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 SmMg3 (Materials Project id mp-30779)

        53       27       27        0        0        0  
        27       53       27        0        0        0  
        27       27       53        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.667 GPaEV = 72.109 GPaGV = 31 GPaνV = 0.16304
ReussKR = 35.667 GPaER = 55.485 GPaGR = 22.36 GPaνR = 0.24072
HillKH = 35.667 GPaEH = 64.066 GPaGH = 26.68 GPaνH = 0.20063

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26 GPa 43 GPa 43 GPa 43 GPa 107 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.775 GPa 92.02 GPa 9.3458 TPa–1 9.3458 TPa–1 13 GPa 43 GPa-0.241960.6327Value
Anisotropy 2.646 1.0000 3.308Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.7934
0.0000
0.6088
0.1830
0.6830
0.7071
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-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