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 SiPd2 (Materials Project id mp-697068)

       235      162      159        0        0        0  
       162      235      159        0        0        0  
       159      159      199        0        0        0  
         0        0        0       94        0        0  
         0        0        0        0       94        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181 GPaEV = 155.74 GPaGV = 57.4 GPaνV = 0.3566
ReussKR = 178.87 GPaER = 121.01 GPaGR = 43.616 GPaνR = 0.38725
HillKH = 179.94 GPaEH = 138.56 GPaGH = 50.508 GPaνH = 0.37166

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 52.311 GPa 73 GPa 94 GPa 94 GPa 543.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 71.64 GPa 172.12 GPa 1.4064 TPa–1 2.7777 TPa–1 28.104 GPa 94 GPa-0.108450.7581Value
Anisotropy 2.403 1.9750 3.345Anisotropy
Axis 0.0000
0.0000
1.0000
0.7568
0.0001
0.6537
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
-0.7071
0.0000
0.0000
1.0000
0.5035
0.5034
-0.7022
0.5068
0.5068
0.6973
Axis
0.4999
-0.5001
-0.7071
0.7660
0.6428
-0.0000
0.4966
0.4965
0.7120
-0.7071
0.7071
-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