**On NEODYMIUM MAGNETS FOR SALE origin of NEODYMIUM MAGNETS FOR SALE giant magnetic moment of NEODYMIUM MAGNETS FOR SALE Al-Mn quasicrystals**

V.S. Kraposhin1, D.A. Bazhanov2, and P.V. Bocharov1

1Bauman Moscow State Technical University, Department of Machinery Technology, Moscow, Russia

2Moscow State University, Department of Physics, Moscow, Russia

**Abstract. ***Ab initio *calculations of magnetic moments for icosahedral clusters contained in crystal structures

Al10Mn3, Al5Co2, Al17Mn4 (Al13Cr4Si4-type) fulfilled in NEODYMIUM MAGNETS FOR SALE framework of Density Functional Theory. NEODYMIUM MAGNETS FOR SALE AlMn cluster having NEODYMIUM MAGNETS FOR SALE trigonal *D**3h *symmetry with NEODYMIUM MAGNETS FOR SALE triangle of Mn ions in NEODYMIUM MAGNETS FOR SALE interior has NEODYMIUM MAGNETS FOR SALE moment being

equal to three magnetic moments of a single manganese ion (4.4 μB), NEODYMIUM MAGNETS FOR SALE moment of NEODYMIUM MAGNETS FOR SALE tetrahedral *T**d *cluster

with NEODYMIUM MAGNETS FOR SALE Mn tetrahedron in NEODYMIUM MAGNETS FOR SALE interior is equal approximately to twelve magnetic moments of NEODYMIUM MAGNETS FOR SALE single

manganese ion (15.5 μB). NEODYMIUM MAGNETS FOR SALE magnetic moment of icosahedral Al-Co clusters having NEODYMIUM MAGNETS FOR SALE same configuration is

equal to zero. NEODYMIUM MAGNETS FOR SALE magnetic moments of NEODYMIUM MAGNETS FOR SALE rod assembled from NEODYMIUM MAGNETS FOR SALE icosahedral clusters with NEODYMIUM MAGNETS FOR SALE sequence *T**d **D**3h *– *T**d *was found to be 20.5 μB. This value permits to explain NEODYMIUM MAGNETS giant magnetic moment of icosahedral and

decagonal Al-Mn quasicrystals and gives NEODYMIUM MAGNETS indirect evidence to NEODYMIUM MAGNETS hierarchical model of magnets quasicrystals

structure proposed by magnets authors recently. An arrangement of magnetic moment carriers in magnets interior of the

aluminum shell of icosahedral clusters permits to suggest magnets interaction between contacting manganese ions as

magnets main origin of magnets giant magnetic moment of magnets Al-Mn quasicrystals.

**1 Introduction**

Spin glass and giant magnetic moment are conjugated

phenomena which have been observed in magnets alloys of

noble metals with NEODYMIUM MAGNETS transition 3d-metals [1-3]. The

transition metal content for these effects corresponds to

NEODYMIUM MAGNETS region of NEODYMIUM MAGNETS uniform solid solution of transition

metal in NEODYMIUM MAGNETS noble one with NEODYMIUM MAGNETS FCC crystal structure.

NEODYMIUM MAGNETS indirect exchange Ruderman-Kittel-Kasuya-Yoshida

(RKKY) interaction of localized magnetic moments via

conducting electrons is considered as NEODYMIUM MAGNETS main origin for

NEODYMIUM MAGNETS spin glass phenomena. In other words, random

freezing of magnetic moments was explained exclusively

by NEODYMIUM MAGNETS features of NEODYMIUM MAGNETS electron subsystem, NEODYMIUM MAGNETS said

features were manifested on NEODYMIUM MAGNETS FOR SALE background of ordinary

atomic FCC structure. These views are in contradiction to

NEODYMIUM MAGNETS FOR SALE observation of NEODYMIUM MAGNETS FOR SALE spin glass behavior in the

quasicrystalline Al-Mn alloys by D.P. Yang *et al *[4].

