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 Mg(Co3P2)2 (Materials Project id mp-10924)

       350      121      146        0        0        0  
       121      350      146        0        0        0  
       146      146      300        0        0        0  
         0        0        0       95        0        0  
         0        0        0        0       95        0  
         0        0        0        0        0      114  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 202.89 GPaEV = 257.52 GPaGV = 99.933 GPaνV = 0.28846
ReussKR = 202.6 GPaER = 253.71 GPaGR = 98.24 GPaνR = 0.29129
HillKH = 202.75 GPaEH = 255.62 GPaGH = 99.087 GPaνH = 0.28987

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
95 GPa 95 GPa 114 GPa 162.02 GPa 229 GPa 608.98 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 209.49 GPa 270 GPa 1.5608 TPa–1 1.8142 TPa–1 87.365 GPa 114.5 GPa0.179050.39953Value
Anisotropy 1.289 1.1623 1.311 2.2313Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5002
0.4998
0.7071
0.7071
0.7071
0.0000
1.0000
0.0007
0.0000
1.0000
-0.0004
-0.0000
Axis
-0.4999
0.5001
-0.7071
-0.7071
0.7071
-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