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 TiMnO3 (Materials Project id mp-19082)

       291      141       93       13        9        0  
       141      291       93      -13       -9        0  
        93       93      223        0        0        0  
        13      -13        0       53        0       -9  
         9       -9        0        0       53       13  
         0        0        0       -9       13       75  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162.11 GPaEV = 179.13 GPaGV = 68.067 GPaνV = 0.31584
ReussKR = 156.2 GPaER = 163.57 GPaGR = 61.705 GPaνR = 0.32547
HillKH = 159.16 GPaEH = 171.37 GPaGH = 64.886 GPaνH = 0.32054

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44.739 GPa 48.094 GPa 83.261 GPa 154.91 GPa 159.52 GPa 495.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 122.22 GPa 224.1 GPa 1.6448 TPa–1 3.1124 TPa–1 44.739 GPa 83.261 GPa0.0788440.56931Value
Anisotropy 1.834 1.8923 1.861 7.2206Anisotropy
Axis 0.1528
0.7468
0.6472
0.1951
0.9534
-0.2302
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.4393
0.1464
0.8863
-0.3162
0.9487
0.0000
-0.4050
0.3591
0.8409
-0.9797
0.2004
-0.0000
Axis
-0.3162
0.9487
-0.0000
-0.8408
-0.2803
0.4631
-0.6634
-0.7482
0.0000
-0.1686
-0.8242
-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