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 PbC2(SN)2 (Materials Project id mp-20605)

        34       27       16        0        5        0  
        27       48       17        0        7        0  
        16       17       41        0        5        0  
         0        0        0       13        0        4  
         5        7        5        0       10        0  
         0        0        0        4        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 27 GPaEV = 33.16 GPaGV = 12.8 GPaνV = 0.29531
ReussKR = 23.137 GPaER = 27.399 GPaGR = 10.517 GPaνR = 0.30263
HillKH = 25.068 GPaEH = 30.281 GPaGH = 11.658 GPaνH = 0.29868

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8.5969 GPa 11.185 GPa 12.892 GPa 21.815 GPa 28.101 GPa 83.41 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 17.356 GPa 51.33 GPa 6.1338 TPa–1 29.389 TPa–1 6.5335 GPa 21.815 GPa0.069860.73606Value
Anisotropy 2.958 4.7913 3.339 10.5362Anisotropy
Axis 0.9805
0.0000
-0.1965
-0.6103
0.7423
-0.2767
0.6728
0.0000
0.7398
-0.7398
-0.0000
0.6728
-0.7026
0.7071
-0.0797
-0.9106
0.0000
-0.4132
-0.0000
1.0000
0.0000
-0.0000
1.0000
0.0000
Axis
-0.7026
-0.7071
-0.0797
0.0000
-1.0000
-0.0000
-0.2290
-0.0000
0.9734
-0.9734
-0.0000
-0.2290
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