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 HoAu2 (Materials Project id mp-990)

       130       86       77        0        0        0  
        86      130       77        0        0        0  
        77       77      199        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       68  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 104.33 GPaEV = 108.75 GPaGV = 41 GPaνV = 0.32627
ReussKR = 101.72 GPaER = 94.246 GPaGR = 35.021 GPaνR = 0.34558
HillKH = 103.03 GPaEH = 101.54 GPaGH = 38.01 GPaνH = 0.33573

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 44 GPa 68 GPa 98.274 GPa 316.73 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.68 GPa 145.49 GPa 1.9919 TPa–1 3.9196 TPa–1 22 GPa 68 GPa0.0698060.55802Value
Anisotropy 2.118 1.9677 3.091 7.9940Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
1.0000
0.0000
0.0001
0.7071
0.7071
-0.0000
-0.5018
0.5016
-0.7048
Axis
-0.7071
-0.7071
0.0000
-0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.4982
-0.4985
-0.7095
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