# 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 SrTiO3 (Materials Project id mp-4651)

297 83 112 0 0 0 83 297 112 0 0 0 112 112 311 0 0 0 0 0 0 102 0 0 0 0 0 0 102 0 0 0 0 0 0 108

### Average properties

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

Voigt | K_{V} = 168.78 GPa | E_{V} = 255.25 GPa | G_{V} = 102.27 GPa | ν_{V} = 0.24795 |

Reuss | K_{R} = 168.04 GPa | E_{R} = 254.2 GPa | G_{R} = 101.85 GPa | ν_{R} = 0.24788 |

Hill | K_{H} = 168.41 GPa | E_{H} = 254.72 GPa | G_{H} = 102.06 GPa | ν_{H} = 0.24791 |

### Eigenvalues of the stiffness matrix

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

102 GPa | 102 GPa | 108 GPa | 183.39 GPa | 214 GPa | 507.61 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 | 244.98 GPa | 258.88 GPa | 1.6758 TPa^{–1} | 2.1377 TPa^{–1} | 95.283 GPa | 108 GPa | 0.1617 | 0.30189 | Value |

Anisotropy | 1.057 | 1.2756 | 1.133 | 1.8670 | Anisotropy | ||||

Axis | 0.0000 0.0000 1.0000 |
-0.5349 0.5349 0.6540 |
0.0000 0.0000 1.0000 |
0.6088 0.7934 0.0000 |
0.7071 -0.0003 0.7071 |
1.0000 -0.0002 -0.0000 |
0.7071 0.7071 0.0000 |
0.7071 0.7071 -0.0000 |
Axis |

0.7071 -0.0005 -0.7071 |
0.0002 1.0000 -0.0000 |
-0.7071 0.7071 -0.0000 |
0.0003 -0.0003 -1.0000 |
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