magnets for sale

neodymium magnets

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 D3h 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 Td 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 Td D3h Td 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 D3h (a) and Td.

(b) symmetries. Grey filled circles designate positions of 3dmetals. D3h clusters is a fragment of   MAGNET WIRE  hexagonal Al10Mn3 or

Al5Co2 structure, Td-cluster is a fragment of   MAGNET WIRE  cubic

Al13Cr4Si4 (Al17Mn4) structure.

It must be noted three features of clusters shown in

Figure 1:

  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


  1. 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   D3h 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    Td-symmetry) shown in

Figure 1b coincides with MAGNETIC BRACELETS    projection started from a

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

  1. 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


Joining of trigonal and tetrahedral clusters in  MAGNETIC BRACELETS    TdD3h-Td-D3h sequence generates a hierarchical

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

model for  MAGNETIC BRACELETS    icosahedral and decagonal quasicrystals [6-


Fig. 2. An hierarchical dodecahedron assembled from rods

obtained by sticking clusters in  MAGNETIC SWEEPER  Td D3h Td 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



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  D3h 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

D3h symmetry belonging to    PUSH PINS   Al10Mn3 intermetallic and

in Figure 6 for    PUSH PINS   tetrahedral Td 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 D3h 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 D3h cluster of   FERROFLUID Al10Mn3

compound. Three-dimensional picture has been reconstructed

from different sections of   FERROFLUID calculated electron density.


EPJ Web of Conferences

Fig. 6. Equatorial section of   FERROFLUID electron density distribution

calculated for   FERROFLUID Td 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


 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 D3h and Td


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 Td D3h Td.

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


TM cluster


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



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


 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.


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.


  1. Mydosh I.A. Spin Glasses, an experimental

introduction. London: Taylor and Francis, 1993.

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

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

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

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

Cambridge University, Cambridge, 1991. 418 p.

  1. 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.


  1. Bendersky L. Quasicrystal with One-Dimensional

Translational Symmetry and a Tenfold Rotation

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

  1. Kraposhin V.S. Assembly of an Icosahedral

Quasicrystal from Hierarchic Atomic

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


  1. Kraposhin V.S. Assembly of an Icosahedral

Quasicrystal from Hierarchic Atomic Clusters:

Decagonal Symmetry//Crystallographic reports.

  1. V.44. P.927-937.
  2. 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).

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

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


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

York: Dover).

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

11169 (1996)

  1. 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-


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

Decagonal Alloys at Room Temperature//Japan. J.

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

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

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