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 CoP2 (Materials Project id mp-14285)

       350       57       80        0       57        0  
        57      422       53        0       12        0  
        80       53      331        0      -26        0  
         0        0        0      139        0       33  
        57       12      -26        0       95        0  
         0        0        0       33        0      114  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 164.78 GPaEV = 309.67 GPaGV = 130.47 GPaνV = 0.18678
ReussKR = 161.85 GPaER = 275.09 GPaGR = 113.05 GPaνR = 0.21671
HillKH = 163.31 GPaEH = 292.56 GPaGH = 121.76 GPaνH = 0.20143

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
75.229 GPa 91.212 GPa 161.79 GPa 277.45 GPa 344.24 GPa 501.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 187.9 GPa 406.87 GPa 1.6707 TPa–1 2.6773 TPa–1 66.933 GPa 171.83 GPa-0.0128950.53748Value
Anisotropy 2.165 1.6025 2.567Anisotropy
Axis -0.8697
-0.0000
0.4936
0.0000
1.0000
0.0000
0.6594
0.0000
0.7518
-0.7518
-0.0000
0.6594
-0.2845
0.0001
0.9587
0.6753
0.7071
0.2097
-0.0446
0.6065
-0.7938
0.4961
-0.0000
0.8683
Axis
-0.9587
0.0000
-0.2845
-0.6753
0.7071
-0.2097
-0.6424
-0.6259
-0.4422
-0.8683
0.0000
0.4961
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