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 KCu4S3 (Materials Project id mp-27677)

        94       19       35        0        0        0  
        19       94       35        0        0        0  
        35       35       62        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47.556 GPaEV = 52.93 GPaGV = 20.133 GPaνV = 0.3145
ReussKR = 46.969 GPaER = 47.328 GPaGR = 17.765 GPaνR = 0.33206
HillKH = 47.262 GPaEH = 50.146 GPaGH = 18.949 GPaνH = 0.32316

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 15 GPa 17 GPa 31.82 GPa 75 GPa 143.18 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.085 GPa 74.234 GPa 5.9263 TPa–1 9.4381 TPa–1 15 GPa 37.5 GPa-0.0102110.57028Value
Anisotropy 1.852 1.5926 2.5Anisotropy
Axis 0.2916
0.2916
0.9110
1.0000
0.0000
0.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
-0.0000
Axis
0.1736
0.9848
-0.0000
-0.7071
0.7071
0.0000
-0.0000
1.0000
-0.0000
-0.0000
-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