An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K.

Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress.

The relation between dislocation velocity and resolved shear stress is:

v = v_o(τ_r/τ_o)^n

where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K.

The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

Metallogenic Provinces of the Southwestern United States and Northern Mexico

Some of the metallogenic provinces of the southwestern United States and northern Mexico are defined by the geographic distribution of trace elements in the primary sulfide minerals chalcopyrite and sphalerite. The elements investigated include antimony, arsenic, bismuth, cadmium, cobalt, gallium, germanium, indium, manganese, molybdenum, nickel, silver, tellurium, thallium, and tin. Of these elements, cobalt, gallium, germanium, indium, nickel, silver, and tin exhibit the best defined geographic distribution.

The data indicate that chalcopyrite is the preferred host for tin and perhaps molybdenum; sphalerite is the preferred host for cadmium, gallium, germanium, indium, and manganese; galena is the preferred host for antimony, bismuth, silver, tellurium, and thallium; and pyrite is the preferred host for cobalt, nickel, and perhaps arsenic. With respect to the two minerals chalcopyrite and sphalerite, antimony, arsenic, molybdenum, nickel, silver, and tin prefer chalcopyrite; and bismuth, cadmium, cobalt, gallium, germanium, indium, manganese, and thallium prefer sphalerite. This distribution probably is the result of the interaction of several factors, among which are these: the various radii of the elements, the association due to chemical similarities of the major and trace elements, and the degree of ionic versus covalent and metallic character of the metal-sulfur bonds in chalcopyrite and sphalerite. The type of deposit, according to a temperature classification, appears to be of minor importance in determining the trace element content of chalcopyrite and sphalerite.

A preliminary investigation of large single crystals of sphalerite and chalcopyrite indicates that the distribution within a single crystal of some elements such as cadmium in sphalerite and indium and silver in chalcopyrite is relatively uniform, whereas the distribution of some other elements such as cobalt and manganese in sphalerite is somewhat less uniform and the distribution of tin in sphalerite is extremely erratic. The variations in trace element content probably are due largely to variations in the composition of the fluids during the growth of the crystals, but the erratic behavior of tin in sphalerite perhaps is related to the presence of numerous cavities and inclusions in the crystal studied.

Maps of the geographic distribution of trace elements in chalcopyrite and sphalerite exhibit three main belts of greater than average trace element content, which are called the Eastern, Central, and Western belts. These belts are consistent in trend and position with a beltlike distribution of copper, gold, lead, zinc, silver, and tungsten deposits and with most of the major tectonic features. However, there appear to be no definite time relationships, for as many as four metallogenic epochs, from Precambrian to late Tertiary, are represented by ore deposits within the Central belt.

The evidence suggests that the beltlike features have a deep seated origin, perhaps in the sub-crust or outer parts of the mantle, and that the deposits within each belt might be genetically related through a beltlike compositional heterogeneity in the source regions of the ores. Hence, the belts are regarded as metallogenic provinces.

Effects of magnetostriction and superlattice formation in ferromagnetic thin films

The contribution to the magnetic uniaxial perpendicular anisotropy which arises from substrate constraint through magnetostrictive effects has been measured in Ni-Fe and Ni-Co thin films evaporated on substrates at room temperature. This was accomplished by measuring the perpendicular anisotropy before and after removal of the film from the substrate. Data are given for the fcc crystal structure regions of both alloy systems, but data for Ni-Co include compositions with less than 60% Ni which have a small percentage of the hcp phase mixed with the fcc phase. The constraint contribution to the perpendicular anisotropy correlates well with the value of the bulk magnetostriction constant using the equation ∆K_˔=3/2λ_sσ. Measured values of isotropic stress for films thicker than 600 Å were 1.6 x 10¹⁰ dyn/cm². In films less than 600 Å thick the isotropic stress decreased with decreasing thickness. After removal of the films from the substrates, the measured perpendicular anisotropy deviated from the expected geometrical shape anisotropy near pure Ni in both alloys. This indicates that additional significant sources of anisotropy exist at these compositions.

