# 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 Nd2O3 (Materials Project id mp-1045)

179 96 96 0 0 0 96 179 96 0 0 0 96 96 179 0 0 0 0 0 0 58 0 0 0 0 0 0 58 0 0 0 0 0 0 58

### Average properties

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

Voigt | K_{V} = 123.67 GPa | E_{V} = 135.44 GPa | G_{V} = 51.4 GPa | ν_{V} = 0.31747 |

Reuss | K_{R} = 123.67 GPa | E_{R} = 132.28 GPa | G_{R} = 50.042 GPa | ν_{R} = 0.32172 |

Hill | K_{H} = 123.67 GPa | E_{H} = 133.86 GPa | G_{H} = 50.721 GPa | ν_{H} = 0.31959 |

### Eigenvalues of the stiffness matrix

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

58 GPa | 58 GPa | 58 GPa | 83 GPa | 83 GPa | 371 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 | 111.97 GPa | 150.48 GPa | 2.6954 TPa^{–1} | 2.6954 TPa^{–1} | 41.5 GPa | 58 GPa | 0.19452 | 0.43199 | Value |

Anisotropy | 1.344 | 1.0000 | 1.398 | 2.2208 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
0.5774 0.5774 0.5773 |
0.2053 0.7663 0.6088 |
0.9914 0.0000 -0.1305 |
0.7071 0.0001 -0.7071 |
0.0000 0.0000 1.0000 |
0.7071 -0.0002 0.7071 |
0.7071 -0.0001 0.7071 |
Axis |

-0.7071 -0.0002 -0.7071 |
-0.1736 0.9848 -0.0000 |
0.7071 -0.0006 -0.7071 |
0.0001 1.0000 0.0001 |
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