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 NbP (Materials Project id mp-9339)

       324      155      122        0        0        0  
       155      324      122        0        0        0  
       122      122      264        0        0        0  
         0        0        0      108        0        0  
         0        0        0        0      108        0  
         0        0        0        0        0      178  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 190 GPaEV = 282.91 GPaGV = 113 GPaνV = 0.25183
ReussKR = 186.3 GPaER = 264.51 GPaGR = 104.69 GPaνR = 0.26336
HillKH = 188.15 GPaEH = 273.74 GPaGH = 108.84 GPaνH = 0.25751

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
108 GPa 108 GPa 168.22 GPa 169 GPa 178 GPa 574.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 201.85 GPa 361.05 GPa 1.4686 TPa–1 2.4305 TPa–1 84.735 GPa 178 GPa0.0141810.45557Value
Anisotropy 1.789 1.6549 2.101 32.1243Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
0.7071
0.7071
0.0000
Axis
-0.7071
0.0002
-0.7071
-0.0000
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.0000
-0.0000
-1.0000
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