# 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 CaBi3 (Materials Project id mp-866006)

53 41 41 -0 -0 -0 41 53 41 -0 -0 -0 41 41 53 -0 -0 -0 -0 -0 -0 14 0 0 -0 -0 -0 0 14 0 -0 -0 -0 0 0 14

### Average properties

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

Voigt | K_{V} = 45 GPa | E_{V} = 30 GPa | G_{V} = 10.8 GPa | ν_{V} = 0.38889 |

Reuss | K_{R} = 45 GPa | E_{R} = 25.656 GPa | G_{R} = 9.1304 GPa | ν_{R} = 0.40498 |

Hill | K_{H} = 45 GPa | E_{H} = 27.841 GPa | G_{H} = 9.9652 GPa | ν_{H} = 0.39689 |

### Eigenvalues of the stiffness matrix

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

12 GPa | 12 GPa | 14 GPa | 14 GPa | 14 GPa | 135 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 | 17.234 GPa | 38.054 GPa | 7.4074 TPa^{–1} | 7.4074 TPa^{–1} | 6 GPa | 14 GPa | 0.043814 | 0.73969 | Value |

Anisotropy | 2.208 | 1.0000 | 2.333 | 16.8823 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5774 0.5773 -0.5774 |
0.0000 0.0000 1.0000 |
0.9239 0.0000 0.3827 |
0.7071 0.0001 -0.7071 |
-0.0000 0.0000 1.0000 |
0.7071 -0.0000 -0.7071 |
-0.0000 0.7071 0.7071 |
Axis |

-0.7071 -0.0002 -0.7071 |
-0.5000 0.8660 -0.0000 |
-0.7071 0.0002 -0.7071 |
-1.0000 -0.0001 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