TABLE I: Cartesian components of switching vectors r , domain wall normals s , and boundary conditions for polarization and strain in adjacent domain states for the inspected domain walls. Vector s$_{O60}$ is defined in Eqn. (3), P$_{0}$ stands for magnitude of spontaneous polarization. As usual, spontaneous quantities are those minimizing GLD functional. Numerical values used in this work are given in Sec˙ V. 4 Wall r s P ( −∞ ) /P$_{0}$ P ( ∞ ) /P$_{0}$ e ( −∞ ) e ( ∞ ) T180 { 001 } (1 , 0 , 0) (0 , 0 , 1) (1 , 0 , 0) ( − 1 , 0 , 0) ( $^{e}$‖$^{, e}$⊥$^{, e}$⊥, 0 , 0 , 0) ( $^{e}$‖$^{, e}$⊥$^{, e}$⊥, 0 , 0 , 0) T180 { 011 } (1 , 0 , 0) (0 , 1 √$_{2}$ , 1 √$_{2}$ ) (1 , 0 , 0) ( − 1 , 0 , 0) ( $^{e}$‖$^{, e}$⊥$^{, e}$⊥, 0 , 0 , 0) ( $^{e}$‖$^{, e}$⊥$^{, e}$⊥, 0 , 0 , 0) T90 ( 1 √$_{2}$ , 1 √$_{2}$ , 0) ( 1 √$_{2}$ , − 1 √$_{2}$ , 0) (1 , 0 , 0) (0 , − 1 , 0) ( $^{e}$‖$^{, e}$⊥$^{, e}$⊥, 0 , 0 , 0) ( $^{e}$⊥$^{, e}$‖$^{, e}$⊥, 0 , 0 , 0) O180 { 1 ¯ 10 } ( 1 √$_{2}$ , 1 √$_{2}$ , 0) ( 1 √$_{2}$ , − 1 √$_{2}$ , 0) ( 1 √$_{2}$ , 1 √$_{2}$ , 0) $_{(}$− 1 √$_{2}$ , − 1 √$_{2}$ , 0) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) O180 { 001 } ( 1 √$_{2}$ , 1 √$_{2}$ , 0) (0 , 0 , 1) ( 1 √$_{2}$ , 1 √$_{2}$ , 0) $_{(}$− 1 √$_{2}$ , − 1 √$_{2}$ , 0) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) O90 (0 , 1 , 0) (1 , 0 , 0) ( 1 √$_{2}$ , 1 √$_{2}$ , 0) ( 1 √$_{2}$ , − 1 √$_{2}$ , 0) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , − 2 e$_{b}$ ) O60 ( 1 √$_{2}$ , 0 , 1 √$_{2}$ ) s$_{O60}$ ( 1 √$_{2}$ , 1 √$_{2}$ , 0) (0 , 1 √$_{2}$ , − 1 √$_{2}$ ) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) ( e$_{c}$, e$_{a}$, e$_{a}$, − 2 e$_{b}$, 0 , 0) O120 ( 1 √$_{6}$ , 2 √$_{6}$ , − 1 √$_{6}$ ) ( 1 √$_{2}$ , 0 , 1 √$_{2}$ ) ( 1 √$_{2}$ , 1 √$_{2}$ , 0) (0 , − 1 √$_{2}$ , 1 √$_{2}$ ) ( e$_{a}$, e$_{a}$, e$_{c}$, 0 , 0 , 2 e$_{b}$ ) ( e$_{c}$, e$_{a}$, e$_{a}$, − 2 e$_{b}$, 0 , 0) R180 { 1 ¯ 10 } ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ ) ( 1 √$_{2}$ , − 1 √$_{2}$ , 0) ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ $_{) (}$− 1 √$_{3}$ , − 1 √$_{3}$ , − 1 √$_{3}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) R180 { ¯ 211 } ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ $_{) (}$− 2 √$_{6}$ , 1 √$_{6}$ , 1 √$_{6}$ ) ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ $_{) (}$− 1 √$_{3}$ , − 1 √$_{3}$ , − 1 √$_{3}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) R109 ( 1 √$_{2}$ , 1 √$_{2}$ , 0) (0 , 0 , 1) ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ $_{) (}$− 1 √$_{3}$ , − 1 √$_{3}$ , 1 √$_{3}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, − 2 e$_{b}$, − 2 e$_{b}$, 2 e$_{b}$ ) R71 (0 , 1 , 0) ( 1 √$_{2}$ , 0 , 1 √$_{2}$ ) ( 1 √$_{3}$ , 1 √$_{3}$ , 1 √$_{3}$ ) ( 1 √$_{3}$ , − 1 √$_{3}$ , 1 √$_{3}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, 2 e$_{b}$, 2 e$_{b}$, 2 e$_{b}$ ) ( e$_{a}$, e$_{a}$, e$_{a}$, − 2 e$_{b}$, 2 e$_{b}$, − 2 e$_{b}$ ) 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 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 − $^{3}$. with The Ginzburg gradient term f$_{G}$ is considered in the form 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 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 α$_{1}$ = 3 . 34 × 10 $^{5}$( T − 381) α$_{11}$ = 4 . 69 10 $^{6}$( T 393) − 2 . 02 × 10 8 α$_{111}$ = − 5 . 52 × 10 $^{7}$( T − 393) + 2 . 76 × 10 9 , (12) f$_{G}$ = 1 2 G$_{11}$ ( P 2 1 , 1 + P 2 , 2 + P 2 3 , $_{3}$) + G$_{12}$ ( P$_{1}$$_{,}$$_{1}$P$_{2}$$_{,}$$_{2}$ + P$_{2}$$_{,}$$_{2}$P$_{3}$$_{,}$$_{3}$ + P$_{1}$$_{,}$$_{1}$P$_{3}$$_{,}$$_{3}$ ) + 1 2 G$_{44}$ (( P$_{1}$$_{,}$$_{2}$ + P$_{2}$$_{,}$$_{1}$ ) 2 + ( P$_{2}$$_{,}$$_{3}$ + P$_{3}$$_{,}$$_{2}$ ) 2 + ( P$_{3}$$_{,}$$_{1}$ + P$_{1}$$_{,}$$_{3}$ ) $^{2}$) . (11) ˆ C$_{11}$ = C$_{11}$ + 2 C$_{12}$ ˆ C$_{12}$ = C$_{11}$ − C$_{12}$ ˆ q$_{11}$ = q$_{11}$ + 2 q$_{12}$ ˆ q$_{12}$ = q$_{11}$ − q$_{12}$ . (10) α ( e ) 11 = α$_{11}$ + 1 6 [ ˆ q 2 11 ˆ C$_{11}$ + 2 ˆ q 2 22 ˆ $_{C$_{22}$}$] α ( e ) 12 = α$_{12}$ + 1 6 [ 2 ˆ q 2 11 ˆ C$_{11}$ − 2 ˆ q 2 22 ˆ C$_{22}$ + 3 q 2 44 C$_{44}$ ] (9) IV. STRAIGHT POLARIZATION PATH APPROXIMATION