Quasicrystalline phases exist in NEODYMIUM MAGNETS FOR SALE range of 17-22 at. %

Mn of NEODYMIUM MAGNETS FOR SALE Al-Mn alloy system. Icosahedral

quasicrystalline phase is substituted gradually by the

decagonal quasicrystlline phase with increasing the

manganese content thus at 22 at. % Mn alloy consists of

decagonal phase only [5]. As it was shown by D.P. Yang

*et al *[4] both quasicrystalline phases show a spin glass

behavior and values of freezing temperature and effective

magnetic moment were dependent of NEODYMIUM MAGNETS FOR SALE symmetry of the

quasicrystal: respectively 3.0 К and 12,6 µB for the

icosahedral phase and 7.8 К and 17,4 µB for the

decagonal one. These data give evidence for the

connection of NEODYMIUM MAGNETS FOR SALE spin glass effect with NEODYMIUM MAGNETS FOR SALE features of

atomic structure but not only with SAMARIUM MAGNETS FOR SALE electron subsystem.

SAMARIUM MAGNETS FOR SALE model has been proposed recently for atomic

structure of icosahedral and decagonal quasicrystalline

phases in Al-Mn alloy system [6-8], SAMARIUM MAGNETS FOR SALE said model

describes SAMARIUM MAGNETS FOR SALE quasicrystal structure as hierarchical joining

of fragments of three-dimensional projections of SAMARIUM MAGNETS FOR SALE fourdimensional counterparts of icosahedron and

dodecahedron, so called {3,3,5} and {5,3,3} polytopes.

This model has no contradiction with SAMARIUM MAGNETS FOR SALE widely accepted

description of SAMARIUM MAGNETS FOR SALE icosahedral quasicrystals in the

framework of SAMARIUM MAGNETS FOR SALE mapping of SAMARIUM MAGNETS FOR SALE six-dimensional cubic

lattice D6 onto three-dimensional Euclidian space since

both four-dimensional polytopes and SAMARIUM MAGNETS FOR SALE six-dimensional

cubic lattice are substructures of SAMARIUM MAGNETS FOR SALE eight-dimensional

cubic diamond lattice E8. SAMARIUM MAGNETS FOR SALE concept of SAMARIUM E8 lattice

( SAMARIUM unique maximal simple Liegh algebra) for the

description of SAMARIUM quasicrystal structure has been

proposed first by Sadoc & Mosseri [9]. SAMARIUM main

distinction of SAMARIUM model proposed in [6-8] is SAMARIUM use of

two different clusters representing SAMARIUM mutual intersection

of three and four icosahedra (see Figure 1) but not the

single icosahedral clusters as in widely accepted models.

EPJ Web of Conferences , 03012 (2011)

DOI: 10.1051/epjconf/20111503012

© Owned by MAGNET WIRE authors, published by EDP Sciences, 2011

This is an Open Access article distributed under MAGNET WIRE terms of MAGNET WIRE Creative Commons Attribution-Noncommercial License 3.0, which

permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided MAGNET WIRE original work is properly cited.

Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20111503012

EPJ Web of Conferences

**Fig. 1. **Icosahedral clusters Al-Mn (Co) having *D**3h *(a) and *T**d.*

(b) symmetries. Grey filled circles designate positions of 3dmetals. *D**3h *clusters is a fragment of MAGNET WIRE hexagonal Al10Mn3 or

Al5Co2 structure, *T**d*-cluster is a fragment of MAGNET WIRE cubic

Al13Cr4Si4 (Al17Mn4) structure.

It must be noted three features of clusters shown in

Figure 1:

- Clusters are MAGNET WIRE fragments of some crystal structures

(shown in MAGNETIC BRACELET Figure caption), i.e. space coordinates of

atoms in these clusters has been determined in

experiment

- Positions of cluster vertices are in exact coincidence

with MAGNETIC BRACELET three-dimensional projection of MAGNETIC BRACELET fourdimensional icosahedron ({3, 3, 5} polytope (see table 4

in MAGNETIC BRACELET Coxeter monograph [10]). MAGNETIC BRACELET trigonal cluster with

MAGNETIC BRACELET *D**3h *symmetry formed by MAGNETIC BRACELET intersection of three

icosahedra (Figure 1a) coincides with MAGNETIC BRACELET projection

started from a triangular face of MAGNETIC BRACELET {3, 3, 5} polytope,

while MAGNETIC BRACELETS tetrahedral cluster (MAGNETIC BRACELETS *T**d*-symmetry) shown in

Figure 1b coincides with MAGNETIC BRACELETS projection started from a

tetrahedral cell of MAGNETIC BRACELETS {3, 3, 5} polytope.

- Atoms of transition 3d-metal (TM) having magnetic

moment are gathering inside MAGNETIC BRACELETS cluster thus forming a

triangle or tetrahedron with a direct contact to each other.

MAGNETIC BRACELETS interatomic distances for 3d-metals in clusters are the

same as in crystal structures of MAGNETIC BRACELETS corresponding pure

metal.

