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strains (in the homogeneous sample). The bar α ( e ) 11 , α ( e ) 12 and the relaxed α$_{11}$, α$_{12}$ coefficients are related as: 4 

with 

The Ginzburg gradient term f$_{G}$ is considered in the form 

<img src='content_image/386928.jpg'>

It was pointed out 4 that the tensor of gradient constants of BaTiO$_{3}$ is highly anisotropic with fundamental conse- quences on predicted domain wall properties. Up to now, the isotropic gradient tensor G$_{i,j}$ was mostly employed in the computations. 

The material-specific coefficients in the model are as- sumed being constant, except for the three Landau po- tential coefficients 

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where T is absolute temperature. 13 The phase transi- tions occur in this model at the temperatures 392.3 K (C → T), 282.5 K (T → O), and 201.8 K (O → R). 13 All phase transitions are of the first order, the local min- ima corresponding to the tetragonal, orthorhombic and rhombohedral phase exist for this Landau potential between 237 K and 393 K, between 104 K and 303 K, and below 256 K, respectively. Full set of temperature independent parameters of the GLD model reads: 4,14 α$_{12}$ = 3 . 230 × 10 $^{8}$Jm$^{5}$C − $^{4}$, α$_{112}$ = 4 . 470 × 10 $^{9}$Jm$^{9}$C − $^{6}$, α$_{123}$ = 4 . 910 10 $^{9}$Jm$^{9}$C − $^{6}$, G$_{11}$ = 51 × 10 − $^{11}$Jm$^{3}$C − $^{2}$, G$_{12}$ = − 2 × 10 − $^{11}$Jm$^{3}$C − $^{2}$, G$_{44}$ = 2 10 − $^{11}$Jm$^{3}$C − $^{2}$, q$_{11}$ = 14 . 20 × 10 $^{9}$JmC − $^{2}$, q$_{12}$ = − 0 . 74 × 10 $^{9}$JmC − $^{2}$, q$_{44}$ = 1 . 57 10 $^{9}$JmC − $^{2}$, C$_{11}$ = 27 . 50 10 $^{10}$Jm − $^{3}$, C$_{12}$ = 17 . 90 × 10 $^{10}$Jm − 3 and C$_{44}$ = 5 . 43 × 10 $^{10}$Jm − $^{3}$. 

## IV. STRAIGHT POLARIZATION PATH APPROXIMATION 

Let us consider a single mechanically compatible and electrically neutral domain wall in a perfect infinite stress-free crystal. Within the continuum GLD theory, such domain wall is associated with a planar kink solution of the Euler-Lagrange equations of the GLD functional for polarization vector and the strain tensor. 1,2,4,16 Do- main wall type is specified by selection of the wall normal s and by the two domain states at s = −∞ and + ∞ . This ideal geometry implies that the polarization and strain vary only along normal to the wall s and domain wall can be thus considered as a trajectory in order-parameter space. 

Even if the domain wall is neutral, in its central part the local electric charges can occur due to the position-dependent polarization. The additional assump- tion ∇ · P = 0 ensures the absence of charges in the whole domain wall. Then the local electric field is zero and the electrostatic contribution vanishes. Such strictly 

