Ferromagnetic thin films of binary alloys

Sukiennicki, A.; Wojtczak, L.; Zasada, I.; Alvarado, F.L. Castillo

doi:10.1016/j.jmmm.2004.09.001

Cited by 8 publications

(8 citation statements)

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“…(vi) if we order the set of numbers (9) to make sequence (11), then we realize that b n with odd n correspond to (7), and (b n ) with even n correspond to (6).…”

Section: From Alloys To Fractals Related To Clifford Structuresmentioning

confidence: 99%

“…The inoculated graded fractal Ξ of the branch type can be decomposed into the bundle of inoculated fractals Ξ 1 and Ξ 2 without gradation, where Ξ 2 is repeated infinitely many times. Here, Ξ 1 corresponds to (6) and Ξ 2 corresponds to (7). Precisely, the embranchments of Ξ 1 are renumbered according to the scheme n → n + 1.…”

Section: From Alloys To Fractals Related To Clifford Structuresmentioning

confidence: 99%

“…Here, resp., g represent members of (6) [resp., (7)]. Only the latter two structures correspond to inoculation at the embranchment.…”

Section: Atomization Theorem For Fractals and Hurwitz Twistor-like Stmentioning

confidence: 99%

“…In this context, Sukiennicki, Wojtczak, Zasada, and Castillo Alvarado [7] investigated an infinite thin film of an AB 3 alloy. As examples we may take Ni 3 Fe or Cu 3 Au.…”

Section: Introductory: Dynamics Of Binary and Ternary Alloysmentioning

confidence: 99%

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Basic properties and applications of graded fractal bundles related to Clifford structures: An introduction

2008

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The idea of fractal modeling of crystals dates back to Bethe [1], who observed its convenience when coming to first, second, and third nearest neighbors of an atom. Taking into account that it is a neighbor of two or more other atoms, even in the case of one layer with a lattice formed by squares, one naturally comes to the notion of cluster [2,3]. It is then natural to cut the plane of the lattice correspondingly to the cluster involved and construct a Riemann surface or a Bethe lattice-a fractal set of the branch type [4,5]. The construction is parallel to that related to the holomorphic function f (z) = exp z 2 in C (Fig. 1). The example already shows the importance of the corresponding group Γ of cover symmetry transformations (Decktransformationengruppe), inoculation (of the branch corresponding to no. 1 on the branch corresponding to no. 4), and gradation related to the points , •, , and •.The next important step was done by Kikuchi [6], who-within his theory of cooperative phenomenadeveloped a method of approximation for order-disorder phenomena.In this context, Sukiennicki, Wojtczak, Zasada, and Castillo Alvarado [7] investigated an infinite thin film of an AB 3 alloy. As examples we may take Ni 3 Fe or Cu 3 Au. They assumed the (111) orientation of the alloy. Let z(j) denote the concentration of A-atoms in the layer j = 0, 1, . . . , where j = 0 corresponds to the surface. Then the concentration of B-atoms in that layer is 1 − z(j). If U is the energy of interaction of the system, T is the absolute temperature, and g is the number of possible configurations, then the entropy S and the free energy F of the system are given byrespectively, where k is the Boltzmann constant, and the conditions for thermodynamic equilibrium at a given temperature T are ∂ ∂τ F τ =τ (j) = 0, ∂ ∂z F z=z(j) = 0 for each j, λ = const. Thus, 1 T ∂ ∂τ U τ =τ (j) = ∂ ∂z S τ =τ (j).

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“…(vi) if we order the set of numbers (9) to make sequence (11), then we realize that b n with odd n correspond to (7), and (b n ) with even n correspond to (6).…”

Section: From Alloys To Fractals Related To Clifford Structuresmentioning

confidence: 99%

Section: From Alloys To Fractals Related To Clifford Structuresmentioning

confidence: 99%

“…Here, resp., g represent members of (6) [resp., (7)]. Only the latter two structures correspond to inoculation at the embranchment.…”

Section: Atomization Theorem For Fractals and Hurwitz Twistor-like Stmentioning

confidence: 99%

“…In this context, Sukiennicki, Wojtczak, Zasada, and Castillo Alvarado [7] investigated an infinite thin film of an AB 3 alloy. As examples we may take Ni 3 Fe or Cu 3 Au.…”

Section: Introductory: Dynamics Of Binary and Ternary Alloysmentioning

confidence: 99%

See 2 more Smart Citations

Basic properties and applications of graded fractal bundles related to Clifford structures: An introduction

2008

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“…The present approach searches for energetically the most favorable equilibrium structure of the surface region described in terms of random-alloy within the Valenta model of the inhomogeneous systems [17][18][19][20][21]. The free energy has contributions: from internal energy defined by the components concentrations and interaction potential of Sutton-Chen (SC) character [22,23] and from the entropy in the standard form.…”

Section: Introductionmentioning

confidence: 99%