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 CeB6 (Materials Project id mp-21343)

       495       15       15        0        0        0  
        15      495       15        0        0        0  
        15       15      495        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       74  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175 GPaEV = 332.33 GPaGV = 140.4 GPaνV = 0.1835
ReussKR = 175 GPaER = 256.86 GPaGR = 102.3 GPaνR = 0.25537
HillKH = 175 GPaEH = 295.7 GPaGH = 121.35 GPaνH = 0.21838

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
74 GPa 74 GPa 74 GPa 480 GPa 480 GPa 525 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 194.57 GPa 494.12 GPa 1.9048 TPa–1 1.9048 TPa–1 74 GPa 240 GPa0.0294120.54953Value
Anisotropy 2.539 1.0000 3.243 18.6840Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8656
0.0000
0.5007
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
Axis
-0.7648
0.6443
0.0000
-0.7071
-0.0002
-0.7071
0.1736
0.9848
-0.0000
-0.7071
0.0002
-0.7071
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