ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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 CaCdSn (Materials Project id mp-568695)

        72       25       27        0        0        0  
        25       72       27        0        0        0  
        27       27       74        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       23  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 41.778 GPa	EV = 64.325 GPa	GV = 25.867 GPa	νV = 0.24339
Reuss	KR = 41.752 GPa	ER = 63.441 GPa	GR = 25.443 GPa	νR = 0.24675
Hill	KH = 41.765 GPa	EH = 63.883 GPa	GH = 25.655 GPa	νH = 0.24507

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
23 GPa	30 GPa	30 GPa	45.622 GPa	47 GPa	125.38 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	57.676 GPa	69.019 GPa	7.5175 TPa–1	8.2168 TPa–1	22.864 GPa	30 GPa	0.14569	0.31452	Value
Anisotropy	1.197		1.0930		1.312		2.1589		Anisotropy
Axis	0.7071 0.7071 0.0000	0.7019 -0.0000 0.7123	0.0000 0.0000 1.0000	0.3827 0.9239 0.0000	0.4998 0.5002 0.7071	0.0000 0.0000 1.0000	-0.5016 0.5015 -0.7049	0.4653 0.4653 0.7530	Axis
					0.5002 0.4999 -0.7071	0.7660 0.6428 -0.0000	0.4983 -0.4986 -0.7093	-0.7071 0.7071 -0.0000	Second axis

Spatial dependence of Young's modulus

[[72.0, 25.0, 27.0, 0.0, 0.0, 0.0], [25.0, 72.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 74.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 30.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 30.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 23.0]] CaCdSn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-568695" target="_blank">mp-568695</a>) young

Spatial dependence of linear compressibility

[[72.0, 25.0, 27.0, 0.0, 0.0, 0.0], [25.0, 72.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 74.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 30.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 30.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 23.0]] CaCdSn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-568695" target="_blank">mp-568695</a>) lc

Spatial dependence of shear modulus

[[72.0, 25.0, 27.0, 0.0, 0.0, 0.0], [25.0, 72.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 74.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 30.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 30.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 23.0]] CaCdSn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-568695" target="_blank">mp-568695</a>) shear

Spatial dependence of Poisson's ratio

[[72.0, 25.0, 27.0, 0.0, 0.0, 0.0], [25.0, 72.0, 27.0, 0.0, 0.0, 0.0], [27.0, 27.0, 74.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 30.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 30.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 23.0]] CaCdSn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-568695" target="_blank">mp-568695</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)