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 Sn3Ru2 (Materials Project id mp-680677)

       194      119       86        0        0        0  
       119      194       86        0        0        0  
        86       86      180        0        0        0  
         0        0        0       64        0        0  
         0        0        0        0       64        0  
         0        0        0        0        0       79  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 127.78 GPaEV = 155.34 GPaGV = 59.867 GPaνV = 0.29738
ReussKR = 126.29 GPaER = 146.74 GPaGR = 56.162 GPaνR = 0.30635
HillKH = 127.03 GPaEH = 151.05 GPaGH = 58.015 GPaνH = 0.30182

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
64 GPa 64 GPa 75 GPa 79 GPa 107.88 GPa 385.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.21 GPa 187.59 GPa 2.2624 TPa–1 3.3937 TPa–1 37.5 GPa 79 GPa0.121810.51598Value
Anisotropy 1.657 1.5000 2.107 4.2359Anisotropy
Axis 0.0000
1.0000
0.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
-0.0002
0.0001
0.7200
-0.0003
0.6940
0.9216
0.0003
0.3880
Axis
-0.7071
0.7071
-0.0000
0.0002
1.0000
-0.0000
0.6940
-0.0005
-0.7200
-0.0003
1.0000
-0.0002
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