Stacked lattice boxes

We study the number of solutions of the Diophantine equationn=x ₁ x ₂+x ₂ x ₃+x ₃ x ₄+...+x _k x _k+1 The combinatorial interpretation of this equation provides the name stacked lattices boxes. The study of these objects unites three separate threads in number theory: (1) the Liouville methods, (2) MacMahon's partitions withk different parts, (3) the asymptotics of divisor sums begun by Ingham.Partially supported by National Science Foundation Grant DMS-9206993, USA.     

Surface reactions of monoethylgermane on Si(100)-(2×1)

The adsorption and decomposition of monoethylgermane (GeH₃Et) on the Si(100)-(2×1) surface was investigated with the intent of elucidating the surface processes leading to the deposition of germanium. The low-temperature adsorption of the molecule was explored, as well as its thermal decomposition. H₂ and C₂H₄ are observed as the desorption products in temperature-programmed desorption experiments. The ethylene is produced by a hydride elimination reaction within the adsorbed ethyl groups. The amount of Ge which can be deposited in a reaction cycle is correlated with the number of sites occupied by the ethyl groups upon the dissociation of GeH₃Et.     

Visible absorption and resonance Raman spectra of alkaline earth metal ozonides in argon and nitrogen matrices at 10 K

Optical and resonance Raman spectra of the reaction products of Mg, Ca, Sr, and Ba with ozone were observed in argon and nitrogen matrices. The visible spectra were characterized by strong, vibronically structured absorptions between 540 and 350 nm, and are assigned to the alkaline earth metal ozonides, $\text{A}{}^{\mathrm{+}}\text{O}{}_3{}^{\mathrm{?}}$. Vibrational analysis yielded ω₁′ and ω₁x₁ values of about 900 and 6 cm^?1, respectively, with only slight variation from metal to metal. Resonance Raman spectra consisted of a strong fundamental near 1020 cm^?1 and two overtones with decreasing intensity. Oxygen-18 substitution confirmed the vibrational assignments, which agree very well with the alkali metal ozonide spectra. These results suggest that the +1 oxidation state plays an important role in the chemistry of the alkaline earth metals under conditions where aggregation does not occur to favor the +2 state. A thorough search was made for absorptions due to the alkaline earth oxide species, but no bands were observed.     

Matrix reactions of Zn,Cd and Mg atoms with NO2. Infrared spectra of M+NO2− species

Matrix reactions of Mg, Zn and Cd atoms and NO₂ have been performed. Infrared absorptions in the 1220 cm^?1 range show isotopic shifts appropriate for M⁺NO₂^? species. Bands near 950 cm^?1 in the zinc experiments are attributed to a different ion-pair structural isomer.     

Argon matrix absorption spectra of ClO, BrO, and IO and emission spectra of IO

Absorption spectra of ClO, BrO, and IO and the emission spectrum of IO have been observed from argon matrix samples prepared by microwave discharging the reagent mixture before condensation. Vibronic progressions were observed for each system. The spectroscopic scopic constants T_e, ω′_e, ω_ex′_e, ω″_e, and ω_ex″_e were evaluated from the absorption and emission data for comparison with gas-phase constants. Very good agreement is found for ClO. The argon matrix observations dictate a revision of the gas-phase vibronic assignments for BrO. The ground-state vibrational fundamental and T_e for argon matrix isolated IO are similar to the gas-phase values, but a lower excited-state spacing is found in the matrix.