# 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 TiZnO3 (Materials Project id mp-14142)

308 154 99 20 -7 0 154 308 99 -20 7 0 99 99 241 0 0 0 20 -20 0 31 0 7 -7 7 0 0 31 20 0 0 0 7 20 77

### Average properties

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

Voigt | K_{V} = 173.44 GPa | E_{V} = 164.92 GPa | G_{V} = 61.467 GPa | ν_{V} = 0.34153 |

Reuss | K_{R} = 167.41 GPa | E_{R} = 112.99 GPa | G_{R} = 40.717 GPa | ν_{R} = 0.38751 |

Hill | K_{H} = 170.43 GPa | E_{H} = 139.35 GPa | G_{H} = 51.092 GPa | ν_{H} = 0.36372 |

### Eigenvalues of the stiffness matrix

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

22.727 GPa | 24.088 GPa | 85.273 GPa | 160.91 GPa | 173.14 GPa | 529.86 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 | 66.85 GPa | 233.48 GPa | 1.5479 TPa^{–1} | 2.8777 TPa^{–1} | 22.727 GPa | 87.337 GPa | -0.10175 | 0.856 | Value |

Anisotropy | 3.493 | 1.8592 | 3.843 | ∞ | Anisotropy | ||||

Axis | -0.0856 0.7594 0.6449 |
0.7907 0.5836 0.1849 |
0.1305 0.9914 0.0000 |
0.0000 0.0000 1.0000 |
0.2926 0.2160 0.9315 |
0.5123 0.3778 0.7713 |
0.4673 0.3449 0.8140 |
-0.0745 0.6604 -0.7472 |
Axis |

-0.5938 0.8046 -0.0000 |
0.6206 0.4579 -0.6365 |
-0.5938 0.8046 0.0000 |
0.0834 -0.7425 -0.6646 |
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