# 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 CrSnRh2 (Materials Project id mp-1018066)

263 106 161 0 0 0 106 263 161 0 0 0 161 161 264 0 0 0 0 0 0 98 0 0 0 0 0 0 98 0 0 0 0 0 0 97

### Average properties

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

Voigt | K_{V} = 182.89 GPa | E_{V} = 215.68 GPa | G_{V} = 82.733 GPa | ν_{V} = 0.30345 |

Reuss | K_{R} = 180.13 GPa | E_{R} = 195.35 GPa | G_{R} = 74.036 GPa | ν_{R} = 0.31926 |

Hill | K_{H} = 181.51 GPa | E_{H} = 205.56 GPa | G_{H} = 78.385 GPa | ν_{H} = 0.31125 |

### Eigenvalues of the stiffness matrix

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

82.837 GPa | 97 GPa | 98 GPa | 98 GPa | 157 GPa | 550.16 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 | 123.51 GPa | 249.23 GPa | 1.0313 TPa^{–1} | 2.2601 TPa^{–1} | 47.074 GPa | 98 GPa | -0.058291 | 0.6454 | Value |

Anisotropy | 2.018 | 2.1915 | 2.082 | ∞ | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5594 0.5593 0.6118 |
0.0000 0.0000 1.0000 |
-0.1305 0.9914 0.0000 |
0.7071 0.0001 -0.7071 |
0.0000 0.0000 1.0000 |
0.7071 0.7071 -0.0000 |
0.7071 0.7071 0.0000 |
Axis |

-0.7071 -0.0002 -0.7071 |
0.7660 0.6428 -0.0000 |
-0.7071 0.7071 -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