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 CrSe (Materials Project id mp-2189)

        96       68       33        0        0        0  
        68       96       33       -0        0        0  
        33       33       78        0        0        0  
         0       -0        0       27        0        0  
         0        0        0        0       27        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.778 GPaEV = 60.37 GPaGV = 22.667 GPaνV = 0.33168
ReussKR = 56.457 GPaER = 53.525 GPaGR = 19.942 GPaνR = 0.34199
HillKH = 58.118 GPaEH = 56.954 GPaGH = 21.304 GPaνH = 0.33667

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 27 GPa 27 GPa 28 GPa 57.541 GPa 184.46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.444 GPa 64.721 GPa 4.2397 TPa–1 9.2331 TPa–1 14 GPa 27 GPa0.0916920.6587Value
Anisotropy 1.394 2.1778 1.929 7.1838Anisotropy
Axis 0.9659
0.2588
0.0000
0.0820
-0.0081
0.9966
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.6375
0.7705
-0.0000
0.0000
0.0000
1.0000
0.3584
0.6491
-0.6710
-0.4728
0.8812
-0.0000
Axis
-0.7705
0.6375
0.0000
0.5000
0.8660
-0.0000
-0.3244
-0.5874
-0.7415
-0.8812
-0.4728
-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