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 NbCr2 (Materials Project id mp-548)

       299      192      192        0        0        0  
       192      299      192        0        0        0  
       192      192      299        0        0        0  
         0        0        0       71        0        0  
         0        0        0        0       71        0  
         0        0        0        0        0       71  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 227.67 GPaEV = 175.55 GPaGV = 64 GPaνV = 0.37149
ReussKR = 227.67 GPaER = 172.5 GPaGR = 62.785 GPaνR = 0.37372
HillKH = 227.67 GPaEH = 174.03 GPaGH = 63.393 GPaνH = 0.3726

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
71 GPa 71 GPa 71 GPa 107 GPa 107 GPa 683 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 148.84 GPa 192.94 GPa 1.4641 TPa–1 1.4641 TPa–1 53.5 GPa 71 GPa0.265040.47194Value
Anisotropy 1.296 1.0000 1.327 1.7806Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.2053
0.7663
0.6088
0.8660
0.0000
0.5000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.9397
0.3420
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
0.0001
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