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 Eu(MnP)2 (Materials Project id mp-21474)

       153       64       56       20        0        0  
        64      153       56      -20        0        0  
        56       56      170        0        0        0  
        20      -20        0       70        0        0  
         0        0        0        0       70       20  
         0        0        0        0       20       45  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92 GPaEV = 141.73 GPaGV = 57 GPaνV = 0.24324
ReussKR = 91.946 GPaER = 124.85 GPaGR = 49.01 GPaνR = 0.27369
HillKH = 91.973 GPaEH = 133.39 GPaGH = 53.005 GPaνH = 0.25828

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.915 GPa 49.663 GPa 81.085 GPa 109.34 GPa 110.89 GPa 276.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 93.497 GPa 187.35 GPa 3.4294 TPa–1 3.7233 TPa–1 33.622 GPa 80.997 GPa0.0626520.52137Value
Anisotropy 2.004 1.0857 2.409 8.3217Anisotropy
Axis 0.0000
0.9349
0.3550
0.6673
0.3868
0.6365
0.0000
0.0000
1.0000
0.9668
0.2557
-0.0000
0.7538
0.4477
0.4809
-0.4177
0.2402
-0.8763
-0.0000
0.8823
-0.4707
1.0000
0.0004
-0.0000
Axis
-0.5190
0.8546
0.0179
-0.4989
-0.8667
0.0002
0.0000
0.4707
0.8823
-0.0004
0.8506
0.5258
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