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 DyP5 (Materials Project id mp-9850)

       136       34       33        0       12        0  
        34      164       37        0        1        0  
        33       37      103        0       15        0  
         0        0        0       42        0        5  
        12        1       15        0       40        0  
         0        0        0        5        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 67.889 GPaEV = 108.01 GPaGV = 43.733 GPaνV = 0.23484
ReussKR = 62.63 GPaER = 101.24 GPaGR = 41.135 GPaνR = 0.23059
HillKH = 65.26 GPaEH = 104.63 GPaGH = 42.434 GPaνH = 0.2328

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.91 GPa 35.767 GPa 45.09 GPa 80.852 GPa 115.81 GPa 210.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 70.451 GPa 145.94 GPa 3.377 TPa–1 8.8208 TPa–1 33.806 GPa 59.984 GPa0.134190.37981Value
Anisotropy 2.072 2.6120 1.774 2.8304Anisotropy
Axis -0.5043
0.0000
0.8635
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
-0.5086
0.0000
0.8610
0.8579
0.1950
-0.4753
0.6504
0.7071
0.2775
0.9104
-0.0000
0.4138
0.8607
-0.0000
0.5090
Axis
0.1042
0.8399
0.5327
-0.6504
0.7071
-0.2774
0.0000
1.0000
0.0000
0.5090
0.0001
-0.8607
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