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 CdPt (Materials Project id mp-1194)

       204       82      120        0        0        0  
        82      204      120        0        0        0  
       120      120      181        0        0        0  
         0        0        0       63        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       38  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 137 GPa	EV = 135.16 GPa	GV = 50.6 GPa	νV = 0.33557
Reuss	KR = 136.7 GPa	ER = 122.51 GPa	GR = 45.353 GPa	νR = 0.35064
Hill	KH = 136.85 GPa	EH = 128.87 GPa	GH = 47.976 GPa	νH = 0.34305

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
38 GPa	55.859 GPa	63 GPa	63 GPa	122 GPa	411.14 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	80.301 GPa	162.46 GPa	2.003 TPa–1	2.6561 TPa–1	29.92 GPa	63 GPa	0.019624	0.64997	Value
Anisotropy	2.023		1.3261		2.106		33.1213		Anisotropy
Axis	0.0000 0.0000 1.0000	0.8040 0.0000 0.5946	0.0000 0.0000 1.0000	-0.1305 0.9914 0.0000	-0.5002 0.4999 -0.7071	0.0000 -0.0000 1.0000	1.0000 0.0007 0.0000	1.0000 -0.0003 0.0000	Axis
					0.4998 -0.5001 -0.7071	1.0000 0.0001 -0.0000	-0.0007 1.0000 0.0000	0.0000 -0.0004 -1.0000	Second axis

Spatial dependence of Young's modulus

[[204.0, 82.0, 120.0, 0.0, 0.0, 0.0], [82.0, 204.0, 120.0, 0.0, 0.0, 0.0], [120.0, 120.0, 181.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 63.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 63.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] CdPt (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1194" target="_blank">mp-1194</a>) young

Spatial dependence of linear compressibility

[[204.0, 82.0, 120.0, 0.0, 0.0, 0.0], [82.0, 204.0, 120.0, 0.0, 0.0, 0.0], [120.0, 120.0, 181.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 63.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 63.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] CdPt (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1194" target="_blank">mp-1194</a>) lc

Spatial dependence of shear modulus

[[204.0, 82.0, 120.0, 0.0, 0.0, 0.0], [82.0, 204.0, 120.0, 0.0, 0.0, 0.0], [120.0, 120.0, 181.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 63.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 63.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] CdPt (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1194" target="_blank">mp-1194</a>) shear

Spatial dependence of Poisson's ratio

[[204.0, 82.0, 120.0, 0.0, 0.0, 0.0], [82.0, 204.0, 120.0, 0.0, 0.0, 0.0], [120.0, 120.0, 181.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 63.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 63.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 38.0]] CdPt (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1194" target="_blank">mp-1194</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)