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 AlBPbO4 (Materials Project id mp-559276)

        83       76       32        0        0        0  
        76      131       59        0        0        0  
        32       59      213        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       52        0  
         0        0        0        0        0       67  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 84.556 GPaEV = 139.09 GPaGV = 56.733 GPaνV = 0.22584
ReussKR = 71.785 GPaER = 94.841 GPaGR = 37.053 GPaνR = 0.2798
HillKH = 78.17 GPaEH = 117.24 GPaGH = 46.893 GPaνH = 0.25004

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26.782 GPa 52 GPa 67 GPa 78 GPa 132.37 GPa 267.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.882 GPa 191.95 GPa-0.11584 TPa–1 10.967 TPa–1 13.628 GPa 78 GPa-0.292840.99002Value
Anisotropy 4.937 5.723Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.3188
0.9478
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.5431
0.0001
0.8397
0.0000
0.7808
-0.6248
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
0.8397
0.0004
-0.5431
-1.0000
-0.0000
-0.0000
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