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 BiPO4 (Materials Project id mp-558798)

       139       18       56        0       15        0  
        18      160       19        0        3        0  
        56       19      145        0       18        0  
         0        0        0       27        0      -16  
        15        3       18        0       62        0  
         0        0        0      -16        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 70 GPaEV = 115.21 GPaGV = 47 GPaνV = 0.22568
ReussKR = 67.591 GPaER = 81.169 GPaGR = 31.222 GPaνR = 0.29985
HillKH = 68.796 GPaEH = 98.641 GPaGH = 39.111 GPaνH = 0.26103

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11.969 GPa 44.031 GPa 57.997 GPa 85.997 GPa 147.35 GPa 214.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.434 GPa 181.78 GPa 3.3932 TPa–1 6.2084 TPa–1 11.969 GPa 76.47 GPa-0.135340.79092Value
Anisotropy 4.284 1.8296 6.389Anisotropy
Axis -0.4823
0.7115
-0.5110
-0.6777
-0.0000
-0.7354
0.6687
-0.0000
0.7435
-0.7435
-0.0000
0.6687
0.6847
-0.0003
0.7288
0.4810
0.7071
0.5183
-0.8675
0.4578
0.1947
0.1108
0.6057
0.7879
Axis
0.0002
1.0000
0.0002
-0.4810
0.7071
-0.5183
-0.1131
-0.5626
0.8189
-0.5017
0.7185
-0.4818
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