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 PrSe (Materials Project id mp-1674)

       176       20       20        0        0        0  
        20      176       20        0        0        0  
        20       20      176        0        0        0  
         0        0        0       12        0        0  
         0        0        0        0       12        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72 GPaEV = 97.811 GPaGV = 38.4 GPaνV = 0.27358
ReussKR = 72 GPaER = 50.203 GPaGR = 18.14 GPaνR = 0.38379
HillKH = 72 GPaEH = 74.994 GPaGH = 28.27 GPaνH = 0.3264

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 12 GPa 12 GPa 156 GPa 156 GPa 216 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.105 GPa 171.92 GPa 4.6296 TPa–1 4.6296 TPa–1 12 GPa 78 GPa0.0253160.77722Value
Anisotropy 5.041 1.0000 6.5 30.7000Anisotropy
Axis 0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.9659
0.0000
0.2588
0.8536
0.3536
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1735
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
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