# 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 LiLuO2 (Materials Project id mp-754605)

270 112 76 0 0 0 112 270 76 0 0 0 76 76 100 0 0 0 0 0 0 74 0 0 0 0 0 0 74 0 0 0 0 0 0 96

### Average properties

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

Voigt | K_{V} = 129.78 GPa | E_{V} = 186.26 GPa | G_{V} = 73.867 GPa | ν_{V} = 0.26079 |

Reuss | K_{R} = 95.856 GPa | E_{R} = 155.1 GPa | G_{R} = 63.034 GPa | ν_{R} = 0.23032 |

Hill | K_{H} = 112.82 GPa | E_{H} = 170.81 GPa | G_{H} = 68.45 GPa | ν_{H} = 0.24766 |

### Eigenvalues of the stiffness matrix

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

63.706 GPa | 74 GPa | 74 GPa | 96 GPa | 158 GPa | 418.29 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 | 69.759 GPa | 224.7 GPa | 0.90063 TPa^{–1} | 8.631 TPa^{–1} | 39.873 GPa | 96 GPa | -0.0058359 | 0.63654 | Value |

Anisotropy | 3.221 | 9.5833 | 2.408 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.6884 0.6884 0.2287 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
1.0000 -0.0002 0.0000 |
0.7088 0.0001 -0.7054 |
-0.7071 0.7071 0.0000 |
Axis |

0.7071 -0.0005 -0.7071 |
0.0002 1.0000 0.0000 |
-0.7054 -0.0002 -0.7088 |
-0.0004 -0.0004 -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