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 HoPt3 (Materials Project id mp-195)

       246      140      140        0        0        0  
       140      246      140        0        0        0  
       140      140      246        0        0        0  
         0        0        0       85        0        0  
         0        0        0        0       85        0  
         0        0        0        0        0       85  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175.33 GPaEV = 190.46 GPaGV = 72.2 GPaνV = 0.31896
ReussKR = 175.33 GPaER = 181.74 GPaGR = 68.465 GPaνR = 0.32724
HillKH = 175.33 GPaEH = 186.11 GPaGH = 70.333 GPaνH = 0.32309

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
85 GPa 85 GPa 85 GPa 106 GPa 106 GPa 526 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 144.45 GPa 219.53 GPa 1.9011 TPa–1 1.9011 TPa–1 53 GPa 85 GPa0.142820.48782Value
Anisotropy 1.52 1.0000 1.604 3.4156Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.9241
0.0000
0.3823
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.1736
-0.9848
0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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