# 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 Ba2YBiO6 (Materials Project id mp-23137)

232 56 56 0 0 0 56 232 56 0 0 0 56 56 232 0 0 0 0 0 0 59 0 0 0 0 0 0 59 0 0 0 0 0 0 59

### Average properties

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

Voigt | K_{V} = 114.67 GPa | E_{V} = 175.73 GPa | G_{V} = 70.6 GPa | ν_{V} = 0.24457 |

Reuss | K_{R} = 114.67 GPa | E_{R} = 170.24 GPa | G_{R} = 67.958 GPa | ν_{R} = 0.25255 |

Hill | K_{H} = 114.67 GPa | E_{H} = 173 GPa | G_{H} = 69.279 GPa | ν_{H} = 0.24855 |

### Eigenvalues of the stiffness matrix

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

59 GPa | 59 GPa | 59 GPa | 176 GPa | 176 GPa | 344 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 | 151.09 GPa | 210.22 GPa | 2.907 TPa^{–1} | 2.907 TPa^{–1} | 59 GPa | 88 GPa | 0.15032 | 0.37725 | Value |

Anisotropy | 1.391 | 1.0000 | 1.492 | 2.5097 | Anisotropy | ||||

Axis | 0.5774 0.5774 0.5773 |
0.0000 0.0000 1.0000 |
0.5000 0.0000 0.8660 |
-0.1206 0.9160 0.3827 |
-0.0000 -0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
-0.7071 0.0000 0.7071 |
0.7071 -0.0000 -0.7071 |
Axis |

1.0000 0.0002 0.0000 |
-0.7071 -0.0002 -0.7071 |
-0.0000 -1.0000 0.0000 |
-0.7071 0.0002 -0.7071 |
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