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The Classical Stefan Problem : Basic Concepts, Modelling and Analysis. (2003)

Gupta, S. C.

San Diego :JAI Press Limited,

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Schlagwort(e): Solid state physics. ; Electronic books.

Materialart: Online-Ressource

Seiten: 1 online resource (404 pages)

Ausgabe: 1st ed.

ISBN: 9780080529165

Serie: Issn Series ; v.Volume 45

URL: https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=313781

DDC: 536/.2

Sprache: Englisch

Anmerkung: Cover -- Contents -- Chapter 1. The Stefan Problem and its Classical Formulation -- 1.1 Some Stefan and Stefan-like Problems -- 1.2 Free Boundary Problems with Free Boundaries of Codimension-two -- 1.3 The Classical Stefan Problem in One-dimension and the Neumann Solution -- 1.4 Classical Formulation of Multi-dimensional Stefan Problems -- Chapter 2. Thermodynamical and Metallurgical Aspects of Stefan Problems -- 2.1 Thermodynamical Aspects -- 2.2 Some Metallurgical Aspects of Stefan Problems -- 2.3 Morphological Instability of the Solid--Liquid Interface -- 2.4 Non-material Singular Surface: Generalized Stefan Condition -- Chapter 3. Extended Classical Formulations of n-phase Stefan Problems with n > -- 1 -- 3.1 One-phase Problems -- 3.2 Extended Classical Formulations of Two-phase Stefan Problems -- 3.3 Stefan problems with Implicit Free Boundary Conditions -- Chapter 4. Stefan Problem with Supercooling: Classical Formulation and Analysis -- 4.1 Introduction -- 4.2 A Phase-field Model for Solidification using Landau Ginzburg Free Energy Functional -- 4.3 Some Thermodynamically Consistent Phase-field and Phase Relaxation Models of Solidification -- 4.4 Solidification of Supercooled Liquid Without Curvature Effect and Kinetic Undercooling: Analysis of the Solution -- 4.5 Analysis of Supercooled Stefan Problems with the Modified Gibbs Thomson Relation -- Chapter 5. Superheating due to Volumetric Heat Sources: The Formulation and Analysis -- 5.1 The Classical Enthalpy Formulation of a One-dimensional Problem -- 5.2 The Weak Solution -- 5.3 Blow-up and Regularization -- Chapter 6. Steady-State and Degenerate Classical Stefan Problems -- 6.1 Some Steady-state Stefan Problems -- 6.2 Degenerate Stefan Problems -- Chapter 7. Elliptic and Parabolic Variational Inequalities -- 7.1 Introduction -- 7.2 The Elliptic Variational Inequality. , 7.3 The Parabolic Variational Inequality -- 7.4 Some Variational Inequality Formulations of Classical Stefan Problems -- Chapter 8. The Hyperbolic Stefan Problem -- 8.1 Introduction -- 8.2 Model I: Hyperbolic Stefan Problem with Temperature Continuity at the Interface -- 8.3 Model II: Formulation with Temperature Discontinuity at the Interface -- 8.4 Model III: Delay in the Response of Energy to Latent and Sensible Heats -- Chapter 9. Inverse Stefan Problems -- 9.1 Introduction -- 9.2 Well-posedness of the solution -- 9.3 Regularization -- 9.4 Determination of Unknown Parameters in Inverse Stefan Problems -- 9.5 Regularization of Inverse Heat Conduction Problems by Imposing Suitable Restrictions on the solution -- 9.6 Regularization of Inverse Stefan Problems Formulated as Equations in the form of Convolution Integrals -- 9.7 Inverse Stefan Problems Formulated as Defect Minimization Problems -- Chapter 10. Analysis of the Classical Solutions of Stefan Problems -- 10.1 One-dimensional One-phase Stefan Problems -- 10.2 One-dimensional Two-phase Stefan Problems -- 10.3 Analysis of the Classical Solutions of Multi-dimensional Stefan Problems -- Chapter 11. Regularity of the Weak Solutions of Some Stefan Problems -- 11.1 Regularity of the Weak solutions of One-dimensional Stefan Problems -- 11.2 Regularity of the Weak solutions of Multi-dimensional Stefan Problems -- Appendix A. Preliminaries -- Appendix B. Some Function Spaces and Norms -- Appendix C. Fixed Point Theorems and Maximum Principles -- Appendix D. Sobolev Spaces -- Bibliography -- Captions for Figures -- Subject Index.

