# 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 LiFeAs2O7 (Materials Project id mp-18878)

139 57 81 0 9 0 57 142 74 0 10 0 81 74 180 0 7 0 0 0 0 54 0 11 9 10 7 0 63 0 0 0 0 11 0 48

### Average properties

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

Voigt | K_{V} = 98.333 GPa | E_{V} = 127.38 GPa | G_{V} = 49.6 GPa | ν_{V} = 0.2841 |

Reuss | K_{R} = 93.794 GPa | E_{R} = 120.57 GPa | G_{R} = 46.888 GPa | ν_{R} = 0.28575 |

Hill | K_{H} = 96.064 GPa | E_{H} = 123.98 GPa | G_{H} = 48.244 GPa | ν_{H} = 0.2849 |

### Eigenvalues of the stiffness matrix

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

39.598 GPa | 61.202 GPa | 62.402 GPa | 76.493 GPa | 86.679 GPa | 299.63 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 | 96.812 GPa | 163.29 GPa | 1.5919 TPa^{–1} | 4.634 TPa^{–1} | 38.156 GPa | 62.524 GPa | 0.14944 | 0.47831 | Value |

Anisotropy | 1.687 | 2.9110 | 1.639 | 3.2006 | Anisotropy | ||||

Axis | 0.9982 -0.0000 -0.0595 |
0.5577 0.4999 0.6626 |
0.2617 0.0000 0.9652 |
0.9652 0.0000 -0.2616 |
0.6796 -0.0000 -0.7336 |
0.0131 0.1879 0.9821 |
0.8111 0.5763 -0.1002 |
-0.0460 0.4087 0.9115 |
Axis |

-0.7336 0.0002 -0.6796 |
-0.9643 -0.2573 0.0621 |
-0.5736 0.7500 -0.3293 |
-0.8883 -0.4342 0.1498 |
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