# 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 Mo2C (Materials Project id mp-1552)

488 169 226 0 0 0 169 489 216 0 0 0 226 216 453 0 0 0 0 0 0 179 0 0 0 0 0 0 167 0 0 0 0 0 0 139

### Average properties

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

Voigt | K_{V} = 294.67 GPa | E_{V} = 388.22 GPa | G_{V} = 151.6 GPa | ν_{V} = 0.28042 |

Reuss | K_{R} = 294.57 GPa | E_{R} = 379.48 GPa | G_{R} = 147.63 GPa | ν_{R} = 0.28529 |

Hill | K_{H} = 294.62 GPa | E_{H} = 383.86 GPa | G_{H} = 149.61 GPa | ν_{H} = 0.28285 |

### Eigenvalues of the stiffness matrix

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

139 GPa | 167 GPa | 179 GPa | 226.02 GPa | 319.86 GPa | 884.12 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 | 304.27 GPa | 431.51 GPa | 1.0771 TPa^{–1} | 1.1739 TPa^{–1} | 118.36 GPa | 179 GPa | 0.15865 | 0.42325 | Value |

Anisotropy | 1.418 | 1.0899 | 1.512 | 2.6679 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.0000 0.7920 0.6105 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
0.5723 0.4153 0.7071 |
-0.0000 0.0000 1.0000 |
-1.0000 -0.0001 -0.0000 |
1.0000 0.0003 0.0000 |
Axis |

0.5724 0.4151 -0.7071 |
0.0000 -1.0000 0.0000 |
0.0001 -1.0000 -0.0000 |
0.0000 0.0002 -1.0000 |
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