# 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 MgNi (Materials Project id mp-1018140)

208 114 135 0 0 0 114 208 135 0 0 0 135 135 164 0 0 0 0 0 0 73 0 0 0 0 0 0 73 0 0 0 0 0 0 61

### Average properties

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

Voigt | K_{V} = 149.78 GPa | E_{V} = 145.73 GPa | G_{V} = 54.467 GPa | ν_{V} = 0.33783 |

Reuss | K_{R} = 148.71 GPa | E_{R} = 114.32 GPa | G_{R} = 41.665 GPa | ν_{R} = 0.37188 |

Hill | K_{H} = 149.24 GPa | E_{H} = 130.22 GPa | G_{H} = 48.066 GPa | ν_{H} = 0.35458 |

### Eigenvalues of the stiffness matrix

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

36.382 GPa | 61 GPa | 73 GPa | 73 GPa | 94 GPa | 449.62 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 | 50.801 GPa | 178.16 GPa | 1.7728 TPa^{–1} | 3.1789 TPa^{–1} | 21.495 GPa | 73 GPa | -0.10037 | 0.90579 | Value |

Anisotropy | 3.507 | 1.7931 | 3.396 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.5776 0.5776 -0.5768 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
0.0000 0.0000 1.0000 |
-0.7071 0.7071 -0.0000 |
0.7071 0.7071 0.0000 |
Axis |

0.7071 -0.0005 -0.7071 |
0.5000 0.8660 -0.0000 |
-0.7071 -0.7071 0.0000 |
0.0001 -0.0000 -1.0000 |
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