# 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 AlRu (Materials Project id mp-542569)

312 148 148 0 0 0 148 312 148 0 0 0 148 148 312 0 0 0 0 0 0 120 0 0 0 0 0 0 120 0 0 0 0 0 0 120

### Average properties

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

Voigt | K_{V} = 202.67 GPa | E_{V} = 268.18 GPa | G_{V} = 104.8 GPa | ν_{V} = 0.27946 |

Reuss | K_{R} = 202.67 GPa | E_{R} = 260.35 GPa | G_{R} = 101.23 GPa | ν_{R} = 0.28589 |

Hill | K_{H} = 202.67 GPa | E_{H} = 264.27 GPa | G_{H} = 103.02 GPa | ν_{H} = 0.28267 |

### Eigenvalues of the stiffness matrix

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

120 GPa | 120 GPa | 120 GPa | 164 GPa | 164 GPa | 608 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 | 216.77 GPa | 300.66 GPa | 1.6447 TPa^{–1} | 1.6447 TPa^{–1} | 82 GPa | 120 GPa | 0.14223 | 0.40689 | Value |

Anisotropy | 1.387 | 1.0000 | 1.463 | 2.8608 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5774 0.5773 -0.5774 |
0.6088 0.0000 0.7934 |
0.0000 0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
0.0000 0.0000 1.0000 |
0.7071 -0.0002 0.7071 |
0.7071 -0.0001 0.7071 |
Axis |

-0.7071 -0.0002 -0.7071 |
0.7660 0.6428 -0.0000 |
0.7071 -0.0006 -0.7071 |
0.0001 1.0000 0.0001 |
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