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 ZnPd (Materials Project id mp-1652)

       222       85      120        0        0        0  
        85      222      120        0        0        0  
       120      120      164        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 139.78 GPaEV = 157.16 GPaGV = 59.867 GPaνV = 0.3126
ReussKR = 139.02 GPaER = 134.46 GPaGR = 50.217 GPaνR = 0.3388
HillKH = 139.4 GPaEH = 145.92 GPaGH = 55.042 GPaνH = 0.32554

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 51.347 GPa 78 GPa 78 GPa 137 GPa 419.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 70.189 GPa 189.75 GPa 2.042 TPa–1 3.1093 TPa–1 29.161 GPa 78 GPa-0.0209010.747Value
Anisotropy 2.703 1.5227 2.675Anisotropy
Axis 0.0000
0.0000
1.0000
0.8183
0.0000
0.5748
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5000
0.5000
0.7071
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
1.0000
-0.0004
0.0000
Axis
0.5000
-0.5000
0.7071
-0.7660
0.6428
-0.0000
-0.0007
1.0000
-0.0000
0.0000
-0.0003
-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