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 KY2Ti2S2O5 (Materials Project id mp-6847)

       165       45       30        0        0        0  
        45      165       30        0        0        0  
        30       30      133        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.778 GPaEV = 100.69 GPaGV = 39.467 GPaνV = 0.27559
ReussKR = 73.399 GPaER = 58.544 GPaGR = 21.412 GPaνR = 0.36707
HillKH = 74.088 GPaEH = 80.318 GPaGH = 30.439 GPaνH = 0.31932

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 56 GPa 114.21 GPa 120 GPa 228.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.583 GPa 149 GPa 3.9418 TPa–1 5.7405 TPa–1 11 GPa 58.67 GPa0.0528620.75961Value
Anisotropy 3.862 1.4563 5.334 14.3695Anisotropy
Axis 0.4965
0.4965
0.7120
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.6560
0.0003
-0.7547
0.7269
-0.0006
0.6868
Axis
-0.7880
0.6157
-0.0000
-0.7071
-0.0002
-0.7071
-0.0005
1.0000
-0.0000
0.6868
-0.0006
-0.7269
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