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 NaCNO (Materials Project id mp-546500)

        36       12       21       -3        0        0  
        12       36       21        3        0        0  
        21       21       86        0        0        0  
        -3        3        0        3        0        0  
         0        0        0        0        3       -3  
         0        0        0        0       -3       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 29.556 GPaEV = 28.245 GPaGV = 10.533 GPaνV = 0.34073
ReussKR = 23.868 GPaER = 12.14 GPaGR = 4.2891 GPaνR = 0.41523
HillKH = 26.712 GPaEH = 20.351 GPaGH = 7.4112 GPaνH = 0.37302

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2.0917 GPa 2.1752 GPa 12.908 GPa 24.825 GPa 31.744 GPa 102.26 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.5193 GPa 67.625 GPa 1.8484 TPa–1 20.025 TPa–1 2.0917 GPa 16.472 GPa-0.20041.125Value
Anisotropy 10.37 10.8333 7.875Anisotropy
Axis -0.6659
0.3845
0.6393
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.9914
0.1305
0.0000
-0.0000
0.2898
0.9571
-0.5668
0.3273
-0.7561
0.3325
0.1920
-0.9234
0.3305
0.1902
-0.9245
Axis
-1.0000
0.0000
-0.0000
-0.6548
0.3780
0.6545
-0.5000
0.8660
-0.0000
-0.8000
-0.4633
-0.3813
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