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.

Two discourses, delivered to the Second Presbyterian Society in Newburyport, August 20, 1812, the day recommended by the President of the United States, for national humiliation and prayer

Printed by W.R. and H. G. Allen

Power of Attorney of Colonel John Butler for Robert Hamilton and Robert Addison, January 4,1797

John Butler (1728-1796) was originally from Connecticut but settled with his family in the Mohawk valley of New York around 1742. His father was a Captain in the British army and well acquainted with William Johnson (superintendent of Northern Indians). Butler impressed Johnson with his aptitude for Indian languages and diplomacy. He began to work with Johnson in 1755, and received several promotions in the department, until his apparent retirement in the early 1770s. At the onset of the Revolutionary War in 1775, Butler relocated to Canada to join the British forces, settling in Niagara. During the War, Butler was instrumental in maintaining the alliance with the Indians. After the War, Butler became prominent in local affairs in Niagara, but failed to secure any important offices when the province of Upper Canada was formed in 1792. In an effort to recoup some of the financial losses his family suffered during the War, Butler illegally attempted to supply trade goods to the Indian department with his son Andrew, his nephew Walter Butler Sheehan, and Samuel Street, a Niagara merchant.