A. An investigation of the relation between the tensile strength and (Brinell) hardness of non-ferrous alloys. B. A design of a fatigue testing machine for a college laboratory

[no abstract]

Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

Quantum Mechanics Studies of Fuel Cell Catalysts and Proton Conducting Ceramics with Validation by Experiment

We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt₃M alloys, where M is a transition metal. We found that only Pt₃Os and Pt₃Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt₃Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O₂ to form H₂O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the O_ad hydration reaction (O_ad + H₂O_ad -> OH_ad + OH_ad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt₃Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt_2ML/Os core-shell) and H₂O formation steps (0.32 eV for Pt, 0.22 eV for Pt_2ML/Os core-shell). We found that Pt_2ML/Os has the highest activity (compared to pure Pt and to the Pt₃Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt_2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO₄ solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni₄Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni₄Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni₄X (X=Fe, Co, Mn, and Mo), showed Ni₄Fe, Ni₄Co, and Fe₄Mn all have better coking resistance than pure Ni, but that only Ni₄Fe and Fe₄Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba₈X₇M₁(OH)₁O₂₃ where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4⁺ X is replace by a 3⁺ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the O_donor-O_acceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.

A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

Nuclear hyperfine interactions in W^(182), W^(183), and Pt^(195) as studies by the Mossbauer effect

The Mössbauer technique has been used to study the nuclear hyperfine interactions and lifetimes in W¹⁸² (2⁺ state) and W¹⁸³ (3/2^- and 5/2^- states) with the following results: g(5/2^-)/g(2⁺) = 1.40 ± 0.04; g(3/2^- = -0.07 ± 0.07; Q(5/2^-)/Q(2⁺) = 0.94 ± 0.04; T_1/2(3/2^-) = 0.184 ± 0.005 nsec; T_1/2(5/2^-) >̰ 0.7 nsec. These quantities are discussed in terms of a rotation-particle interaction in W¹⁸³ due to Coriolis coupling. From the measured quantities and additional information on γ-ray transition intensities magnetic single-particle matrix elements are derived. It is inferred from these that the two effective g-factors, resulting from the Nilsson-model calculation of the single-particle matrix elements for the spin operators ŝ_z and ŝ₊, are not equal, consistent with a proposal of Bochnacki and Ogaza.

The internal magnetic fields at the tungsten nucleus were determined for substitutional solid solutions of tungsten in iron, cobalt, and nickel. With g(2⁺) = 0.24 the results are: |H_eff(W-Fe)| = 715 ± 10 kG; |H_eff(W-Co)| = 360 ± 10 kG; |H_eff(W-Ni)| = 90 ± 25 kG. The electric field gradients at the tungsten nucleus were determined for WS₂ and WO₃. With Q(2⁺) = -1.81b the results are: for WS₂, eq = -(1.86 ± 0.05) 10¹⁸ V/cm²; for WO₃, eq = (1.54 ± 0.04) 10¹⁸ V/cm² and ƞ = 0.63 ± 0.02.

The 5/2^- state of Pt¹⁹⁵ has also been studied with the Mössbauer technique, and the g-factor of this state has been determined to be -0.41 ± 0.03. The following magnetic fields at the Pt nucleus were found: in an Fe lattice, 1.19 ± 0.04 MG; in a Co lattice, 0.86 ± 0.03 MG; and in a Ni lattice, 0.36 ± 0.04 MG. Isomeric shifts have been detected in a number of compounds and alloys and have been interpreted to imply that the mean square radius of the Pt¹⁹⁵ nucleus in the first-excited state is smaller than in the ground state.

Heteroepitaxy of Group IV and Group III-V semiconductor alloys for photovoltaic applications

Photovoltaic energy conversion represents a economically viable technology for realizing collection of the largest energy resource known to the Earth -- the sun. Energy conversion efficiency is the most leveraging factor in the price of energy derived from this process. This thesis focuses on two routes for high efficiency, low cost devices: first, to use Group IV semiconductor alloy wire array bottom cells and epitaxially grown Group III-V compound semiconductor alloy top cells in a tandem configuration, and second, GaP growth on planar Si for heterojunction and tandem cell applications.

