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 NaGa4 (Materials Project id mp-454)

        92       33       17        0        0        0  
        33       92       17        0        0        0  
        17       17       90        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45.333 GPaEV = 73.332 GPaGV = 29.8 GPaνV = 0.2304
ReussKR = 45.03 GPaER = 69.294 GPaGR = 27.862 GPaνR = 0.24353
HillKH = 45.181 GPaEH = 71.322 GPaGH = 28.831 GPaνH = 0.2369

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 31 GPa 31 GPa 59 GPa 77.764 GPa 137.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.232 GPa 85.376 GPa 6.8403 TPa–1 8.527 TPa–1 18 GPa 36.245 GPa0.0876880.53422Value
Anisotropy 1.546 1.2466 2.014 6.0922Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
0.7071
-0.0000
-0.7071
-0.6752
0.6751
0.2972
0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
0.0000
-0.7071
0.0002
-0.7071
-0.2101
0.2102
-0.9548
-0.7071
0.7071
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