# 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 K (Materials Project id mp-604318)

6 3 2 0 0 0 3 6 2 0 0 0 2 2 7 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1

### Average properties

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

Voigt | K_{V} = 3.6667 GPa | E_{V} = 3.7258 GPa | G_{V} = 1.4 GPa | ν_{V} = 0.33065 |

Reuss | K_{R} = 3.6667 GPa | E_{R} = 3.3177 GPa | G_{R} = 1.2295 GPa | ν_{R} = 0.3492 |

Hill | K_{H} = 3.6667 GPa | E_{H} = 3.5232 GPa | G_{H} = 1.3148 GPa | ν_{H} = 0.33986 |

### Eigenvalues of the stiffness matrix

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

1 GPa | 1 GPa | 1 GPa | 3 GPa | 5 GPa | 11 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 | 2.75 GPa | 6.1111 GPa | 90.909 TPa^{–1} | 90.909 TPa^{–1} | 1 GPa | 2.1429 GPa | 0.11594 | 0.5942 | Value |

Anisotropy | 2.222 | 1.0000 | 2.143 | 5.1250 | Anisotropy | ||||

Axis | 0.5773 0.5773 0.5774 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.9239 0.0000 0.3827 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
-0.7071 0.7071 0.0000 |
-0.7071 0.7071 0.0000 |
Axis |

1.0000 0.0000 -0.0000 |
0.7071 -0.0005 -0.7071 |
-0.0004 -0.0004 -1.0000 |
-0.7071 -0.7071 -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