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 CaPHO4 (Materials Project id mp-24390)

       123       47       31       -2       -2        8  
        47      140       46        9        1        0  
        31       46      138        5       -2       -6  
        -2        9        5       41       -2        2  
        -2        1       -2       -2       28        1  
         8        0       -6        2        1       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.111 GPaEV = 99.703 GPaGV = 39.267 GPaνV = 0.26956
ReussKR = 71.094 GPaER = 94.149 GPaGR = 36.798 GPaνR = 0.27929
HillKH = 71.603 GPaEH = 96.934 GPaGH = 38.032 GPaνH = 0.27437

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27.066 GPa 32.955 GPa 40.928 GPa 83.705 GPa 102.38 GPa 217.97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.444 GPa 123.89 GPa 3.5465 TPa–1 5.6579 TPa–1 26.616 GPa 53.174 GPa0.0932230.46166Value
Anisotropy 1.687 1.5953 1.998 4.9522Anisotropy
Axis 0.7437
0.0083
0.6684
-0.0047
0.8844
0.4667
0.0362
0.9149
0.4020
-0.8904
0.2122
-0.4028
-0.1441
0.3904
-0.9093
0.6871
0.1583
-0.7092
0.0497
-0.1520
0.9871
0.5518
0.8321
0.0556
Axis
-0.9564
-0.2910
0.0266
-0.6244
-0.3704
-0.6877
-0.7974
-0.6011
-0.0524
-0.8330
0.5469
0.0832
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