# 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-4481)

147 62 64 0 0 0 62 123 59 0 0 0 64 59 177 0 0 0 0 0 0 56 0 0 0 0 0 0 59 0 0 0 0 0 0 45

### Average properties

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

Voigt | K_{V} = 90.778 GPa | E_{V} = 125.59 GPa | G_{V} = 49.467 GPa | ν_{V} = 0.26942 |

Reuss | K_{R} = 88.794 GPa | E_{R} = 121.46 GPa | G_{R} = 47.744 GPa | ν_{R} = 0.27202 |

Hill | K_{H} = 89.786 GPa | E_{H} = 123.53 GPa | G_{H} = 48.605 GPa | ν_{H} = 0.2707 |

### Eigenvalues of the stiffness matrix

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

45 GPa | 56 GPa | 59 GPa | 71.353 GPa | 100.47 GPa | 275.18 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 | 89.981 GPa | 142.87 GPa | 2.6959 TPa^{–1} | 5.0794 TPa^{–1} | 36.123 GPa | 59 GPa | 0.13483 | 0.41733 | Value |

Anisotropy | 1.588 | 1.8842 | 1.633 | 3.0953 | Anisotropy | ||||

Axis | 0.0000 1.0000 0.0000 |
-0.4502 0.2429 0.8593 |
0.0000 0.0000 1.0000 |
0.0000 1.0000 0.0000 |
0.7071 0.7071 -0.0000 |
0.0000 0.0000 1.0000 |
0.0000 0.7470 0.6649 |
-0.7923 0.0000 0.6101 |
Axis |

-0.7071 0.7071 0.0000 |
-1.0000 0.0000 0.0000 |
-0.0001 -0.6649 0.7470 |
-0.0000 -1.0000 0.0000 |
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