# 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 HfBe2 (Materials Project id mp-2553)

252 38 90 0 0 0 38 252 90 0 0 0 90 90 219 0 0 0 0 0 0 130 0 0 0 0 0 0 130 0 0 0 0 0 0 107

### Average properties

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

Voigt | K_{V} = 128.78 GPa | E_{V} = 251.5 GPa | G_{V} = 107.07 GPa | ν_{V} = 0.1745 |

Reuss | K_{R} = 128.56 GPa | E_{R} = 236.7 GPa | G_{R} = 99.19 GPa | ν_{R} = 0.19314 |

Hill | K_{H} = 128.67 GPa | E_{H} = 244.15 GPa | G_{H} = 103.13 GPa | ν_{H} = 0.18374 |

### Eigenvalues of the stiffness matrix

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

107 GPa | 122.36 GPa | 130 GPa | 130 GPa | 214 GPa | 386.64 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 | 163.14 GPa | 278.72 GPa | 2.3251 TPa^{–1} | 2.7267 TPa^{–1} | 68.562 GPa | 130 GPa | 0.0047146 | 0.40902 | Value |

Anisotropy | 1.709 | 1.1727 | 1.896 | 86.7568 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.3713 0.6851 0.6267 |
0.0000 0.0000 1.0000 |
1.0000 0.0000 0.0000 |
0.7071 -0.0003 0.7071 |
0.0000 0.0000 1.0000 |
0.7134 0.7007 0.0000 |
-0.5872 0.8094 0.0000 |
Axis |

0.7071 -0.0005 -0.7071 |
0.7660 0.6428 -0.0000 |
-0.7007 0.7134 -0.0000 |
-0.0000 -0.0000 -1.0000 |
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