Surface energy and pressure of diamond and silicon nanocrystals

Based on the pair potential of interatomic interaction, we study the dependence of various properties of diamond and silicon nanocrystals with a free surface on size, surface shape, and temperature. A model nanocrystal has the form of a parallelepiped faceted by {100} planes with a square base. The number of atoms N in the nanocrystals is varied from 5 to infinity. The Debye temperature, Gruneisen parameter, specific surface energy, isochoric derivative of specific surface energy with respect to temperature, and surface pressure are calculated as a function of the size and shape of diamond and silicon nanocrystals at temperatures ranging from 20 K to the melting point. The surface pressure P _sf(N) ∼ N ^−1/3 is much lower than the pressure calculated by the Laplace formula for similar nanocrystals for given values of density, temperature, and number of atoms. As the temperature increases from 20 K to the melting point, the isotherm P _sf(N) lowers and changes the shape of the dependence on N; at high temperatures, it goes to the region of extension of small nanocrystals of diamond and silicon.     

Change in the size dependences of the surface properties of nanodiamond upon variation in the isotope composition

The isothermal-isomorphic dependences of the specific surface energy (σ), its isochoric temperature derivative (σ′), and surface pressure (P _sf) on the size of nanodiamonds ¹²C and ¹³C at 100 and 4300 K are calculated. It is shown that the ratio σ(¹²C)/σ(¹³C) decreases with decreasing size along both isotherms, and σ′(¹²C)/σ′(¹³C) increases with decreasing size, and this effect is higher at lower temperatures. The ratio P _sf(¹²C)/P _sf(¹³C) increases with decreasing size. The effect is stronger at higher temperatures.     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

The temperature dependence of nanocrystal heat capacity

The temperature dependence of the specific (per atom) entropy and heat capacity of a nanocrystal is studied using a nanocrystal model in the form of a rectangular parallelepiped with variable surface shape. Accounting for the temperature dependence of the surface energy showed that the temperature dependence of the surface contribution to specific entropy is described by the same function that determines the temperature dependence of the isochoric heat capacity of a macrocrystal. Thus, at T → 0 K at T/Θ > 2 the surface contribution to the specific heat is zero. The maximal surface contribution to specific heat is reached at T/Θ = 0.2026 and is equal to c _st/k _B = 1.0115 (where k _B is the Boltzmann constant, Θ is the characteristic temperature depending both on the size and the shape of the nanocrystal). The applicability of the Grüneisen rule for a nanocrystal both at low and high temperatures is studied. It has been found that a case when the surface contribution to specific heat would be negative c(N) < c(∞), i.e. c _st(N) < 0 can occur for nanocrystals with a noncubic habitus.     

Electron-vibrational energy exchange in collisions of Ar atoms in the 3P2 metastable state with N2(X1S g+ ) molecules

Rate constants for electron-vibrational energy exchange Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) → Ar(¹ S ₀) + N₂(C ³Π _u , ν′), where ν′ = 0, 1, 2, were calculated. Calculations were performed taking into account the presence of a resonance in electron scattering by N₂(X ¹Σ _g ⁺). As a result, the interaction of Ar(³ P ₂) with N₂(X ¹Σ _g ⁺, ν = 0) was characterized by attraction and, in the end, intersection of electron-vibrational potential surfaces correlating with Ar(³ P ₂) + N₂(X ¹Σ _g ⁺, ν = 0) and Ar(¹ S ₀) + N₂(C ³Π _u , ν′) at interparticle distances of 2.5–3.5 ?. Exchange interaction at which electron-vibrational transitions in the region of intersection of electron-vibrational transitions in the region of intersection of electron-vibrational potential surfaces accompanied by spin exchange were induced was calculated by the asymptotic method. The rate constants determined at 300–600 K were on the order of 10⁻¹¹−10⁻¹² cm³/s and weakly increased as the temperature grew. Mainly the C ³Π _u , ν′ = 0 state of the N₂ molecule was populated. The calculation results were in satisfactory agreement with the experimental data obtained at 300 K.     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)     

Buffer-gas pressure broadening for the 2ν3 band of methane measured with continuous-wave cavity ring-down spectroscopy

Buffer-gas pressure broadening for the P(1), Q(1), R(0) and R(1) transitions in the 2ν ₃ band of CH₄ was investigated in the 1660 nm region. The pressure broadening coefficients, γ(gas), were determined for a variety of buffer gases: N₂, O₂, He, Ne, Ar, Kr and Xe. The γ values generally increased with increasing polarizability of the buffer gases. γ(air) are 0.056(2) for P(1), 0.056(1) for R(0), 0.061(1) for R(1) and 0.059(1) for Q(1) in units of cm⁻¹ atm⁻¹ where numbers in parentheses are one standard deviation in units of the last digits quoted. The temperature dependent parameter (broadening exponent) for air is 0.84(7) for P(1) within the temperature range 233–298 K.     

