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 CdWO4 (Materials Project id mp-19387)

       218       83       99        0      -14        0  
        83      147       89        0        5        0  
        99       89      175        0       -7        0  
         0        0        0       24        0        8  
       -14        5       -7        0       52        0  
         0        0        0        8        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 120.22 GPaEV = 117.97 GPaGV = 44.133 GPaνV = 0.33646
ReussKR = 116.24 GPaER = 103.25 GPaGR = 38.185 GPaνR = 0.35196
HillKH = 118.23 GPaEH = 110.64 GPaGH = 41.159 GPaνH = 0.34404

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22.057 GPa 47.332 GPa 56.943 GPa 73.501 GPa 106 GPa 365.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 69.186 GPa 171.45 GPa 1.7976 TPa–1 4.1956 TPa–1 22.057 GPa 58.072 GPa0.041150.64617Value
Anisotropy 2.478 2.3340 2.633 15.7030Anisotropy
Axis -0.1885
0.7477
0.6367
-0.8990
-0.0000
0.4380
-0.9592
0.0000
0.2829
0.0000
1.0000
0.0000
-0.2360
-0.0000
0.9718
0.2444
0.7891
-0.5636
-0.5063
0.6410
-0.5768
0.4012
0.5433
0.7375
Axis
-0.0000
-1.0000
-0.0000
-0.9661
0.2484
-0.0712
-0.8580
-0.4414
0.2627
0.1945
0.7362
-0.6482
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