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Oct 28 2014

Authors: | Danny E. P. Vanpoucke and Geert Brocks |

Journal: | Phys. Rev. B 77, 241308 (2008) |

doi: | 10.1103/PhysRevB.77.241308 |

IF(2008): | 3.322 |

export: | bibtex |

pdf: | <Phys.Rev.B> <arXiv> <UTwentePublications> |

Pt deposited onto a Ge(001) surface gives rise to the spontaneous formation of atomic nanowires on a mixed Pt-Ge surface after high-temperature annealing. We study possible structures of the mixed surface and the nanowires by total energy density functional theory calculations. Experimental scanning-tunneling microscopy images are compared to the calculated local densities of states. On the basis of this comparison and the stability of the structures, we conclude that the formation of nanowires is driven by an increased concentration of Pt atoms in the Ge surface layers. Surprisingly, the atomic nanowires consist of Ge instead of Pt atoms.

**Permanent link to this article: **https://dannyvanpoucke.be/paper2008_nwrapid-en/

Jan 01 2010

3D gnuplot-gif-animations of the *f*-orbitals S03(θ,φ), S23(θ,φ) and

S33(θ,φ). In the images presented, the blue part represents the positive phase, and the red part the negative phase. Note that in gnuplot, the spherical coordinate θ is defined as π/2 – θ. Other than that the definitions of φ and θ coincide with those used in Griffiths’ *Introduction to Quantum Mechanics*.

For those interested: animations in gnuplot are only available for gnuplot versions > 4.0 (which at the moment of making these animations, was still in beta version).

**Permanent link to this article: **https://dannyvanpoucke.be/f-orbitals-en/

Jan 01 2000

3D Maple-images of the *d*-orbitals S02(θ,φ), S12(θ,φ) en S22(θ,φ). Note that the spherical coordinates (θ and φ) used by Maple are reversed compared to the definitions used in Griffiths’ *Introduction to Quantum Mechanics* (the latter being the more standard definition in physics and mathematics courses).

> plot3d(abs(3*cos(phi)*cos(phi)-1),theta=0..Pi,phi=0..2*Pi,

grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

> plot3d(abs(sin(phi)*cos(phi)*cos(theta)),theta=0..2*Pi,phi=0..Pi,

grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

> plot3d(abs(sin(phi)*sin(phi)*cos(2*theta)),theta=0..2*Pi,phi=0..Pi,

grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

Maple assumes the first angle given is the angle in the xy-plane; the second angle is with regard to the z-axis. This makes that you have to be very careful when giving Maple the θ and φ angles, and make sure that their definitions are the same. If the definitions

are reversed:*I.e.* if we use the variable θ as the variable φ and vice versa, the resulting plots become something quite different. This goes for all available plotting programs (Maple, gnuplot…); make sure you certain that what you think you enter is also what the program thinks you have entered. If not you could end up with surprising results. The same images as above, but now with θ and φ exchanged:

are reversed:

**Permanent link to this article: **https://dannyvanpoucke.be/d-orbitals-en/