# 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 YCo3 (Materials Project id mp-2588)

201 136 115 2 -0 1 136 200 113 -1 1 -0 115 113 245 -0 -0 2 2 -1 -0 39 -1 -0 -0 1 -0 -1 38 1 1 -0 2 -0 1 33

### Average properties

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

Voigt | K_{V} = 152.67 GPa | E_{V} = 112.39 GPa | G_{V} = 40.8 GPa | ν_{V} = 0.37731 |

Reuss | K_{R} = 152.32 GPa | E_{R} = 106.63 GPa | G_{R} = 38.541 GPa | ν_{R} = 0.38333 |

Hill | K_{H} = 152.5 GPa | E_{H} = 109.51 GPa | G_{H} = 39.67 GPa | ν_{H} = 0.38031 |

### Eigenvalues of the stiffness matrix

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

32.76 GPa | 37.511 GPa | 39.488 GPa | 64.697 GPa | 123.19 GPa | 458.35 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 | 95.683 GPa | 167.67 GPa | 1.9185 TPa^{–1} | 2.4231 TPa^{–1} | 31.672 GPa | 51.809 GPa | 0.19166 | 0.56773 | Value |

Anisotropy | 1.752 | 1.2630 | 1.636 | 2.9622 | Anisotropy | ||||

Axis | -0.8548 0.2841 -0.4342 |
-0.0057 -0.0058 1.0000 |
0.1039 0.0850 0.9910 |
-0.5242 0.8514 -0.0181 |
-0.5371 0.8435 -0.0007 |
-0.3743 0.5962 -0.7102 |
-0.5291 0.8486 -0.0016 |
0.2121 0.9772 0.0044 |
Axis |

-0.8265 -0.5264 -0.1994 |
0.3632 -0.6104 -0.7039 |
-0.0344 -0.0234 -0.9991 |
-0.9750 0.2119 -0.0673 |
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