Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Special report of New York State Survey on the preservation of the scenery of Niagara Falls ; and fourth annual report on the triangulation of State. For the Year 1879 /

Notes by F. L. Olmsted.

Letter from the Secretary of State to Mr. Monroe, on the subject of the attack on the Chesapeake : the correspondence of Mr. Monroe with the British Government ; and also Mr. Madison's correspondence with Mr. Rose on the same subject. --

March 23, 1808. Printed by order of the House of Representatives.

Message from the President of the United States, transmitting of a report of the Secretary of State, in relation to individuals selected from American prisoners of war, and sent to Great Britain for trial, and also in relation to any orders for retaliation, &c., &c.--

April 16, 1814. Printed by order of the Senate of the United States.

Message from the President of the United States, transmitting a report of the Secretary of State, in obedience to a resolution of the thirteenth inst. "requesting the President to lay before this House such documents relative to the Russian mediation as in his opinion it may not be improper to communicate." --

United States,13th Congress, 2d session, 1813-1814. House. Doc. no. 35.

Message from the President of the United States, transmitting copies of a letter from the British Secretary of State for Foreign Affairs, to the Secretary of State, with the answer of the latter.--

January 6, 1814. Ordered to lie on the table.

Report of the Committee to whom was Referred the Correspondence between Mr. Monroe and Mr. Canning, and between Mr. Madison and Mr. Rose, relative to the attacked of Chesapeake : and also a communication from the President of the United States of the 30 March last, with a letter from Mr. Erskine to the Secretary of State, and a letter from M. Champagny to Gen. Armstrong.--

April 16, 1808. Printed by Order of the Senate.

Advocating recognition and redistribution in poverty alleviation programs in Ghana : an examination of state and NGO programs and policies

Abstract This thesis argues that poverty alleviation strategies and programs carried out by the government and Non Governmental Organizations in Ghana provide affirmative solutions to poverty. This is because, these intervention strategies have been influenced by conventional discourses on poverty that fail to adequately address non-economic issues of poverty such as powerlessness, marginalization and tmder-representation. The study is carried out in a two-pronged manner; first, it analyses state policies and strategies, particularly the Ghana Poverty Reduction Strategy (GPRS), on poverty alleviation and compares these to NGO programs, implemented with funds and support from external donor organizations. Specifically, I focus on how NGOs and the governnlent of Ghana negotiate autonomy and financial dependency with their funding donor-partners and how these affect their policies and programs. Findings from this study reveal that while external influences dominate poverty alleviation policies and strategies, NGOs and the government of Ghana exercise varying degrees of agency in navigating these issues. In particular, NGOs have been able to adapt their programs to the changing needs of donor markets, and are also actively engaged in re-orienting poverty back to the political domain through advocacy campaigns. Overall, rural communities in Ghana depend on charitable NGOs for the provision of essential social services, while the Ghanaian government depends on international donor assistance for its development projects.

Letter from the Secretary of State to Mr. Monroe, on the subject of the attack on the Chesapeake : the correspondence of Mr. Monroe with the British Government; and also Mr. Madison's correspondence with Mr. Rose on the same subject

March 23, 1808. Printed by order of the House of Representatives.

Message from the President of the United States, transmitting a report of the Secretary of State, in obedience to a resolution of the thirteenth inst.

Full Title: 47. Message from the President of the United States, transmitting a report of the Secretary of State, in obedience to a resolution of the thirteenth inst. "requesting the President to lay before this House such documents relative to the Russian mediation as in his opinion it may not be improper to communicate." United States,13th Congress, 2d session, 1813-1814. House. Doc. no. 35. January 18, 1814. Ordered to lie on the table. One letter in French with English translation Printed by Roger C. Weightman

Message from the President of the United States, transmitting copies of a letter from the British Secretary of State for Foreign Affairs, to the Secretary of State, with the answer of the latter

January 6, 1814. Ordered to lie on the table. -------------------------------------------------------------------------------- At head of title: [22]. -------------------------------------------------------------------------------- 13th Congress, 2nd Session, House. Doc. 22. Printed by Roger C. Weightman

A report of the Secretary of State, in relation to individuals selected from American prisoners of war, and sent to Great Britain for trial, and also in relation to any orders for retaliation

Printed by Roger C. Weightman

The American Weekly Messenger; or Register of State Papers, History and Politics for 1813 - 1814 Volume 1

Register of state papers, history, and politics for the years 1813 - 1814.

The measurement of the optical absorption cross section of photosystem 1 and photosystem 2 from whole live cells of porphyridium cruentum, in light state 1 and light state 2

The optical cross section of PS I in whole cells of Porphyridium cruentum (UTEX 161), held in either state 1 or state 2, was determined by measuring the change in absorbance at 820nm, an indication of P700+; the X-section of PS2 was determined by measuring the variable fluorescence, (Fv-Fo)/Fo, from PS2. Both cross-sections were 7 determined by fitting Poisson distribution equations to the light saturation curves obtained with single turnover laser flashes which varied in intensity from zero to a level where maximum yield occurred. Flash wavelengths of 574nm, 626nm, and 668nm were used, energy absorbed by PBS, by PBS and chla, and by chla respectively. There were two populations of both PSi and PS2. A fraction of PSi is associated with PBS, and a fraction of PS2 is free from PBS. On the transition S1->S2, only with PBS-absorbed energy (574nm) did the average X-section of PSi increase (27%), and that of PS2 decrease (40%). The fraction of PSi associated with PBS decreased, from 0.65 to 0.35, and the Xsection of this associated PS 1 increased, from 135±65 A2 to 400±300A2. The cross section of PS2 associated with PBS decreased from 150±50 A2 to 85±45 A2, but the fraction of PS2 associated with PBS, approximately 0.75, did not change significantly. The increase in PSi cross section could not be completely accounted for by postulating that several PSi are associated with a single PBS and that in the transition to state2, fewer PSi share the same number of PBS, resulting in a larger X-section. It is postulated that small changes occur in the attachment of PS2 to PBS causing energy to be diverted to the attached PSi. These experiments support neither the mobile-PBS model of state transitions nor that of spillover. From cross section changes there was no evidence of energy transfer from PS2 to PSi with 668nm light. The decrease in PS2 fluorescence which occurred at this wavelength cannot be explained by energy transfer; another explanation must be sought. No explanation was found for an observed decrease in PSi yield at high flash intensities.