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 CrN2 (Materials Project id mp-1014993)

       390      116      116       -0       -0        0  
       116      390      116       -0       -0        0  
       116      116      390       -0       -0        0  
        -0       -0       -0       53        0        0  
        -0       -0       -0        0       53       -0  
         0        0        0        0       -0       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 207.33 GPaEV = 228.05 GPaGV = 86.6 GPaνV = 0.31668
ReussKR = 207.33 GPaER = 189.3 GPaGR = 70.222 GPaνR = 0.34783
HillKH = 207.33 GPaEH = 208.9 GPaGH = 78.411 GPaνH = 0.33207

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 53 GPa 53 GPa 274 GPa 274 GPa 622 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 146.52 GPa 336.81 GPa 1.6077 TPa–1 1.6077 TPa–1 53 GPa 137 GPa0.116130.60957Value
Anisotropy 2.299 1.0000 2.585 5.2492Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
-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
1.0000
0.0002
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