The surface energy density of the domain wall is where The domain wall characteristics depend on the coeffi- cients g, a$_{1}$, a$_{11}$, a$_{111}$ through Eqs. (19, 20, 23, 25). The explicit expressions for these coefficients are summarized for various domain walls in Table II. The expressions are simplified using the notation inspired by Ref. 1. For all phases we are using: for tetragonal and orthorhombic phases we are abbrevi- ating and for the rhombohedral phase Advantage of the GLD approach is that domain wall properties can be obtained at any temperature. In Ta- ble III we give numerical results for domain wall param- eters at one particular temperature for each of the ferro- electric phases: at 298 K, 208 K, and 118 K for the tetrag- onal, orthorhombic, and rhombohedral phase, resp. Cor- responding numerical values of the spontaneous quanti- ties appearing in Table I are: P$_{0}$ = 0 . 265 C m − $^{2}$, e$_{‖}$ = Q$_{11}$P 2 0 = 7 . 77 × 10 − 3 and e$_{⊥}$ = Q$_{12}$P 2 0 = − 3 . 18 × 10 − 3 (the tetragonal phase, 298 K); P$_{0}$ = 0 . 331 C m − $^{2}$, e$_{a}$ = Q$_{11}$ + Q$_{12}$ 2 P 2 0 = 3 . 58 × 10 − $^{3}$, e$_{c}$ = Q$_{12}$P 2 0 = − 4 . 96 × 10 − 3 and e$_{b}$ = Q$_{44}$ 4 P 2 0 = 0 . 79 × 10 − 3 (the orthorhombic phase, 208 K); P$_{0}$ = 0 . 381 C m − $^{2}$, e$_{a}$ = Q$_{11}$ +2 Q$_{12}$ 3 P 2 0 = 0 . 97 × 10 − 3 and e$_{b}$ = Q$_{44}$ 4 P 2 0 = 0 . 70 × 10 − 3 (the rhom- The expressions for the coefficients of the T180 and T90 domain walls are equivalent to the previously pub- lished expressions. 1,4 Derivations for O60, O120, and R180 { ¯ 211 } walls lead to complicated formulas, and there- fore only numerical results for g, a$_{1}$, a$_{11}$ , and a$_{111}$ coeffi- cients are presented here. C ′ 33 = C$_{11}$ + C$_{12}$ + 2 C$_{44}$ 2 q ′ 11 = q$_{11}$ + 2 q$_{12}$ + 2 q$_{44}$ 3 q ′ 13 = q$_{11}$ + 2 q$_{12}$ − q$_{44}$ 3 . (27) C ′ 11 = C$_{11}$ + C$_{12}$ + 2 C$_{44}$ 2 C ′ 12 = C$_{11}$ + C$_{12}$ − 2 C$_{44}$ 2 C ′ 66 = C$_{11}$ − C$_{12}$ 2 q ′ 11 = q$_{11}$ + q$_{12}$ + q$_{44}$ 2 q ′ 12 = q$_{11}$ + q$_{12}$ − q$_{44}$ 2 q ′ 66 = q$_{11}$ − q$_{12}$ , a r 1 = α$_{1}$ − [ 1 3 ˆ q 2 11 ˆ C$_{11}$ + 1 6 ˆ q 2 22 ˆ C$_{22}$ − ( q$_{11}$ + q$_{12}$ ) q ′ 12 2 C ′ 11 ] P 2 0 a r 11 = α ( e ) 11 2 + α ( e ) 12 4 − q ′ 2 12 2 C ′ 11 a rs 12 = 3 α ( e ) 11 − α ( e ) 12 2 − q ′ $_{11}$q ′ 12 C ′ 11 − ˆ q 2 22 2 ˆ C$_{22}$ a ′ 111 = 1 4 ( α$_{111}$ + α$_{112}$ ) a ′ 112 = 1 4 (15 α$_{111}$ − α$_{112}$ ) , I ( A ) = 3 4 ∫ ∞ −∞ cosh $^{2}$( h ) dh ( A + cosh $^{2}$( h ) − 1) 3 . (26) Σ = ∫ ∞ −∞ ( f$_{EL}$ ( s ) − f$_{EL}$ ( p$_{∞}$ )) ds = 4 3 p$_{∞}$ √ 2 gU [ A 5 / $^{2}$I ( A ) ] , (25) FIG. 4: Dependence of correction factor in the expression for domain wall energy density (25) as a function of the shape coefficient A . Full points indicate values of A for particular domain walls considered in Table III. FIG. 5: Course of strain components along the domain wall normal coordinate s for the T90 domain wall. Indices refer to cubic axes of the parent phase. V. QUANTITATIVE RESULTS 6