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 K2ReF6 (Materials Project id mp-7824)

        61       14       21       -3        0        0  
        14       61       21        3        0        0  
        21       21       41        0        0        0  
        -3        3        0       13        0        0  
         0        0        0        0       13       -3  
         0        0        0        0       -3       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 30.556 GPaEV = 42.879 GPaGV = 16.933 GPaνV = 0.26611
ReussKR = 30.041 GPaER = 38.828 GPaGR = 15.113 GPaνR = 0.28458
HillKH = 30.298 GPaEH = 40.866 GPaGH = 16.023 GPaνH = 0.2752

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12.169 GPa 12.479 GPa 23.78 GPa 23.831 GPa 47.521 GPa 92.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 29.24 GPa 52.16 GPa 9.1199 TPa–1 15.048 TPa–1 12.136 GPa 24.228 GPa0.0454510.50773Value
Anisotropy 1.784 1.6500 1.996 11.1709Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.9770
0.2131
0.9676
0.2525
-0.0000
0.0000
0.0000
1.0000
0.2181
0.1557
0.9634
0.7752
0.5870
0.2332
-0.0000
0.9574
0.2886
1.0000
0.0003
0.0000
Axis
-0.8527
-0.4497
0.2657
-0.6181
0.7811
0.0885
-1.0000
-0.0000
-0.0000
-0.0001
0.2792
-0.9602
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