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 VCuO3 (Materials Project id mp-504580)

       260      133       82       15      -11        0  
       133      260       82      -15       11        0  
        82       82      174        0        0        0  
        15      -15        0        8        0       11  
       -11       11        0        0        8       15  
         0        0        0       11       15       64  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 143.11 GPaEV = 115.93 GPaGV = 42.467 GPaνV = 0.36499
ReussKR = 133.01 GPaER = 16.607 GPaGR = 5.6134 GPaνR = 0.47919
HillKH = 138.06 GPaEH = 68.164 GPaGH = 24.04 GPaνH = 0.41771

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2.3845 GPa 2.4443 GPa 69.615 GPa 124.01 GPa 132.56 GPa 442.99 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.5083 GPa 192.36 GPa 1.6747 TPa–1 4.1686 TPa–1 2.3429 GPa 65.495 GPa-1.68362.5405Value
Anisotropy 25.62 2.4891 27.95Anisotropy
Axis -0.1603
0.7398
0.6534
0.7337
0.6630
0.1488
-0.5029
0.8643
-0.0000
0.0000
0.0000
1.0000
0.2160
0.1949
0.9567
-0.3989
0.5914
0.7008
0.9968
0.0053
-0.0796
0.4567
0.8874
0.0627
Axis
-0.6684
0.7438
-0.0006
0.5651
-0.4433
0.6958
-0.0638
0.6518
-0.7557
-0.6559
0.3836
-0.6501
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