# 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 Mg2Au (Materials Project id mp-11250)

61 39 46 0 0 0 39 106 58 0 0 0 46 58 104 0 0 0 0 0 0 27 0 0 0 0 0 0 32 0 0 0 0 0 0 16

### Average properties

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

Voigt | K_{V} = 61.889 GPa | E_{V} = 62.658 GPa | G_{V} = 23.533 GPa | ν_{V} = 0.33126 |

Reuss | K_{R} = 54.837 GPa | E_{R} = 56.825 GPa | G_{R} = 21.406 GPa | ν_{R} = 0.32729 |

Hill | K_{H} = 58.363 GPa | E_{H} = 59.742 GPa | G_{H} = 22.47 GPa | ν_{H} = 0.32939 |

### Eigenvalues of the stiffness matrix

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

16 GPa | 27 GPa | 31.606 GPa | 32 GPa | 48.559 GPa | 190.84 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 | 38.221 GPa | 74.713 GPa | 2.0042 TPa^{–1} | 12.49 TPa^{–1} | 16 GPa | 32 GPa | 0.10513 | 0.54702 | Value |

Anisotropy | 1.955 | 6.2317 | 2 | 5.2033 | Anisotropy | ||||

Axis | 0.9855 0.1695 0.0000 |
0.5862 0.0000 0.8102 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
1.0000 -0.0009 0.0000 |
0.0000 0.0000 1.0000 |
0.6880 0.2160 -0.6928 |
0.3499 0.5609 0.7503 |
Axis |

0.0009 1.0000 0.0000 |
-1.0000 0.0000 0.0000 |
-0.6672 -0.1874 -0.7210 |
-0.7390 0.6575 -0.1469 |
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