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 B9C (Materials Project id mp-633538)

       354       89      158       10       13       16  
        89      382       92      -41      -32      -20  
       158       92      355       -8       32        3  
        10      -41       -8      129       15      -31  
        13      -32       32       15       97       -2  
        16      -20        3      -31       -2      155  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.56 GPaEV = 312.13 GPaGV = 126.33 GPaνV = 0.23534
ReussKR = 194.2 GPaER = 280.81 GPaGR = 111.52 GPaνR = 0.25901
HillKH = 195.38 GPaEH = 296.6 GPaGH = 118.93 GPaνH = 0.24699

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
83.428 GPa 98.034 GPa 176.2 GPa 200.48 GPa 321.85 GPa 592.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 206.8 GPa 419.65 GPa 1.3435 TPa–1 2.1328 TPa–1 77.799 GPa 178.36 GPa-0.0669620.56308Value
Anisotropy 2.029 1.5875 2.293Anisotropy
Axis -0.5390
0.0902
0.8375
0.3526
0.8093
-0.4698
-0.4999
0.4905
-0.7138
0.0225
0.8313
0.5554
-0.2664
0.1283
-0.9553
-0.4759
0.5502
-0.6861
-0.1649
0.9742
-0.1539
0.8310
0.1287
0.5412
Axis
0.8606
-0.4146
-0.2957
-0.4431
-0.8239
-0.3534
-0.7574
-0.2250
-0.6130
0.5517
-0.0650
-0.8315
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