The effect of substrate constraint on the crystalline anisotropy K₁ of Ni-Fe epitaxial films has been studied by use of a film removal technique, which involves the evaporation of an epitaxial layer of LiF on MgO, the epitaxial growth of the metallic film on the LiF, and the stripping of the film with water soluble tape. Films ranging in composition from 50% to 100% Ni have been studied. For compositions below 90% Ni the experimental values agree reasonably well with the first order theoretical prediction, ∆K₁=[-9/4(C₁₁-C₁₂)λ² 100+9/2C₄₄λ²111].

In order to compare the magnetic properties of epitaxial thin films more completely with the properties of bulk single crystals, Ni-Fe films ranging in composition from 60% to 90% Ni, which were evaporated epitaxially on (100) MgO substrates, have been subsequently annealed at 400°C in a vacuum of less than 10^-7 Torr to form the ordered Ni₃Fe structure near the 75% composition. This ordered structure has been confirmed by electron diffraction.

The saturation magnetization at Ni₃Fe increased about 6% with ordering which is in good agreement with previous bulk data. Measurements of the magnetocrystalline anisotropy energy K₁ for the epitaxial films show the same large changes with ordering as observed in bulk single crystal samples. In the (001) plane the magnetostriction constants ^λ100, ^λ111 are directly related to the induced anisotropy due to a uniform uniaxial strain in the [100] and [110] directions respectively. Assuming that the elastic constants of a film are the same as in bulk material and are unchanged by ordering, the changes in strain sensitivity with ordering for the epitaxial films are found to be in good agreement with values predicted from bulk data. The exchange constant A as measured by ferromagnetic resonance has been measured at the Ni₃Fe composition and found to increase 25% with ordering. This seems to indicate a significant increase in the Curie temperature which has only been inferred indirectly for bulk material.

Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly

Algorithmic DNA tiles systems are fascinating. From a theoretical perspective, they can result in simple systems that assemble themselves into beautiful, complex structures through fundamental interactions and logical rules. As an experimental technique, they provide a promising method for programmably assembling complex, precise crystals that can grow to considerable size while retaining nanoscale resolution. In the journey from theoretical abstractions to experimental demonstrations, however, lie numerous challenges and complications.

In this thesis, to examine these challenges, we consider the physical principles behind DNA tile self-assembly. We survey recent progress in experimental algorithmic self-assembly, and explain the simple physical models behind this progress. Using direct observation of individual tile attachments and detachments with an atomic force microscope, we test some of the fundamental assumptions of the widely-used kinetic Tile Assembly Model, obtaining results that fit the model to within error. We then depart from the simplest form of that model, examining the effects of DNA sticky end sequence energetics on tile system behavior. We develop theoretical models, sequence assignment algorithms, and a software package, StickyDesign, for sticky end sequence design.

As a demonstration of a specific tile system, we design a binary counting ribbon that can accurately count from a programmable starting value and stop growing after overflowing, resulting in a single system that can construct ribbons of precise and programmable length. In the process of designing the system, we explain numerous considerations that provide insight into more general tile system design, particularly with regards to tile concentrations, facet nucleation, the construction of finite assemblies, and design beyond the abstract Tile Assembly Model.

Finally, we present our crystals that count: experimental results with our binary counting system that represent a significant improvement in the accuracy of experimental algorithmic self-assembly, including crystals that count perfectly with 5 bits from 0 to 31. We show some preliminary experimental results on the construction of our capping system to stop growth after counters overflow, and offer some speculation on potential future directions of the field.

Geochemistry and resonance ionization of platinum-group elements

Experimental studies were conducted with the goals of 1) determining the origin of Pt- group element (PGE) alloys and associated mineral assemblages in refractory inclusions from meteorites and 2) developing a new ultrasensitive method for the in situ chemical and isotopic analysis of PGE. A general review of the geochemistry and cosmochemistry of the PGE is given, and specific research contributions are presented within the context of this broad framework.

