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 SmAl3Pd2 (Materials Project id mp-11539)

       163       65       70        0        0        0  
        65      163       70        0        0        0  
        70       70      220        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 106.22 GPaEV = 140.57 GPaGV = 54.933 GPaνV = 0.27944
ReussKR = 104.02 GPaER = 138.45 GPaGR = 54.158 GPaνR = 0.27817
HillKH = 105.12 GPaEH = 139.51 GPaGH = 54.546 GPaνH = 0.27881

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 56 GPa 56 GPa 98 GPa 124.92 GPa 323.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 127.75 GPa 177.02 GPa 2.1804 TPa–1 3.7166 TPa–1 49 GPa 59.013 GPa0.221580.30702Value
Anisotropy 1.386 1.7045 1.204 1.3856Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
0.9573
0.2890
0.0000
0.5928
0.3855
0.7071
-0.6255
0.7802
0.0000
0.0000
0.0000
1.0000
Axis
-0.2890
0.9573
-0.0000
0.5928
0.3855
-0.7071
-0.0000
0.0000
-1.0000
0.1736
0.9848
-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