# 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 LiB (Materials Project id mp-16726)

41 32 -19 0 0 0 32 57 -27 0 0 0 -19 -27 400 0 0 0 0 0 0 14 0 0 0 0 0 0 20 0 0 0 0 0 0 40

### Average properties

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

Voigt | K_{V} = 52.222 GPa | E_{V} = 111.86 GPa | G_{V} = 48.933 GPa | ν_{V} = 0.143 |

Reuss | K_{R} = 31.168 GPa | E_{R} = 44.93 GPa | G_{R} = 17.833 GPa | ν_{R} = 0.25974 |

Hill | K_{H} = 41.695 GPa | E_{H} = 79.052 GPa | G_{H} = 33.383 GPa | ν_{H} = 0.18401 |

### Eigenvalues of the stiffness matrix

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

14 GPa | 16.008 GPa | 20 GPa | 40 GPa | 78.602 GPa | 403.39 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 | 22.997 GPa | 386.57 GPa | 4.0015 TPa^{–1} | 19.708 TPa^{–1} | 8.0972 GPa | 73.2 GPa | -0.38005 | 0.76607 | Value |

Anisotropy | 16.81 | 4.9252 | 9.04 | ∞ | Anisotropy | ||||

Axis | 1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
-0.7071 0.7071 0.0000 |
0.4659 0.5320 -0.7071 |
-0.0000 -0.0000 1.0000 |
-0.0000 1.0000 -0.0000 |
Axis |

-0.7071 -0.7071 -0.0000 |
0.4659 0.5320 0.7071 |
-0.0000 1.0000 0.0000 |
-1.0000 -0.0000 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