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 MnCoP (Materials Project id mp-20249)

       290      121      138        0        0        0  
       121      385      148        0        0        0  
       138      148      312        0        0        0  
         0        0        0      122        0        0  
         0        0        0        0      117        0  
         0        0        0        0        0      111  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 200.11 GPaEV = 276.03 GPaGV = 108.67 GPaνV = 0.2701
ReussKR = 197.27 GPaER = 269.79 GPaGR = 106.05 GPaνR = 0.27206
HillKH = 198.69 GPaEH = 272.91 GPaGH = 107.36 GPaνH = 0.27107

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
111 GPa 117 GPa 122 GPa 161.14 GPa 220.76 GPa 605.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 219.16 GPa 310.02 GPa 1.2955 TPa–1 2.1215 TPa–1 81.023 GPa 122 GPa0.171680.3737Value
Anisotropy 1.415 1.6376 1.506 2.1767Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.8875
0.4608
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
0.0001
0.0002
1.0000
0.8759
0.4825
0.0000
-0.0000
0.4991
0.8666
Axis
0.7071
-0.0005
-0.7071
-0.0000
1.0000
-0.0002
-0.4825
0.8759
0.0000
-1.0000
-0.0000
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