# 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 MoS2 (Materials Project id mp-1434)

179 45 1 0 0 0 45 179 1 -0 0 0 1 1 3 0 0 0 0 -0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 67

### Average properties

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

Voigt | K_{V} = 50.556 GPa | E_{V} = 84.784 GPa | G_{V} = 34.733 GPa | ν_{V} = 0.22049 |

Reuss | K_{R} = 2.9646 GPa | E_{R} = 4.9265 GPa | G_{R} = 2.014 GPa | ν_{R} = 0.22304 |

Hill | K_{H} = 26.76 GPa | E_{H} = 44.855 GPa | G_{H} = 18.374 GPa | ν_{H} = 0.22063 |

### Eigenvalues of the stiffness matrix

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

1 GPa | 1 GPa | 2.991 GPa | 67 GPa | 134 GPa | 224.01 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 | 2.664 GPa | 167.5 GPa | 2.9851 TPa^{–1} | 331.34 TPa^{–1} | 1 GPa | 67 GPa | 0.0044643 | 0.619 | Value |

Anisotropy | 62.88 | 111.0000 | 67 | 138.6559 | Anisotropy | ||||

Axis | 0.3044 0.3967 0.8660 |
0.6088 0.7934 0.0000 |
0.7934 0.6088 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
1.0000 0.0006 0.0000 |
0.0000 0.0000 1.0000 |
-0.5981 0.7405 0.3063 |
Axis |

1.0000 0.0000 -0.0000 |
-0.0006 1.0000 0.0000 |
0.5000 0.8660 -0.0000 |
0.1925 -0.2383 0.9519 |
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