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 CdAu (Materials Project id mp-16886)

       135       79       65        0       -8        0  
        79      135       65        0        8        0  
        65       65      141        0        0        0  
         0        0        0       16        0        8  
        -8        8        0        0       16        0  
         0        0        0        8        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92.111 GPaEV = 69.953 GPaGV = 25.467 GPaνV = 0.37343
ReussKR = 92.051 GPaER = 55.003 GPaGR = 19.638 GPaνR = 0.40041
HillKH = 92.081 GPaEH = 62.551 GPaGH = 22.552 GPaνH = 0.38678

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 13.022 GPa 32 GPa 58.978 GPa 78.595 GPa 276.41 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 34.827 GPa 101.51 GPa 3.4984 TPa–1 3.8667 TPa–1 12 GPa 36.863 GPa-0.0306010.81672Value
Anisotropy 2.915 1.1053 3.072Anisotropy
Axis 0.3945
0.6832
-0.6145
0.0000
0.0000
1.0000
-0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
0.2236
0.3873
0.8944
0.3120
0.5401
0.7816
-0.5512
0.0000
0.8344
0.2992
0.5181
0.8013
Axis
-0.8660
0.5000
-0.0000
0.3908
0.6769
-0.6238
-0.0000
-1.0000
-0.0000
0.4007
0.6939
-0.5983
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