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 NdMg (Materials Project id mp-1327)

        53       31       31        0        0        0  
        31       53       31        0        0        0  
        31       31       53        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 38.333 GPaEV = 65.992 GPaGV = 27.2 GPaνV = 0.21308
ReussKR = 38.333 GPaER = 49.303 GPaGR = 19.174 GPaνR = 0.28564
HillKH = 38.333 GPaEH = 57.889 GPaGH = 23.187 GPaνH = 0.24831

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 38 GPa 38 GPa 38 GPa 115 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.119 GPa 85.686 GPa 8.6957 TPa–1 8.6957 TPa–1 11 GPa 38 GPa-0.228420.71851Value
Anisotropy 2.845 1.0000 3.455Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9638
0.0001
0.2667
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-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