P W. Dondl, J. Zimmer/J. Mech. Phys. Solids 52(2004)2057-2077 Fig. 2. Tetragonal reference configuration. The axes c1, c2 and c3 of rotations in the tetragonal point group Fig. 3. Schematic of the three-dimensional P3=0 is shown. The bo tetragonal minimum is marked with a t. the orthorhombic is marked with an‘o’.Th ce in scaling of Pi and p2 in the real esh is too large to be accurately displayed here. The mor is not in the plan We study this phase transformation using a continuum theory by invoking the Cauchy-Born rule(Ericksen in Gurtin, 1984). Let 22 CR3 reference configura tion. The deformation of the crystal is given by y(r). The displacement is defined as u(x): =y(x)-x. The deformation gradient is F According to the Cauchy-Born rule, this deformation gradient serves as a measure of the deformation of the lattice It is well known that there are several variants of the low-symmetry phases, where the number of variants is given by the quotient of the order of the high symmet group and the low symmetry group(see, e.g., Bhattacharya, 2003, Section 4.3)2062 P.W. Dondl, J. Zimmer / J. Mech. Phys. Solids 52 (2004) 2057 – 2077 Fig. 2. Tetragonal reference con3guration. The axes c1, c2 and c3 of rotations in the tetragonal point group are shown. Fig. 3. Schematic representation of the three-dimensional mesh used for the interpolation of the energy. A two-dimensional cut in the plane 3 = 0 is shown. The box with the tetragonal minimum is marked with a ‘t’, the orthorhombic minimum is marked with an ‘o’. The diIerence in scaling of 1 and 2 in the real mesh is too large to be accurately displayed here. The monoclinic minimum is not in the plane 3 = 0. We study this phase transformation using a continuum theory by invoking the Cauchy–Born rule (Ericksen in Gurtin, 1984). Let  ⊂ R3 be the reference con3gura￾tion. The deformation of the crystal is given by y(x). The displacement is de3ned as u(x) := y(x) − x. The deformation gradient is Fij := @yj @xi : According to the Cauchy–Born rule, this deformation gradient serves as a measure of the deformation of the lattice. It is well known that there are several variants of the low-symmetry phases, where the number of variants is given by the quotient of the order of the high symmetry group and the low symmetry group (see, e.g., Bhattacharya, 2003, Section 4.3)