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 NaHF2 (Materials Project id mp-27837)

        57       21       31       -4        0        0  
        21       57       31        4        0        0  
        31       31      111        0        0        0  
        -4        4        0       12        0        0  
         0        0        0        0       12       -4  
         0        0        0        0       -4       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 43.444 GPaEV = 47.138 GPaGV = 17.867 GPaνV = 0.31916
ReussKR = 38.273 GPaER = 39.242 GPaGR = 14.762 GPaνR = 0.32911
HillKH = 40.859 GPaEH = 43.195 GPaGH = 16.315 GPaνH = 0.3238

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10.734 GPa 20 GPa 37.266 GPa 47.657 GPa 141.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 27.887 GPa 86.359 GPa 2.3753 TPa–1 11.876 TPa–1 10 GPa 23.842 GPa0.0242440.73453Value
Anisotropy 3.097 5.0000 2.384 30.2970Anisotropy
Axis -0.7111
0.4106
0.5708
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7934
0.6088
0.0000
-0.0000
0.4472
0.8944
0.5465
0.3155
-0.7758
0.5510
0.3181
-0.7715
0.0002
0.5043
0.8635
Axis
-1.0000
-0.0000
0.0000
0.6719
0.3879
0.6310
-0.5000
0.8660
-0.0000
-0.0003
0.8635
-0.5043
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