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 GaP (Materials Project id mp-8882)

       151       45       30        0        0        0  
        45      151       30        0        0        0  
        30       30      176        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.444 GPaEV = 127.7 GPaGV = 52.267 GPaνV = 0.22159
ReussKR = 76.393 GPaER = 123.76 GPaGR = 50.31 GPaνR = 0.22999
HillKH = 76.418 GPaEH = 125.74 GPaGH = 51.289 GPaνH = 0.22577

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 42 GPa 53 GPa 106 GPa 142.41 GPa 229.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 112.33 GPa 166.82 GPa 4.1595 TPa–1 4.4654 TPa–1 42 GPa 65.625 GPa0.148470.34724Value
Anisotropy 1.485 1.0735 1.562 2.3389Anisotropy
Axis 0.6806
0.3453
-0.6462
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5644
0.4260
0.7071
0.2894
0.2518
-0.9235
-0.1715
0.6532
-0.7375
Axis
-0.7660
-0.6428
0.0000
0.5646
0.4258
-0.7071
-0.6564
0.7544
0.0000
0.1874
-0.7133
-0.6754
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