# 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 Ag2BiO3 (Materials Project id mp-23558)

162 82 88 0 0 0 82 114 81 0 0 0 88 81 132 0 0 0 0 0 0 15 0 0 0 0 0 0 19 0 0 0 0 0 0 22

### Average properties

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

Voigt | K_{V} = 101.11 GPa | E_{V} = 60.667 GPa | G_{V} = 21.667 GPa | ν_{V} = 0.4 |

Reuss | K_{R} = 98.073 GPa | E_{R} = 57.137 GPa | G_{R} = 20.364 GPa | ν_{R} = 0.4029 |

Hill | K_{H} = 99.592 GPa | E_{H} = 58.903 GPa | G_{H} = 21.015 GPa | ν_{H} = 0.40143 |

### Eigenvalues of the stiffness matrix

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

15 GPa | 19 GPa | 22 GPa | 41.32 GPa | 61.3 GPa | 305.38 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 | 47.317 GPa | 91.14 GPa | 1.8112 TPa^{–1} | 5.2204 TPa^{–1} | 15 GPa | 28.637 GPa | 0.21751 | 0.58648 | Value |

Anisotropy | 1.926 | 2.8822 | 1.909 | 2.6963 | Anisotropy | ||||

Axis | -0.0000 0.7523 0.6588 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 1.0000 0.0000 |
-0.0003 -0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
0.0000 0.7190 -0.6950 |
0.0001 0.6376 0.7704 |
Axis |

0.0000 1.0000 0.0000 |
0.7071 -0.0005 -0.7071 |
-1.0000 -0.0000 -0.0000 |
-0.0001 0.7704 -0.6376 |
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