# 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 KNbO3 (Materials Project id mp-7375)

196 73 49 -28 0 0 73 196 49 28 0 0 49 49 191 0 0 0 -28 28 0 32 0 0 0 0 0 0 32 -28 0 0 0 0 -28 61

### Average properties

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

Voigt | K_{V} = 102.78 GPa | E_{V} = 134.51 GPa | G_{V} = 52.467 GPa | ν_{V} = 0.28187 |

Reuss | K_{R} = 102.37 GPa | E_{R} = 79.739 GPa | G_{R} = 29.098 GPa | ν_{R} = 0.37017 |

Hill | K_{H} = 102.57 GPa | E_{H} = 108.03 GPa | G_{H} = 40.782 GPa | ν_{H} = 0.32447 |

### Eigenvalues of the stiffness matrix

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

14.968 GPa | 17.182 GPa | 78.032 GPa | 137.82 GPa | 150.48 GPa | 309.52 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 | 43 GPa | 190.25 GPa | 3.0487 TPa^{–1} | 3.6713 TPa^{–1} | 14.968 GPa | 76.53 GPa | -0.30603 | 0.99054 | Value |

Anisotropy | 4.425 | 1.2042 | 5.113 | ∞ | Anisotropy | ||||

Axis | -0.6934 0.4010 0.5986 |
-0.0000 0.9578 0.2873 |
0.9659 0.2588 0.0000 |
0.0000 0.0000 1.0000 |
-0.0000 0.5197 0.8544 |
0.6490 0.0001 -0.7608 |
0.5254 0.3031 -0.7950 |
0.5298 0.3049 -0.7914 |
Axis |

-1.0000 -0.0000 -0.0000 |
0.7070 0.3691 0.6032 |
-0.5002 0.8659 -0.0003 |
-0.6848 -0.3968 -0.6113 |
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