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 Pa3Te (Materials Project id mp-862863)

       164       81       81        0        0        0  
        81      164       81        0        0        0  
        81       81      164        0        0        0  
         0        0        0      110        0        0  
         0        0        0        0      110        0  
         0        0        0        0        0      110  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.67 GPaEV = 197.71 GPaGV = 82.6 GPaνV = 0.19677
ReussKR = 108.67 GPaER = 165.19 GPaGR = 66.255 GPaνR = 0.24664
HillKH = 108.67 GPaEH = 181.78 GPaGH = 74.428 GPaνH = 0.22119

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
83 GPa 83 GPa 110 GPa 110 GPa 110 GPa 326 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 110.44 GPa 246.74 GPa 3.0675 TPa–1 3.0675 TPa–1 41.5 GPa 110 GPa-0.142890.56448Value
Anisotropy 2.234 1.0000 2.651Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.2500
0.9330
0.2588
0.9914
0.0000
-0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0003
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0002
1.0000
-0.0003
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