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 SbPd2 (Materials Project id mp-542106)

       208      105      108        0        0        0  
       105      197      108        0        0        0  
       108      108      131        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       46        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 130.89 GPaEV = 110.22 GPaGV = 40.533 GPaνV = 0.35965
ReussKR = 123.29 GPaER = 100.44 GPaGR = 36.812 GPaνR = 0.36422
HillKH = 127.09 GPaEH = 105.33 GPaGH = 38.673 GPaνH = 0.36186

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 42.714 GPa 44 GPa 46 GPa 97.562 GPa 395.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.06 GPa 128.88 GPa 1.2831 TPa–1 5.3914 TPa–1 24.241 GPa 48.634 GPa0.134180.71381Value
Anisotropy 2.341 4.2018 2.006 5.3199Anisotropy
Axis 0.0000
0.0000
1.0000
0.8838
-0.0000
-0.4678
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.3146
0.6333
0.7071
0.7071
0.7057
-0.0451
-0.0000
1.0000
-0.0000
0.0000
1.0000
-0.0000
Axis
-0.3142
0.6335
-0.7071
-0.7071
0.7057
-0.0450
-1.0000
-0.0000
0.0000
-0.0008
-0.0000
-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