# 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 Cu (Materials Project id mp-30)

180 127 127 0 0 0 127 180 127 0 0 0 127 127 180 0 0 0 0 0 0 78 0 0 0 0 0 0 78 0 0 0 0 0 0 78

### Average properties

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

Voigt | K_{V} = 144.67 GPa | E_{V} = 152.09 GPa | G_{V} = 57.4 GPa | ν_{V} = 0.32479 |

Reuss | K_{R} = 144.67 GPa | E_{R} = 119.57 GPa | G_{R} = 43.885 GPa | ν_{R} = 0.36225 |

Hill | K_{H} = 144.67 GPa | E_{H} = 136.05 GPa | G_{H} = 50.643 GPa | ν_{H} = 0.34326 |

### Eigenvalues of the stiffness matrix

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

53 GPa | 53 GPa | 78 GPa | 78 GPa | 78 GPa | 434 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 | 74.925 GPa | 198.35 GPa | 2.3041 TPa^{–1} | 2.3041 TPa^{–1} | 26.5 GPa | 78 GPa | -0.099409 | 0.77569 | Value |

Anisotropy | 2.647 | 1.0000 | 2.943 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5774 0.5773 -0.5774 |
0.7934 0.0000 0.6088 |
0.3314 0.8001 0.5000 |
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 |
-0.7660 0.6428 -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