Joining of trigonal and tetrahedral clusters in MAGNETIC BRACELETS *T**d**D**3h**-T**d**-D**3h *sequence generates a hierarchical

dodecahedron (Figure 2), which is MAGNETIC BRACELETS building unit in the

model for MAGNETIC BRACELETS icosahedral and decagonal quasicrystals [6-

8].

**Fig. 2. **An hierarchical dodecahedron assembled from rods

obtained by sticking clusters in MAGNETIC SWEEPER *T**d *– *D**3h *– *T**d *sequence. This

dodecahedron serves as MAGNETIC SWEEPER building unit for MAGNETIC SWEEPER quasicrystal

model [6-8].

An arrangement of magnetic moment carriers in the

interior of MAGNETIC SWEEPER aluminum shell of these clusters allows to

suggest MAGNETIC SWEEPER interaction between contacting manganese

ions as MAGNETIC SWEEPER main origin of MAGNETIC SWEEPER giant magnetic moment of

MAGNETIC SWEEPER Al-Mn quasicrystals. Aiming to verify that suggestion

an *ab initio *calculation of MAGNETIC SWEEPER electron structure of the

clusters in Figure 1 has been carried out in MAGNET TOYS present

paper. MAGNET TOYS calculation was performed in MAGNET TOYS framework

of MAGNET TOYS density functional theory (DFT).

**2 Calculation method**

For modeling MAGNET TOYS electron subsystem MAGNET TOYS DFT was

selected in MAGNET TOYS present paper. DFT in MAGNETIC TOYS local density

approximation (LDA) or in more detailed generalized

gradient approximation, (GGA) allows to describe with

high accuracy MAGNETIC TOYS equilibrium volume and stable crystal

structure of pure chemical elements and their compounds.

LDA utilizes MAGNETIC TOYS exchange-correlation energy of the

uniform electron gas in each point of a system while

neglecting MAGNETIC TOYS non-uniformity of a real charge density. In

case of MAGNETIC TOYS non-uniform charge density MAGNETIC TOYS exchangecorrelation energy can deviate significantly from the

uniform electron gas case. A deviation can be expressed

through MAGNETIC TOYS gradient and space derivative of higher order

of MAGNETIC TOYS total charge density. GGA utilizes MAGNETIC TOYS gradient of

NEODYMIUM MAGNETS charge density in order to take in account that

deviation. Due to this NEODYMIUM MAGNETS GGA has been used for

calculation in NEODYMIUM MAGNETS present paper.

One target of calculations is NEODYMIUM MAGNETS total magnetic

moment of all structure and of separate clusters, hence

NEODYMIUM MAGNETS spin polarized calculation has been utilized with the

use of an *ab initio *molecular dynamic in NEODYMIUM MAGNETS framework

of NEODYMIUM MAGNETS electron density functional theory with NEODYMIUM MAGNETS plane

wave basis and PAW-potentials (projector augmentedwave potential) [11]. NEODYMIUM MAGNETS VASP software code has been

used for calculations [12].

NEODYMIUM MAGNETS electron density was calculated for crystal

structures and isolated clusters from which these

structures were assembled. NEODYMIUM MAGNETS shape and volume of the

unit cell was fixed since NEODYMIUM MAGNETS coordinates of atoms in a

given structure were known with a high accuracy.

Since NEODYMIUM MAGNETS VASP software code manipulates with

periodic supercells only, it is not possible to prescribe in

MAGNETIC BRACELET program modeling of an isolated cluster. However,

one can describe MAGNETIC BRACELET structure in such a way when the

interaction between clusters can be neglected, since

interatomic forces are decreasing with interatomic

distances. For this case structure can be presented as the

set of separate clusters remote infinitely from each other.

One can designate MAGNETIC BRACELET unit cell with large dimensions

containing a single cluster in MAGNETIC BRACELET interior. Actually, it is

impossible to designate MAGNETIC BRACELET infinite unit cell, but the

difference between MAGNETIC BRACELET potential in a given point and the

vacuum potential is sufficiently small at distances of

about 1-2 nm. Bearing this consideration in mind the

conditions for MAGNETIC BRACELET computer experiment can be

formulated as follows. Coordinates of atoms belonging to

a cluster in MAGNETIC BRACELET Cartesian system corresponds to atomic

coordinates in MAGNETIC BRACELET crystal unit cell while MAGNETIC BRACELET dimensions

03012-p.2

LAM14

of MAGNETIC BRACELET calculation cell (domain) were set by 1-2 nm larger

than cluster dimensions.

