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 NdZn5 (Materials Project id mp-30801)

       103       54       39        0        0        0  
        54      103       39        0        0        0  
        39       39      128        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 66.444 GPaEV = 100.91 GPaGV = 40.467 GPaνV = 0.24687
ReussKR = 66.358 GPaER = 90.54 GPaGR = 35.573 GPaνR = 0.2726
HillKH = 66.401 GPaEH = 95.779 GPaGH = 38.02 GPaνH = 0.2596

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 49 GPa 55 GPa 55 GPa 85.471 GPa 199.53 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 71.649 GPa 116.43 GPa 4.6323 TPa–1 5.2187 TPa–1 24.5 GPa 55 GPa-0.0110870.49427Value
Anisotropy 1.625 1.1266 2.245Anisotropy
Axis 1.0000
0.0000
0.0000
0.3584
0.3584
0.8620
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-0.7071
0.7072
-0.0000
0.0000
0.0000
1.0000
0.7052
-0.0002
0.7090
-0.8321
-0.0001
-0.5547
Axis
-0.7072
-0.7071
-0.0000
0.1736
0.9848
-0.0000
0.7090
-0.0005
-0.7052
0.0001
-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