# 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 AlBPbO4 (Materials Project id mp-559276)

83 76 32 0 0 0 76 131 59 0 0 0 32 59 213 0 0 0 0 0 0 78 0 0 0 0 0 0 52 0 0 0 0 0 0 67

### Average properties

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

Voigt | K_{V} = 84.556 GPa | E_{V} = 139.09 GPa | G_{V} = 56.733 GPa | ν_{V} = 0.22584 |

Reuss | K_{R} = 71.785 GPa | E_{R} = 94.841 GPa | G_{R} = 37.053 GPa | ν_{R} = 0.2798 |

Hill | K_{H} = 78.17 GPa | E_{H} = 117.24 GPa | G_{H} = 46.893 GPa | ν_{H} = 0.25004 |

### Eigenvalues of the stiffness matrix

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

26.782 GPa | 52 GPa | 67 GPa | 78 GPa | 132.37 GPa | 267.85 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 | 38.882 GPa | 191.95 GPa | -0.11584 TPa^{–1} | 10.967 TPa^{–1} | 13.628 GPa | 78 GPa | -0.29284 | 0.99002 | Value |

Anisotropy | 4.937 | ∞ | 5.723 | ∞ | Anisotropy | ||||

Axis | 1.0000 0.0000 0.0000 |
0.0000 0.3188 0.9478 |
0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
-0.7071 0.7071 0.0000 |
0.0000 0.0000 1.0000 |
0.5431 0.0001 0.8397 |
0.0000 0.7808 -0.6248 |
Axis |

-0.7071 -0.7071 -0.0000 |
0.0000 1.0000 -0.0000 |
0.8397 0.0004 -0.5431 |
-1.0000 -0.0000 -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