# 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 BeSe (Materials Project id mp-1008524)

149 94 40 0 0 0 94 149 40 0 0 0 40 40 189 0 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 28

### Average properties

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

Voigt | K_{V} = 92.778 GPa | E_{V} = 77.476 GPa | G_{V} = 28.467 GPa | ν_{V} = 0.36082 |

Reuss | K_{R} = 92.683 GPa | E_{R} = 29.816 GPa | G_{R} = 10.307 GPa | ν_{R} = 0.44638 |

Hill | K_{H} = 92.731 GPa | E_{H} = 54.371 GPa | G_{H} = 19.387 GPa | ν_{H} = 0.40228 |

### Eigenvalues of the stiffness matrix

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

5 GPa | 5 GPa | 28 GPa | 55 GPa | 153.32 GPa | 278.68 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 | 18.579 GPa | 175.83 GPa | 3.4873 TPa^{–1} | 3.8149 TPa^{–1} | 5 GPa | 53.472 GPa | 0.057994 | 0.86509 | Value |

Anisotropy | 9.464 | 1.0940 | 10.69 | 14.9168 | Anisotropy | ||||

Axis | 0.7180 0.0000 0.6961 |
0.0000 0.0000 1.0000 |
0.2390 0.9710 -0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.5236 0.4753 -0.7071 |
-0.3465 0.3465 -0.8717 |
-0.4492 0.4492 -0.7723 |
Axis |

-0.7660 0.6428 -0.0000 |
-0.5235 -0.4753 -0.7071 |
-0.7071 -0.7071 -0.0000 |
-0.5461 0.5461 0.6353 |
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