# 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 LaGaO3 (Materials Project id mp-3336)

289 138 113 10 0 0 138 289 113 -10 0 0 113 113 299 0 0 0 10 -10 0 78 0 0 0 0 0 0 78 10 0 0 0 0 10 75

### Average properties

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

Voigt | K_{V} = 178.33 GPa | E_{V} = 209.69 GPa | G_{V} = 80.4 GPa | ν_{V} = 0.30403 |

Reuss | K_{R} = 178.25 GPa | E_{R} = 205.62 GPa | G_{R} = 78.615 GPa | ν_{R} = 0.30774 |

Hill | K_{H} = 178.29 GPa | E_{H} = 207.66 GPa | G_{H} = 79.508 GPa | ν_{H} = 0.30588 |

### Eigenvalues of the stiffness matrix

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

66.388 GPa | 75.356 GPa | 86.612 GPa | 153.64 GPa | 190.85 GPa | 535.15 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 | 179 GPa | 239.19 GPa | 1.8211 TPa^{–1} | 1.968 TPa^{–1} | 66.388 GPa | 91.809 GPa | 0.18942 | 0.43505 | Value |

Anisotropy | 1.336 | 1.0806 | 1.383 | 2.2967 | Anisotropy | ||||

Axis | 0.7355 0.4290 -0.5244 |
0.0000 0.0000 1.0000 |
0.3827 0.9239 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.7577 -0.6526 |
0.4923 0.2659 0.8288 |
0.5019 0.8649 0.0026 |
0.5050 0.8631 0.0011 |
Axis |

-1.0000 0.0000 -0.0000 |
0.7198 0.4109 -0.5594 |
-0.3446 0.1972 0.9178 |
-0.7920 0.4639 -0.3969 |
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