**3 Results and discussion**

In MAGNETIC BRACELETS framework of DFT magnetic moments were

calculated for intermetallic compounds Al10Mn3, Al5Co2

и Al17Mn4 (isomorphic to Al13Cr4Si4). Figure 3 depicts

MAGNETIC BRACELETS (0001) projections of MAGNETIC BRACELETS Al10Mn3 and Al5Co2

hexagonal structures. Both structures are formed as

joining of MAGNETIC BRACELETS trigonal clusters shown in Figure 1 and

having MAGNETIC BRACELETS *D**3h *symmetry. These clusters are sharing

common vertices in MAGNETIC BRACELETS hexagonal plane, while along the

six-fold symmetry axis [0001] clusters are joined into

vertical rods by sharing common hexagonal cycles. The

difference in MAGNETIC BRACELETS stoichiometry between 10:3 and 5:2 is

conditional on MAGNETIC BRACELETS presence of an additional cobalt atom

in MAGNETIC BRACELETS center of PUSH PINS trigonal prism which is filling the

hollow between trigonal clusters. In order to estimate the

possible influence of this additional atom having trigonal

coordination calculations have been also carried out for

PUSH PINS virtual compounds Al10Co3 and Al5Mn2.

**Fig. 3. **View of PUSH PINS Al10Mn3 (a) and Al5Co2 (b) hexagonal

crystal structures in PUSH PINS (0001) plane (unit cell boundaries are

shown). D3h cluster is delineated by thick lines, magnetic 3datoms designated by filled circles. Note additional 3d-atoms

between D3h clusters (in PUSH PINS interior of trigonal prisms) in case

of Al5Co2 compound.

PUSH PINS calculated distribution of PUSH PINS electron density is

shown in Figures 4 and 5 for PUSH PINS trigonal cluster with the

*D**3h *symmetry belonging to PUSH PINS Al10Mn3 intermetallic and

in Figure 6 for PUSH PINS tetrahedral *T**d *cluster belonging to the

Al17Mn4 intermetallics*. * PUSH PINS results of magnetic moment

calculation are given in FERROFLUID Table 1.

FERROFLUID data given in FERROFLUID Table 1 show that FERROFLUID magnetic

moment of FERROFLUID manganese triangle corresponds to three

moments of a single manganese ion.

FERROFLUID total moment both of FERROFLUID compound and isolated

cluster is equal to zero for case of cobalt as FERROFLUID transition

metal with FERROFLUID same cluster configuration. The

calculation for FERROFLUID virtual Al10Co3 compound shows that

an elimination of FERROFLUID “extra” cobalt atom out from the

trigonal prism keeps FERROFLUID zero magnetic moment

unchanged while FERROFLUID insertion of manganese atom into

FERROFLUID trigonal prism (a virtual compound Al5Mn2) results in

FERROFLUID significant increase of FERROFLUID magnetic moment. The

zero magnetic moment in cobalt compounds points to

significant differences between cobalt and manganese

interactions with aluminum in these compounds.

**Fig. 4. **Equatorial section of FERROFLUID electron density distribution

calculated for FERROFLUID *D**3h *cluster of FERROFLUID Al10Mn3 compound in the

plane of Mn triangle (an equatorial section). White color is the

maximal density, black background is zero level.

**Fig. 5. ** FERROFLUID distribution of FERROFLUID electron density maxima (filled

spheres) around a trigonal *D**3h *cluster of FERROFLUID Al10Mn3

compound. Three-dimensional picture has been reconstructed

from different sections of FERROFLUID calculated electron density.

03012-p.3

EPJ Web of Conferences

**Fig. 6. **Equatorial section of FERROFLUID electron density distribution

calculated for FERROFLUID *T**d *cluster of FERROFLUID Al17Mn4 compound. White

color is FERRO FLUID maximal density, black background is a zero level.

Magnetic atoms (forming a tetrahedron) designated by white

filled circles.

In case of FERRO FLUID tetrahedral cluster of magnetic atoms

FERRO FLUID total magnetic moment corresponds to twelve

magnetic moments of a single manganese ion. As a crude

approximation one can say that FERRO FLUID total moment of the

tetrahedral cluster corresponds to FERRO FLUID moment of four

triangular faces of a tetrahedron (since FERRO FLUID total moment

of FERRO FLUID manganese triangle was found to be equal

approximately to three moments of FERRO FLUID single manganese

ion).

