# 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 Fe2N (Materials Project id mp-248)

355 160 208 -0 -19 -1 160 355 208 -0 18 1 208 208 336 -1 -0 -0 -0 -0 -1 102 0 19 -19 18 -0 0 102 0 -1 1 -0 19 0 99

### Average properties

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

Voigt | K_{V} = 244.22 GPa | E_{V} = 245.05 GPa | G_{V} = 91.933 GPa | ν_{V} = 0.33277 |

Reuss | K_{R} = 243.69 GPa | E_{R} = 230.06 GPa | G_{R} = 85.674 GPa | ν_{R} = 0.34266 |

Hill | K_{H} = 243.96 GPa | E_{H} = 237.58 GPa | G_{H} = 88.804 GPa | ν_{H} = 0.33769 |

### Eigenvalues of the stiffness matrix

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

81.419 GPa | 95.141 GPa | 117.84 GPa | 119.76 GPa | 201.87 GPa | 732.97 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 | 167.95 GPa | 305.21 GPa | 1.1441 TPa^{–1} | 1.4814 TPa^{–1} | 64.243 GPa | 119.57 GPa | 0.11881 | 0.55451 | Value |

Anisotropy | 1.817 | 1.2948 | 1.861 | 4.6673 | Anisotropy | ||||

Axis | -0.0038 0.0093 0.9999 |
-0.4147 0.7040 -0.5765 |
-0.0223 -0.0175 0.9996 |
-0.9564 0.2914 -0.0163 |
0.6367 0.0903 0.7658 |
0.6788 0.0082 0.7342 |
-0.8557 0.5173 -0.0154 |
0.8515 0.5244 -0.0028 |
Axis |

0.7655 0.0460 -0.6418 |
-0.0068 1.0000 -0.0049 |
-0.4980 -0.8311 -0.2476 |
-0.1363 0.2264 0.9645 |
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