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 NaAl11O17 (Materials Project id mp-3405)

       315      124       65        0        0        0  
       124      315       65        0        0        0  
        65       65      258        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       35        0  
         0        0        0        0        0       96  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 155.11 GPaEV = 194.81 GPaGV = 75.467 GPaνV = 0.29068
ReussKR = 150.81 GPaER = 153.12 GPaGR = 57.531 GPaνR = 0.33078
HillKH = 152.96 GPaEH = 174.25 GPaGH = 66.499 GPaνH = 0.31014

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 35 GPa 96 GPa 191 GPa 219.5 GPa 477.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.08 GPa 260.76 GPa 1.8414 TPa–1 2.9481 TPa–1 35 GPa 107.95 GPa0.103980.61646Value
Anisotropy 2.306 1.6010 3.084 5.9285Anisotropy
Axis 0.7009
-0.0000
0.7133
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5236
0.4753
-0.7071
0.3894
0.3894
-0.8347
0.5073
0.5073
0.6966
Axis
-0.9397
0.3420
0.0000
-0.5235
-0.4753
-0.7071
-0.7071
0.7071
0.0000
0.4926
0.4926
-0.7174
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