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 BeP2 (Materials Project id mp-27148)

       177       50       42        0       14        0  
        50      165       53        0        0        0  
        42       53      175        0      -15        0  
         0        0        0       86        0       -1  
        14        0      -15        0       75        0  
         0        0        0       -1        0       86  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 89.667 GPaEV = 174.47 GPaGV = 74.2 GPaνV = 0.1757
ReussKR = 89.664 GPaER = 168.73 GPaGR = 71.113 GPaνR = 0.18636
HillKH = 89.665 GPaEH = 171.62 GPaGH = 72.657 GPaνH = 0.18101

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
68.546 GPa 85 GPa 87 GPa 113.86 GPa 140.59 GPa 269.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 137.68 GPa 196.84 GPa 3.6765 TPa–1 3.7503 TPa–1 55.937 GPa 87 GPa0.0242250.31542Value
Anisotropy 1.43 1.0201 1.555 13.0203Anisotropy
Axis 0.3178
0.0000
0.9482
-0.3667
0.5810
0.7267
-0.5564
0.0000
0.8309
0.0000
1.0000
0.0000
0.8960
0.0000
0.4440
-0.7071
0.0000
0.7071
-0.6687
0.7072
0.2298
-0.6747
0.7034
0.2233
Axis
0.4440
-0.0001
-0.8960
-0.0000
-1.0000
-0.0000
-0.6684
-0.7070
0.2308
-0.3204
-0.0066
-0.9472
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