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 MnCoGe (Materials Project id mp-20565)

       299      158       78        0        0        0  
       158      299       78        0        0        0  
        78       78      252        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 164.22 GPaEV = 173.99 GPaGV = 65.733 GPaνV = 0.32342
ReussKR = 158.7 GPaER = 152.22 GPaGR = 56.794 GPaνR = 0.34013
HillKH = 161.46 GPaEH = 163.16 GPaGH = 61.264 GPaνH = 0.33158

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40 GPa 40 GPa 70 GPa 141 GPa 203.92 GPa 505.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 122.23 GPa 225.37 GPa 1.6894 TPa–1 2.9224 TPa–1 40 GPa 93.274 GPa0.157230.52957Value
Anisotropy 1.844 1.7299 2.332 3.3681Anisotropy
Axis 0.5062
0.5062
0.6982
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.4037
-0.0000
0.9149
0.6978
-0.0002
0.7163
Axis
-0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
0.0001
1.0000
-0.0000
0.7163
-0.0004
-0.6978
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