# 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 ErSi (Materials Project id mp-378)

171 42 77 0 0 0 42 203 28 0 0 0 77 28 187 0 0 0 0 0 0 46 0 0 0 0 0 0 107 0 0 0 0 0 0 60

### Average properties

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

Voigt | K_{V} = 95 GPa | E_{V} = 168.98 GPa | G_{V} = 70.2 GPa | ν_{V} = 0.20355 |

Reuss | K_{R} = 94.862 GPa | E_{R} = 155.08 GPa | G_{R} = 63.167 GPa | ν_{R} = 0.22754 |

Hill | K_{H} = 94.931 GPa | E_{H} = 162.1 GPa | G_{H} = 66.683 GPa | ν_{H} = 0.21541 |

### Eigenvalues of the stiffness matrix

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

46 GPa | 60 GPa | 99.823 GPa | 107 GPa | 175.51 GPa | 285.66 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 | 120.81 GPa | 228.41 GPa | 3.3847 TPa^{–1} | 3.7555 TPa^{–1} | 46 GPa | 107 GPa | 0.030133 | 0.43871 | Value |

Anisotropy | 1.891 | 1.1096 | 2.326 | 14.5593 | Anisotropy | ||||

Axis | -0.0000 0.6528 0.7576 |
0.6779 -0.0000 0.7351 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
0.0002 0.0001 1.0000 |
-0.0000 0.0000 1.0000 |
-0.7011 0.3767 0.6054 |
0.0000 0.0000 1.0000 |
Axis |

-0.0000 1.0000 -0.0001 |
-1.0000 0.0000 -0.0000 |
-0.7120 -0.3234 -0.6233 |
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