# 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 NiAg3 (Materials Project id mp-976772)

81 56 56 0 0 0 56 81 56 0 0 0 56 56 81 0 0 0 0 0 0 38 0 0 0 0 0 0 38 0 0 0 0 0 0 38

### Average properties

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

Voigt | K_{V} = 64.333 GPa | E_{V} = 72.899 GPa | G_{V} = 27.8 GPa | ν_{V} = 0.31114 |

Reuss | K_{R} = 64.333 GPa | E_{R} = 56.635 GPa | G_{R} = 20.925 GPa | ν_{R} = 0.35328 |

Hill | K_{H} = 64.333 GPa | E_{H} = 64.896 GPa | G_{H} = 24.363 GPa | ν_{H} = 0.33188 |

### Eigenvalues of the stiffness matrix

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

25 GPa | 25 GPa | 38 GPa | 38 GPa | 38 GPa | 193 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 | 35.219 GPa | 95.247 GPa | 5.1813 TPa^{–1} | 5.1813 TPa^{–1} | 12.5 GPa | 38 GPa | -0.12121 | 0.77516 | Value |

Anisotropy | 2.704 | 1.0000 | 3.04 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5774 0.5773 -0.5774 |
0.9239 0.0000 0.3827 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
0.0000 0.7071 0.7071 |
Axis |

0.7071 -0.0005 -0.7071 |
-0.7660 0.6428 -0.0000 |
0.7071 -0.0005 -0.7071 |
-1.0000 0.0000 -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