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 NaCl (Materials Project id mp-22862)

        46       11       11        0        0        0  
        11       46       11        0        0        0  
        11       11       46        0        0        0  
         0        0        0       12        0        0  
         0        0        0        0       12        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 22.667 GPaEV = 35.241 GPaGV = 14.2 GPaνV = 0.24088
ReussKR = 22.667 GPaER = 34.261 GPaGR = 13.725 GPaνR = 0.24808
HillKH = 22.667 GPaEH = 34.752 GPaGH = 13.963 GPaνH = 0.24447

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 12 GPa 12 GPa 35 GPa 35 GPa 68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.6 GPa 41.754 GPa 14.706 TPa–1 14.706 TPa–1 12 GPa 17.5 GPa0.151550.36625Value
Anisotropy 1.365 1.0000 1.458 2.4167Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.5909
0.7655
0.2549
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0000
-0.7071
Axis
0.1735
0.9848
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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