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Physical Review

Heat Capacity of Atoms Adsorbed on a Close-Packed Substrate

Michael Bretz

Published Aug 5, 1969• 5 citations
Publisher

Abstract

The specific heat is calculated for noninteracting Fermi atoms adsorbed into deep potential wells on a close-packed substrate at low temperatures. The atoms have a small, but finite, probability of tunneling to adjacent localized sites, which creates a low-lying energy band. It is shown that in this tight-binding approximation, the band structure is identical with the two-dimensional electronic band structure in graphite, and this is used to calculate the specific heat of the adsorbed particles. For comparison, the specific heat is obtained for a constant density of states. There is a general correspondence between the two cases, with the constant density of states smoothing out the actual specific heat at the lowest temperatures. A short discussion explains how hard-core repulsion between adsorbed particles will affect the surface coverage and the mobility.

DOI
10.1103/physrev.184.162

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The specific heat is calculated for noninteracting Fermi atoms adsorbed into deep potential wells on a close-packed substrate at low temperatures. The atoms have a small, but finite, probability of tunneling to adjacent localized sites, which creates a low-lying energy band. It is shown that in this tight-binding approximation, the band structure is identical with the two-dimensional electronic band structure in graphite, and this is used to calculate the specific heat of the adsorbed particles. For comparison, the specific heat is obtained for a constant density of states. There is a general correspondence between the two cases, with the constant density of states smoothing out the actual specific heat at the lowest temperatures. A short discussion explains how hard-core repulsion between adsorbed particles will affect the surface coverage and the mobility.
We have calculated the heat capacity and entropy of Bose and Fermi atoms adsorbed on crystalline surfaces at low temperatures. The treatment is quantum mechanical at the outset, the influence of tunneling of atoms between adsorption sites being discussed in detail. It is shown by general qualitative arguments that the energy spectrum of a low-coverage monolayer contains a low-lying tunneling band of translational surface states. The finite energy width of the tunneling band ensures that the monolayer entropy due to the distribution of particles among the translational states will vanish at 0\ifmmode^\circ\else\textdegree\fi{}K. This entropy is shown to be equivalent to the configuration entropy at relatively high temperatures and therefore demonstrates the manner in which the configuration entropy is removed at 0\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures, particles become excited to higher bands which may be separated from the tunneling band by an energy gap. Quantum-statistical properties of non-interacting bosons and fermions in a two-band model are analyzed in terms of the number of adsorption sites, the tunneling band width, and the interband energy gap. When the interband gap is larger than the tunneling band width, the monolayer heat capacity displays two distinct peaks, at temperatures kT\mathrm{kT}kT characteristic of the interband energy gap and of the tunneling band width. The heat capacity approaches ideal two-dimensional gas behavior at zero interband gap. The systems are studied over a range of other parameters, including the ratios of densities of states in the two bands and the number of atoms adsorbed on the surface. A qualitative discussion is given of the influence of interactions among the adsorbed atoms, and of their modifications by the substrate. The relevance of the theory to current experiments on helium monolayers is discussed.
We have measured the heat capacity of submonolayers of 4He^{4}\mathrm{He}4He adsorbed on Ag films between 1.7 and 3.3 K. Good fits to the results are obtained with a model of a noninteracting two-dimensional Bose gas. The sticking probability for room-temperature 4He^{4}\mathrm{He}4He atoms on cold Ag has been measured as a function of substrate temperature and 4He^{4}\mathrm{He}4He coverage. The sticking probability is 4% at low coverage, and abruptly drops to 1% for coverages above 0.5 monolayer.
The effect of finite number of trapped atoms is discussed in Bose-Einstein condensation without interaction, according to Thomas-Fermi approximation. We obtain the state density by high-temperature expansion and calculate the critical temperature in one-dimensional(1D) and two-dimensional(2D) trap potentials. Then the temperature dependence of specific heat are analyzed. The results show that: in 2D case, the specific heat c is proportional to T2; in 1D case,c increases linearly with temperature.
Spin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« less
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