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 MgPd3 (Materials Project id mp-7753)

       163      128      128        0        0        0  
       128      163      128        0        0        0  
       128      128      163        0        0        0  
         0        0        0       63        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 139.67 GPaEV = 121.42 GPaGV = 44.8 GPaνV = 0.35511
ReussKR = 139.67 GPaER = 86.287 GPaGR = 30.882 GPaνR = 0.39703
HillKH = 139.67 GPaEH = 104.12 GPaGH = 37.841 GPaνH = 0.37575

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 35 GPa 63 GPa 63 GPa 63 GPa 419 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.395 GPa 164.3 GPa 2.3866 TPa–1 2.3866 TPa–1 17.5 GPa 63 GPa-0.166830.91629Value
Anisotropy 3.26 1.0000 3.6Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.3536
0.8536
0.3827
0.7071
-0.0003
0.7071
0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0001
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
-0.0000
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