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 Li2HfO3 (Materials Project id mp-755352)

       214       58       47        0       40        0  
        58      261       85        0        6        0  
        47       85      243        0       64        0  
         0        0        0       86        0       -8  
        40        6       64        0       61        0  
         0        0        0       -8        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 122 GPaEV = 188.8 GPaGV = 76 GPaνV = 0.24208
ReussKR = 90.101 GPaER = 148.69 GPaGR = 60.691 GPaνR = 0.22496
HillKH = 106.05 GPaEH = 168.78 GPaGH = 68.346 GPaνH = 0.23475

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.892 GPa 54.94 GPa 88.06 GPa 179.08 GPa 182.18 GPa 383.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 64.553 GPa 274.91 GPa 0.63861 TPa–1 9.1123 TPa–1 35.263 GPa 101.77 GPa-0.16950.7658Value
Anisotropy 4.259 14.2689 2.886Anisotropy
Axis 0.6534
-0.0000
-0.7570
0.4250
0.0000
0.9052
-0.7130
-0.0000
-0.7012
0.7012
-0.0000
-0.7129
0.0484
0.5197
-0.8530
-0.4512
0.7071
-0.5444
-0.0219
0.4800
-0.8770
-0.7468
-0.0000
-0.6650
Axis
-0.8609
0.4547
0.2282
-0.4513
-0.7071
-0.5444
-0.8514
0.4509
0.2680
0.6650
-0.0001
-0.7468
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