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-22003)

        35       12       19       -3        0        0  
        12       35       19        3        0        0  
        19       19       87        0        0        0  
        -3        3        0        3        0        0  
         0        0        0        0        3       -3  
         0        0        0        0       -3       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.556 GPaEV = 28.14 GPaGV = 10.533 GPaνV = 0.33576
ReussKR = 23.221 GPaER = 11.768 GPaGR = 4.1568 GPaνR = 0.41553
HillKH = 25.888 GPaEH = 20.131 GPaGH = 7.3451 GPaνH = 0.3704

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2.1372 GPa 12 GPa 23.863 GPa 33.504 GPa 100.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.2102 GPa 71.638 GPa 2.673 TPa–1 20.196 TPa–1 2 GPa 16.885 GPa-0.241291.1516Value
Anisotropy 11.54 7.5556 8.443Anisotropy
Axis 0.6687
0.3876
0.6345
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
-0.0000
0.3162
0.9487
-0.6549
0.1286
-0.7447
0.2772
0.1598
-0.9474
0.3077
0.1774
-0.9348
Axis
-1.0000
-0.0000
0.0000
-0.6975
0.2765
0.6611
-0.5029
0.8643
-0.0013
-0.8080
-0.4700
-0.3552
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