# 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 KCu4S3 (Materials Project id mp-27677)

94 19 35 0 0 0 19 94 35 0 0 0 35 35 62 0 0 0 0 0 0 15 0 0 0 0 0 0 15 0 0 0 0 0 0 17

### Average properties

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

Voigt | K_{V} = 47.556 GPa | E_{V} = 52.93 GPa | G_{V} = 20.133 GPa | ν_{V} = 0.3145 |

Reuss | K_{R} = 46.969 GPa | E_{R} = 47.328 GPa | G_{R} = 17.765 GPa | ν_{R} = 0.33206 |

Hill | K_{H} = 47.262 GPa | E_{H} = 50.146 GPa | G_{H} = 18.949 GPa | ν_{H} = 0.32316 |

### Eigenvalues of the stiffness matrix

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

15 GPa | 15 GPa | 17 GPa | 31.82 GPa | 75 GPa | 143.18 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 | 40.085 GPa | 74.234 GPa | 5.9263 TPa^{–1} | 9.4381 TPa^{–1} | 15 GPa | 37.5 GPa | -0.010211 | 0.57028 | Value |

Anisotropy | 1.852 | 1.5926 | 2.5 | ∞ | Anisotropy | ||||

Axis | 0.2916 0.2916 0.9110 |
1.0000 0.0000 0.0000 |
0.6088 0.7934 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.7071 0.7071 -0.0000 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 -0.0000 |
Axis |

0.1736 0.9848 -0.0000 |
-0.7071 0.7071 0.0000 |
-0.0000 1.0000 -0.0000 |
-0.0000 -0.0000 -1.0000 |
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