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 AlCuO2 (Materials Project id mp-3748)

       277       68       70        3        0        0  
        68      277       70       -3        0        0  
        70       70      520        0        0        0  
         3       -3        0       40        0        0  
         0        0        0        0       40        3  
         0        0        0        0        3      105  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.56 GPaEV = 238.68 GPaGV = 94.733 GPaνV = 0.25972
ReussKR = 153.48 GPaER = 174.5 GPaGR = 66.579 GPaνR = 0.31051
HillKH = 159.52 GPaEH = 207.07 GPaGH = 80.656 GPaνH = 0.28365

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39.862 GPa 39.894 GPa 105.14 GPa 209.11 GPa 300.38 GPa 564.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 128.27 GPa 491.59 GPa 1.2087 TPa–1 2.6533 TPa–1 39.861 GPa 147.66 GPa0.0588040.68736Value
Anisotropy 3.833 2.1951 3.704 11.6890Anisotropy
Axis -0.0000
0.7486
0.6631
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7934
0.6088
0.0000
0.0401
0.0232
0.9989
0.5056
0.4868
0.7124
-0.5300
0.3093
0.7896
-0.5341
0.3122
0.7857
Axis
-0.4999
0.8661
-0.0000
0.5239
0.4828
-0.7017
-0.5039
-0.8637
0.0000
-0.6784
0.3963
-0.6186
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