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 PmCdPd2 (Materials Project id mp-862898)

        91       88       88        0        0        0  
        88       91       88        0        0        0  
        88       88       91        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 89 GPaEV = 44.217 GPaGV = 15.6 GPaνV = 0.4172
ReussKR = 89 GPaER = 10.19 GPaGR = 3.4404 GPaνR = 0.48092
HillKH = 89 GPaEH = 27.577 GPaGH = 9.5202 GPaνH = 0.44836

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 3 GPa 25 GPa 25 GPa 25 GPa 267 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.4749 GPa 68.579 GPa 3.7453 TPa–1 3.7453 TPa–1 1.5 GPa 25 GPa-0.700621.6828Value
Anisotropy 15.33 1.0000 16.67Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
1.0000
0.0000
-0.0006
-0.0393
0.9990
-0.0196
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.6748
0.6748
0.2988
Axis
-0.7071
-0.0002
-0.7071
-0.5000
-0.8660
0.0000
-0.7071
-0.0002
-0.7071
0.2111
0.2115
-0.9543
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