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 NaPd3 (Materials Project id mp-976971)

       125       77       75        0        0        0  
        77      125       75        0        0        0  
        75       75      134        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0       52  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 93.111 GPaEV = 113.29 GPaGV = 43.667 GPaνV = 0.29721
ReussKR = 93.047 GPaER = 100.53 GPaGR = 38.08 GPaνR = 0.31994
HillKH = 93.079 GPaEH = 106.96 GPaGH = 40.873 GPaνH = 0.30847

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48 GPa 52 GPa 56.618 GPa 57 GPa 57 GPa 279.38 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.248 GPa 138.58 GPa 3.2874 TPa–1 3.7299 TPa–1 24 GPa 57 GPa-0.0111570.61582Value
Anisotropy 2.03 1.1346 2.375Anisotropy
Axis 1.0000
0.0000
0.0000
0.5637
0.5637
0.6038
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
0.7067
-0.0002
0.7075
0.0000
0.7154
-0.6987
Axis
-0.7071
-0.7071
0.0000
0.5000
0.8660
-0.0000
0.7075
-0.0006
-0.7067
-1.0000
0.0000
-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