ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-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 Yb (Materials Project id mp-141)

        29       11        7        0        0        0  
        11       29        7        0        0        0  
         7        7       29        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 15.222 GPaEV = 24.476 GPaGV = 9.9333 GPaνV = 0.23201
ReussKR = 15.171 GPaER = 24.269 GPaGR = 9.8382 GPaνR = 0.23339
HillKH = 15.197 GPaEH = 24.372 GPaGH = 9.8858 GPaνH = 0.2327

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 10 GPa 10 GPa 18 GPa 23.175 GPa 45.825 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.845 GPa 26.55 GPa 20.716 TPa–1 24.482 TPa–1 9 GPa 10.837 GPa0.159090.34091Value
Anisotropy 1.113 1.1818 1.204 2.1429Anisotropy
Axis 0.4481
0.7370
0.5061
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.9573
0.2890
0.0000
0.6000
0.3742
0.7071
0.4552
0.8904
0.0000
-0.6864
0.7272
-0.0000
Axis
-0.2890
0.9573
-0.0000
0.6000
0.3742
-0.7071
0.0000
0.0000
-1.0000
-0.7272
-0.6864
-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