# 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 SmTaO4 (Materials Project id mp-12931)

280 89 116 0 -10 0 89 194 99 0 16 0 116 99 278 0 -13 0 0 0 0 66 0 9 -10 16 -13 0 71 0 0 0 0 9 0 64

### Average properties

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

Voigt | K_{V} = 151.11 GPa | E_{V} = 182.06 GPa | G_{V} = 70.067 GPa | ν_{V} = 0.2992 |

Reuss | K_{R} = 144.7 GPa | E_{R} = 173.68 GPa | G_{R} = 66.803 GPa | ν_{R} = 0.29995 |

Hill | K_{H} = 147.9 GPa | E_{H} = 177.87 GPa | G_{H} = 68.435 GPa | ν_{H} = 0.29957 |

### Eigenvalues of the stiffness matrix

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

55.945 GPa | 63.446 GPa | 74.055 GPa | 133.95 GPa | 164.29 GPa | 461.31 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 | 136.11 GPa | 225.98 GPa | 1.512 TPa^{–1} | 3.5558 TPa^{–1} | 52.21 GPa | 81.676 GPa | 0.08963 | 0.44712 | Value |

Anisotropy | 1.66 | 2.3517 | 1.564 | 4.9885 | Anisotropy | ||||

Axis | -0.3825 0.8656 0.3231 |
-0.4518 -0.0000 0.8921 |
0.4410 0.0000 0.8975 |
0.0000 1.0000 0.0000 |
0.6140 0.6770 0.4058 |
0.6495 -0.0001 0.7604 |
-0.0000 1.0000 -0.0000 |
0.4434 -0.0000 0.8963 |
Axis |

-0.2874 0.6706 -0.6839 |
0.7604 0.0001 -0.6495 |
-0.7818 -0.0000 0.6235 |
-0.0000 1.0000 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