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 ZnSb (Materials Project id mp-753)

        95       26       30        0        0        0  
        26       85       29        0        0        0  
        30       29       82        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48 GPaEV = 72.416 GPaGV = 29 GPaνV = 0.24855
ReussKR = 47.871 GPaER = 68.651 GPaGR = 27.221 GPaνR = 0.26099
HillKH = 47.936 GPaEH = 70.542 GPaGH = 28.111 GPaνH = 0.25473

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 30 GPa 38 GPa 53.479 GPa 64.214 GPa 144.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.062 GPa 84.965 GPa 6.197 TPa–1 7.3714 TPa–1 18 GPa 38 GPa0.0488830.47392Value
Anisotropy 1.632 1.1895 2.111 9.6950Anisotropy
Axis 0.6843
0.7292
0.0000
-0.0000
0.7409
0.6716
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.0004
0.0003
1.0000
0.4321
0.5675
0.7009
-0.6453
0.5719
-0.5064
Axis
0.0001
1.0000
0.0000
0.0000
1.0000
-0.0003
0.4063
0.5714
-0.7131
-0.7196
-0.6775
0.1518
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