An important step toward understanding the cosmochemistry of the PGE is the determination of the origin of POE-rich metallic phases (most commonly εRu-Fe) that are found in Ca, AJ-rich refractory inclusions (CAI) in C3V meteorites. These metals occur along with γNi-Fe metals, Ni-Fe sulfides and Fe oxides in multiphase opaque assemblages. Laboratory experiments were used to show that the mineral assemblages and textures observed in opaque assemblages could be produced by sulfidation and oxidation of once homogeneous Ni-Fe-PGE metals. Phase equilibria, partitioning and diffusion kinetics were studied in the Ni-Fe-Ru system in order to quantify the conditions of opaque assemblage formation. Phase boundaries and tie lines in the Ni-Fe-Ru system were determined at 1273, 1073 and 873K using an experimental technique that allowed the investigation of a large portion of the Ni-Fe-Ru system with a single experiment at each temperature by establishing a concentration gradient within which local equilibrium between coexisting phases was maintained. A wide miscibility gap was found to be present at each temperature, separating a hexagonal close-packed εRu-Fe phase from a face-centered cubic γNi-Fe phase. Phase equilibria determined here for the Ni-Fe-Ru system, and phase equilibria from the literature for the Ni-Fe-S and Ni-Fe-O systems, were compared with analyses of minerals from opaque assemblages to estimate the temperature and chemical conditions of opaque assemblage formation. It was determined that opaque assemblages equilibrated at a temperature of ~770K, a sulfur fugacity 10 times higher than an equilibrium solar gas, and an oxygen fugacity 10⁶ times higher than an equilibrium solar gas.

Diffusion rates between -γNi-Fe and εRu-Fe metal play a critical role in determining the time (with respect to CAI petrogenesis) and duration of the opaque assemblage equilibration process. The diffusion coefficient for Ru in Ni (D^Ru_Ni) was determined as an analog for the Ni-Fe-Ru system by the thin-film diffusion method in the temperature range of 1073 to 1673K and is given by the expression:

D^Ru_Ni (cm² sec^-1) = 5.0(±0.7) x 10^-3 exp(-2.3(±0.1) x 10¹² erg mole^-1/RT) where R is the gas constant and T is the temperature in K. Based on the rates of dissolution and exsolution of metallic phases in the Ni-Fe-Ru system it is suggested that opaque assemblages equilibrated after the melting and crystallization of host CAI during a metamorphic event of ≥ 10³ years duration. It is inferred that opaque assemblages originated as immiscible metallic liquid droplets in the CAI silicate liquid. The bulk compositions of PGE in these precursor alloys reflects an early stage of condensation from the solar nebula and the partitioning of V between the precursor alloys and CAI silicate liquid reflects the reducing nebular conditions under which CAI were melted. The individual mineral phases now observed in opaque assemblages do not preserve an independent history prior to CAI melting and crystallization, but instead provide important information on the post-accretionary history of C3V meteorites and allow the quantification of the temperature, sulfur fugacity and oxygen fugacity of cooling planetary environments. This contrasts with previous models that called upon the formation of opaque assemblages by aggregation of phases that formed independently under highly variable conditions in the solar nebula prior to the crystallization of CAI.

Analytical studies were carried out on PGE-rich phases from meteorites and the products of synthetic experiments using traditional electron microprobe x-ray analytical techniques. The concentrations of PGE in common minerals from meteorites and terrestrial rocks are far below the ~100 ppm detection limit of the electron microprobe. This has limited the scope of analytical studies to the very few cases where PGE are unusually enriched. To study the distribution of PGE in common minerals will require an in situ analytical technique with much lower detection limits than any methods currently in use. To overcome this limitation, resonance ionization of sputtered atoms was investigated for use as an ultrasensitive in situ analytical technique for the analysis of PGE. The mass spectrometric analysis of Os and Re was investigated using a pulsed primary Ar⁺ ion beam to provide sputtered atoms for resonance ionization mass spectrometry. An ionization scheme for Os that utilizes three resonant energy levels (including an autoionizing energy level) was investigated and found to have superior sensitivity and selectivity compared to nonresonant and one and two energy level resonant ionization schemes. An elemental selectivity for Os over Re of ≥ 10³ was demonstrated. It was found that detuning the ionizing laser from the autoionizing energy level to an arbitrary region in the ionization continuum resulted in a five-fold decrease in signal intensity and a ten-fold decrease in elemental selectivity. Osmium concentrations in synthetic metals and iron meteorites were measured to demonstrate the analytical capabilities of the technique. A linear correlation between Os⁺ signal intensity and the known Os concentration was observed over a range of nearly 10⁴ in Os concentration with an accuracy of ~ ±10%, a millimum detection limit of 7 parts per billion atomic, and a useful yield of 1%. Resonance ionization of sputtered atoms samples the dominant neutral-fraction of sputtered atoms and utilizes multiphoton resonance ionization to achieve high sensitivity and to eliminate atomic and molecular interferences. Matrix effects should be small compared to secondary ion mass spectrometry because ionization occurs in the gas phase and is largely independent of the physical properties of the matrix material. Resonance ionization of sputtered atoms can be applied to in situ chemical analysis of most high ionization potential elements (including all of the PGE) in a wide range of natural and synthetic materials. The high useful yield and elemental selectivity of this method should eventually allow the in situ measurement of Os isotope ratios in some natural samples and in sample extracts enriched in PGE by fire assay fusion.

