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 C (Materials Project id mp-1095534)

       878       -1      151        0        0        0  
        -1        6       -1        0        0        0  
       151       -1      878        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0      357        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 228.89 GPaEV = 426.97 GPaGV = 179.53 GPaνV = 0.1891
ReussKR = 5.9062 GPaER = 7.4618 GPaGR = 2.8934 GPaνR = 0.28944
HillKH = 117.4 GPaEH = 217.35 GPaGH = 91.213 GPaνH = 0.19143

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 2 GPa 5.998 GPa 357 GPa 727 GPa 1029 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.3302 GPa 851.92 GPa 1.1342 TPa–1 167.04 TPa–1 1 GPa 363.5 GPa-1.9352.3407Value
Anisotropy 255.8147.2857 363.5Anisotropy
Axis -0.0000
0.7742
-0.6329
0.0000
0.0000
1.0000
0.9914
0.0000
0.1305
0.0000
1.0000
0.0000
-0.0003
-0.0000
1.0000
0.7071
0.0000
0.7071
0.7683
0.0379
0.6389
0.7613
0.0449
0.6468
Axis
0.0000
1.0000
0.0000
0.7071
-0.0000
-0.7071
-0.4818
0.6914
0.5383
0.4179
0.7288
-0.5424
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