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 Gd (Materials Project id mp-155)

        67       22       20        0        0        0  
        22       67       20        0        0        0  
        20       20       80        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.556 GPaEV = 59.22 GPaGV = 23.933 GPaνV = 0.23719
ReussKR = 37.396 GPaER = 58.8 GPaGR = 23.749 GPaνR = 0.23794
HillKH = 37.476 GPaEH = 59.01 GPaGH = 23.841 GPaνH = 0.23756

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 23 GPa 45 GPa 55.86 GPa 113.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 56.597 GPa 71.011 GPa 7.7532 TPa–1 9.4937 TPa–1 22.5 GPa 26.589 GPa0.181450.27322Value
Anisotropy 1.255 1.2245 1.182 1.5057Anisotropy
Axis 0.8935
-0.0000
0.4490
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
0.4998
0.5002
0.7071
1.0000
0.0002
0.0000
-0.4473
0.4473
0.7745
Axis
-0.7071
-0.7071
-0.0000
0.5003
0.4997
-0.7071
-0.0000
0.0002
-1.0000
0.5477
-0.5476
0.6326
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