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 K3Mo (Materials Project id mp-973974)

        21       10       15        0        0        0  
        10       21       15        0        0        0  
        15       15       16        0        0        0  
         0        0        0        6        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 15.333 GPaEV = 10.53 GPaGV = 3.8 GPaνV = 0.38554
ReussKR = 15.333 GPaER = 4.1392 GPaGR = 1.4224 GPaνR = 0.45501
HillKH = 15.333 GPaEH = 7.4128 GPaGH = 2.6112 GPaνH = 0.41943

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 6 GPa 6 GPa 11 GPa 46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.4839 GPa 15.508 GPa 21.739 TPa–1 21.739 TPa–1 0.57143 GPa 6 GPa-0.599171.4865Value
Anisotropy 10.45 1.0000 10.5Anisotropy
Axis 0.0000
0.0000
1.0000
0.8154
-0.0000
-0.5789
0.0000
0.0000
1.0000
0.3794
0.9160
0.1305
-0.5002
0.4998
0.7071
-0.0000
0.0000
1.0000
0.9695
0.0002
0.2451
1.0000
-0.0000
-0.0001
Axis
-0.4998
0.5002
-0.7071
-0.7660
0.6428
-0.0000
-0.0002
1.0000
-0.0001
-0.0001
-0.0000
-1.0000
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