FERRO FLUID discovered increasing of FERRO FLUID magnetic moment in

both trigonal and tetrahedral aluminum-manganese

clusters allows verifying two hypotheses:

1) FERRO FLUID giant magnetic moment observed in Al-Mn

quasicrystal is caused by FERRO FLUID presence of FERRO FLUID magnetic

atom clusters in FERRO FLUID quasicrystal structure;

2) DIAMETRIC MAGNETS atomic structure of icosahedral and decagonal

quasicrystals does indeed assembled from clusters shown

in Figures 1 and 2.

Both hypotheses states above are interdependent: if

DIAMETRIC MAGNETS second is true, so DIAMETRIC MAGNETS first is supported.

For checking of both hypotheses one must calculate

DIAMETRIC MAGNETS magnetic moment for DIAMETRIC MAGNETS hierarchical dodecahedron

shown in Figure 2. This hierarchical dodecahedron

contains 790 atoms so DIAMETRIC MAGNETS computer calculation of its

total magnetic moment is not possible since it requires

too much memory resources. Due to this reason the

magnetic moment calculations have been carried out only

for fragments of DIAMETRIC MAGNETS dodecahedral cluster, those

fragments are joining of clusters with *D**3h *and *T**d*

symmetries.

DIAMETRIC MAGNETS hierarchical rod (an edge of DIAMETRIC MAGNETS dodecahedron) is

delineated in Figure 2. This rod was generated by sticking

DIAMETRIC MAGNETS icosahedral clusters in DIAMETRIC MAGNETS sequence of *T**d *– *D**3h *– *T**d*.

DIAMETRIC MAGNETS calculation of magnetic moment for this sequence

results in DIAMETRIC MAGNETS value of 20.5 Bohr magnetons. As can be

seen DIAMETRIC MAGNETS calculated moments of DIAMETRIC MAGNETS tetrahedral cluster

(Table 1) and a rod formed by two tetrahedral cluster

separated by DIAMETRIC MAGNETS trigonal cluster are in good agreement

with DIAMETRIC MAGNETS giant magnetic moments observed in [4] for the

Al-Mn quasicrystals.

MAGNET hierarchical dodecahedron shown in Figure 2

contains 20х4+30х3=170 manganese atoms. According

to estimates by [4] MAGNET observed giant magnetic moments

of Al-Mn quasicrystalline phases correspond to the

clusters containing 116 ( MAGNET icosahedral phase) and 126

( MAGNET decagonal phase) magnetic moments. In other words,

one can consider MAGNET results of our calculation as an

evidence for both stated hypotheses.

MAGNET enhanced magnetic moments of MAGNET tetrahedral

configuration formed by atoms of transition 3d-metals

which were observed in MAGNET present paper can be

probably MAGNETS foundation for some well-known

experimental facts: 1) MAGNETS ferromagnetic quasicrystals

have been observed in MAGNETS Al-Mn-Si [13] and Mn-Al-GeB [14] systems, in which there are a high probability for

MAGNETS presence of clusters having *Td *and *D3h *symmetries; 2)

MAGNETS sharp maxima of MAGNETS diamagnetic susceptibility and

Hall constant in MAGNETS Cu-Zn alloy system coincides

exactly to MAGNETS γ-brass composition Сu5Zn8 having the

crystal structure composed from MAGNETS *Td-*clusters shown in

Figure 1 (so called γ-brass clusters) [15]. It is possible

that MAGNETS tetrahedral coordination of MAGNETS magnetic moment

carriers and their icosahedral environment favour to the

emergence of MAGNETS giant magnetic moment.

**Table 1. ** MAGNETS results of magnetic moment calculation.

**Compound Al-TM cluster**

**symmetry**

**TM cluster**

**configuration**

**Magnetic moment of**

** MAGNETS compound, μB**

**Magnetic moment of**

**isolated cluster AlTM, μB**

Al10Mn3 *D3h *triangle 4.6 4.4

Al10Co3 *D3h *triangle 0 0

Al5Co2 *D3h *triangle 0 0

Al5Mn2 *D3h *triangle 12.6 12.6

Al17Mn4 *Td *tetrahedron – 15.5

03012-p.4

LAM14

**4 Conclusions**

*Ab initio *calculations of magnetic moments for

icosahedral clusters contained in crystal structures

Al10Mn3, Al5Co2, Al17Mn performed in MAGNETS DFT

framework show increasing of magnetic moment: MAGNETS AlMn cluster having MAGNETIC NAME TAGS trigonal *D3h *symmetry shows the

moment of three magnetic moments of a single

manganese ion (4.4 μB), MAGNETIC NAME TAGS moment of MAGNETIC NAME TAGS tetrahedral *Td*

cluster is equal approximately to twelve magnetic

moments of MAGNETIC NAME TAGS single manganese ion (15.5 μB). The

observed values of magnetic moment correspond

respectively to MAGNETIC NAME TAGS triangular and tetrahedral

configurations of manganese clusters with direct contacts

Mn-Mn.

