# 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 Au (Materials Project id mp-81)

144 134 134 0 0 0 134 144 134 0 0 0 134 134 144 0 0 0 0 0 0 29 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} = 137.33 GPa | E_{V} = 55.583 GPa | G_{V} = 19.4 GPa | ν_{V} = 0.43255 |

Reuss | K_{R} = 137.33 GPa | E_{R} = 29.093 GPa | G_{R} = 9.9315 GPa | ν_{R} = 0.46469 |

Hill | K_{H} = 137.33 GPa | E_{H} = 42.485 GPa | G_{H} = 14.666 GPa | ν_{H} = 0.44844 |

### Eigenvalues of the stiffness matrix

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

10 GPa | 10 GPa | 29 GPa | 29 GPa | 29 GPa | 412 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 | 14.82 GPa | 81.279 GPa | 2.4272 TPa^{–1} | 2.4272 TPa^{–1} | 5 GPa | 29 GPa | -0.33932 | 1.2463 | Value |

Anisotropy | 5.484 | 1.0000 | 5.8 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.5774 0.5774 -0.5773 |
0.9992 -0.0001 -0.0393 |
0.0000 0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
0.0000 0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
0.0000 0.7071 -0.7071 |
Axis |

-0.7071 -0.0002 -0.7071 |
-0.1736 0.9848 -0.0000 |
-0.7071 -0.0002 -0.7071 |
-1.0000 0.0000 -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