# 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 ZrO2 (Materials Project id mp-2858)

256 140 99 0 -1 0 140 357 152 0 3 0 99 152 301 0 -40 0 0 0 0 114 0 8 -1 3 -40 0 80 0 0 0 0 8 0 70

### Average properties

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

Voigt | K_{V} = 188.44 GPa | E_{V} = 227.69 GPa | G_{V} = 87.667 GPa | ν_{V} = 0.29862 |

Reuss | K_{R} = 177.56 GPa | E_{R} = 211.51 GPa | G_{R} = 81.257 GPa | ν_{R} = 0.30147 |

Hill | K_{H} = 183 GPa | E_{H} = 219.6 GPa | G_{H} = 84.462 GPa | ν_{H} = 0.3 |

### Eigenvalues of the stiffness matrix

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

68.459 GPa | 68.591 GPa | 115.41 GPa | 157.3 GPa | 192.17 GPa | 576.07 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 | 146.73 GPa | 280.29 GPa | 0.83877 TPa^{–1} | 2.9826 TPa^{–1} | 61.918 GPa | 115.41 GPa | 0.069562 | 0.52362 | Value |

Anisotropy | 1.91 | 3.5559 | 1.864 | 7.5274 | Anisotropy | ||||

Axis | 0.5465 0.0000 0.8374 |
0.0504 0.7893 0.6119 |
0.0000 1.0000 0.0000 |
0.8239 0.0000 0.5668 |
0.1156 0.5239 -0.8439 |
0.1735 0.0002 0.9848 |
-0.8243 0.4177 -0.3822 |
0.0000 1.0000 -0.0000 |
Axis |

-0.8470 -0.3918 -0.3593 |
0.0005 1.0000 -0.0003 |
0.2318 -0.3669 -0.9009 |
-0.6774 -0.0000 -0.7356 |
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