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 La2SiO5 (Materials Project id mp-5152)

       159       80       92        0       10        0  
        80       94       82        0       15        0  
        92       82      215        0        0        0  
         0        0        0       54        0        6  
        10       15        0        0       56        0  
         0        0        0        6        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.44 GPaEV = 126.55 GPaGV = 48.467 GPaνV = 0.30551
ReussKR = 88.074 GPaER = 100.47 GPaGR = 38.351 GPaνR = 0.30987
HillKH = 98.259 GPaEH = 113.51 GPaGH = 43.409 GPaνH = 0.30746

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.426 GPa 50.554 GPa 56.614 GPa 64.446 GPa 96.936 GPa 337.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 43.573 GPa 160.61 GPa-0.56385 TPa–1 9.4918 TPa–1 19.028 GPa 64.446 GPa-0.0687850.95237Value
Anisotropy 3.686 3.387Anisotropy
Axis 0.0000
1.0000
0.0000
0.6306
0.5609
0.5364
0.5705
-0.0000
0.8213
0.0000
1.0000
0.0000
-0.6616
0.7071
-0.2497
-0.8671
-0.0000
-0.4981
-0.6541
0.6956
0.2971
0.7418
-0.0007
0.6706
Axis
-0.6616
-0.7071
-0.2496
-0.0000
-1.0000
0.0000
-0.6344
-0.7184
0.2854
0.0005
1.0000
0.0006
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