# 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 Mn2Sb (Materials Project id mp-6912)

92 76 2 0 0 0 76 92 2 0 0 0 2 2 125 0 0 0 0 0 0 11 0 0 0 0 0 0 11 0 0 0 0 0 0 8

### Average properties

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

Voigt | K_{V} = 52.111 GPa | E_{V} = 56.16 GPa | G_{V} = 21.267 GPa | ν_{V} = 0.32038 |

Reuss | K_{R} = 51.2 GPa | E_{R} = 31.298 GPa | G_{R} = 11.193 GPa | ν_{R} = 0.39812 |

Hill | K_{H} = 51.656 GPa | E_{H} = 44.073 GPa | G_{H} = 16.23 GPa | ν_{H} = 0.3578 |

### Eigenvalues of the stiffness matrix

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

8 GPa | 11 GPa | 11 GPa | 16 GPa | 124.81 GPa | 168.19 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 | 27.186 GPa | 124.95 GPa | 5.8594 TPa^{–1} | 7.8125 TPa^{–1} | 8 GPa | 23.573 GPa | 0.011905 | 0.82603 | Value |

Anisotropy | 4.596 | 1.3333 | 2.947 | 69.3862 | Anisotropy | ||||

Axis | 0.4479 0.7548 0.4791 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
1.0000 -0.0008 -0.0000 |
-0.4023 0.5815 -0.7071 |
0.0000 0.0000 1.0000 |
0.9430 0.3328 -0.0000 |
Axis |

0.0008 1.0000 -0.0000 |
0.4024 -0.5815 -0.7071 |
0.1736 0.9848 -0.0000 |
-0.3328 0.9430 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