# 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 C (Materials Project id mp-568286)

879 -1 160 0 0 0 -1 6 -1 0 0 0 160 -1 879 0 0 0 0 0 0 2 0 0 0 0 0 0 360 0 0 0 0 0 0 1

### Average properties

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

Voigt | K_{V} = 231.11 GPa | E_{V} = 428.07 GPa | G_{V} = 179.67 GPa | ν_{V} = 0.19129 |

Reuss | K_{R} = 5.9071 GPa | E_{R} = 7.4619 GPa | G_{R} = 2.8934 GPa | ν_{R} = 0.28947 |

Hill | K_{H} = 118.51 GPa | E_{H} = 217.9 GPa | G_{H} = 91.28 GPa | ν_{H} = 0.19356 |

### Eigenvalues of the stiffness matrix

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

1 GPa | 2 GPa | 5.9981 GPa | 360 GPa | 719 GPa | 1039 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 | 3.3302 GPa | 850.46 GPa | 1.1232 TPa^{–1} | 167.04 TPa^{–1} | 1 GPa | 360 GPa | -1.9438 | 2.3501 | Value |

Anisotropy | 255.4 | 148.7143 | 360 | ∞ | Anisotropy | ||||

Axis | 0.6329 0.7742 0.0000 |
0.7071 0.0000 0.7071 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
1.0000 -0.0002 -0.0000 |
0.0000 0.0000 -1.0000 |
0.6399 0.0378 -0.7675 |
0.6472 0.0446 -0.7610 |
Axis |

0.0002 1.0000 0.0000 |
-1.0000 0.0000 -0.0000 |
0.5377 0.6915 0.4823 |
-0.5422 0.7286 -0.4184 |
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