# ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by **Romain Gaillac** and **François-Xavier Coudert** at CNRS / Chimie
ParisTech.

If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (*J. Phys. Condens. Matter*, 2016, 28, 275201) and give the
website URL.

ELATE is open source software. Any queries or comments are welcome at

## Summary of the properties

### Input: stiffness matrix (coefficients in GPa) of SiC (Materials Project id mp-568619)

494 98 50 -31 0 0 98 494 50 31 0 0 50 50 534 0 0 0 -31 31 0 159 0 0 0 0 0 0 159 -31 0 0 0 0 -31 198

### Average properties

Averaging scheme | Bulk modulus | Young's modulus | Shear modulus | Poisson's ratio |
---|---|---|---|---|

Voigt | K_{V} = 213.11 GPa | E_{V} = 442.02 GPa | G_{V} = 191.47 GPa | ν_{V} = 0.15431 |

Reuss | K_{R} = 213.1 GPa | E_{R} = 424.63 GPa | G_{R} = 181.8 GPa | ν_{R} = 0.16789 |

Hill | K_{H} = 213.11 GPa | E_{H} = 433.38 GPa | G_{H} = 186.63 GPa | ν_{H} = 0.16106 |

### Eigenvalues of the stiffness matrix

λ_{1} |
λ_{2} |
λ_{3} |
λ_{4} |
λ_{5} |
λ_{6} |
---|---|---|---|---|---|

141.88 GPa | 151.15 GPa | 215.12 GPa | 403.85 GPa | 486.57 GPa | 639.43 GPa |

### Variations of the elastic moduli

Young's modulus | Linear compressibility | Shear modulus | Poisson's ratio | ||||||
---|---|---|---|---|---|---|---|---|---|

E_{min} | E_{max} |
β_{min} | β_{max} | G_{min} | G_{max} |
ν_{min} | ν_{max} | ||

Value | 349.13 GPa | 525.55 GPa | 1.5556 TPa^{–1} | 1.5813 TPa^{–1} | 141.88 GPa | 234.28 GPa | 0.0051615 | 0.3098 | Value |

Anisotropy | 1.505 | 1.0165 | 1.651 | 60.0222 | Anisotropy | ||||

Axis | 0.6900 0.3983 0.6044 |
0.0000 0.0000 1.0000 |
0.9220 0.3872 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.4835 0.8753 |
0.0000 0.6233 0.7820 |
0.4404 0.2543 -0.8610 |
0.5313 0.3074 -0.7894 |
Axis |

-1.0000 0.0000 -0.0000 |
0.0000 0.7820 -0.6233 |
-0.5000 0.8660 0.0000 |
-0.6839 -0.3944 -0.6138 |
Second axis |

## Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

## Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

## Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

## Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane