bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element. Other examples are partially ordered sets, where (INT) is satisfied because of reflexivity. We will shortly identify posets as being exactly the bases of compact elements of algebraic domains. In what follows we will use the terminology developed at the beginning of this chapter, even though the relation ≺ on an abstract basis need neither be reflexive nor antisymmetric. This is convenient but in some instances looks more innocent than it is. An idealA in a basis, for example, has the property (following from directedness) that for everyx ∈ A there is another element y ∈ A with x ≺ y. In posets this doesn’t mean anything but here it becomes an important feature. Sometimes this is stressed by using the expression ‘ A is a round ideal’. Note that a set of the form↓x is always an ideal because of (INT) but that it need not contain x itself. We will refrain from calling ↓x ‘principal’ in these circumstances. Definition 2.2.21. For a basis〈B,≺〉 let Idl(B) be the set of all ideals ordered by inclusion. It is called theideal completionof B. Furthermore, leti : B → Idl(B) denote the function which maps x ∈ B to ↓x. If we want to stress the relation with whichB is equipped then we write Idl(B,≺) for the ideal completion. Proposition 2.2.22.Let 〈B,≺〉 be an abstract basis.

Domain theory

Physical vapor deposition under conditions of obliquely incident flux and limited adatom diffusion results in a film with a columnar microstructure. These columns will be oriented toward the vapor source and substrate rotation can be used to sculpt the columns into various morphologies. This is the basis for glancing angle deposition (GLAD), a technique for fabricating porous thin films with engineered structures. The origin of the columnar structure characteristic of GLAD films is discussed in terms of nucleation processes and structure zone models. As deposition continues, the columnar structures are influenced by atomic-scale ballistic shadowing and surface diffusion. Competitive growth is observed where the tallest columns grow at the expense of smaller features. The column shape evolves during growth, and power-law scaling behavior is observed as shown in both experimental results and theoretical simulations. Due to the porous nature of the films and the increased surface area, a variety of chemical applications and sensor device architectures are possible. Because the GLAD process provides precise nanoscale control over the film structure, characteristics such as the mechanical, magnetic, and optical properties of the deposited film may be engineered for various applications. Depositing onto prepatterned substrates forces the columns to adopt a planar ordering, an important requirement for photonic crystal applications.

Glancing angle deposition: Fabrication, properties, and applications of micro- and nanostructured thin films

Columnar microstructure in vapor-deposited thin films

Perspectives on oblique angle deposition of thin films: From fundamentals to devices

Magnetic anisotropy has been observed in evaporated Permalloy films deposited at oblique incidence of the vapor. Electron micrographs of such films reveal chains of crystallites whose long axes are oriented perpendicular to the vapor beam. A ``self‐shadowing'' model is proposed to explain chain growth, i.e., the area behind a crystallite is left vacant because it is in the crystallite's shadow. Oriented crystallite chains are thus caused by a purely geometric process; their existence has also been demonstrated for Au, Pt, W, and Mg. Oriented chains give rise to a number of macroscopic effects: magnetic anisotropy, anisotropic resistance, dichroism, and anisotropic resonance linewidth. Experiments involving the stripping of oblique‐incidence Permalloy films from their substrates indicate the presence of an anisotropic strain which, in conjunction with magnetostriction, gives another contribution to the magnetic anisotropy; this contribution explains the observed compositional dependence of the magnetic ani...

Oblique‐Incidence Anisotropy in Evaporated Permalloy Films

Domain‐wall structure in Permalloy films in the thickness range 25 to 2000 A has been studied by the Bitter technique. A new type of 180° wall has been observed: the main wall is cut at regular intervals by short, right‐angle ``cross ties'' which terminate in free, single ends. The cross‐tie period and length are dependent on film thickness, each becoming shorter with decreasing thickness. These patterns can be understood in terms of a new model for the structure of domain walls in thin films of low‐anisotropy material. In the conventional model the atomic moments within the wall rotate about an axis perpendicular to the wall. In a thin film such a configuration leads to a large energy contribution from the large demagnetization factor normal to the film. In the new model, the axis of rotation is itself thought to rotate about the axis of the wall to give a ``corkscrew'' configuration of spins and a large decrease in associated magnetostatic energy. Of several experiments which have been performed which s...

Domain‐Wall Structure in Permalloy Films

Internal isotropic strain in Permalloy films having a negative magnetoelastic constant creates a magnetoelastic easy axis normal to the film. Below a critical thickness tc such films are single domain in the film plane and have a square B‐H loop; above this thickness new configurations are established, characterized by a B‐H loop of special form and having relaxation properties. Above tc the Bitter pattern is “mottled” and continues so even in the presence of a 10 000 oe field. A domain structure is proposed in qualitative agreement with experiment; mottling is interpreted in terms of centers of microstrain.

Properties of Permalloy Films Having a Magnetoelastic Easy Axis Normal to the Film

Isotropic stress measurements in Permalloy films have been carried out as a function of thickness, rate of deposition, and substrate temperature. The measurements were made by clamping one end of a substrate consisting of a thin strip of glass or mica and observing the deflection of the free end during deposition. Results indicate that the stress is independent of thickness in the range 100–2000 A. However, depending upon the values of the other deposition parameters, one may observe either tensile, compressive, or zero stress.

D. O. Smith

Papers

Oblique‐Incidence Anisotropy in Evaporated Permalloy Films

Domain‐Wall Structure in Permalloy Films

Properties of Permalloy Films Having a Magnetoelastic Easy Axis Normal to the Film

Isotropic Stress Measurements in Permalloy Films

Erratum: Oblique‐Incidence Anisotropy in Evaporated Films