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 K2NaAlAs2 (Materials Project id mp-9069)

        38       12        6        0        0        0  
        12       30       11        0        0        0  
         6       11       48        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 19.333 GPaEV = 38.355 GPaGV = 16.4 GPaνV = 0.16935
ReussKR = 19.047 GPaER = 36.158 GPaGR = 15.275 GPaνR = 0.18361
HillKH = 19.19 GPaEH = 37.262 GPaGH = 15.837 GPaνH = 0.17639

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 16 GPa 20.082 GPa 22 GPa 36.855 GPa 59.063 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.449 GPa 44.156 GPa 13.771 TPa–1 21.32 TPa–1 10.592 GPa 22 GPa-0.0553290.40845Value
Anisotropy 1.806 1.5482 2.077Anisotropy
Axis 0.0000
1.0000
0.0000
0.3451
0.0000
0.9386
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.0000
0.0000
1.0000
0.6928
-0.0002
0.7211
-0.7698
-0.0000
0.6383
Axis
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
-0.0000
0.7211
-0.0004
-0.6928
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