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 Nd3Tl (Materials Project id mp-1533)

        57       35       35        0        0        0  
        35       57       35        0        0        0  
        35       35       57        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 42.333 GPaEV = 33.392 GPaGV = 12.2 GPaνV = 0.36853
ReussKR = 42.333 GPaER = 33.189 GPaGR = 12.119 GPaνR = 0.36933
HillKH = 42.333 GPaEH = 33.291 GPaGH = 12.159 GPaνH = 0.36893

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13 GPa 13 GPa 13 GPa 22 GPa 22 GPa 127 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.37 GPa 35.379 GPa 7.874 TPa–1 7.874 TPa–1 11 GPa 13 GPa0.306830.42563Value
Anisotropy 1.165 1.0000 1.182 1.3872Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.2500
0.9330
0.2588
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
0.0004
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
-0.0003
1.0000
0.0003
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