# 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 Zn3Cu (Materials Project id mp-972042)

135 72 72 0 0 0 72 135 72 0 0 0 72 72 170 0 0 0 0 0 0 48 0 0 0 0 0 0 48 0 0 0 0 0 0 32

### Average properties

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

Voigt | K_{V} = 96.889 GPa | E_{V} = 106.72 GPa | G_{V} = 40.533 GPa | ν_{V} = 0.31643 |

Reuss | K_{R} = 95.838 GPa | E_{R} = 103.11 GPa | G_{R} = 39.037 GPa | ν_{R} = 0.32068 |

Hill | K_{H} = 96.363 GPa | E_{H} = 104.92 GPa | G_{H} = 39.785 GPa | ν_{H} = 0.31854 |

### Eigenvalues of the stiffness matrix

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

32 GPa | 48 GPa | 48 GPa | 63 GPa | 85.01 GPa | 291.99 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 | 88.021 GPa | 122.1 GPa | 2.5381 TPa^{–1} | 3.9481 TPa^{–1} | 31.5 GPa | 48 GPa | 0.19693 | 0.4283 | Value |

Anisotropy | 1.387 | 1.5556 | 1.524 | 2.1749 | Anisotropy | ||||

Axis | 0.0000 1.0000 0.0000 |
0.3010 0.3010 0.9049 |
0.0000 0.0000 1.0000 |
0.5000 0.8660 0.0000 |
-0.7071 0.7071 0.0000 |
-0.0000 0.0000 1.0000 |
0.7611 0.0001 0.6486 |
0.7612 -0.0005 -0.6486 |
Axis |

-0.7071 -0.7071 0.0000 |
-0.7660 0.6428 -0.0000 |
0.6486 0.0003 -0.7611 |
0.0006 1.0000 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