# 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 LiCuO2 (Materials Project id mp-25372)

247 88 65 -6 0 0 88 247 65 6 0 0 65 65 185 0 0 0 -6 6 0 50 0 0 0 0 0 0 50 -6 0 0 0 0 -6 80

### Average properties

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

Voigt | K_{V} = 123.89 GPa | E_{V} = 169.73 GPa | G_{V} = 66.733 GPa | ν_{V} = 0.27167 |

Reuss | K_{R} = 120.28 GPa | E_{R} = 160.57 GPa | G_{R} = 62.846 GPa | ν_{R} = 0.2775 |

Hill | K_{H} = 122.08 GPa | E_{H} = 165.15 GPa | G_{H} = 64.79 GPa | ν_{H} = 0.27454 |

### Eigenvalues of the stiffness matrix

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

48.845 GPa | 49.343 GPa | 81.155 GPa | 141.36 GPa | 159.66 GPa | 378.64 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 | 131.21 GPa | 207.66 GPa | 2.2419 TPa^{–1} | 3.83 TPa^{–1} | 48.831 GPa | 81.155 GPa | 0.13208 | 0.41888 | Value |

Anisotropy | 1.583 | 1.7083 | 1.662 | 3.1715 | Anisotropy | ||||

Axis | -0.0000 0.6775 -0.7355 |
0.8495 0.5195 -0.0924 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
-0.1654 0.0960 -0.9815 |
0.0000 0.9820 -0.1891 |
0.5082 0.2960 -0.8088 |
-0.6190 0.3648 -0.6955 |
Axis |

-0.5005 -0.8657 -0.0003 |
-1.0000 0.0000 0.0000 |
-0.5029 0.8643 0.0003 |
0.5993 -0.3530 -0.7185 |
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