# 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 Ta (Materials Project id mp-569794)

302 148 148 0 0 0 148 290 140 0 0 0 148 140 290 0 0 0 0 0 0 67 0 0 0 0 0 0 44 0 0 0 0 0 0 44

### Average properties

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

Voigt | K_{V} = 194.89 GPa | E_{V} = 165.05 GPa | G_{V} = 60.733 GPa | ν_{V} = 0.35885 |

Reuss | K_{R} = 194.69 GPa | E_{R} = 156.47 GPa | G_{R} = 57.272 GPa | ν_{R} = 0.36605 |

Hill | K_{H} = 194.79 GPa | E_{H} = 160.78 GPa | G_{H} = 59.003 GPa | ν_{H} = 0.36244 |

### Eigenvalues of the stiffness matrix

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

44 GPa | 44 GPa | 67 GPa | 147.13 GPa | 150 GPa | 584.87 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 | 134.24 GPa | 200.12 GPa | 1.5572 TPa^{–1} | 1.7896 TPa^{–1} | 44 GPa | 75 GPa | 0.22416 | 0.54754 | Value |

Anisotropy | 1.491 | 1.1493 | 1.705 | 2.4426 | Anisotropy | ||||

Axis | 0.6872 0.5137 0.5137 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 0.9660 0.2587 |
0.0000 0.0000 1.0000 |
0.0002 0.7071 -0.7071 |
-0.6788 -0.0000 0.7343 |
0.7113 -0.0002 0.7028 |
Axis |

1.0000 0.0000 -0.0000 |
0.0002 -0.7071 -0.7071 |
0.0000 -1.0000 -0.0000 |
0.7028 -0.0006 -0.7113 |
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