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 NbRu (Materials Project id mp-432)

       308      207      196        0        0        0  
       207      308      196        0        0        0  
       196      196      319        0        0        0  
         0        0        0       49        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 237 GPaEV = 147.97 GPaGV = 53 GPaνV = 0.39594
ReussKR = 237 GPaER = 146.93 GPaGR = 52.598 GPaνR = 0.39668
HillKH = 237 GPaEH = 147.45 GPaGH = 52.799 GPaνH = 0.39631

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 49 GPa 55 GPa 101 GPa 123 GPa 711 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 138.75 GPa 169.81 GPa 1.4065 TPa–1 1.4065 TPa–1 49 GPa 59.735 GPa0.330840.46154Value
Anisotropy 1.224 1.0000 1.219 1.3951Anisotropy
Axis 0.7973
0.0000
-0.6036
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
0.9659
0.0000
0.2588
-0.0000
0.0000
1.0000
0.4998
0.5002
0.7071
1.0000
-0.0004
-0.0000
-1.0000
-0.0000
0.0000
Axis
-0.7660
-0.6428
-0.0000
0.5003
0.4998
-0.7071
-0.0000
-0.0003
-1.0000
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