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 K3As (Materials Project id mp-14018)

        31       11        4        0        0        0  
        11       31        4        0        0        0  
         4        4       26        0        0        0  
         0        0        0        6        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 14 GPaEV = 22.235 GPaGV = 9 GPaνV = 0.23529
ReussKR = 13.59 GPaER = 20.402 GPaGR = 8.1622 GPaνR = 0.24979
HillKH = 13.795 GPaEH = 21.322 GPaGH = 8.5811 GPaνH = 0.24239

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 6 GPa 10 GPa 20 GPa 24.202 GPa 43.798 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.944 GPa 26.835 GPa 20.755 TPa–1 32.075 TPa–1 6 GPa 11.844 GPa0.0952380.41247Value
Anisotropy 1.584 1.5455 1.974 4.3310Anisotropy
Axis 0.6914
0.0873
0.7172
1.0000
0.0002
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
0.0000
0.0000
1.0000
0.7142
0.0001
-0.7000
Axis
0.1735
0.9848
-0.0000
-0.5291
-0.4692
-0.7071
0.1736
0.9848
-0.0000
-0.7000
-0.0001
-0.7142
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