TY - JOUR

T1 - Domain walls in ω-phase transformations

AU - Sanati, Mahdi

AU - Saxena, Avadh

N1 - Funding Information:
The authorsa cknowledgues efuld iscussionws ith S.D. Cai. This work was supporteidn partb y the US NSF and in partb y the US DOE. One of us (MS) acknowledgefisn ancials upporfto r this work from NSF GrantD MR95-31223.

PY - 1998

Y1 - 1998

N2 - The β-phase (body-centered cubic: b.c.c.) to ω-phase transformation in certain elements (e.g. Zr) and alloys (e.g. Zr-Nb) is induced either by quenching or application of pressure. The ω-phase is a metastable state and usually coexists with the β-matrix in the form of small particles. To study the formation of domain walls in these materials we have extended the Landau model of Cook for the ω-phase transition by including a spatial gradient (Ginzburg) term of the scalar order parameter. In general, the Landau free energy is an asymmetric double-well potential. From the variational derivative of the total free energy we obtain a static equilibrium condition. By solving this equation for different physical parameters and boundary conditions, we obtained different quasi-one-dimensional soliton-like solutions. These solutions correspond to three different types of domain walls between the ω-phase and the β-matrix. In addition, we obtained soliton lattice (domain wall array) solutions, calculated their formation energy and the asymptotic interaction between the solitons.

AB - The β-phase (body-centered cubic: b.c.c.) to ω-phase transformation in certain elements (e.g. Zr) and alloys (e.g. Zr-Nb) is induced either by quenching or application of pressure. The ω-phase is a metastable state and usually coexists with the β-matrix in the form of small particles. To study the formation of domain walls in these materials we have extended the Landau model of Cook for the ω-phase transition by including a spatial gradient (Ginzburg) term of the scalar order parameter. In general, the Landau free energy is an asymmetric double-well potential. From the variational derivative of the total free energy we obtain a static equilibrium condition. By solving this equation for different physical parameters and boundary conditions, we obtained different quasi-one-dimensional soliton-like solutions. These solutions correspond to three different types of domain walls between the ω-phase and the β-matrix. In addition, we obtained soliton lattice (domain wall array) solutions, calculated their formation energy and the asymptotic interaction between the solitons.

KW - Asymmetric double-well potential

KW - Domain wall arrays and interaction

KW - Ginzburg-Landau model

KW - ω-phase transformation

UR - http://www.scopus.com/inward/record.url?scp=0012289750&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(98)00135-3

DO - 10.1016/S0167-2789(98)00135-3

M3 - Article

AN - SCOPUS:0012289750

VL - 123

SP - 368

EP - 379

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-4

ER -