# 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 SiC2 (Materials Project id mp-1019097)

327 5 87 0 0 0 5 327 87 0 0 0 87 87 502 0 0 0 0 0 0 36 0 0 0 0 0 0 36 0 0 0 0 0 0 14

### Average properties

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

Voigt | K_{V} = 168.22 GPa | E_{V} = 212.36 GPa | G_{V} = 82.333 GPa | ν_{V} = 0.28961 |

Reuss | K_{R} = 153.37 GPa | E_{R} = 99.52 GPa | G_{R} = 35.751 GPa | ν_{R} = 0.39185 |

Hill | K_{H} = 160.79 GPa | E_{H} = 157.81 GPa | G_{H} = 59.042 GPa | ν_{H} = 0.33643 |

### Eigenvalues of the stiffness matrix

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

14 GPa | 36 GPa | 36 GPa | 267.46 GPa | 322 GPa | 566.54 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 | 51.246 GPa | 456.4 GPa | 1.0427 TPa^{–1} | 2.7388 TPa^{–1} | 14 GPa | 152.7 GPa | -0.032308 | 0.83022 | Value |

Anisotropy | 8.906 | 2.6266 | 10.91 | ∞ | Anisotropy | ||||

Axis | 0.7071 0.7071 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.5000 0.8660 0.0000 |
1.0000 -0.0002 -0.0000 |
0.7071 -0.0000 -0.7071 |
-1.0000 0.0000 -0.0001 |
0.7071 0.7071 -0.0000 |
Axis |

0.0002 1.0000 -0.0000 |
-0.7071 0.0002 -0.7071 |
-0.0000 -1.0000 -0.0000 |
-0.7071 0.7071 0.0000 |
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