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 Ca(CoP)2 (Materials Project id mp-3210)

       243       50       57        0        0        0  
        50      243       57        0        0        0  
        57       57      129        0        0        0  
         0        0        0       91        0        0  
         0        0        0        0       91        0  
         0        0        0        0        0       79  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 104.78 GPaEV = 195.61 GPaGV = 82.267 GPaνV = 0.18886
ReussKR = 96.901 GPaER = 182.29 GPaGR = 76.823 GPaνR = 0.18646
HillKH = 100.84 GPaEH = 188.95 GPaGH = 79.545 GPaνH = 0.1877

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
79 GPa 91 GPa 91 GPa 96.013 GPa 193 GPa 325.99 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 106.82 GPa 221.83 GPa 2.3004 TPa–1 5.719 TPa–1 54.858 GPa 96.5 GPa0.00203540.39152Value
Anisotropy 2.077 2.4861 1.759192.3575Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.9237
0.3830
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
-0.5002
0.4998
-0.7071
0.7071
0.7071
-0.0000
0.4997
0.4997
0.7075
1.0000
0.0002
0.0000
Axis
0.4999
-0.5001
-0.7071
-0.7071
0.7071
0.0000
0.5003
0.5003
-0.7067
-0.0000
0.0002
-1.0000
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