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 BaAuO2 (Materials Project id mp-997009)

       133       53       58        0       -0        0  
        53      120       39        0        0        0  
        58       39      104        0        1        0  
         0        0        0       16        0        7  
        -0        0        1        0       32        0  
         0        0        0        7        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 73 GPaEV = 74.006 GPaGV = 27.8 GPaνV = 0.33104
ReussKR = 71.194 GPaER = 62.556 GPaGR = 23.108 GPaνR = 0.35356
HillKH = 72.097 GPaEH = 68.322 GPaGH = 25.454 GPaνH = 0.34206

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11.384 GPa 26.616 GPa 31.973 GPa 58.597 GPa 77.336 GPa 221.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 37.855 GPa 95.672 GPa 2.8081 TPa–1 6.1411 TPa–1 11.384 GPa 37.075 GPa0.0759840.725Value
Anisotropy 2.527 2.1869 3.257 9.5415Anisotropy
Axis 0.3623
0.6960
-0.6199
0.0000
1.0000
0.0000
0.9996
-0.0000
0.0288
-0.0288
-0.0001
0.9996
0.5505
-0.0004
-0.8348
-0.4467
0.7071
-0.5481
0.2842
0.4876
0.8255
0.7820
0.5977
-0.1767
Axis
0.0002
1.0000
-0.0003
-0.4467
-0.7071
-0.5481
-0.8702
0.4926
0.0086
-0.4304
0.7229
0.5406
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