Body-Centered Tetragonal (tI)

Stiffness Matrix

\[\begin{split}\begin{pmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ & C_{11} & C_{13} & 0 & 0 & 0 \\ & & C_{33} & 0 & 0 & 0 \\ & & & C_{44} & 0 & 0 \\ & & & & C_{44} & 0 \\ & & & & & C_{66} \end{pmatrix}\end{split}\]

Atom Arrangement

Figure 1: Body-centered tetragonal structure. X, Y, and Z crystal frame axes are colored red, green, and blue, respectively.

Slip Systems

index	slip direction	plane normal
1	\([0 0 1]\)	\((1 0 0)\)
2	\([0 0 1]\)	\((0 1 0)\)

Figure 2: \(\langle 0 0 1\rangle\,\{1 0 0\}\) slip system

index	slip direction	plane normal
3	\([0 0 1]\)	\(( 1 1 0)\)
4	\([0 0 1]\)	\((\bar 1 1 0)\)

Figure 3: \(\langle 0 0 1\rangle\,\{1 1 0\}\) slip system

index	slip direction	plane normal
5	\([0 1 0]\)	\((1 0 0)\)
6	\([1 0 0]\)	\((0 1 0)\)

Figure 4: \(\langle 0 1 0\rangle\,\{1 0 0\}\) slip system

index	slip direction	plane normal
7	\([ 1 \bar 1 1]\)	\(( 1 1 0)\)
8	\([ 1 \bar 1 \bar 1]\)	\(( 1 1 0)\)
9	\([\bar 1 \bar 1 \bar 1]\)	\((\bar 1 1 0)\)
10	\([\bar 1 \bar 1 1]\)	\((\bar 1 1 0)\)

Figure 5: \(\langle 1 \bar 1 1\rangle\,\{1 1 0\}\) slip system

index	slip direction	plane normal
11	\([1 \bar 1 0 ]\)	\((1 1 0)\)
12	\([1 1 0 ]\)	\((1 \bar 1 0)\)

Figure 6: \(\langle 1 \bar 1 0\rangle\,\{1 1 0\}\) slip system

index	slip direction	plane normal
13	\([ 0 1 1]\)	\((1 0 0)\)
14	\([ 0 \bar 1 1]\)	\((1 0 0)\)
15	\([\bar 1 0 1]\)	\((0 1 0)\)
16	\([ 1 0 1]\)	\((0 1 0)\)

Figure 7: \(\langle 0 1 1 \rangle\,\{1 0 0\}\) slip system

index	slip direction	plane normal
17	\([0 1 0]\)	\((0 0 1)\)
18	\([1 0 0]\)	\((0 0 1)\)

Figure 8: \(\langle 0 1 0 \rangle\,\{0 0 1\}\) slip system

index	slip direction	plane normal
19	\([ 1 1 0]\)	\((0 0 1)\)
20	\([\bar 1 1 0]\)	\((0 0 1)\)

Figure 9: \(\langle 1 \bar 1 0 \rangle\,\{0 0 1\}\) slip system

index	slip direction	plane normal
21	\([ 0 1 \bar 1]\)	\(( 0 1 1)\)
22	\([ 0 \bar 1 \bar 1]\)	\(( 0 \bar 1 1)\)
23	\([\bar 1 0 \bar 1]\)	\((\bar 1 0 1)\)
24	\([ 1 0 \bar 1]\)	\(( 1 0 1)\)

Figure 10: \(\langle 0 1 \bar 1 \rangle\,\{0 1 1\}\) slip system

index	slip direction	plane normal
25	\([ 1 \bar 1 1]\)	\((0 1 1)\)
26	\([ 1 1 \bar 1]\)	\((0 1 1)\)
27	\([ 1 1 1]\)	\((0 1 \bar 1)\)
28	\([\bar 1 1 1]\)	\((0 1 \bar 1)\)
29	\([ 1 \bar 1 \bar 1]\)	\((1 0 1)\)
30	\([\bar 1 \bar 1 1]\)	\((1 0 1)\)
31	\([ 1 1 1]\)	\((1 0 \bar 1)\)
32	\([ 1 \bar 1 1]\)	\((1 0 \bar 1)\)

Figure 11: \(\langle 1 \bar 1 1 \rangle\,\{0 1 1\}\) slip system

index	slip direction	plane normal
33	\([1 0 0]\)	\((0 1 1)\)
34	\([1 0 0]\)	\((0 1 \bar 1)\)
35	\([0 1 0]\)	\((1 0 1)\)
36	\([0 1 0]\)	\((1 0 \bar 1)\)

Figure 12: \(\langle 1 0 0 \rangle\,\{0 1 1\}\) slip system

index	slip direction	plane normal
37	\([ 0 1 \bar 1]\)	\(( 2 1 1)\)
38	\([ 0 \bar 1 \bar 1]\)	\(( 2 \bar 1 1)\)
39	\([ 1 0 \bar 1]\)	\(( 1 2 1)\)
40	\([\bar 1 0 \bar 1]\)	\((\bar 1 2 1)\)
41	\([ 0 1 \bar 1]\)	\((\bar 2 1 1)\)
42	\([ 0 \bar 1 \bar 1]\)	\((\bar 2 \bar 1 1)\)
43	\([\bar 1 0 \bar 1]\)	\((\bar 1 \bar 2 1)\)
44	\([ 1 0 \bar 1]\)	\(( 1 \bar 2 1)\)

index	slip direction	plane normal
45	\([\bar 1 1 1]\)	\(( 2 1 1)\)
46	\([\bar 1 \bar 1 1]\)	\(( 2 \bar 1 1)\)
47	\([ 1 \bar 1 1]\)	\(( 1 2 1)\)
48	\([\bar 1 \bar 1 1]\)	\((\bar 1 2 1)\)
49	\([ 1 1 1]\)	\((\bar 2 1 1)\)
50	\([ 1 \bar 1 1]\)	\((\bar 2 \bar 1 1)\)
51	\([\bar 1 1 1]\)	\((\bar 1 \bar 2 1)\)
52	\([ 1 1 1]\)	\(( 1 \bar 2 1)\)