# 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 P2O5 (Materials Project id mp-990076)

797 70 31 -0 0 0 70 344 142 -0 0 0 31 142 531 -1 0 0 -0 -0 -1 43 0 0 0 0 0 0 251 -0 0 0 0 0 -0 158

### Average properties

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

Voigt | K_{V} = 239.78 GPa | E_{V} = 442.73 GPa | G_{V} = 185.67 GPa | ν_{V} = 0.19227 |

Reuss | K_{R} = 225.12 GPa | E_{R} = 291.6 GPa | G_{R} = 113.54 GPa | ν_{R} = 0.28411 |

Hill | K_{H} = 232.45 GPa | E_{H} = 369.53 GPa | G_{H} = 149.6 GPa | ν_{H} = 0.23504 |

### Eigenvalues of the stiffness matrix

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

42.998 GPa | 158 GPa | 251 GPa | 263.27 GPa | 590.37 GPa | 818.35 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 | 147.68 GPa | 782.75 GPa | 1.0142 TPa^{–1} | 2.1895 TPa^{–1} | 42.997 GPa | 293.61 GPa | -0.24535 | 0.79568 | Value |

Anisotropy | 5.3 | 2.1588 | 6.829 | ∞ | Anisotropy | ||||

Axis | -0.0000 0.7316 0.6818 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 0.0000 |
-0.0000 0.9999 0.0151 |
-0.0000 -0.0022 1.0000 |
0.7071 -0.0017 0.7071 |
-0.8143 0.3587 0.4563 |
0.6324 0.4845 -0.6044 |
Axis |

0.0000 1.0000 0.0022 |
0.7071 0.0022 -0.7071 |
-0.5798 -0.5400 -0.6102 |
0.0426 0.7574 0.6516 |
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