# 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 Ti4O5 (Materials Project id mp-10734)

466 103 103 0 0 0 103 361 134 27 0 0 103 134 361 -27 0 0 0 27 -27 113 0 0 0 0 0 0 56 0 0 0 0 0 0 56

### Average properties

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

Voigt | K_{V} = 207.56 GPa | E_{V} = 261.89 GPa | G_{V} = 101.53 GPa | ν_{V} = 0.2897 |

Reuss | K_{R} = 206.36 GPa | E_{R} = 219.1 GPa | G_{R} = 82.803 GPa | ν_{R} = 0.32304 |

Hill | K_{H} = 206.96 GPa | E_{H} = 240.76 GPa | G_{H} = 92.168 GPa | ν_{H} = 0.30611 |

### Eigenvalues of the stiffness matrix

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

56 GPa | 56 GPa | 101.39 GPa | 238.61 GPa | 334.12 GPa | 626.88 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 | 170.17 GPa | 423.14 GPa | 1.3798 TPa^{–1} | 1.7331 TPa^{–1} | 56 GPa | 160.21 GPa | 0.10443 | 0.61478 | Value |

Anisotropy | 2.487 | 1.2561 | 2.861 | 5.8869 | Anisotropy | ||||

Axis | 0.6492 0.2927 0.7020 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.9914 -0.1305 |
0.0000 0.0000 1.0000 |
0.7071 0.6539 0.2691 |
-0.7420 0.2551 -0.6199 |
-0.7325 0.6296 0.2590 |
Axis |

1.0000 0.0000 -0.0000 |
-0.7071 0.6539 0.2691 |
-0.0000 -0.9247 -0.3806 |
-0.6808 -0.6774 -0.2788 |
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