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 NaBr (Materials Project id mp-22916)

        47       17       17        0        0        0  
        17       47       17        0        0        0  
        17       17       47        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 27 GPaEV = 31.355 GPaGV = 12 GPaνV = 0.30645
ReussKR = 27 GPaER = 30.299 GPaGR = 11.538 GPaνR = 0.31297
HillKH = 27 GPaEH = 30.828 GPaGH = 11.769 GPaνH = 0.3097

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 10 GPa 30 GPa 30 GPa 81 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.703 GPa 37.969 GPa 12.346 TPa–1 12.346 TPa–1 10 GPa 15 GPa0.201780.44214Value
Anisotropy 1.422 1.0000 1.5 2.1912Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
0.7071
-0.0005
-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