Relations between the Concentrations of Imperfections in Crystalline Solids

Kröger, F. A.; Vink, Hans

doi:10.1016/s0081-1947(08)60135-6

Cited by 1,831 publications

(844 citation statements)

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“…It is known that TB structured compounds lose oxygen during high temperature sintering [33,34] which, follows the Kroger and Vink relation: Oo→1/2O 2 ↑+Vo+2e  , where Vo denotes oxygen vacancy [35]. Some oxygen vacancies created during high temperature processing induce disordering in the system [36]. As a result Bragg angle diffuse type of ferroelectric to paraelectric phase transition occurs.…”

Section: Dielectric Studymentioning

confidence: 99%

Dielectric and electrical properties of Na2Pb2La2W2Ti4Ta4O30 electroceramics

et al. 2012

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Abstract:The polycrystalline sample of complex tungsten-bronze type compound (Na 2 Pb 2 La 2 W 2 Ti 4 Ta 4 O 30 ) was prepared by a high-temperature solid-state reaction technique. Room temperature preliminary structural study using X-ray diffraction (XRD) data exhibits the formation of a single-phase new compound. The SEM micrograph of the compound exhibits non uniform rectangular grains distributed throughout the sample surface. Detailed studies of dielectric parameters (ε r , tan δ) as a function of temperature and frequency, and P-E hysteresis (spontaneous polarization) confirmed the existence of ferroelectricity in the material. Complex impedance spectroscopy analysis, carried out as a function of frequency at different temperatures, established a correlation between the microstructure and electrical properties of the material. The electrical relaxation process occurring in the material is temperature dependent. The activation energy found from the Arrhenius plot that the conduction process in the material is of mixed type. The nature of frequency dependence of ac conductivity suggests that the material obeys Jonscher's universal power law.

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Section: Dielectric Studymentioning

confidence: 99%

Dielectric and electrical properties of Na2Pb2La2W2Ti4Ta4O30 electroceramics

et al. 2012

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“…In that respect radiation damage can be visualized as an accumulation of defects formed by displacement cascades [39,40]. The three key Frenkel reactions in Kröger-Vink notation (for example in this notation V ′′′′ Zr and Zr ⋅⋅⋅⋅ i will denote a vacant Zr site and a Zr interstitial defect respectively) [41] are…”

Section: Intrinsic Defect Processesmentioning

confidence: 99%

Defect processes in Li2ZrO3: insights from atomistic modelling

Kordatos

Christopoulos

Kelaidis

et al. 2017

J Mater Sci: Mater Electron

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density functional theory (DFT) simulations in conjunction with experimental nuclear magnetic resonance (NMR) in order to investigate the Li ion migration mechanisms. Disorder in the anion sublattice can impact the material properties and the diffusion of point defects [14,15]. This is a common future in energy related materials where intrinsic disorder and doping can influence the formation (i.e. concentration of point defects mediating diffusion) and the migration (i.e. the energy barriers for diffusion) [16][17][18][19]. Controlling point defects such as vacancies is important for semiconductors, superconductors, and oxides [20][21][22][23][24][25][26][27][28]. A way to defect engineer the concentration and clustering of point defects in the anion sublattice (for example oxygen vacancies) is via the introduction of dopants. This is effectively to maintain charge balance in the lattice [29]. For example the introduction of two trivalent dopants in the tetravalent cerium site in CeO 2 can be charge balanced by the formation of an oxygen vacancy. Therefore the introduction of trivalent dopants in CeO 2 is an efficient way to form oxygen vacancies at concentrations higher than the equilibrium concentration [29].Atomistic simulation is an efficient and powerful way to understand the energetics of point defects in energy materials [30][31][32]. The main aim of the present study is to systematically investigate the intrinsic defect processes and impact of doping in Li 2 ZrO 3 using DFT. In particular, we consider here divalent (Mg, Zn, Ca, Cd, Sr, Ba), trivalent (Al, Ga, Sc, In, Y) and tetravalent (Si, Ge, Ti, Sn, Pb, Ce) substitutionals and their association with oxygen vacancies.Abstract Lithium zirconate (Li 2 ZrO 3 ) is an important material that is considered as an anode in lithium-ion batteries and as a nuclear reactor breeder material. The intrinsic defect processes and doping can impact its material properties. In the present study we employ density functional theory calculations to calculate the defect processes and doping in Li 2 ZrO 3 . Here we show that the lithium Frenkel is the dominant intrinsic defect process and that dopants substituting in the zirconium site strongly associate with oxygen vacancies. In particular, it is calculated that divalent dopants more strongly bind with oxygen vacancies, with trivalent dopants following in binding energies and even tetravalent dopands having significant binding energies. The results are discussed in view of the application of Li 2 ZrO 3 in energy applications.

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“…The charge transference in (Ca 1Àx Cu x ) TiO 3 crystals is also represented by KrögereVink notation [49] by means of clusters notations in Equation (2):…”

Section: X-ray Absorption Near Edge Structure Spectroscopy Analysesmentioning

confidence: 99%

“…Also, the proposed model for the lattice former can be extended for the network modifiers, and is represented by KrögereVink notation [49] by means of clusters notations in Equation (3): …”

Section: X-ray Absorption Near Edge Structure Spectroscopy Analysesmentioning

confidence: 99%