# 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 CdAuO2 (Materials Project id mp-997037)

170 87 62 0 0 0 87 222 106 0 0 0 62 106 189 0 0 0 0 0 0 36 0 0 0 0 0 0 15 0 0 0 0 0 0 23

### Average properties

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

Voigt | K_{V} = 121.22 GPa | E_{V} = 99.595 GPa | G_{V} = 36.533 GPa | ν_{V} = 0.36307 |

Reuss | K_{R} = 116.3 GPa | E_{R} = 78.86 GPa | G_{R} = 28.428 GPa | ν_{R} = 0.38699 |

Hill | K_{H} = 118.76 GPa | E_{H} = 89.301 GPa | G_{H} = 32.481 GPa | ν_{H} = 0.37468 |

### Eigenvalues of the stiffness matrix

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

15 GPa | 23 GPa | 36 GPa | 94.421 GPa | 116.98 GPa | 369.6 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 | 50.405 GPa | 144.32 GPa | 1.4181 TPa^{–1} | 3.995 TPa^{–1} | 15 GPa | 58.339 GPa | 0.15054 | 0.68016 | Value |

Anisotropy | 2.863 | 2.8172 | 3.889 | 4.5181 | Anisotropy | ||||

Axis | 0.7081 -0.0000 0.7061 |
0.0000 1.0000 0.0000 |
0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.7071 -0.0000 -0.7071 |
0.0000 0.0000 1.0000 |
0.7051 0.0002 -0.7091 |
Axis |

1.0000 0.0000 -0.0000 |
-0.7071 0.0002 -0.7071 |
-1.0000 0.0000 0.0000 |
-0.7091 -0.0002 -0.7051 |
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