# 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 BaPt5 (Materials Project id mp-811)

204 97 112 0 0 0 97 204 112 0 0 0 112 112 308 0 0 0 0 0 0 68 0 0 0 0 0 0 68 0 0 0 0 0 0 53

### Average properties

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

Voigt | K_{V} = 150.89 GPa | E_{V} = 168.52 GPa | G_{V} = 64.133 GPa | ν_{V} = 0.31385 |

Reuss | K_{R} = 144.18 GPa | E_{R} = 163.19 GPa | G_{R} = 62.22 GPa | ν_{R} = 0.31136 |

Hill | K_{H} = 147.53 GPa | E_{H} = 165.86 GPa | G_{H} = 63.177 GPa | ν_{H} = 0.31264 |

### Eigenvalues of the stiffness matrix

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

53 GPa | 68 GPa | 68 GPa | 107 GPa | 146.07 GPa | 462.93 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 | 142.97 GPa | 224.65 GPa | 1.1387 TPa^{–1} | 2.8986 TPa^{–1} | 53 GPa | 68 GPa | 0.23681 | 0.37209 | Value |

Anisotropy | 1.571 | 2.5455 | 1.283 | 1.5713 | Anisotropy | ||||

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

0.0002 1.0000 0.0000 |
0.7660 0.6428 -0.0000 |
0.0003 0.0003 -1.0000 |
0.5150 0.8572 0.0000 |
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