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 Mg3P2 (Materials Project id mp-8085)

       108       32       32        0        0        0  
        32      108       32        0        0        0  
        32       32      108        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.333 GPaEV = 95.773 GPaGV = 39.2 GPaνV = 0.22159
ReussKR = 57.333 GPaER = 95.723 GPaGR = 39.175 GPaνR = 0.22173
HillKH = 57.333 GPaEH = 95.748 GPaGH = 39.188 GPaνH = 0.22166

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40 GPa 40 GPa 40 GPa 76 GPa 76 GPa 172 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 93.371 GPa 97.358 GPa 5.814 TPa–1 5.814 TPa–1 38 GPa 40 GPa0.204130.23581Value
Anisotropy 1.043 1.0000 1.053 1.1552Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.1294
0.4830
0.8660
0.3314
0.8001
0.5000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
0.0000
1.0000
0.0000
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