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 NpSn3 (Materials Project id mp-881)

       165       20       20        0        0        0  
        20      165       20        0        0        0  
        20       20      165        0        0        0  
         0        0        0       88        0        0  
         0        0        0        0       88        0  
         0        0        0        0        0       88  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.333 GPaEV = 175.41 GPaGV = 81.8 GPaνV = 0.072176
ReussKR = 68.333 GPaER = 174.28 GPaGR = 81.067 GPaνR = 0.074922
HillKH = 68.333 GPaEH = 174.85 GPaGH = 81.434 GPaνH = 0.073547

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
88 GPa 88 GPa 88 GPa 145 GPa 145 GPa 205 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 160.68 GPa 184.71 GPa 4.878 TPa–1 4.878 TPa–1 72.5 GPa 88 GPa0.0116570.1198Value
Anisotropy 1.15 1.0000 1.214 10.2774Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.3827
0.0000
0.9239
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.7071
0.0002
-0.7071
0.0000
1.0000
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