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 K2NaAlP2 (Materials Project id mp-9068)

        42       18       14        0        0        0  
        18       45       20        0        0        0  
        14       20       62        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.111 GPaEV = 43.82 GPaGV = 17.667 GPaνV = 0.2402
ReussKR = 27.403 GPaER = 41.343 GPaGR = 16.556 GPaνR = 0.24855
HillKH = 27.757 GPaEH = 42.584 GPaGH = 17.112 GPaνH = 0.24431

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 17 GPa 24.94 GPa 25 GPa 37.994 GPa 86.067 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 33.867 GPa 53.234 GPa 8.6816 TPa–1 15.745 TPa–1 12.605 GPa 25 GPa-0.0230910.42965Value
Anisotropy 1.572 1.8136 1.983Anisotropy
Axis 0.0000
1.0000
0.0000
0.4075
-0.0000
0.9132
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.7017
-0.0002
0.7124
-0.6324
0.0000
-0.7746
Axis
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
0.0000
0.7124
-0.0005
-0.7017
-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