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 NaN3 (Materials Project id mp-570538)

        59       30       17        0       16        0  
        30       64       24        0       10        0  
        17       24       45        0        9        0  
         0        0        0       13        0       -2  
        16       10        9        0       18        0  
         0        0        0       -2        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.444 GPaEV = 38.531 GPaGV = 14.667 GPaνV = 0.31356
ReussKR = 24.999 GPaER = 32.781 GPaGR = 12.791 GPaνR = 0.28145
HillKH = 29.722 GPaEH = 35.691 GPaGH = 13.729 GPaνH = 0.29986

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 12.042 GPa 14 GPa 28.609 GPa 35.235 GPa 110.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.912 GPa 58.425 GPa 4.0496 TPa–1 30.73 TPa–1 9 GPa 18.196 GPa0.0103980.67885Value
Anisotropy 2.666 7.5885 2.022 65.2874Anisotropy
Axis -0.7643
0.0000
0.6448
-0.8719
-0.0000
-0.4897
0.7400
0.0000
0.6726
-0.6726
-0.0000
0.7400
0.8945
-0.0004
0.4472
0.8446
-0.0001
-0.5353
-0.1825
0.2989
0.9367
-0.6837
0.6109
-0.3992
Axis
0.0003
1.0000
0.0001
-0.5353
0.0001
-0.8446
-0.9479
-0.3065
-0.0868
-0.5459
-0.7912
-0.2759
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