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 NaFeO2 (Materials Project id mp-19359)

       251       80       47        1        0        0  
        80      251       47       -1        0        0  
        47       47      195        0        0        0  
         1       -1        0       55        0        0  
         0        0        0        0       55        1  
         0        0        0        0        1       85  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 116.11 GPaEV = 182.83 GPaGV = 73.867 GPaνV = 0.23757
ReussKR = 112.81 GPaER = 174.02 GPaGR = 70.005 GPaνR = 0.2429
HillKH = 114.46 GPaEH = 178.43 GPaGH = 71.936 GPaνH = 0.24019

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
54.967 GPa 54.983 GPa 85.033 GPa 167.91 GPa 171.02 GPa 358.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 148.11 GPa 220.04 GPa 2.4615 TPa–1 3.9417 TPa–1 54.983 GPa 86.112 GPa0.132740.36723Value
Anisotropy 1.486 1.6014 1.566 2.7666Anisotropy
Axis 0.5679
0.3382
-0.7504
0.0000
0.9999
-0.0141
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
-0.0071
-0.0040
1.0000
0.0000
0.7014
-0.7128
-0.0000
0.4153
-0.9097
0.0001
0.7307
-0.6826
Axis
0.8624
0.5062
0.0081
-0.0000
-0.7128
-0.7014
-1.0000
-0.0000
0.0000
0.0001
-0.6826
-0.7307
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