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 CsNa2BO3 (Materials Project id mp-8871)

       123       18       16        0        0        0  
        18       80       28        0        0        0  
        16       28       96        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47 GPaEV = 64.137 GPaGV = 25.2 GPaνV = 0.27256
ReussKR = 46.337 GPaER = 48.472 GPaGR = 18.282 GPaνR = 0.32566
HillKH = 46.669 GPaEH = 56.456 GPaGH = 21.741 GPaνH = 0.29838

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 16 GPa 22 GPa 58.472 GPa 96.524 GPa 144 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.524 GPa 117.86 GPa 5.9551 TPa–1 8.7554 TPa–1 9 GPa 45.243 GPa0.0650380.70576Value
Anisotropy 3.861 1.4702 5.027 10.8514Anisotropy
Axis 0.6829
0.7305
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.7071
-0.0000
-0.7071
0.8547
0.5192
0.0004
-0.7620
0.6476
0.0000
Axis
0.0001
1.0000
0.0000
-0.7071
0.0002
-0.7071
0.0001
0.0006
-1.0000
-0.6476
-0.7620
-0.0000
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