# 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 C (Materials Project id mp-1008374)

494 27 14 0 0 0 27 1102 170 0 0 0 14 170 1134 0 0 0 0 0 0 500 0 0 0 0 0 0 117 0 0 0 0 0 0 55

### Average properties

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

Voigt | K_{V} = 350.22 GPa | E_{V} = 704.33 GPa | G_{V} = 302.33 GPa | ν_{V} = 0.16482 |

Reuss | K_{R} = 289.62 GPa | E_{R} = 375.92 GPa | G_{R} = 146.42 GPa | ν_{R} = 0.28367 |

Hill | K_{H} = 319.92 GPa | E_{H} = 545.59 GPa | G_{H} = 224.38 GPa | ν_{H} = 0.21577 |

### Eigenvalues of the stiffness matrix

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

55 GPa | 117 GPa | 492.73 GPa | 500 GPa | 947.49 GPa | 1289.8 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 | 189.35 GPa | 1127.2 GPa | 0.74427 TPa^{–1} | 1.9625 TPa^{–1} | 55 GPa | 500 GPa | -0.17374 | 0.75425 | Value |

Anisotropy | 5.953 | 2.6368 | 9.091 | ∞ | Anisotropy | ||||

Axis | 0.7323 0.6810 0.0000 |
-0.0000 0.6142 0.7891 |
0.0000 1.0000 0.0000 |
1.0000 0.0000 0.0000 |
1.0000 -0.0002 -0.0001 |
-0.0000 0.0000 1.0000 |
0.2142 0.6068 0.7655 |
-0.5376 0.6603 0.5244 |
Axis |

0.0002 1.0000 -0.0000 |
-0.0000 -1.0000 0.0000 |
0.5685 0.5598 -0.6029 |
-0.7976 -0.5999 -0.0625 |
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