Absolute cross sections of electron attachment to molecular clusters. Part II: Formation of (H2O) N? , (N2O) N? , and (N2) N?

Absolute cross sections σ⁻(E, N) of electron attachment to clusters (H₂O) _N , (N₂O) _N , and (N₂) _N for varying electron energy E and cluster size N are measured by using crossed electron and cluster beams in a vacuum. Continua of σ⁻(E) are found that correlate well with the functions of electron impact excitation of molecules’ internal degrees of freedom. The electron is attached through its solvation in a cluster. In the formation of (H₂O) _N ⁻ , (N₂O) _N ⁻ , and (N₂) _N ⁻ , the curves σ⁻(N) have a well-defined threshold because of a rise in the electron thermalization and solvation probability with N. For (H₂O)₉₀₀, (N₂O)₃₅₀, and (N₂)₂₆₀ clusters at E = 0.2 eV, the energy losses by the slow electron in the cluster are estimated as 3.0 × 10⁷, 2.7 × 10⁷, and 6.0 × 10⁵ eV/m, respectively. It is found that the growth of σ⁻ with N is the fastest for (H₂O) _N and (N₂) _N clusters at E → 0 as a result of polarization capture of the s-electron. Specifically, at E = 0.1 eV and N = 260, σ⁻ = 3.0 × 10⁻¹³ cm² for H₂O clusters, 8.0 × 10⁻¹⁴ cm² for N₂O clusters, and 1.4 × 10⁻¹⁵ cm² for N₂ clusters; at E = 11 eV, σ⁻ = 9.0 × 10⁻¹⁶ cm² for (H₂O)₂₀₀ clusters, 2.4 × 10⁻¹⁴ cm² for (N₂O)₃₅₀ clusters, and 5.0 × 10⁻¹⁷ cm² for (N₂)₂₆₀ clusters; finally, at E = 30 eV, σ⁻ = 3.6 × 10⁻¹⁷ cm² for (N₂O)₁₀ clusters and 3.0 × 10⁻¹⁷ cm² for (N₂)₁₂₅ clusters. Original Russian Text ? A.A. Vostrikov, D.Yu. Dubov, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 12, pp. 1–15.     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Aerosol deposition of detonation nanodiamonds used as nucleation centers for the growth of nanocrystalline diamond films and isolated particles

The aerosol deposition of detonation nanodiamonds (DNDs) on a silicon substrate is comprehensively studied, and the possibility of subsequent growth of nanocrystalline diamond films and isolated particles on substrates coated with DNDs is demonstrated. It is shown that a change in the deposition time and the weight concentration of DNDs in a suspension in the range 0.001–1% results in a change in the shape of DND agglomerates and their number per unit substrate surface area N _s from 10⁸ to 10¹¹ cm⁻². Submicron isolated diamond particles are grown on a substrate coated with DND agglomerates at N _s ≈ 108 cm⁻² using microwave plasma-enhanced chemical vapor deposition. At N _s ≈ 10¹⁰ cm⁻², thin (∼100 nm) nanodiamond films with a root-mean-square surface roughness less than 15 nm are grown.     

Intrinsic inhomogeneities of low-doped lanthanum manganites in the paramagnetic temperature range

The nature of the electrical resistivity for low-doped lanthanum manganites is elucidated. The electrical resistivity is described by the Efros-Shklovskii law (lnρ √ (T ₀/T)^−1/2, where T ₀ √ 1/R _ls) in the temperature range from T* ≈ 300 K ≈ T _C (T _C is the Curie temperature for conducting manganites) to their T _C and is explained by the tunneling of carriers between localized states. The magnetoresistance is explained by a change in the size of localized states R _ls in a magnetic field. The patterns of change in R _ls with temperature and magnetic field strength determined from magnetotransport properties are satisfactorily described in the model of phase separation into small-radius metallic droplets in a paramagnetic matrix. The sizes R _ls and their temperature dependence have been estimated through magnetic measurements. The results confirm the existence of a Griffith phase. The intrinsic inhomogeneities produced by thermodynamic phase separation determine the electrical resistivity and magnetoresistance of lanthanum manganites.     

