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 NbNO (Materials Project id mp-754495)

       209       76      113        0       14        0  
        76      230       96        0        2        0  
       113       96      269        0       24        0  
         0        0        0       45        0       -6  
        14        2       24        0       46        0  
         0        0        0       -6        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 142 GPaEV = 145.19 GPaGV = 54.6 GPaνV = 0.32959
ReussKR = 135.69 GPaER = 133.55 GPaGR = 49.984 GPaνR = 0.33596
HillKH = 138.84 GPaEH = 139.38 GPaGH = 52.292 GPaνH = 0.33269

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36.675 GPa 42.872 GPa 49.325 GPa 122.13 GPa 156.8 GPa 432.19 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 106.78 GPa 205.35 GPa 1.1712 TPa–1 3.5324 TPa–1 36.675 GPa 79.075 GPa0.134290.63068Value
Anisotropy 1.923 3.0160 2.156 4.6963Anisotropy
Axis -0.6133
0.6770
-0.4069
-0.2365
0.0000
-0.9716
-0.4531
0.0000
-0.8915
0.8915
0.0000
-0.4531
0.8112
0.0002
0.5847
-0.2474
0.7071
-0.6624
0.8313
0.0000
0.5559
-0.6885
-0.0000
-0.7253
Axis
-0.0002
1.0000
-0.0001
-0.2474
-0.7071
-0.6624
-0.0000
1.0000
0.0000
0.7253
-0.0001
-0.6885
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