Metal catalyzed vapor-liquid-solid grown microwire arrays are an intriguing alternative for wafer-free Si and SiGe materials which can be removed as flexible membranes. Selected area Cu-catalyzed vapor-liquid solid growth of SiGe microwires is achieved using chlorosilane and chlorogermane precursors. The composition can be tuned up to 12% Ge with a simultaneous decrease in the growth rate from 7 to 1 μm/min^-1. Significant changes to the morphology were observed, including tapering and faceting on the sidewalls and along the lengths of the wires. Characterization of axial and radial cross sections with transmission electron microscopy revealed no evidence of defects at facet corners and edges, and the tapering is shown to be due to in-situ removal of catalyst material during growth. X-ray diffraction and transmission electron microscopy reveal a Ge-rich crystal at the tip of the wires, strongly suggesting that the Ge incorporation is limited by the crystallization rate.

Tandem Ga_1-xIn_xP/Si microwire array solar cells are a route towards a high efficiency, low cost, flexible, wafer-free solar technology. Realizing tandem Group III-V compound semiconductor/Si wire array devices requires optimization of materials growth and device performance. GaP and Ga_1-xIn_xP layers were grown heteroepitaxially with metalorganic chemical vapor deposition on Si microwire array substrates. The layer morphology and crystalline quality have been studied with scanning electron microscopy and transmission electron microscopy, and they provide a baseline for the growth and characterization of a full device stack. Ultimately, the complexity of the substrates and the prevalence of defects resulted in material without detectable photoluminescence, unsuitable for optoelectronic applications.

Coupled full-field optical and device physics simulations of a Ga_0.51In_0.49P/Si wire array tandem are used to predict device performance. A 500 nm thick, highly doped "buffer" layer between the bottom cell and tunnel junction is assumed to harbor a high density of lattice mismatch and heteroepitaxial defects. Under simulated AM1.5G illumination, the device structure explored in this work has a simulated efficiency of 23.84% with realistic top cell SRH lifetimes and surface recombination velocities. The relative insensitivity to surface recombination is likely due to optical generation further away from the free surfaces and interfaces of the device structure.

Finally, GaP has been grown free of antiphase domains on Si (112) oriented substrates using metalorganic chemical vapor deposition. Low temperature pulsed nucleation is followed by high temperature continuous growth, yielding smooth, specular thin films. Atomic force microscopy topography mapping showed very smooth surfaces (4-6 Å RMS roughness) with small depressions in the surface. Thin films (~ 50 nm) were pseudomorphic, as confirmed by high resolution x-ray diffraction reciprocal space mapping, and 200 nm thick films showed full relaxation. Transmission electron microscopy showed no evidence of antiphase domain formation, but there is a population of microtwin and stacking fault defects.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Part I: Total yield measurements for the ^(21)Ne(α,n)^)(24)Mg reaction. Part II: A study of the ^(12)C(He,p)^(14)N reaction

PART I

The total cross-section for the reaction ²¹Ne(α, n)²⁴Mg has been measured in the energy range 1.49 Mev ≤ E_cm ≤ 2.6 Mev. The cross-section factor, S(O), for this reaction has been determined, by means of an optical model calculation, to be in the range 1.52 x 10¹² mb-Mev to 2.67 x 10¹² mb-Mev, for interaction radii in the range 5.0 fm to 6.6 fm. With S(O) ≈ 2 x 10¹² mb-Mev, the reaction ²¹Ne(α, n)²⁴Mg can produce a large enough neutron flux to be a significant astrophysical source of neutrons.

PART II

The reaction¹²C(³He, p)¹⁴N has been studied over the energy range 12 Mev ≤ E_lab ≤ 18 Mev. Angular distributions of the proton groups leading to the lowest seven levels in ¹⁴N were obtained.

Distorted wave calculations, based on two-nucleon transfer theory, were performed, and were found to be reliable for obtaining the value of the orbital angular momentum transferred. The present work shows that such calculations do not yield unambiguous values for the spectroscopic factors.