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 NbCr3 (Materials Project id mp-999390)

       345       79       79        0        0        0  
        79      345       79        0        0        0  
        79       79      345        0        0        0  
         0        0        0       50        0        0  
         0        0        0        0       50        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 167.67 GPaEV = 214.17 GPaGV = 83.2 GPaνV = 0.2871
ReussKR = 167.67 GPaER = 176.52 GPaGR = 66.633 GPaνR = 0.32454
HillKH = 167.67 GPaEH = 195.62 GPaGH = 74.917 GPaνH = 0.30555

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
50 GPa 50 GPa 50 GPa 266 GPa 266 GPa 503 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 136.44 GPa 315.56 GPa 1.9881 TPa–1 1.9881 TPa–1 50 GPa 133 GPa0.0938810.59001Value
Anisotropy 2.313 1.0000 2.66 6.2847Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1734
0.9849
-0.0000
0.7071
-0.0005
-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