# 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 PbCl2 (Materials Project id mp-862871)

46 25 25 0 0 0 25 33 28 0 0 0 25 28 33 0 0 0 0 0 0 27 0 0 0 0 0 0 7 0 0 0 0 0 0 7

### Average properties

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

Voigt | K_{V} = 29.778 GPa | E_{V} = 28.107 GPa | G_{V} = 10.467 GPa | ν_{V} = 0.34269 |

Reuss | K_{R} = 29.358 GPa | E_{R} = 16.772 GPa | G_{R} = 5.9696 GPa | ν_{R} = 0.40479 |

Hill | K_{H} = 29.568 GPa | E_{H} = 22.564 GPa | G_{H} = 8.2181 GPa | ν_{H} = 0.37281 |

### Eigenvalues of the stiffness matrix

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

5 GPa | 7 GPa | 7 GPa | 17.358 GPa | 27 GPa | 89.642 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 | 8.7122 GPa | 41.596 GPa | 7.0694 TPa^{–1} | 13.496 TPa^{–1} | 2.5 GPa | 27 GPa | -0.2297 | 0.7774 | Value |

Anisotropy | 4.774 | 1.9091 | 10.8 | ∞ | Anisotropy | ||||

Axis | 0.0000 1.0000 0.0000 |
0.0000 0.7071 0.7071 |
1.0000 0.0000 0.0000 |
0.0000 0.9914 0.1305 |
0.0002 0.7071 -0.7071 |
0.0000 -0.0000 1.0000 |
-0.0000 0.7071 -0.7071 |
0.5877 0.0002 0.8091 |
Axis |

0.0002 -0.7071 -0.7071 |
-0.0000 -1.0000 -0.0000 |
-0.0000 0.7071 0.7071 |
-0.0003 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