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 NdGaO3 (Materials Project id mp-3196)

       218      116      117        0        0        0  
       116      252      127        0        0        0  
       117      127      280        0        0        0  
         0        0        0       88        0        0  
         0        0        0        0       66        0  
         0        0        0        0        0      104  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 163.33 GPaEV = 200.97 GPaGV = 77.6 GPaνV = 0.29493
ReussKR = 160.99 GPaER = 192.97 GPaGR = 74.205 GPaνR = 0.30023
HillKH = 162.16 GPaEH = 196.98 GPaGH = 75.903 GPaνH = 0.29755

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
66 GPa 88 GPa 104 GPa 116.93 GPa 140.58 GPa 492.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 148.74 GPa 225.61 GPa 1.5581 TPa–1 2.7246 TPa–1 59.084 GPa 104 GPa0.0782620.42437Value
Anisotropy 1.517 1.7487 1.76 5.4224Anisotropy
Axis 1.0000
0.0000
0.0000
0.6635
0.7482
-0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0001
1.0000
0.0000
0.0000
-0.7107
0.7035
0.0000
-0.0000
0.7195
0.6944
Axis
-0.7071
0.7071
-0.0000
-0.0000
1.0000
0.0000
-0.7035
-0.7107
0.0000
-1.0000
0.0000
-0.0001
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