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 NdP (Materials Project id mp-2823)

       178       26       26        0        0        0  
        26      178       26        0        0        0  
        26       26      178        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.667 GPaEV = 130.8 GPaGV = 53.8 GPaνV = 0.21564
ReussKR = 76.667 GPaER = 120.02 GPaGR = 48.431 GPaνR = 0.23908
HillKH = 76.667 GPaEH = 125.46 GPaGH = 51.116 GPaνH = 0.22725

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 39 GPa 39 GPa 152 GPa 152 GPa 230 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 100.04 GPa 171.37 GPa 4.3478 TPa–1 4.3478 TPa–1 39 GPa 76 GPa0.083040.4315Value
Anisotropy 1.713 1.0000 1.949 5.1963Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.9397
0.3420
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
-0.7071
0.0002
-0.7071
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