# 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 NdBrO (Materials Project id mp-23068)

107 25 4 0 0 0 25 107 4 0 0 0 4 4 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0 41

### Average properties

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

Voigt | K_{V} = 31.667 GPa | E_{V} = 55.551 GPa | G_{V} = 23 GPa | ν_{V} = 0.20763 |

Reuss | K_{R} = 4.9841 GPa | E_{R} = 14.719 GPa | G_{R} = 7.3029 GPa | ν_{R} = 0.0077875 |

Hill | K_{H} = 18.325 GPa | E_{H} = 35.634 GPa | G_{H} = 15.151 GPa | ν_{H} = 0.17592 |

### Eigenvalues of the stiffness matrix

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

4.7485 GPa | 6 GPa | 6 GPa | 41 GPa | 82 GPa | 132.25 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 | 4.7576 GPa | 99.222 GPa | 1.5924 TPa^{–1} | 197.45 TPa^{–1} | 4.2917 GPa | 41 GPa | -0.13517 | 0.63198 | Value |

Anisotropy | 20.86 | 124.0000 | 9.553 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.2588 0.9659 0.0000 |
0.2588 0.9659 0.0000 |
0.0000 0.0000 1.0000 |
0.6705 0.2246 0.7071 |
-0.6863 0.7273 -0.0000 |
-0.2136 0.7962 0.5660 |
0.0911 0.9958 0.0000 |
Axis |

0.6706 0.2243 -0.7071 |
-0.7273 -0.6863 -0.0000 |
-0.1467 0.5467 -0.8244 |
0.0000 0.0000 -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