# 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 LiCrO2 (Materials Project id mp-18793)

351 106 69 -9 0 0 106 351 69 9 0 0 69 69 203 0 0 0 -9 9 0 54 0 0 0 0 0 0 54 -9 0 0 0 0 -9 122

### Average properties

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

Voigt | K_{V} = 154.78 GPa | E_{V} = 226.3 GPa | G_{V} = 90.067 GPa | ν_{V} = 0.25631 |

Reuss | K_{R} = 141.82 GPa | E_{R} = 194.89 GPa | G_{R} = 76.669 GPa | ν_{R} = 0.27097 |

Hill | K_{H} = 148.3 GPa | E_{H} = 210.63 GPa | G_{H} = 83.368 GPa | ν_{H} = 0.26328 |

### Eigenvalues of the stiffness matrix

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

52.829 GPa | 53.156 GPa | 123.17 GPa | 169.84 GPa | 245.84 GPa | 490.16 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 | 145.4 GPa | 308.58 GPa | 1.6096 TPa^{–1} | 3.8319 TPa^{–1} | 53.175 GPa | 123.65 GPa | 0.078722 | 0.47928 | Value |

Anisotropy | 2.122 | 2.3806 | 2.325 | 6.0882 | Anisotropy | ||||

Axis | 0.5573 0.3226 0.7651 |
0.0000 0.9979 0.0647 |
0.0948 0.9955 0.0000 |
0.0000 0.0000 1.0000 |
0.0358 0.0203 0.9992 |
0.7070 0.7013 0.0907 |
-0.0000 0.6377 0.7703 |
-0.0000 0.7590 0.6510 |
Axis |

0.8638 0.5022 -0.0412 |
-0.7072 0.7012 0.0907 |
-1.0000 -0.0000 0.0000 |
0.0000 0.6510 -0.7590 |
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