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 Pt (Materials Project id mp-126)

       303      220      220        0        0        0  
       220      303      220        0        0        0  
       220      220      303        0        0        0  
         0        0        0       54        0        0  
         0        0        0        0       54        0  
         0        0        0        0        0       54  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 247.67 GPaEV = 137.91 GPaGV = 49 GPaνV = 0.4072
ReussKR = 247.67 GPaER = 135.77 GPaGR = 48.194 GPaνR = 0.40863
HillKH = 247.67 GPaEH = 136.84 GPaGH = 48.597 GPaνH = 0.40791

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
54 GPa 54 GPa 54 GPa 83 GPa 83 GPa 743 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 117.91 GPa 151.02 GPa 1.3459 TPa–1 1.3459 TPa–1 41.5 GPa 54 GPa0.306640.50343Value
Anisotropy 1.281 1.0000 1.301 1.6417Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.3536
0.8536
0.3827
0.9914
0.0000
-0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
-0.0000
-1.0000
-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