# 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 ZnO (Materials Project id mp-2133)

188 109 92 0 0 0 109 188 92 0 0 0 92 92 205 0 0 0 0 0 0 37 0 0 0 0 0 0 37 0 0 0 0 0 0 39

### Average properties

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

Voigt | K_{V} = 129.67 GPa | E_{V} = 113.23 GPa | G_{V} = 41.8 GPa | ν_{V} = 0.35446 |

Reuss | K_{R} = 129.67 GPa | E_{R} = 110.65 GPa | G_{R} = 40.746 GPa | ν_{R} = 0.35778 |

Hill | K_{H} = 129.67 GPa | E_{H} = 111.94 GPa | G_{H} = 41.273 GPa | ν_{H} = 0.35612 |

### Eigenvalues of the stiffness matrix

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

37 GPa | 37 GPa | 39 GPa | 79 GPa | 113 GPa | 389 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 | 102.89 GPa | 148 GPa | 2.5707 TPa^{–1} | 2.5707 TPa^{–1} | 37 GPa | 51.011 GPa | 0.23941 | 0.46653 | Value |

Anisotropy | 1.438 | 1.0000 | 1.379 | 1.9486 | Anisotropy | ||||

Axis | 0.5636 0.5636 -0.6040 |
0.0000 0.0000 1.0000 |
0.2391 0.8924 -0.3827 |
0.9659 0.0000 0.2588 |
0.0000 0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
0.7071 0.7071 0.0000 |
-0.7071 0.7071 -0.0000 |
Axis |

-0.7662 0.6426 -0.0000 |
0.7071 -0.0005 -0.7071 |
0.0004 -0.0004 -1.0000 |
-0.7071 -0.7071 -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