# 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 Nb (Materials Project id mp-75)

233 145 145 0 0 0 145 233 145 0 0 0 145 145 233 0 0 0 0 0 0 11 0 0 0 0 0 0 11 0 0 0 0 0 0 11

### Average properties

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

Voigt | K_{V} = 174.33 GPa | E_{V} = 69.389 GPa | G_{V} = 24.2 GPa | ν_{V} = 0.43366 |

Reuss | K_{R} = 174.33 GPa | E_{R} = 45.768 GPa | G_{R} = 15.714 GPa | ν_{R} = 0.45625 |

Hill | K_{H} = 174.33 GPa | E_{H} = 57.671 GPa | G_{H} = 19.957 GPa | ν_{H} = 0.44487 |

### Eigenvalues of the stiffness matrix

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

11 GPa | 11 GPa | 11 GPa | 88 GPa | 88 GPa | 523 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 | 32.32 GPa | 121.76 GPa | 1.912 TPa^{–1} | 1.912 TPa^{–1} | 11 GPa | 44 GPa | 0.12473 | 0.79957 | Value |

Anisotropy | 3.767 | 1.0000 | 4 | 6.4103 | Anisotropy | ||||

Axis | -0.5774 0.5774 0.5773 |
1.0000 0.0000 0.0000 |
0.9659 0.0000 0.2588 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.7071 0.0001 -0.7071 |
0.7071 0.0000 -0.7072 |
0.7071 -0.0002 0.7071 |
Axis |

-0.7880 0.6157 -0.0000 |
-0.7071 -0.0002 -0.7071 |
-0.0000 1.0000 0.0000 |
0.7071 -0.0001 -0.7071 |
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