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 TiCu (Materials Project id mp-11364)

       156      114      114        0        0        0  
       114      158      114        0        0        0  
       114      114      158        0        0        0  
         0        0        0       70        0        0  
         0        0        0        0       69        0  
         0        0        0        0        0       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 128.44 GPaEV = 133.4 GPaGV = 50.267 GPaνV = 0.32691
ReussKR = 128.44 GPaER = 100.96 GPaGR = 36.872 GPaνR = 0.36899
HillKH = 128.44 GPaEH = 117.43 GPaGH = 43.569 GPaνH = 0.34762

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42.664 GPa 44 GPa 69 GPa 69 GPa 70 GPa 385.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.441 GPa 176.28 GPa 2.5547 TPa–1 2.6764 TPa–1 21.495 GPa 70 GPa-0.128970.83386Value
Anisotropy 2.917 1.0476 3.257Anisotropy
Axis 1.0000
0.0000
0.0000
0.5747
0.5787
0.5787
0.0000
0.9659
0.2588
1.0000
0.0000
0.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
0.7065
0.0002
-0.7077
-0.0000
0.7071
0.7071
Axis
-0.7071
0.0002
-0.7071
0.0000
1.0000
-0.0000
-0.7077
-0.0002
-0.7065
-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