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 CaHgO2 (Materials Project id mp-7041)

        82       24       59       -3        0        0  
        24       82       59        3        0        0  
        59       59      251        0        0        0  
        -3        3        0        1        0        0  
         0        0        0        0        1       -3  
         0        0        0        0       -3       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 77.667 GPaEV = 66.261 GPaGV = 24.4 GPaνV = 0.35781
ReussKR = 52.806 GPaER = 4.9095 GPaGR = 1.6536 GPaνR = 0.4845
HillKH = 65.237 GPaEH = 36.641 GPaGH = 13.027 GPaνH = 0.40639

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.68218 GPa0.68594 GPa 29.318 GPa 58.314 GPa 67.964 GPa 289.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.4638 GPa 185.32 GPa-0.61087 TPa–1 9.774 TPa–1 0.68218 GPa 37.964 GPa-1.74571.2539Value
Anisotropy 75.22 55.65Anisotropy
Axis -0.6302
0.3638
0.6859
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.2588
0.9659
0.0000
0.0912
-0.0527
0.9944
-0.5967
0.3430
-0.7255
1.0000
0.0001
-0.0000
0.0000
0.1014
0.9949
Axis
-0.5000
-0.8660
0.0000
0.6288
-0.3619
-0.6883
-0.0000
0.6923
0.7216
0.0000
-0.9949
0.1014
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