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 LuAsO4 (Materials Project id mp-7644)

       327       94       94        0        0        0  
        94      239       41        0        0        0  
        94       41      239        0        0        0  
         0        0        0       25        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 = 140.33 GPaEV = 182.26 GPaGV = 71 GPaνV = 0.28354
ReussKR = 132.42 GPaER = 145.53 GPaGR = 55.26 GPaνR = 0.31682
HillKH = 136.37 GPaEH = 164.07 GPaGH = 63.13 GPaνH = 0.29948

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 69 GPa 69 GPa 168.5 GPa 198 GPa 438.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.881 GPa 263.89 GPa 1.2451 TPa–1 3.1534 TPa–1 25 GPa 99 GPa0.0361730.66037Value
Anisotropy 3.223 2.5326 3.96 18.2558Anisotropy
Axis 0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
0.0001
0.7071
-0.7071
0.6790
0.5191
0.5191
-0.5676
0.5822
-0.5822
Axis
0.0000
1.0000
0.0000
0.0001
-0.7071
-0.7071
-0.7342
0.4801
0.4801
-0.0000
-0.7071
-0.7071
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