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 CaP (Materials Project id mp-1345)

        95       33       22        0        0        0  
        33       95       22        0        0        0  
        22       22       95        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       34        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.778 GPaEV = 82.109 GPaGV = 33.667 GPaνV = 0.21944
ReussKR = 48.661 GPaER = 81.637 GPaGR = 33.447 GPaνR = 0.22039
HillKH = 48.719 GPaEH = 81.873 GPaGH = 33.557 GPaνH = 0.21992

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 34 GPa 34 GPa 62 GPa 76.283 GPa 146.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 80.541 GPa 87.438 GPa 6.5225 TPa–1 7.5054 TPa–1 31 GPa 36.131 GPa0.15970.31039Value
Anisotropy 1.086 1.1507 1.166 1.9435Anisotropy
Axis 0.8668
0.0001
0.4987
0.0000
0.0000
1.0000
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.9573
0.2890
0.0000
0.5291
0.4691
-0.7071
0.6837
0.7297
-0.0000
0.8420
0.5395
-0.0000
Axis
-0.2890
0.9573
-0.0000
-0.5291
-0.4692
-0.7071
0.0000
-0.0000
-1.0000
-0.5395
0.8420
0.0000
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