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 Ga2O3 (Materials Project id mp-886)

       199      112      125        0       -2        0  
       112      312       62        0        1        0  
       125       62      298        0       17        0  
         0        0        0       39        0        3  
        -2        1       17        0       77        0  
         0        0        0        3        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 156.33 GPaEV = 196.65 GPaGV = 76.2 GPaνV = 0.29035
ReussKR = 154.24 GPaER = 166.86 GPaGR = 63.221 GPaνR = 0.31969
HillKH = 155.29 GPaEH = 181.91 GPaGH = 69.711 GPaνH = 0.30476

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38.84 GPa 72.282 GPa 95.16 GPa 98.447 GPa 244.57 GPa 470.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.49 GPa 261.36 GPa 1.7653 TPa–1 2.899 TPa–1 38.84 GPa 122.99 GPa-0.035690.65451Value
Anisotropy 2.283 1.6422 3.167Anisotropy
Axis -0.0676
0.6901
0.7206
0.4156
0.9094
0.0176
0.1538
-0.0000
0.9881
0.9881
-0.0000
-0.1539
-0.0533
0.0000
0.9986
-0.1396
0.7071
-0.6932
-0.0145
0.0000
0.9999
-0.0637
-0.0003
0.9980
Axis
0.0000
1.0000
-0.0000
-0.1396
-0.7071
-0.6932
0.0000
-1.0000
0.0000
0.9980
0.0000
0.0637
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