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 Ta4N5 (Materials Project id mp-8046)

       718      133      133        0        0        0  
       133      559      140       58        0        0  
       133      140      559      -58        0        0  
         0       58      -58      167        0        0  
         0        0        0        0      133        0  
         0        0        0        0        0      133  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 294.22 GPaEV = 452.53 GPaGV = 181.93 GPaνV = 0.24366
ReussKR = 291.02 GPaER = 411.47 GPaGR = 162.72 GPaνR = 0.26435
HillKH = 292.62 GPaEH = 432.15 GPaGH = 172.33 GPaνH = 0.25386

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
133 GPa 133 GPa 142.65 GPa 443.35 GPa 520.17 GPa 896.83 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 339.88 GPa 667.39 GPa 0.92818 TPa–1 1.254 TPa–1 126.48 GPa 260.55 GPa0.0991220.47273Value
Anisotropy 1.964 1.3510 2.06 4.7692Anisotropy
Axis 0.5189
0.7580
-0.3951
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.5000
0.8660
-0.0000
0.3002
-0.9539
0.7071
0.6745
0.2122
0.6230
0.2348
-0.7461
0.7301
0.6518
0.2051
Axis
-0.0000
0.9539
0.3002
-0.7071
0.6745
0.2123
0.0000
0.9539
0.3002
-0.6834
0.6964
0.2192
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