# 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 NaF (Materials Project id mp-682)

95 24 24 0 0 0 24 95 24 0 0 0 24 24 95 0 0 0 0 0 0 27 0 0 0 0 0 0 27 0 0 0 0 0 0 27

### Average properties

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

Voigt | K_{V} = 47.667 GPa | E_{V} = 75.211 GPa | G_{V} = 30.4 GPa | ν_{V} = 0.23702 |

Reuss | K_{R} = 47.667 GPa | E_{R} = 74.105 GPa | G_{R} = 29.86 GPa | ν_{R} = 0.24089 |

Hill | K_{H} = 47.667 GPa | E_{H} = 74.659 GPa | G_{H} = 30.13 GPa | ν_{H} = 0.23895 |

### Eigenvalues of the stiffness matrix

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

27 GPa | 27 GPa | 27 GPa | 71 GPa | 71 GPa | 143 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 | 68.135 GPa | 85.319 GPa | 6.993 TPa^{–1} | 6.993 TPa^{–1} | 27 GPa | 35.5 GPa | 0.1696 | 0.32867 | Value |

Anisotropy | 1.252 | 1.0000 | 1.315 | 1.9379 | Anisotropy | ||||

Axis | -0.5774 0.5774 -0.5773 |
1.0000 0.0000 0.0000 |
0.8924 0.3696 0.2588 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
-0.7071 0.0000 0.7071 |
0.7071 -0.0002 0.7071 |
Axis |

-0.9404 0.3402 -0.0000 |
0.7071 -0.0005 -0.7071 |
-0.0000 -1.0000 -0.0000 |
0.7071 -0.0005 -0.7071 |
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