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 LiZnPS4 (Materials Project id mp-11175)

        49       14       26        0        0        3  
        14       49       26        0        0       -3  
        26       26       43        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         3       -3        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 30.333 GPaEV = 42.972 GPaGV = 17 GPaνV = 0.26389
ReussKR = 30.156 GPaER = 37.137 GPaGR = 14.341 GPaνR = 0.29475
HillKH = 30.244 GPaEH = 40.088 GPaGH = 15.671 GPaνH = 0.27909

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.895 GPa 15.096 GPa 22 GPa 22 GPa 35.904 GPa 91.105 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.54 GPa 51.794 GPa 8.1061 TPa–1 12.528 TPa–1 8.4108 GPa 22 GPa-0.114070.67362Value
Anisotropy 2.405 1.5455 2.616Anisotropy
Axis 0.0000
0.0000
1.0000
-0.2588
0.7521
0.6060
0.0000
0.0000
1.0000
-0.9102
0.4142
0.0000
0.3101
0.6355
-0.7071
0.0000
0.0000
1.0000
0.9456
0.3254
0.0000
0.9456
0.3254
-0.0000
Axis
-0.3101
-0.6355
-0.7071
0.1736
0.9848
-0.0000
-0.3254
0.9456
0.0000
0.0001
-0.0004
-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