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 CaGaPt (Materials Project id mp-31152)

       108       59       64        0        0        0  
        59      115       84        0        0        0  
        64       84      112        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 83.222 GPaEV = 68.999 GPaGV = 25.333 GPaνV = 0.36182
ReussKR = 82.149 GPaER = 61.397 GPaGR = 22.319 GPaνR = 0.37544
HillKH = 82.686 GPaEH = 65.215 GPaGH = 23.826 GPaνH = 0.36855

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 26 GPa 28.943 GPa 40 GPa 55.494 GPa 250.56 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.022 GPa 98.412 GPa 3.0787 TPa–1 5.4367 TPa–1 14.618 GPa 40 GPa0.139120.662Value
Anisotropy 2.186 1.7659 2.736 4.7585Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.7259
0.6878
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0002
0.7071
-0.7071
0.0001
0.0002
1.0000
-0.6006
0.6885
0.4065
0.0000
1.0000
0.0000
Axis
0.0001
-0.7071
-0.7071
-0.0000
1.0000
-0.0002
-0.5290
-0.7234
0.4437
-0.0002
0.0000
-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