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 NbRh3 (Materials Project id mp-2449)

       394      176      176        0        0        0  
       176      394      176        0        0        0  
       176      176      394        0        0        0  
         0        0        0      178        0        0  
         0        0        0        0      178        0  
         0        0        0        0        0      178  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 248.67 GPaEV = 375.5 GPaGV = 150.4 GPaνV = 0.24833
ReussKR = 248.67 GPaER = 357.95 GPaGR = 142.04 GPaνR = 0.26009
HillKH = 248.67 GPaEH = 366.77 GPaGH = 146.22 GPaνH = 0.25418

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
178 GPa 178 GPa 178 GPa 218 GPa 218 GPa 746 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 285.31 GPa 431.13 GPa 1.3405 TPa–1 1.3405 TPa–1 109 GPa 178 GPa0.0738350.41372Value
Anisotropy 1.511 1.0000 1.633 5.6033Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.2053
0.7663
0.6088
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
0.0001
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