Schematic illustrating the relief produced on a surface by twinning. This is a cross-section of a twin perpendicular to the direction. The orientation of the orthorhombic unit cell is indicated. The thick black lines are twin boundaries. The twin sequence is CAC (the letters indicate which crystallographic direction is perpendicular to the surface) and the relief angle and twinning angle are equal, .
(a) The twin found in Fig. 1(a) after polishing and (b) at a temperature above the martensitic transformation where a double kink appears at the position of the former A twin domain. The relief angles are equal and opposite to the relief angles in Fig. 1.
Reliefs generated on a surface by different transformation paths through twinning when cooling from the situation shown in Fig. 2(b). (a) Twinning on the same planes as in Fig. 2(a) and the same twin sequence ACA changes the relief angle by and results in a flat surface; (b) reversal of the twin sequence to ACA increases the relief angle by to a total relief angle of ; (c) changing the twinning planes also doubles the final relief angle when keeping the sequence CAC; and (d) changing both the twinning sequence (from CAC to ACA) and the twinning plane orientation results in a flat surface.
Reliefs generated on a surface by different transformation paths with twinning upon cooling when starting from the situation shown in Fig. 2(b). (a) Twin sequence CBC and the same twin plane orientation as before heating leads to a final relief angle ; (b) twin sequence BCB and the same twin plane orientation as before heating leads to a final relief angle of ; (c) twin sequence CBC with a different twinning plane orientation results in ; and (d) twin sequence BCB with twinning planes inclined to the right results in .
Loading geometry for the thermomechanical treatment. The sample was compressed parallel to the shortest edge which is the direction. Cartesian coordinates were defined as indicated. The crystallographic direction is parallel to the axis over most of the sample. There are two possibilities for the orientation of the crystallographic and directions. The AFM and MFM experiments were performed on the shaded surface normal to the axis.
Representative (a) AFM height image, (b) amplitude error image, and (c) MFM magnetic image of the face showing surface relief bands taken at room temperature. In the amplitude error image, the three shades of gray each indicate areas of relatively equivalent slope values. The strong contrast of the magnetic image indicates out-of-plane magnetization while the weak (neutral) contrast indicates in-plane magnetization (Ref. 15). The angle, (defined in b), between the surface relief bands measures 8.4°.
Representative (a) AFM height image, (b) amplitude error image, and (c) MFM magnetic image of the surface relief at . (d) A cross-section of the surface with a relief angle [the subscript H3 refers to the labeling in Fig. 8(b)]. The position of the cross-section (d) is marked with a white line in (a). Regions R1 and R2 point out an uncommon trait found in this image. Most often similar twin domains have parallel and equivalent slope values (i.e., for R1 and for R2). Thus, the difference between the slopes of R1 and R2 is 0.9°.
(a) AFM amplitude error image is overlaid with a small section of the MFM magnetic image to define the location of the P twin boundaries. ( from left to right) indicate the names of each P twin boundary. The twin domains alternate from A to B to A across each boundary. (b) AFM amplitude error image with H twin boundaries defined. ( from left to right) indicate the names of each H twin boundary. The twin domains alternate from K to L to K across each boundary.
The combination of Figs. 8(a) and 8(b) onto the AFM height image. The solid black lines mark P twin boundaries and the long dashed black lines mark H twin boundaries. Lines 1–5 (dotted lines) indicate cross-sections used to measure the slope angles for the H twins and lines 6–10 (short dashed line) indicate cross-sections used to measure the slope angles for the P twins. The angle between the traces of H and P twins measures 8.4°. Labels are as defined in Fig. 8.
Twinning angles for specific twinning systems in orthorhombic (14M) and tetragonal (10M) martensite calculated with Eq. (1) and using lattice parameter of Ref. 5.
Total relief angles going from twinning mode 1 to twinning mode 2 (or vice versa) upon heating and cooling for surface planes parallel to . The relief angles are with , the sign is positive for additive shear and negative for subtractive shear).
Slope angles and relief angles for the H and P twinning events. The subscript letters stand for H, P, and the areas as described in Fig. 8. The values for the relief angles (last four rows) were obtained with Eqs. (2)–(5).
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