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 PrSe2 (Materials Project id mp-1018940)

       117       55       43        0        0        0  
        55      117       43        0        0        0  
        43       43      116        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 70.222 GPaEV = 78.167 GPaGV = 29.733 GPaνV = 0.31448
ReussKR = 70.06 GPaER = 71.044 GPaGR = 26.689 GPaνR = 0.33099
HillKH = 70.141 GPaEH = 74.628 GPaGH = 28.211 GPaνH = 0.32267

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 32 GPa 32 GPa 62 GPa 77.052 GPa 210.95 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 49.419 GPa 94.5 GPa 4.4912 TPa–1 5.291 TPa–1 15 GPa 36.356 GPa0.0972760.64731Value
Anisotropy 1.912 1.1781 2.424 6.6544Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
0.7071
-0.0002
0.7071
-0.5510
0.5509
-0.6268
-0.7071
0.7071
0.0000
Axis
0.0002
1.0000
0.0000
0.7071
0.0001
-0.7071
0.4431
-0.4433
-0.7792
-0.7071
-0.7071
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