# 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 Zn2SbN3 (Materials Project id mp-1029334)

222 93 75 0 0 0 93 222 75 0 0 0 75 75 254 0 0 0 0 0 0 55 0 0 0 0 0 0 56 0 0 0 0 0 0 63

### Average properties

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

Voigt | K_{V} = 131.56 GPa | E_{V} = 167.72 GPa | G_{V} = 65.133 GPa | ν_{V} = 0.28752 |

Reuss | K_{R} = 131.47 GPa | E_{R} = 163.8 GPa | G_{R} = 63.375 GPa | ν_{R} = 0.29235 |

Hill | K_{H} = 131.51 GPa | E_{H} = 165.77 GPa | G_{H} = 64.254 GPa | ν_{H} = 0.28993 |

### Eigenvalues of the stiffness matrix

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

55 GPa | 56 GPa | 63 GPa | 129 GPa | 174.14 GPa | 394.86 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 | 150.62 GPa | 218.29 GPa | 2.3997 TPa^{–1} | 2.6033 TPa^{–1} | 55 GPa | 80.092 GPa | 0.18757 | 0.3845 | Value |

Anisotropy | 1.449 | 1.0848 | 1.456 | 2.0500 | Anisotropy | ||||

Axis | 0.3631 0.6902 -0.6259 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
0.6088 0.7934 0.0000 |
-0.0003 -0.0000 1.0000 |
0.7071 -0.0003 0.7071 |
-0.7071 0.7071 0.0000 |
0.0000 0.6614 -0.7501 |
Axis |

-0.0000 1.0000 0.0000 |
0.7071 -0.0005 -0.7071 |
-0.0002 -0.0002 -1.0000 |
-0.0000 -0.7501 -0.6614 |
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