Theory Background

Crystal type and independent elastic constants

  • 3D crystal

The different crystal symmetry of 3D materials are illustrated in Fig. 1, and the corresponding independent elastic constants are shown in Fig. 2.

_images/CrystalType_3D.png

Fig. 1 Symmetry in 3D crystal

(a)Triclinic; (b)Monoclinic; (c)Orthorhombic; (d)Tetragonal; (e)Cubic; (f)Trigonal; (g)Hexagonal

_images/IndependentCIJ_3D.png

Fig. 2 The independent elastic constants in 3D crystals

  • 2D crystal

The different crystal symmetry of 2D materials are illustrated in Fig. 3, and the corresponding independent elastic constants are shown in Fig. 4.

_images/CrystalType_2D.png

Fig. 3 Symmetry in 2D crystal

  1. Oblique; (b) Rectangular; (c) Square; (d)Hexagonal
_images/IndependentCIJ_2D.png

Fig. 4 The independent elastic constants in 2D crystals