Domain shape instabilities and dendrite domain growth in uniaxial ferroelectrics

Shur, V. Ya.; Ахматханов, А. Р.

doi:10.1098/rsta.2017.0204

Cited by 16 publications

(6 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since BaTiO 3 is a semiconductor, the strong electric fields near a domain needle-tip are expected to promote local conduction, leading to a redistribution of charge, and partially screening the effect of the polarization jump. This charge screening provides an essential contribution to the local fields [36,23].…”

Section: Stability Of Needle Domain Pairs With Reduced Effective Linementioning

confidence: 99%

“…However, application of this analogy to BaTiO 3 produces a puzzle: Firstly, the material is strongly anisotropic, and electromechanically coupled, so the equilibrium positions of dislocations should not be expected to correspond to those of an isotropic elastic medium. Secondly, there is a jump in polarization between the needle and its surroundings; the resulting depolarization fields strongly affect the configuration and stability of domain needles [23]. Yet, in observations, the needle-tips commonly line up as if they behaved like dislocations in an isotropic elastic medium.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling and interaction of needle domains in barium titanate single crystals

Sui

Huber

2020

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Needle domains are thin, lamellar domains that can appear as fine lines or stripes in a ferroelectric crystal. They affect the poling, switching, and other properties of ferroelectrics. A model is established to study the stress and electric fields caused by needle domains and their interaction. Considering the electrical and mechanical compatibility conditions at the tip of a needle domain, the fields are represented using equivalent edge dislocations and line charges. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are employed. A modified Peach-Koehler force and calculations of the total energy due to the needle domains are used to study the formation, interaction and stability of needle patterns, taking full account of the strong anisotropy and electromechanical coupling present. The interaction of pairs of needle domains in an infinite piezoelectric with properties of barium titanate is found to be dominated by the electrostatic terms. This makes comb-like arrays of needle domains unstable if perfectly insulating properties are assumed. By considering redistribution of charge, stable equilibrium states for arrays of needle domains are found; these agree well with experimental observations. The model explains the stability of various observed needle patterns and also how unstable patterns evolve.

show abstract

Section: Stability Of Needle Domain Pairs With Reduced Effective Linementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling and interaction of needle domains in barium titanate single crystals

Sui

Huber

2020

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

show abstract

“…The phase interface in such problems is assumed to be atomically rough with thickness of the order of several interatomic distances. Not discussing this problem in detail (see works on phase-field modelling [13][14][15][16][17][18][19][20][21][22][23][24][25][26]) we shall neglect this atomic roughness and assume a sharp interface on the macroscopic length scale. Methods of analytical and numerical description of the Stefan-type moving boundary problems can be classified as two problem-solving approaches: (i) to find the bulk temperature and solute concentration fields taking into account the phase interface conditions [9][10][11] and (ii) to formulate and solve the free-boundary problem for the phase interface function (deformation of the interfacial surface) [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

Galenko

Alexandrov

Титова

2018

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

show abstract

“…Two principally new and unusual tasks finalize this topical section. These are directly attributed to pattern formation of graphene islands in two-dimensional films by Elder et al [39] and exotic dendrites in ferroelectrics by Shur & Akhmatkhanov [40]. Using the two-dimensional PFC model, Elder et al reproduce the phenomenon of disappearance of graphene flakes due to hydrogen gas pressure.…”

Section: (A) Microscopic Description and Analysis Of Interfacial Patternsmentioning

confidence: 99%

From atomistic interfaces to dendritic patterns

Galenko

Alexandrov

2018

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

One contribution of 16 to a theme issue 'From atomistic interfaces to dendritic patterns' . Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters. Great benefits can be attained from the development of micro-, meso-and macrolevels of analysis when investigating the dynamics of interfaces, interpreting experimental data and designing the macrostructure of samples. The review and research articles in this theme issue cover the spectrum of scales (from nano-to macro-length scales) in order to exhibit recently developing trends in the theoretical analysis and computational modelling of dendrite pattern formation. Atomistic modelling, the flow effect on interface dynamics, the transition from diffusion-limited to thermally controlled growth existing at a considerable driving force, two-phase (mushy) layer formation, the growth of eutectic dendrites, the formation of a secondary dendritic network due to coalescence, computational methods, including boundary integral and phase-field methods, and experimental tests for theoretical models-all these themes are highlighted in the present issue.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

show abstract

Domain shape instabilities and dendrite domain growth in uniaxial ferroelectrics

Cited by 16 publications

References 59 publications

Modelling and interaction of needle domains in barium titanate single crystals

Modelling and interaction of needle domains in barium titanate single crystals

The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

From atomistic interfaces to dendritic patterns

Contact Info

Product

Resources

About