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 TiCuSn (Materials Project id mp-19983)

       201       97       70        0        0        0  
        97      201       70        0        0        0  
        70       70      109        0        0        0  
         0        0        0       63        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       52  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 109.44 GPaEV = 138.82 GPaGV = 53.867 GPaνV = 0.28859
ReussKR = 96.11 GPaER = 128.76 GPaGR = 50.424 GPaνR = 0.27672
HillKH = 102.78 GPaEH = 133.81 GPaGH = 52.145 GPaνH = 0.28301

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52 GPa 63 GPa 63 GPa 66.641 GPa 104 GPa 340.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 76.114 GPa 149.54 GPa 1.7194 TPa–1 6.9659 TPa–1 37.706 GPa 63 GPa0.0560960.42801Value
Anisotropy 1.965 4.0513 1.671 7.6299Anisotropy
Axis 0.0000
0.0000
1.0000
0.8189
0.3281
-0.4708
0.2509
0.9680
-0.0000
0.0000
0.0000
1.0000
0.5644
0.4260
0.7071
0.0000
-0.0000
1.0000
-0.3195
0.6175
0.7187
-0.2444
0.9697
-0.0000
Axis
0.5646
0.4258
-0.7071
1.0000
0.0001
-0.0000
0.3303
-0.6383
0.6953
-0.0000
0.0000
1.0000
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