# 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 Yb3Tc (Materials Project id mp-979938)

46 19 28 0 0 0 19 46 28 0 0 0 28 28 37 0 0 0 0 0 0 25 0 0 0 0 0 0 25 0 0 0 0 0 0 19

### Average properties

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

Voigt | K_{V} = 31 GPa | E_{V} = 43.973 GPa | G_{V} = 17.4 GPa | ν_{V} = 0.26359 |

Reuss | K_{R} = 31 GPa | E_{R} = 31.076 GPa | G_{R} = 11.657 GPa | ν_{R} = 0.33293 |

Hill | K_{H} = 31 GPa | E_{H} = 37.696 GPa | G_{H} = 14.528 GPa | ν_{H} = 0.29733 |

### Eigenvalues of the stiffness matrix

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

9 GPa | 19 GPa | 25 GPa | 25 GPa | 27 GPa | 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 | 12.877 GPa | 54.677 GPa | 10.753 TPa^{–1} | 10.753 TPa^{–1} | 5.4 GPa | 25 GPa | -0.25368 | 0.94873 | Value |

Anisotropy | 4.246 | 1.0000 | 4.63 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.5708 0.5708 0.5903 |
0.9239 0.0000 0.3827 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
-0.0000 0.0000 1.0000 |
-0.7071 0.7071 -0.0000 |
0.7071 0.7071 0.0000 |
Axis |

0.7071 -0.0005 -0.7071 |
-0.5000 -0.8660 0.0000 |
-0.7071 -0.7071 0.0000 |
-0.0000 -0.0000 1.0000 |
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