# 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 GdSe (Materials Project id mp-510404)

201 35 35 0 0 0 35 201 35 0 0 0 35 35 201 0 0 0 0 0 0 20 0 0 0 0 0 0 20 0 0 0 0 0 0 20

### Average properties

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

Voigt | K_{V} = 90.333 GPa | E_{V} = 116.22 GPa | G_{V} = 45.2 GPa | ν_{V} = 0.28558 |

Reuss | K_{R} = 90.333 GPa | E_{R} = 77.903 GPa | G_{R} = 28.72 GPa | ν_{R} = 0.35627 |

Hill | K_{H} = 90.333 GPa | E_{H} = 97.572 GPa | G_{H} = 36.96 GPa | ν_{H} = 0.31998 |

### Eigenvalues of the stiffness matrix

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

20 GPa | 20 GPa | 20 GPa | 166 GPa | 166 GPa | 271 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 | 55.876 GPa | 190.62 GPa | 3.69 TPa^{–1} | 3.69 TPa^{–1} | 20 GPa | 83 GPa | 0.052804 | 0.69675 | Value |

Anisotropy | 3.411 | 1.0000 | 4.15 | 13.1950 | Anisotropy | ||||

Axis | 0.5774 0.5773 -0.5774 |
1.0000 0.0000 0.0000 |
0.9239 0.0000 0.3827 |
0.4830 0.6294 -0.6088 |
0.0000 0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
-0.7071 0.0000 0.7071 |
0.7071 -0.0000 -0.7071 |
Axis |

-0.7660 0.6428 -0.0000 |
-0.7071 -0.0002 -0.7071 |
0.0000 -1.0000 0.0000 |
-0.7071 0.0002 -0.7071 |
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