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Microstructural studies of diamond thin films grown by electron cyclotron resonance-assisted chemical vapor deposition (2000)

Gupta, S. ; Katiyar, R. S.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 88 (2000), S. 5695-5702

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: A detailed investigation of the correlation among intrinsic stress (σint), nonuniform stress (σnu), and phonon lifetime (1/Γ) was performed in order to obtain a coherent and comprehensive picture of the microstructure of diamond thin films grown by the electron cyclotron resonance-assisted chemical vapor deposition (ECR-CVD) technique. It was found that the diamond growth taking place by the ECR-CVD is different to that taking place by the microwave CVD and hot-filament CVD. Point and line defects, rather than sp2 C bonds, were found to be the dominant source of both nonuniform stress and reduced phonon lifetime. The surface relaxation mechanism in these films yields sp2 C at the expense of strained sp3 C, resulting in a trade off between diamond yield and crystalline quality. The diamond precursor that spontaneously forms on the unseeded substrates yielded higher quality diamond than planted diamond seeds. The grain boundary relaxation model proposed by Hoffman accounts well for the observed behavior of the intrinsic stress, thus indicating that microstructural restructuration takes place at the grain boundaries when sufficient time and thermal energy are provided. © 2000 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1318387

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Collimated deposition of hard bias magnetic films via long-throw techniques (2000)

Rook, K. ; Gupta, S. ; Feng, Y. ; [weitere]

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 87 (2000), S. 5738-5740

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: We present an optimization of long-throw sputter-deposited Cr/CoCrPt films, specifically for (lifted-off) hard bias applications in an AMR/GMR head. Deposition was carried out in the target-to-substrate (T/S) range of 7–9 in., with pressure down to 0.25 mTorr. On increasing the T/S by 1 in., a 5% reduction in coercivity was observed, and shown to be only partially explained by the deposition rate reduction. On the other hand, lower gas pressure during the CoCrPt deposition significantly increased the coercivity. Higher target power and higher substrate bias also increased the coercivity. All the observed T/S, pressure, target power, and bias dependencies suggest enhanced coercivity is associated with higher CoCrPt adatom mobility. X-ray diffraction data showed the relative intensity of the (0002) to the (1010) peak to be decreased both with higher CoCrPt deposition power or substrate bias; more in-plane c-axis texture could explain the increased coercivity. A sputter etch of the wafer before Cr deposition increased the coercivity by about 300 Oe. A combination of these techniques may be used to compensate for the deterioration in magnetic properties due to the long-throw. Optimal properties of 1790 Oe coercivity and 3.5 memu/cm2 Mrt were achieved. © 2000 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.372506

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Ex situ spectroscopic ellipsometry investigation of the layered structure of polycrystalline diamond thin films grown by electron cyclotron resonance-assisted chemical vapor deposition (2001)

Gupta, S.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 90 (2001), S. 1280-1285

