# 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 Mn(PtO2)3 (Materials Project id mp-18971)

317 147 117 0 0 0 147 318 133 0 0 0 117 133 291 0 0 0 0 0 0 37 0 0 0 0 0 0 58 0 0 0 0 0 0 103

### Average properties

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

Voigt | K_{V} = 191.11 GPa | E_{V} = 198.66 GPa | G_{V} = 74.867 GPa | ν_{V} = 0.32675 |

Reuss | K_{R} = 190.03 GPa | E_{R} = 175.27 GPa | G_{R} = 65.095 GPa | ν_{R} = 0.34627 |

Hill | K_{H} = 190.57 GPa | E_{H} = 187.05 GPa | G_{H} = 69.981 GPa | ν_{H} = 0.33641 |

### Eigenvalues of the stiffness matrix

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

37 GPa | 58 GPa | 103 GPa | 164.92 GPa | 186.31 GPa | 574.77 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 | 120.73 GPa | 261.58 GPa | 1.4937 TPa^{–1} | 2.0713 TPa^{–1} | 37 GPa | 103 GPa | 0.11741 | 0.63448 | Value |

Anisotropy | 2.167 | 1.3867 | 2.784 | 5.4041 | Anisotropy | ||||

Axis | 0.0000 0.7063 0.7080 |
0.7423 0.6701 0.0000 |
0.0000 1.0000 0.0000 |
0.0000 0.0000 1.0000 |
-0.0003 -0.0000 1.0000 |
1.0000 -0.0001 0.0000 |
0.5753 0.5566 0.5993 |
0.3198 0.6599 -0.6799 |
Axis |

0.0000 1.0000 0.0000 |
0.0001 1.0000 -0.0000 |
-0.7939 0.5563 0.2454 |
-0.1394 -0.6770 -0.7226 |
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