk properties, including interaction between point defects, but also energies and structures of clean (1 1 0) and (1 1 1) surfaces. We confirmed that the highly perturbed structure of (1 1 0) surface doped by yttria is in a good agreement with results of DFT calculations. Yttrium segregation at (1 1 1) surface was predicted and discussed by comparison with results of DFT simulations. Keywords: yttria-stabilized zirconia, surface, dipole model (Some figures may appear in colour only in the online journal)
due to temperature cycling during SOFC operation. This may eventually trigger mechanical failure because of induced local stress fields. Therefore, stabilization of the cubic phase at operating temperatures of SOFC helps to avoid this problem. Due to the aforementioned prominent unique properties c-YSZ is still the most widely used electrolyte in SOFC. Computer simulations have been extensively used to investigate some aspects of YSZ properties, which are often inaccessible directly in experiments. First principles calculations were successively used to describe bulk properties of different phases of YSZ [7, 8], properties of defects and their interactions [7], surface structures and properties [9–12], etc. However, because of high computational cost, first principles calculations can be efficiently used neither for large systems nor for evaluation of YSZ structure at operating conditions. Therefore, for instance, to study oxygen ion conductivity or Ni sintering, classical molecular dynamics (MD) and MonteCarlo (MC) methods with empirical potentials are employed [13–16]. Though being able to treat larger systems, these methods must use adequate interatomic potentials to describe correctly properties of interest to obtain reliable results.
1. Introduction
Yttria-stabilized zirconia (YSZ) is a ceramic material that plays an important role in many technological applications. Besides thermal barrier coatings in a gas-turbine engines [1], oxygen sensors [2], etc solid oxide fuel cells (SOFC) [3] is a major application of YSZ. In particular, high oxygen vacancy concentration makes YSZ a fast solid-state oxygen ion conductor, which is attractive for using it in oxygen sensors [4] and as an electrolyte in SOFCs. High anion conductivity of YSZ in anode facilitates oxygen ion movement towards triple phase boundaries (TPB), the only place where fuel oxidation can take place. In addition, YSZ is used very commonly as a part of porous Ni/YSZ anode. Another effect of doping zironia with yttria is stabilization of the cubic (c-) phase at low temperatures, while pure zirconia is in the cubic phase only above 2650 K. Zirconia undergoes phase transition to tetragonal (t-) (below 2650 K) or, at even lower temperatures (below 1450 K) to (m-) monoclinic phase [5, 6]. Such phase transitions are highly undesirable because they are inevitably accompanied by volume changes 0953-8984/15/015005+09$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 015005
A M Iskandarov et al
Since the spectrum of properties of interest is very wide for YSZ and it turned out to be impossible to study all of them using a single potential, there are many interatomic potentials that have been designed for particular problems. For instance, for c ↔ t phase transition problem, Schelling et al [17] modified parameters of the Zacate potential [18] for c-YSZ. The calculated values of the phase transition temperature and the c/a ratio are underestimated compared with experimental data [19–22]. Lau and Dunlap [14] combined slightly modified parameters of Zacate [18], Lewis [23], Minervini [24] potentials and incorporated the shell-model [25] to study anion and cation diffusion in crystalline and amorphous YSZ. Ion diffusion in c-YSZ has also been widely studied with the pairwise potential developed by Dwivedi and Cormack [26] and obtained results [16, 27–29] agree with experimental data. However, the abovementioned potentials were fitted to the properties of bulk YSZ crystals, and their validity for studying complex YSZ structures was only assumed. For instance, under this assumption Lee et al performed an analysis of Y segregation at free (1 0 0) surface [16]. Therefore, the necessity to perform MD and MC studies of more complicated structures, e.g. free surfaces, interfaces, triple phase boundaries [16, 30], and processes, such as fuel oxidation, urges to develop more sophisticated and transferable models. The ReaxFF method is probably the most complicated, and was originally developed to account for chemical reactions [31]. For YSZ a ReaxFF potential was first parameterized by van Duin et al [32]. However, even this rather complicated potential model was reparameterized to perform accurate simulations of a free (1 1 1)YSZ surface [33]. In this study we develop, to the best of our knowledge, the first interatomic potential for YSZ based on the dipole model originally proposed by Tangney and Scandolo (TS) [34]. The distinct feature of the TS model is incorporation of electric polarization of ions, which is especially large for oxygen ions in oxides. Tangney and Scandolo demonstrated that introducing the polarizability effect for liquid silica leads to better reproduction of the equation of state and the Si–O–Si angle distribution [34], as compared to the pairwise potential proposed by Beest, Kramer, and van Santen (BKS) [35]. Besides being applicable for liquid silica, developed interatomic potentials were reported to be highly transferable. Indeed, though not included in fitting, silica polymorphs, such as quartz, cristobalite, and coesite, were better described by the TS model than by the BKS potential. Recently, the TS model was also successfully implemented for liquid magnesia [36]. High transferability of the TS model makes it attractive for parameterizing for YSZ, because of its numerous properties of interest. In this paper, we illustrate that with the TS model one can achieve improvement in a wider spectrum of properties compared with pairwise potentials, while the TS model is simpler and less expensive than the ReaxFF approach. The developed potential was designed to be able to reproduce bulk properties, such as the lattice constant and the cohesive energy, and energies of (1 1 1) and (1 1 0) surfaces. Details of the model and the procedure of its parameter determination are described in the next section (section 2). Validation of the potential is performed in
section 3 by comparison of reproduced properties with those obtained from first principles calculations and experimental data. Among examined properties are the energy of defect interactions, surface energies and structures and yttrium surface segregation. We also examine how results derived with our potential compare with those obtained by widely used the Dwivedi and Cormack interatomic potential [26]. For this purpose in section 3 we present and discuss properties calculated using both potentials if corresponding data for the Dwivedi and Cormack potential is available in literature. 2. Potential fitting 2.1. Dipole potential model
Total potential energy, Etot , of a condensed ionic system, according to the TS model, is calculated as a sum of two contributions: energy of short-range pairwise interactions sr , and energy of long-range electrostatic between ions, Etot el interactions, Etot . The short range interactions are described by the Buckingham potential, which for a pair of atoms i and j can be written as 6 bij Eijsr (rij ) = aij e−rij /bij − cij , (1) rij where rij is the distance between the atoms, aij , bij , and cij are parameters of the Buckingham potential that depend only sr is calculated as a on types of atoms i and j . The value of Etot sr sum of Eij (rij ) for all pairs of atoms i and j located within a cut-off radius, Rcsr = 10 Å, from each other, i.e. sr Etot =
N
N
i=1
j >i,rij Rcsr
Eijsr ,
(2)
where N is the number of atoms in the system. A distinctive feature of theTSmodel is incorporation of electrostatic dipole moments, pi , induced on ions. This allows to account for charge polarization of the ions. Thus, el , consists not total energy of electrostatic interactions, Etot only of energies ofelectrostatic interactions, E qq , between ions’ point charges, qj , but includes two more energy terms, namely el = E qq + E pq + E pp , (3) Etot where E pq is energy of electrostatic interactions between point charges and dipoles, and E pp —between dipoles. In order to calculate the two latter terms in equation (3), one has to determine dipole moments, {pi }, which are formed by two contributions. first contribution to pi comes from The the point charges qj of surrounding ions within cut-off radius, Rcel = 14 Å, and can be written as j =N
pPi = αi
j =1,j =i,rij
