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 AlPt (Materials Project id mp-10903)

       195      181      181        0        0        0  
       181      195      181        0        0        0  
       181      181      195        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       78  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 185.67 GPaEV = 136.63 GPaGV = 49.6 GPaνV = 0.37735
ReussKR = 185.67 GPaER = 45.024 GPaGR = 15.424 GPaνR = 0.45958
HillKH = 185.67 GPaEH = 92.156 GPaGH = 32.512 GPaνH = 0.41727

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 14 GPa 78 GPa 78 GPa 78 GPa 557 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 20.739 GPa 205.26 GPa 1.7953 TPa–1 1.7953 TPa–1 7 GPa 78 GPa-0.591921.4776Value
Anisotropy 9.897 1.0000 11.14Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
-0.0023
0.9999
-0.0105
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.7071
0.0000
Axis
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
-0.0000
1.0000
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