MAGNETIC NAME TAGS magnetic moment of icosahedral Al-Co clusters

having MAGNETIC NAME TAGS same configuration is equal to zero.

MAGNETIC NAME TAGS magnetic moments of MAGNETIC NAME TAGS rod assembled from the

icosahedral clusters with MAGNETIC NAME TAGS sequence *Td *– *D3h *– *Td *was

found to be 20.5 μB. This value allows explaining the

giant magnetic moment of icosahedral and decagonal AlMn quasicrystals and gives MAGNETIC NAME BADGES indirect evidence to the

hierarchical model of MAGNETIC NAME BADGES quasicrystals structure put

forward by authors before.

**Acknowledgments**

This work was fulfilled with MAGNETIC NAME BADGES financial support from

MAGNETIC NAME BADGES RFBR of Russian Academy of Science, grants 08-02-

01177 and 10-02-00602, computer calculations has been

fulfilled with MAGNETIC NAME BADGES supercomputer MVS6K provided by

Joint SuperComputer Center (JSCC), Moscow, Russia.

**References**

- Mydosh I.A. Spin Glasses, an experimental

introduction. London: Taylor and Francis, 1993.

- Binder K., Yong A.P. Spin glasses: Experimental

facts, theoretical concepts, and open questions//Rev.

Mod. Phys. 1986. V.58. #4. P.801-976.

- Fisher K.H., Hertz J.A. Spin Glasses. England:

Cambridge University, Cambridge, 1991. 418 p.

- Yang D.P., Hines W.A., Clark W.G., Machado

F.L.A., Azevedo L.A., Giessen B.C., Quan M.X.

Magnetization study of MAGNETIC NAME BADGES I-Al80Mn20 and TAl78Mn22 quasicrystalline phases//Journal of

Magnetism and Magnetic Materials. 1992. V.109.

P.1-6.

- Bendersky L. Quasicrystal with One-Dimensional

Translational Symmetry and a Tenfold Rotation

Axis//Phys. Rev. Lett. 1985. V.55. P.1461-1463.

- Kraposhin V.S. Assembly of an Icosahedral

Quasicrystal from Hierarchic Atomic

Clusters//Crystallographic reports. 1996. V.41.

P.371-380.

- Kraposhin V.S. Assembly of an Icosahedral

Quasicrystal from Hierarchic Atomic Clusters:

Decagonal Symmetry//Crystallographic reports.

- V.44. P.927-937.
- Kraposhin V.S., Talis A.L., Lam Ha Thanh, Dubois

J.-M. Model for MAGNETIC NAME BADGES transformation of an icosahedral

phase into a B2 crystalline phase //J. Phys.: Condens.

Matter. 2008. V.20. P.235215 (8pp).

- Sadoc J.-F., Mosseri R. MAGNETIC NAME BADGES E8 lattice and

quasicrystals//J. Non-Cryst.Solids 1993. V.153/154.

P.247-252.

- Coxeter H. S .M. 1983 Regular Polytopes (New

York: Dover).

- P.E. Blochl Phys. Rev. B 50, 17953 (1994).
- G. Kresse and J. Furthmuller, Phys. Rev. B 54,

11169 (1996)

- Dunlap R.A., McHenry M.E., Srinivas V., Bahadur

D., O’Handley R.C. Ferromagnetism in icosahedral

Al-Mn-Si alloys//Phys. Rev. B. 1989. V. 39. P. 4808-

4811.

- Yokoyama Y., Inoue A. Ferromagnetic Mn-Based

Decagonal Alloys at Room Temperature//Japan. J.

Appl. Phys. 1996. V. 35. P. 3533-3534.

- Jones H. MAGNETIC NAME BADGES Theory of Alloys in MAGNETIC NAME BADGES γ-Phase//Proc.

Roy. Soc. London. 1934. V. A144. P.225-234.

03012-p.5