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 Na3Sb (Materials Project id mp-7956)

        37       12        0        0        0        0  
        12       37        0        0        0        0  
         0        0       33        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 14.556 GPaEV = 27.371 GPaGV = 11.533 GPaνV = 0.18659
ReussKR = 14.061 GPaER = 24.132 GPaGR = 9.9392 GPaνR = 0.21396
HillKH = 14.308 GPaEH = 25.765 GPaGH = 10.736 GPaνH = 0.19989

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 7 GPa 12 GPa 25 GPa 33 GPa 49 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.588 GPa 33.108 GPa 20.408 TPa–1 30.303 TPa–1 7 GPa 16.527 GPa00.40494Value
Anisotropy 1.69 1.4848 2.361Anisotropy
Axis 0.5022
0.5023
0.7039
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7074
-0.0003
0.7068
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
1.0000
0.0000
-0.0000
0.7068
-0.0005
-0.7074
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