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.

The effect of social skills training on grade 3 students' self-esteem, moral development and perceptions of classroom environment

Two Grade 3 classes were used to study the effects of a formal social skills training program. Specifically, comparisons were made on self-esteem, classroom environment, and moral development to see whether changes occurred as a direct result of social skills training. One group participated in the social skills program, while the other group did not. It was hypothesized that formal social skills training would improve students' selfesteem, moral development, and the classroom environment. At the end of the program, however, data from class observations, teacher interviews, journal of the social skills training group teacher, and measures of self-esteem, classroom environment and moral development did not support this hypothesis. Although the social skills training group scored significantly higher in class cohesiveness, they did not show marked improvement in the other measures. In fact, in some measures (e.g., friction and competitiveness), they demonstrated greater scores at both pretest and posttests. The social skills training group was, however, able to vocalize and utilize the strategies of several skills which had been a focus of the program, suggesting that formal social skills training is a useful tool for presenting and reinforcing some specific behaviours.