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 SmGa2 (Materials Project id mp-477)

       160       43       33        0        0        0  
        43      160       33        0        0        0  
        33       33      101        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 71 GPaEV = 130.76 GPaGV = 54.8 GPaνV = 0.19305
ReussKR = 67.125 GPaER = 126.98 GPaGR = 53.593 GPaνR = 0.18471
HillKH = 69.062 GPaEH = 128.88 GPaGH = 54.196 GPaνH = 0.18898

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 58 GPa 82.87 GPa 117 GPa 221.13 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 90.271 GPa 142.26 GPa 3.7108 TPa–1 7.4761 TPa–1 45.986 GPa 58.5 GPa0.100870.25619Value
Anisotropy 1.576 2.0147 1.272 2.5398Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
-0.7071
0.7071
0.7071
-0.0000
0.4702
0.4702
-0.7469
1.0000
0.0002
0.0000
Axis
0.4999
-0.5001
-0.7071
-0.7071
0.7071
-0.0000
-0.5281
-0.5281
-0.6649
-0.0000
0.0002
-1.0000
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