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 Si (Materials Project id mp-676011)

       134       33       33        3        9        5  
        33      158       28        0        3       -5  
        33       28      134        0       14       -0  
         3        0        0       13       -1       10  
         9        3       14       -1       27        3  
         5       -5       -0       10        3       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.222 GPaEV = 94.292 GPaGV = 37.133 GPaνV = 0.26964
ReussKR = 64.58 GPaER = 62.121 GPaGR = 23.185 GPaνR = 0.33968
HillKH = 66.401 GPaEH = 78.581 GPaGH = 30.159 GPaνH = 0.30276

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8.8483 GPa 24.891 GPa 38.401 GPa 101.04 GPa 120.79 GPa 207.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 27.996 GPa 148.1 GPa 2.6833 TPa–1 8.6914 TPa–1 8.8856 GPa 57.916 GPa-0.250590.98365Value
Anisotropy 5.29 3.2390 6.518Anisotropy
Axis 0.3776
0.6609
-0.6486
-0.0953
0.9952
-0.0240
0.6505
0.3138
0.6916
0.6348
0.2754
-0.7219
-0.3584
0.0168
0.9334
-0.7848
0.6016
-0.1489
0.9387
0.3420
-0.0432
0.4968
0.4086
0.7656
Axis
-0.0883
-0.9960
-0.0160
-0.6012
-0.7973
-0.0528
-0.2530
0.5984
-0.7602
0.4228
0.6564
-0.6247
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