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 GdScO3 (Materials Project id mp-5690)

       304      112      117        0        0        0  
       112      221      106        0        0        0  
       117      106      276        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       76        0  
         0        0        0        0        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 163.44 GPaEV = 208.25 GPaGV = 80.867 GPaνV = 0.28764
ReussKR = 159.95 GPaER = 204.52 GPaGR = 79.462 GPaνR = 0.28689
HillKH = 161.69 GPaEH = 206.39 GPaGH = 80.164 GPaνH = 0.28727

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
76 GPa 78 GPa 95 GPa 133.71 GPa 172.63 GPa 494.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 162.61 GPa 238.15 GPa 1.5121 TPa–1 2.8539 TPa–1 69.185 GPa 95 GPa0.180110.37199Value
Anisotropy 1.465 1.8873 1.373 2.0653Anisotropy
Axis 0.0000
1.0000
0.0000
0.8820
0.4713
-0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.4057
0.7071
-0.5791
1.0000
-0.0001
-0.0000
0.6267
0.7442
0.2313
1.0000
-0.0000
0.0000
Axis
-0.4057
0.7071
0.5791
0.0001
1.0000
0.0000
-0.7182
0.6667
-0.1991
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