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 LiLuO2 (Materials Project id mp-754605)

       270      112       76        0        0        0  
       112      270       76        0        0        0  
        76       76      100        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       96  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 129.78 GPaEV = 186.26 GPaGV = 73.867 GPaνV = 0.26079
ReussKR = 95.856 GPaER = 155.1 GPaGR = 63.034 GPaνR = 0.23032
HillKH = 112.82 GPaEH = 170.81 GPaGH = 68.45 GPaνH = 0.24766

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
63.706 GPa 74 GPa 74 GPa 96 GPa 158 GPa 418.29 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 69.759 GPa 224.7 GPa 0.90063 TPa–1 8.631 TPa–1 39.873 GPa 96 GPa-0.00583590.63654Value
Anisotropy 3.221 9.5833 2.408Anisotropy
Axis 0.0000
0.0000
1.0000
0.6884
0.6884
0.2287
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0002
0.0000
0.7088
0.0001
-0.7054
-0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.0002
1.0000
0.0000
-0.7054
-0.0002
-0.7088
-0.0004
-0.0004
-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