Phase equilibria and diffusion experiments have provided the basis for a reinterpretation of the origin of opaque assemblages in CAI and have yielded quantitative information on conditions in the primitive solar nebula and cooling planetary environments. Development of the method of resonance ionization of sputtered atoms for the analysis of Os has shown that this technique has wide applications in geochemistry and will for the first time allow in situ studies of the distribution of PGE at the low concentration levels at which they occur in common minerals.

I. Electronic states of heavily-doped molecular crystals--naphthalene. I. Theoretical. II. Experimental. II. Lowest singlet and triplet excited states of pyrazine

PART I

The energy spectrum of heavily-doped molecular crystals was treated in the Green’s function formulation. The mixed crystal Green’s function was obtained by averaging over all possible impurity distributions. The resulting Green’s function, which takes the form of an infinite perturbation expansion, was further approximated by a closed form suitable for numerical calculations. The density-of-states functions and optical spectra for binary mixtures of normal naphthalene and deuterated naphthalene were calculated using the pure crystal density-of-state functions. The results showed that when the trap depth is large, two separate energy bands persist, but when the trap depth is small only a single band exists. Furthermore, in the former case it was found that the intensities of the outer Davydov bands are enhanced whereas the inner bands are weakened. Comparisons with previous theoretical calculations and experimental results are also made.

PART II

The energy states and optical spectra of heavily-doped mixed crystals are investigated. Studies are made for the following binary systems: (1) naphthalene-h₈ and d₈, (2) naphthalene--h₈ and αd₄, and (3) naphthalene--h₈ and βd₁, corresponding to strong, medium and weak perturbations. In addition to ordinary absorption spectra at 4˚K, band-to-band transitions at both 4˚K and 77˚K are also analyzed with emphasis on their relations to cooperative excitation and overall density-of-states functions for mixed crystals. It is found that the theoretical calculations presented in a previous paper agree generally with experiments except for cluster states observed in system (1) at lower guest concentrations. These features are discussed semi-quantitatively. As to the intermolecular interaction parameters, it is found that experimental results compare favorably with calculations based on experimental density-of-states functions but not with those based on octopole interactions or charge-transfer interactions. Previous experimental results of Sheka and the theoretical model of Broude and Rashba are also compared with present investigations.

PART III

The phosphorescence, fluorescence and absorption spectra of pyrazine-h₄ and d₄ have been obtained at 4˚K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h₄ in d₄ were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.

The analysis of the weak fluorescence spectrum resolves the long-disputed question of whether one or two transitions are involved in the near-ultraviolet absorption of pyrazine. The “mirror-image relationship” between absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as ¹B_3u ← ¹A_1g. The forbidden component ¹B_2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.

The phosphorescence spectrum when compared with the excitation phosphorescence spectra, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and a “mirror-image relationship” between absorption and emission. In accordance with previous work, the triplet state is designated as ³B_3u.

The vibronic structure of the phosphorescence spectrum is very complicated. Previous work on the analysis of this spectrum all concluded that a long progression of v_6a exists. Under the high resolution attainable in our work, the supposed v_6a progression proves to have a composite triplet structure, starting from the second member of the progression. Not only is the v_9a hydrogen-bending mode present as shown by the appearance of the C-D bending mode in the d₄ spectrum, but a band of 1207 cm^-1 in the pyrazine in benzene system and 1231 cm^-1 in the mixed crystal system is also observed. This band is assigned as 2v_6b and of a_1g symmetry. Its anonymously strong intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with the 2v_6a and v_9a band.

To help resolve the present controversy over the crystal phosphorescence spectrum of pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.