On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Christopher Newton Collection, 1955-1998 (non-inclusive)

Christopher Newton was born in England in June of 1936. He received his education at Sir Roger Manwood’s School in Kent, the University of Leeds, Purdue University in Indiana and the University of Illinois where he received his M.A. He founded Theatre Calgary in 1968 and was the artistic director there until 1971. He was appointed as the artistic director of the Vancouver Playhouse where he established the Playhouse Acting School with Powys Thomas. Mr. Newton has also performed and directed at Stratford Festivals and on Broadway. He became the artistic director at Shaw Festival in Niagara-on-the-Lake in 1979 and remained there for 23 seasons until 2002. Mr. Newton has many television, radio and film credits to his name as well as having written many stage plays. Mr. Newton has received honorary degrees from Brock University (1986), the University of Guelph (1989), Wilfrid Laurier University (1997) and Buffalo State University. He was made an Honorary Fellow at the Royal Conservatory of Music of Toronto (1993) and of Ryerson Polytechnic University (1995). He has won the Governor General’s performing arts award (2000), the Molson Prize and the Thomas DeGaetani Award from the United States Institute for Theatre Technology. In 1996 he was made an Honorary Life Member of the Association for Canadian Theatre Research and in the same year he received the M. Joan Chalmers Award for Artistic Direction. In 1995, he was made a Member of the Order of Canada and he won a Governor General's Performing Arts Award in 2000. Christopher Newton is currently the Artistic Director Emeritus at the Shaw Festival. Sources: http://www.shawfest.com/the-ensemble/christopher-newton/ http://www.thecanadianencyclopedia.com/articles/christopher-newton