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 KCrS2 (Materials Project id mp-4026)

       109       23       24       13        0        0  
        23      109       24      -13        0        0  
        24       24       85        0        0        0  
        13      -13        0       34        0        0  
         0        0        0        0       34       13  
         0        0        0        0       13       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 49.444 GPaEV = 90.116 GPaGV = 37.667 GPaνV = 0.19624
ReussKR = 48.874 GPaER = 82.115 GPaGR = 33.654 GPaνR = 0.21998
HillKH = 49.159 GPaEH = 86.15 GPaGH = 35.661 GPaνH = 0.20792

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24.743 GPa 28.157 GPa 52.257 GPa 67.217 GPa 91.843 GPa 149.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 63.369 GPa 115.33 GPa 6.0588 TPa–1 8.3433 TPa–1 24.743 GPa 52.257 GPa-0.0138150.45222Value
Anisotropy 1.82 1.3770 2.112Anisotropy
Axis 0.6804
0.3928
-0.6187
-0.0000
0.9285
-0.3714
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.0000
0.5801
-0.8146
0.5000
0.8660
0.0001
0.6204
0.3582
0.6978
-0.5000
0.8660
-0.0000
Axis
-1.0000
0.0000
-0.0000
-0.7054
0.4073
-0.5800
-0.5000
0.8660
-0.0000
-0.6105
-0.3524
0.7093
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