# 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 PbF4 (Materials Project id mp-341)

199 4 0 0 0 0 4 199 0 0 0 0 0 0 16 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 11

### Average properties

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

Voigt | K_{V} = 46.889 GPa | E_{V} = 80.45 GPa | G_{V} = 33.133 GPa | ν_{V} = 0.21404 |

Reuss | K_{R} = 13.821 GPa | E_{R} = 28.27 GPa | G_{R} = 12.195 GPa | ν_{R} = 0.1591 |

Hill | K_{H} = 30.355 GPa | E_{H} = 54.443 GPa | G_{H} = 22.664 GPa | ν_{H} = 0.20108 |

### Eigenvalues of the stiffness matrix

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

9 GPa | 9 GPa | 11 GPa | 16 GPa | 195 GPa | 203 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 | 16 GPa | 198.92 GPa | 4.9261 TPa^{–1} | 62.5 TPa^{–1} | 9 GPa | 97.5 GPa | 0 | 0.80444 | Value |

Anisotropy | 12.43 | 12.6875 | 10.83 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
-0.3827 0.9239 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
-0.7071 0.7071 0.0000 |
0.0000 0.0000 1.0000 |
-0.7071 0.7071 -0.0000 |
Axis |

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