# 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 NaMgF3 (Materials Project id mp-2955)

130 40 48 0 0 0 40 130 37 0 0 0 48 37 119 0 0 0 0 0 0 38 0 0 0 0 0 0 44 0 0 0 0 0 0 42

### Average properties

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

Voigt | K_{V} = 69.889 GPa | E_{V} = 104.42 GPa | G_{V} = 41.733 GPa | ν_{V} = 0.25099 |

Reuss | K_{R} = 69.735 GPa | E_{R} = 103.8 GPa | G_{R} = 41.456 GPa | ν_{R} = 0.25192 |

Hill | K_{H} = 69.812 GPa | E_{H} = 104.11 GPa | G_{H} = 41.595 GPa | ν_{H} = 0.25146 |

### Eigenvalues of the stiffness matrix

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

38 GPa | 42 GPa | 44 GPa | 76.144 GPa | 92.912 GPa | 209.94 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 | 94.735 GPa | 112.81 GPa | 4.28 TPa^{–1} | 5.1505 TPa^{–1} | 38 GPa | 45.842 GPa | 0.18889 | 0.33756 | Value |

Anisotropy | 1.191 | 1.2034 | 1.206 | 1.7871 | Anisotropy | ||||

Axis | -0.0000 0.5287 0.8488 |
0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
-0.0003 -0.0000 1.0000 |
0.5468 0.7071 0.4484 |
-0.0006 -0.0006 1.0000 |
1.0000 0.0002 0.0000 |
Axis |

0.0000 1.0000 0.0000 |
-0.5468 0.7071 -0.4484 |
0.0000 1.0000 0.0006 |
0.0000 0.0003 -1.0000 |
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