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: Polycrystalline diamond thin films deposited by electron cyclotron resonance-assisted chemical vapor deposition on Si (111) were investigated using spectroscopic phase-modulated ellipsometry from the near IR to UV range (830–270 nm). Analysis of the raw ellipsometry data [ψ(λi), Δ(λi)] by applying the conventional Bruggeman effective medium theory and linear regression analysis provided details about the film microstructure: (i) the multilayer structure and the component layer thickness of the films; (ii) the volume fraction of the constituents (sp3- and sp2- bonded carbon) and of voids (fv) in the bulk layer (L2); (iii) the inhomogeneity of the structure along the growth axis and its variation with the seeding density; and (iv) the surface roughness layer thickness (dS). A simplified three-layer structural model consisting of an interfacial layer, an intermediate (or bulk) layer, and a top surface roughness layer has been proposed that simulates the ellipsometry data reasonably well. The results obtained through ellipsometry modeling, such as surface roughness and overall film thickness, were compared with those from atomic force microscopy and profilometry, respectively, in order to validate the model employed. Typically, high surface roughness values around 60 nm were found for films grown under different substrate temperatures and oxygen-to-carbon ratios. It was also found that a combination of relatively high substrate temperature and O/C ratio can be used to reduce the surface roughness to around 25 nm. In general, the void fraction (fv) of the bulk layer decreases as a function of seeding density, indicating the formation of a denser film. The sp2-bonded carbon fraction (fsp〈sup ARRANGE="STAGGER"〉2 C) also varies with the process parameters. These results (fv and fsp〈sup ARRANGE="STAGGER"〉2 C) for the bulk layer and its behavior with respect to process parameters are discussed. © 2001 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1384487

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Sputter deposition of 45% Ni-55% Fe for high moment top pole applications (2000)

Rook, K. ; Gupta, S. ; Hieronymi, R.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 87 (2000), S. 5843-5845

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: We present the properties of dc magnetron sputter-deposited 45% Ni-55% Fe. Optimal magnetic properties obtained in 1.4 μm films were: 4πMs∼16.4 kG, Hce∼3.7 Oe, Hch∼0.8 Oe, Hk∼9.6 Oe, at a deposition rate of 29 Å/s. A linear designed experiment revealed that: higher gas pressure significantly lowers both Hce and Hk; higher (rf) substrate bias increases α90 and Hch, while decreasing Hk; and higher substrate magnetic field worsens Hch and α90. Augmentation of the experimental matrix and analysis of higher order terms implied that a combination of intermediate pressure and small bias provides optimal magnetic properties. From x-ray diffraction, the 45–55 NiFe is fcc, with lattice parameter 3.578–3.584 Å, in fair agreement with the bulk value of ∼3.585 Å. Grain sizes in the range 150–180 Å were estimated. Analysis of the (111): (200) peak intensity ratio showed that higher substrate bias or lower pressure both significantly enhance the (111) texture. Correlation was observed between the magnetics and the crystalline texture; less [111] texture gives lower coercivity. Data on 2000 Å films for seedlayer applications are also presented. © 2000 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.372541

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Study of the electron field emission and microstructure correlation in nanocrystalline carbon thin films (2001)

Gupta, S. ; Weiss, B. L.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 89 (2001), S. 5671-5675

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: Nanocrystalline carbon thin films were deposited by hot-filament chemical vapor deposition using a 2% concentration of methane in hydrogen. The films were deposited on molybdenum substrates under various substrate biasing conditions. A positive bias produced a continuous flow of electrons from the filament onto the substrate, while a negative bias caused the substrate to be bombarded with positive ions. Films were also grown under no bias, for comparison. Differences in the electron field emission properties (turn-on fields and emitted currents) of these films were characterized. Correspondingly, microstructural differences were also studied, as characterized with atomic force microscopy and Raman spectroscopy. Films grown under electron bombardment showed lower turn-on fields, smoother surfaces, and smaller grains than those grown under ion bombardment or no bias. A correlation between the enhanced emission properties and the nanocrystalline carbon material produced by the low-energy particle bombardment was found through the parameters obtained using spectroscopic ellipsometry modeling. The results confirm the significant role of defects on the electron field emission mechanism. © 2001 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1367873

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Electrical conductivity studies of chemical vapor deposited sulfur-incorporated nanocomposite carbon thin films (2002)

Gupta, S. ; Martínez, A.

