# 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 YCo (Materials Project id mp-865373)

118 57 25 5 0 0 57 118 25 -5 0 0 25 25 69 0 0 0 5 -5 0 14 0 0 0 0 0 0 14 5 0 0 0 0 5 30

### Average properties

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

Voigt | K_{V} = 57.667 GPa | E_{V} = 65.072 GPa | G_{V} = 24.8 GPa | ν_{V} = 0.31193 |

Reuss | K_{R} = 50.822 GPa | E_{R} = 52.293 GPa | G_{R} = 19.681 GPa | ν_{R} = 0.32851 |

Hill | K_{H} = 54.244 GPa | E_{H} = 58.699 GPa | G_{H} = 22.241 GPa | ν_{H} = 0.31965 |

### Eigenvalues of the stiffness matrix

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

12.566 GPa | 12.959 GPa | 31.434 GPa | 58.29 GPa | 62.041 GPa | 185.71 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 | 35.656 GPa | 90.04 GPa | 4.0647 TPa^{–1} | 11.547 TPa^{–1} | 12.566 GPa | 31.894 GPa | 0.018582 | 0.60281 | Value |

Anisotropy | 2.525 | 2.8409 | 2.538 | 32.4408 | Anisotropy | ||||

Axis | 0.6244 0.3628 -0.6918 |
0.0000 0.9921 -0.1254 |
0.5000 0.8660 0.0000 |
0.0000 0.0000 1.0000 |
-0.0000 0.2757 -0.9613 |
0.7071 0.6790 -0.1974 |
-0.4548 0.2608 0.8516 |
-0.6145 0.3499 0.7070 |
Axis |

-1.0000 -0.0000 0.0000 |
-0.7071 0.6790 -0.1974 |
-0.4987 -0.8668 -0.0008 |
-0.6143 0.3500 -0.7072 |
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