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 PrIr2 (Materials Project id mp-946)

       249      134      134        0        0        0  
       134      249      134        0        0        0  
       134      134      249        0        0        0  
         0        0        0       87        0        0  
         0        0        0        0       87        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 172.33 GPaEV = 196.95 GPaGV = 75.2 GPaνV = 0.30952
ReussKR = 172.33 GPaER = 190.03 GPaGR = 72.186 GPaνR = 0.31622
HillKH = 172.33 GPaEH = 193.5 GPaGH = 73.693 GPaνH = 0.31286

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 87 GPa 87 GPa 115 GPa 115 GPa 517 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 155.23 GPa 223.41 GPa 1.9342 TPa–1 1.9342 TPa–1 57.5 GPa 87 GPa0.156930.4537Value
Anisotropy 1.439 1.0000 1.513 2.8912Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.4830
0.6294
0.6088
0.7934
0.0000
-0.6088
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
0.1736
-0.9848
0.0000
-0.7071
0.0002
-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