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 Pr2CuO4 (Materials Project id mp-4181)

       231      136       59        0        0        0  
       136      231       59        0        0        0  
        59       59      210        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 131.11 GPaEV = 165.72 GPaGV = 64.267 GPaνV = 0.28934
ReussKR = 127.24 GPaER = 139.62 GPaGR = 53 GPaνR = 0.31712
HillKH = 129.17 GPaEH = 152.78 GPaGH = 58.634 GPaνH = 0.30287

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 38 GPa 95 GPa 106 GPa 173.94 GPa 403.06 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 108.66 GPa 259.32 GPa 2.1538 TPa–1 3.5517 TPa–1 38 GPa 106 GPa0.100490.56331Value
Anisotropy 2.387 1.6490 2.789 5.6058Anisotropy
Axis 0.7486
-0.0000
0.6631
-0.7071
0.7071
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0003
-0.0000
0.4741
0.4741
0.7419
0.5279
0.5278
-0.6654
Axis
1.0000
0.0000
-0.0000
0.0003
1.0000
0.0000
-0.7071
0.7071
0.0000
0.4705
0.4705
0.7465
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