# 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 TbZr (Materials Project id mp-978918)

104 32 47 0 0 0 32 104 47 -0 0 0 47 47 120 -0 0 0 0 -0 -0 30 0 0 0 0 0 0 30 0 0 0 0 0 0 36

### Average properties

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

Voigt | K_{V} = 64.444 GPa | E_{V} = 83.835 GPa | G_{V} = 32.667 GPa | ν_{V} = 0.28319 |

Reuss | K_{R} = 63.309 GPa | E_{R} = 82.857 GPa | G_{R} = 32.319 GPa | ν_{R} = 0.28187 |

Hill | K_{H} = 63.876 GPa | E_{H} = 83.346 GPa | G_{H} = 32.493 GPa | ν_{H} = 0.28253 |

### Eigenvalues of the stiffness matrix

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

30 GPa | 30 GPa | 36 GPa | 61.052 GPa | 72 GPa | 194.95 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 | 81.629 GPa | 87.515 GPa | 3.5288 TPa^{–1} | 6.1334 TPa^{–1} | 30 GPa | 36 GPa | 0.1588 | 0.36545 | Value |

Anisotropy | 1.072 | 1.7381 | 1.2 | 2.3014 | Anisotropy | ||||

Axis | 0.7988 0.0004 0.6016 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.7889 0.6145 -0.0000 |
-0.4115 0.9114 0.0000 |
0.6082 0.2247 0.7613 |
Axis |

0.1736 0.9848 -0.0000 |
-0.6145 0.7889 0.0000 |
-0.9114 -0.4115 0.0000 |
0.7141 0.2638 -0.6484 |
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