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 NaH2N (Materials Project id mp-23850)

        38       20        9        0        0        0  
        20       17        0        0        0        0  
         9        0       12        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 13.889 GPaEV = 16.943 GPaGV = 6.5333 GPaνV = 0.29668
ReussKR = 3.9474 GPaER = 8.3106 GPaGR = 3.6161 GPaνR = 0.14911
HillKH = 8.9181 GPaEH = 12.797 GPaGH = 5.0747 GPaνH = 0.26085

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2.3373 GPa 4 GPa 7 GPa 9 GPa 13.058 GPa 51.604 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.1997 GPa 21.804 GPa -120 TPa–1 200 TPa–1 1.4873 GPa 9 GPa-0.731711.3071Value
Anisotropy 5.192 6.051Anisotropy
Axis -0.0000
0.9929
-0.1189
0.7762
0.6305
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
-0.0002
0.0001
1.0000
-0.9015
-0.0000
-0.4328
Axis
-0.7071
-0.7071
0.0000
-1.0000
0.0000
0.0000
0.0000
-1.0000
0.0001
0.0000
-1.0000
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