# 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 BaCO3 (Materials Project id mp-675324)

96 23 46 0 0 0 23 100 25 0 0 0 46 25 71 0 0 0 0 0 0 6 0 0 0 0 0 0 21 0 0 0 0 0 0 6

### Average properties

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

Voigt | K_{V} = 50.556 GPa | E_{V} = 48.59 GPa | G_{V} = 18.133 GPa | ν_{V} = 0.33981 |

Reuss | K_{R} = 49.771 GPa | E_{R} = 30.227 GPa | G_{R} = 10.805 GPa | ν_{R} = 0.39878 |

Hill | K_{H} = 50.163 GPa | E_{H} = 39.6 GPa | G_{H} = 14.469 GPa | ν_{H} = 0.36843 |

### Eigenvalues of the stiffness matrix

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

6 GPa | 6 GPa | 21 GPa | 35.179 GPa | 79.243 GPa | 152.58 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 | 20.666 GPa | 90.498 GPa | 4.6245 TPa^{–1} | 8.7083 TPa^{–1} | 6 GPa | 35.033 GPa | 0.074595 | 0.7601 | Value |

Anisotropy | 4.379 | 1.8831 | 5.839 | 10.1897 | Anisotropy | ||||

Axis | -0.0000 0.6781 0.7349 |
0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.8474 0.0000 -0.5309 |
-0.7071 0.7071 -0.0001 |
-1.0000 -0.0000 0.0001 |
0.5185 0.7449 0.4198 |
Axis |

-0.0000 1.0000 0.0000 |
-0.7071 -0.7071 -0.0001 |
0.0000 -1.0000 0.0000 |
-0.5780 0.6671 -0.4699 |
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