# 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 NbNO (Materials Project id mp-754495)

209 76 113 0 14 0 76 230 96 0 2 0 113 96 269 0 24 0 0 0 0 45 0 -6 14 2 24 0 46 0 0 0 0 -6 0 41

### Average properties

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

Voigt | K_{V} = 142 GPa | E_{V} = 145.19 GPa | G_{V} = 54.6 GPa | ν_{V} = 0.32959 |

Reuss | K_{R} = 135.69 GPa | E_{R} = 133.55 GPa | G_{R} = 49.984 GPa | ν_{R} = 0.33596 |

Hill | K_{H} = 138.84 GPa | E_{H} = 139.38 GPa | G_{H} = 52.292 GPa | ν_{H} = 0.33269 |

### Eigenvalues of the stiffness matrix

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

36.675 GPa | 42.872 GPa | 49.325 GPa | 122.13 GPa | 156.8 GPa | 432.19 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 | 106.78 GPa | 205.35 GPa | 1.1712 TPa^{–1} | 3.5324 TPa^{–1} | 36.675 GPa | 79.075 GPa | 0.13429 | 0.63068 | Value |

Anisotropy | 1.923 | 3.0160 | 2.156 | 4.6963 | Anisotropy | ||||

Axis | -0.6133 0.6770 -0.4069 |
-0.2365 0.0000 -0.9716 |
-0.4531 0.0000 -0.8915 |
0.8915 0.0000 -0.4531 |
0.8112 0.0002 0.5847 |
-0.2474 0.7071 -0.6624 |
0.8313 0.0000 0.5559 |
-0.6885 -0.0000 -0.7253 |
Axis |

-0.0002 1.0000 -0.0001 |
-0.2474 -0.7071 -0.6624 |
-0.0000 1.0000 0.0000 |
0.7253 -0.0001 -0.6885 |
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