# 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 Ca2SiO4 (Materials Project id mp-758006)

184 69 72 0 0 0 69 134 68 0 0 0 72 68 163 0 0 0 0 0 0 54 0 0 0 0 0 0 36 0 0 0 0 0 0 42

### Average properties

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

Voigt | K_{V} = 99.889 GPa | E_{V} = 116.31 GPa | G_{V} = 44.533 GPa | ν_{V} = 0.30593 |

Reuss | K_{R} = 97.983 GPa | E_{R} = 113.21 GPa | G_{R} = 43.294 GPa | ν_{R} = 0.30744 |

Hill | K_{H} = 98.936 GPa | E_{H} = 114.76 GPa | G_{H} = 43.914 GPa | ν_{H} = 0.30667 |

### Eigenvalues of the stiffness matrix

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

36 GPa | 42 GPa | 54 GPa | 77.082 GPa | 101.95 GPa | 301.97 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 | 95.657 GPa | 137.82 GPa | 2.4909 TPa^{–1} | 4.5987 TPa^{–1} | 36 GPa | 54 GPa | 0.17282 | 0.44377 | Value |

Anisotropy | 1.441 | 1.8462 | 1.5 | 2.5679 | Anisotropy | ||||

Axis | 0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
1.0000 0.0000 0.0000 |
0.0000 1.0000 0.0000 |
0.0000 0.0000 1.0000 |
0.0001 0.0002 1.0000 |
0.4086 0.7067 0.5776 |
0.7042 0.4467 0.5519 |
Axis |

1.0000 0.0000 -0.0000 |
-0.0000 1.0000 -0.0002 |
-0.3047 0.7021 -0.6436 |
-0.7022 0.3236 0.6342 |
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