# 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 ZrCr2 (Materials Project id mp-1919)

273 131 139 0 0 0 131 273 139 0 0 0 139 139 252 0 0 0 0 0 0 37 0 0 0 0 0 0 37 0 0 0 0 0 0 71

### Average properties

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

Voigt | K_{V} = 179.56 GPa | E_{V} = 149.55 GPa | G_{V} = 54.933 GPa | ν_{V} = 0.36119 |

Reuss | K_{R} = 179.45 GPa | E_{R} = 138.16 GPa | G_{R} = 50.363 GPa | ν_{R} = 0.37168 |

Hill | K_{H} = 179.5 GPa | E_{H} = 143.88 GPa | G_{H} = 52.648 GPa | ν_{H} = 0.36641 |

### Eigenvalues of the stiffness matrix

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

37 GPa | 37 GPa | 71 GPa | 117.24 GPa | 142 GPa | 538.76 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 | 115.57 GPa | 181.3 GPa | 1.7889 TPa^{–1} | 1.9947 TPa^{–1} | 37 GPa | 71 GPa | 0.21281 | 0.56663 | Value |

Anisotropy | 1.569 | 1.1150 | 1.919 | 2.6626 | Anisotropy | ||||

Axis | 0.2398 0.6336 0.7356 |
0.7934 0.6088 0.0000 |
0.5000 0.8660 0.0000 |
0.0000 0.0000 1.0000 |
-0.0000 -0.0000 1.0000 |
-0.0836 0.9965 0.0000 |
0.5885 0.5103 -0.6271 |
0.6106 0.4253 0.6681 |
Axis |

-0.7648 0.6443 0.0000 |
-0.9965 -0.0836 -0.0000 |
-0.6551 0.7555 -0.0000 |
-0.5482 -0.3818 0.7441 |
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