# 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 Sn (Materials Project id mp-949028)

55 20 20 0 0 0 20 55 20 0 0 0 20 20 55 0 0 0 0 0 0 18 0 0 0 0 0 0 18 0 0 0 0 0 0 18

### Average properties

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

Voigt | K_{V} = 31.667 GPa | E_{V} = 44.973 GPa | G_{V} = 17.8 GPa | ν_{V} = 0.2633 |

Reuss | K_{R} = 31.667 GPa | E_{R} = 44.966 GPa | G_{R} = 17.797 GPa | ν_{R} = 0.26334 |

Hill | K_{H} = 31.667 GPa | E_{H} = 44.97 GPa | G_{H} = 17.798 GPa | ν_{H} = 0.26332 |

### Eigenvalues of the stiffness matrix

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

18 GPa | 18 GPa | 18 GPa | 35 GPa | 35 GPa | 95 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 | 44.333 GPa | 45.398 GPa | 10.526 TPa^{–1} | 10.526 TPa^{–1} | 17.5 GPa | 18 GPa | 0.25353 | 0.27144 | Value |

Anisotropy | 1.024 | 1.0000 | 1.029 | 1.0706 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.5774 0.5774 0.5773 |
0.3827 0.0000 0.9239 |
0.3794 0.9160 -0.1305 |
0.7071 -0.0003 0.7071 |
0.0000 0.0000 1.0000 |
0.7071 -0.0000 -0.7071 |
-0.7071 -0.0000 -0.7071 |
Axis |

0.7071 -0.0005 -0.7071 |
0.4962 0.8682 -0.0000 |
-0.7071 0.0002 -0.7071 |
-0.0000 -1.0000 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