# 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 Si3Rh5 (Materials Project id mp-21012)

250 142 182 0 0 0 142 236 181 0 0 0 182 181 357 0 0 0 0 0 0 94 0 0 0 0 0 0 114 0 0 0 0 0 0 77

### Average properties

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

Voigt | K_{V} = 205.89 GPa | E_{V} = 211.38 GPa | G_{V} = 79.533 GPa | ν_{V} = 0.32889 |

Reuss | K_{R} = 191.63 GPa | E_{R} = 191.75 GPa | G_{R} = 71.912 GPa | ν_{R} = 0.33323 |

Hill | K_{H} = 198.76 GPa | E_{H} = 201.57 GPa | G_{H} = 75.723 GPa | ν_{H} = 0.33098 |

### Eigenvalues of the stiffness matrix

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

77 GPa | 94 GPa | 99.648 GPa | 114 GPa | 115.23 GPa | 628.12 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 | 128.5 GPa | 256.49 GPa | 0.30225 TPa^{–1} | 2.6299 TPa^{–1} | 50.394 GPa | 114 GPa | 0.062383 | 0.64437 | Value |

Anisotropy | 1.996 | 8.7009 | 2.262 | 10.3293 | Anisotropy | ||||

Axis | 0.0000 1.0000 0.0000 |
0.5527 0.4041 -0.7288 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
-0.7071 0.7071 -0.0000 |
-0.0000 0.0000 -1.0000 |
0.7119 -0.0003 0.7023 |
0.6135 0.0002 0.7897 |
Axis |

-0.7071 -0.7071 -0.0000 |
-1.0000 0.0000 0.0000 |
0.7023 -0.0005 -0.7119 |
-0.0001 1.0000 -0.0001 |
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