# 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 MnF2 (Materials Project id mp-560902)

158 67 67 0 0 0 67 99 77 0 0 0 67 77 99 0 0 0 0 0 0 68 0 0 0 0 0 0 29 0 0 0 0 0 0 29

### Average properties

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

Voigt | K_{V} = 86.444 GPa | E_{V} = 92.203 GPa | G_{V} = 34.867 GPa | ν_{V} = 0.32223 |

Reuss | K_{R} = 84.063 GPa | E_{R} = 67.582 GPa | G_{R} = 24.737 GPa | ν_{R} = 0.36601 |

Hill | K_{H} = 85.253 GPa | E_{H} = 80.075 GPa | G_{H} = 29.802 GPa | ν_{H} = 0.34346 |

### Eigenvalues of the stiffness matrix

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

22 GPa | 29 GPa | 29 GPa | 68 GPa | 71.821 GPa | 262.18 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 | 37.143 GPa | 127.03 GPa | 2.2305 TPa^{–1} | 4.8327 TPa^{–1} | 11 GPa | 68 GPa | -0.065926 | 0.70979 | Value |

Anisotropy | 3.42 | 2.1667 | 6.182 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.0000 0.7071 0.7071 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.0002 0.7071 -0.7071 |
0.0000 -0.0000 1.0000 |
0.0000 0.7071 -0.7071 |
0.5498 0.0004 0.8353 |
Axis |

0.0002 -0.7071 -0.7071 |
-0.0000 1.0000 0.0000 |
-0.0000 0.7071 0.7071 |
-0.0005 1.0000 -0.0001 |
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