Internal friction in directed-crystallization (Cu-Sn)-Nb alloys

The distinctive features of the low-frequency internal friction Q ⁻¹(T) of (Cu-Sn)-Nb composites at high temperatures (up to 400°C) are investigated for strains in the range 10⁻⁵–10⁻⁴. Considerable hysteresis of Q ⁻¹(T) in the heating-cooling cycle is recorded, including the presence of a minimum at ∼175°C when the sample is heated to 400°C and two peaks P ₂ (at 280°C) and P ₁ (at ∼100°C) when the sample is cooled from 400°C. The activation energy of the anomalous internal friction background (up to 175°C), the oxygen diffusion parameters, and the oxygen concentration in the niobium fibers (all of which govern the peak P ₂) are calculated, and the value and temperature dependence of the yield point of the bronze matrix (which govern the peak P ₁) are estimated. Zh. Tekh. Fiz. 68, 114–117 (November 1998)     

On Ruelle’s Construction of the Thermodynamic Limit for the Classical Microcanonical Entropy

In 1969 Ruelle published his construction of the thermodynamic limit, in the sense of Fisher, for the quasi-microcanonical entropy density of classical Hamiltonian N-body systems with stable and tempered pair interactions. Here, “quasi-microcanonical” refers to the fact that he discussed the entropy defined with a regularized microcanonical measure as ln (N!⁻¹ ∫ χ _{{ℰ−▵ℰ<H<ℰ}}d^6N X) rather than defined with the proper microcanonical measure as ln (N!⁻¹ ∫ δ(ℰ−H) d^6N X). Replacing δ(ℰ−H) by χ _{{ℰ−▵ℰ<H<ℰ}} seems to have become the standard procedure for rigorous treatments of the microcanonical ensemble hence. In this note we make a very elementary technical observation to the effect that Ruelle’s proof (still based on regularization) does establish the thermodynamic limit also for the entropy density defined with the proper microcanonical measure. We also show that with only minor changes in the proof the regularization of δ(ℰ−H) is actually not needed at all.     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

A Note on Classical Ground State Energies

The pair-specific ground state energy ε _g (N):=ℰ _g (N)/(N(N−1)) of Newtonian N body systems grows monotonically in N. This furnishes a whole family of simple new tests for minimality of putative ground state energies ℰ _g ^x (N) obtained through computer experiments. Inspection of several publicly available lists of such computer-experimentally obtained putative ground state energies ℰ _g ^x (N) has yielded several dozen instances of ℰ _g ^x (N) which failed one of these tests; i.e., for those N one concludes that ℰ _g ^x (N)>ℰ _g (N) strictly. Although the correct ℰ _g (N) is not revealed by this method, it does yield a better upper bound on ℰ _g (N) than ℰ _g ^x (N) whenever ℰ _g ^x (N) fails a monotonicity test. The surveyed N-body systems include in particular N point charges with 2- or 3-dimensional Coulomb pair interactions, placed either on the unit 2-sphere or on a 2-torus (a.k.a. Thomson, Fekete, or Riesz problems).     

Fine and hyperfine structure of the muonic <Superscript>3</Superscript>He ion

On the basis of quasipotential approach to the bound state problem in QED we calculate the vacuum polarization, relativistic, recoil, structure corrections of orders α ⁵ and α ⁶ to the fine structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and to the hyperfine structure of the energy levels 2P _1/2 and 2P _3/2 in muonic ₂³He ion. The resulting values ΔE ^fs = 144 803.15 μeV, Δ$ \tilde E $ \tilde E ^hfs(2P _1/2) = −58 712.90 μeV, Δ$ \tilde E $ \tilde E ^hfs(2P _3/2) = −24 290.69 μeV provide reliable guidelines in performing a comparison with the relevant experimental data.     

Kinetics of formation of O2(1Σ) molecules in reactions involving excited O2(1Δ) oxygen molecules and I(2P1/2) iodine atoms

The results of our experimental study of the kinetics of formation of O₂(¹Σ) molecules in energy-exchange reactions O₂(¹Δ) + I(⁵ p,² P _1/2) and O₂(a,¹Δ) + O₂(a,¹Δ) are presented. The ratio of rate constants was obtained for these reactions (4800 ± 300). Setting the rate constant of the deactivation of O₂(¹Σ) molecules on CO₂ molecules at 4.1 · 10^–13 cm³/s, we evaluated the rate constants for these reactions at a temperature of approximately 330 K: (1.7 ± 0.2) · 10⁻¹³ and (3.6 ± 0.5) · 10⁻¹⁷ cm³/s, respectively.     

Progress in pion-decay channelling: Refractory bcc metals at high and low temperatures

By means of π⁺/μ⁺ channelling, positive pions (π⁺) implanted intoTa, Mo, andW are investigated up to high temperatures. A striking observation is that the channelling effect disappears in a rather narrow temperature interval centred at 0.26 (Ta) to 0.51 (W) of the melting temperature. From studies of π⁺ trapping by oxygen atoms inTa estimates for the low-temperature π⁺ diffusivity inTa [D _π(23K)=1.4·10^−10±0.3 m²s⁻¹,D _π(47K)=5.7·10^−10±0.3 m²s⁻¹] as well as for the binding enthalpy of π⁺ to 0 atoms (H _B=7·10⁻² eV) have been obtained. The diffusion data are in reasonable agreement with the theory of phonon-assisted tunnelling.     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.