Woodbury, NY : American Institute of Physics (AIP)

Applied Physics Letters 81 (2002), S. 283-285

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ISSN: 1077-3118

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The room-temperature electrical conductivity of sulfur-incorporated nanocomposite carbon (n-C:S) thin films synthesized by hot-filament chemical vapor deposition was investigated as a function of the sulfur concentration. The films were prepared using a 2% CH4/H2 gas mixture and H2S as the dopant source. The n-C:S films exhibited an increase in conductivity by four orders of magnitude (up to 160 S cm−1) with an increase in sulfur content compared with those grown without sulfur (n-C). The films grown at the highest [H2S] possess the highest carrier concentration (∼5×1019/cm3) and the lowest carrier mobility (0.005 cm2 V−1 s−1). These findings are discussed in terms of the multiple roles of sulfur atoms in the films: (i) induction of structural defects and their corresponding midgap states, (ii) enhancement of the spatial connectivity of the sp2-bonded carbon network, and (iii) electrical activity of only a small fraction of the sulfur atoms. © 2002 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1491600

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Enhanced room-temperature magnetoresistance in La0.7Sr0.3MnO3-glass composites (2001)

Gupta, S. ; Ranjit, R. ; Mitra, C. ; [weitere]

Woodbury, NY : American Institute of Physics (AIP)

Applied Physics Letters 78 (2001), S. 362-364

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ISSN: 1077-3118

Quelle: AIP Digital Archive

Thema: Physik

Notizen: In this letter, we report the improved magnetotransport properties of La0.7Sr0.3MnO3-borosilicate glass composite with different weight percents of glass. All the composites showed ferromagnetic nature at room temperature. The microstructure of these composites was seen using a scanning electron microscope. The microstructure was reconfirmed using spot energy dispersive x-ray analysis. We observe an enhancement of the low-field magnetoresistance (〈200 Oe) at room temperature for the optimal composition of 25 wt % of glass. It is argued that glass layer separating the grain boundaries may be acting as barrier for spin-polarized tunneling, thereby enhancing the low-field magnetoresistance. © 2001 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1342044

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Role of sp2 C cluster size on the field emission properties of sulfur-incorporated nanocomposite carbon thin films (2002)

Gupta, S.

Woodbury, NY : American Institute of Physics (AIP)

Applied Physics Letters 80 (2002), S. 1471-1473

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ISSN: 1077-3118

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The electron field emission properties of sulfur-incorporated nanocomposite carbon thin films grown by hot-filament chemical vapor deposition were investigated as a function of film microstructure. The in-plane correlation length (La) of the sp2 C clusters in these films was determined from the intensity ratio of the D and G bands [I(D)/I(G)] in the visible Raman spectra using a phenomenological model. The turn-on field was found to decrease with increasing sp2 C cluster size in the range of 0.8–1.4 nm. The lowest turn-on field found was 4.0 V/μm corresponding to films having sp2 C clusters of around 1.4 nm and conductivity of 30 Ω−1 cm−1. These findings are discussed in terms of a reduced field emission barrier brought about by the incorporation of sulfur and the need for relatively longer conductive paths capable of withstanding the relatively large emission currents. © 2002 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1451985

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Electron field emission from sulfur-incorporated nanocrystalline carbon thin films (2001)

Gupta, S. ; Weiss, B. L.

Woodbury, NY : American Institute of Physics (AIP)

Applied Physics Letters 79 (2001), S. 3446-3448

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ISSN: 1077-3118

Quelle: AIP Digital Archive

Thema: Physik

Notizen: Results are reported on the electron field emission properties of sulfur-incorporated nanocrystalline carbon (n-C:S) thin films grown by hot-filament chemical vapor deposition technique. The lowest turn-on field values observed were around 4.0–4.5 V/μm, which are about half of those measured for films grown without sulfur. Associated to the effect of addition of sulfur on field emission properties, there are interesting microstructural changes, as characterized with scanning electron microscopy, atomic force microscopy, and Raman spectroscopy techniques. The sulfur-incorporated films show smoother and finer-grained surfaces than those grown without sulfur. These results are similar to those found for the introduction of nitrogen, but different to those produced by oxygen addition to the chemical vapor deposition process. These findings are attributed to changes in the electronic band structure. © 2001 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.1411988

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