# 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 TmBi2BrO4 (Materials Project id mp-546350)

162 86 27 0 0 0 86 162 27 0 0 0 27 27 76 0 0 0 0 0 0 21 0 0 0 0 0 0 21 0 0 0 0 0 0 83

### Average properties

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

Voigt | K_{V} = 75.556 GPa | E_{V} = 107.01 GPa | G_{V} = 42.333 GPa | ν_{V} = 0.26394 |

Reuss | K_{R} = 59.555 GPa | E_{R} = 79.933 GPa | G_{R} = 31.314 GPa | ν_{R} = 0.2763 |

Hill | K_{H} = 67.555 GPa | E_{H} = 93.486 GPa | G_{H} = 36.824 GPa | ν_{H} = 0.26936 |

### Eigenvalues of the stiffness matrix

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

21 GPa | 21 GPa | 67.904 GPa | 76 GPa | 83 GPa | 256.1 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 | 58.017 GPa | 192.41 GPa | 2.8177 TPa^{–1} | 11.156 TPa^{–1} | 21 GPa | 83 GPa | 0.074369 | 0.51713 | Value |

Anisotropy | 3.316 | 3.9592 | 3.952 | 6.9535 | Anisotropy | ||||

Axis | 0.6100 -0.0000 0.7924 |
0.7071 0.7071 0.0000 |
0.2588 0.9659 0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.0000 1.0000 |
1.0000 -0.0003 -0.0000 |
0.5069 0.5069 0.6972 |
-0.5889 0.5890 0.5534 |
Axis |

-0.7660 -0.6428 0.0000 |
0.0003 1.0000 0.0000 |
-0.7071 0.7071 0.0000 |
-0.3915 0.3912 -0.8329 |
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