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.

Novices' learning from the Internet : an exploration of navigation behaviours, learner-related factors, and mental effort

The current study was an exploration of why some novices are more successful than their peers when learning from the Internet by examining the relations among time spent with relevant information and changes in invested mental effort during Internet navigations as well as achievement. Navigation behaviours and learner characteristics were investigated as predictors of time spent with relevant information and changes in mental effort. Undergraduates (N = 85, Mage = 20 years, 5 months) searched the Internet for information corresponding to a low knowledge topic for 20 min while their eye gaze and pupil size were recorded. Pupil diameter was used as an objective, continuous measure of mental effort. Participants also completed questionnaires or computer tasks pertaining to s e l f-regulated learning characteristics (general intrinsic goal orientation and effort regulation) and cognitive factors (working memory control, distractibility and cognitive style). All analyses controlled for general mental ability, reading comprehension, topic and Internet knowledge, and overall motivation. A greater proportion of time spent with relevant information predicted higher scores on an achievement test. Interestingly, time spent with relevant information partially mediated the positive relation between the frequency of increases in invested mental effort and achievement. Surprisingly, intrinsic goal orientation was negatively related to time spent with relevant information and effort regulation was negatively related to the frequency of increases in invested mental effort. These findings have implications for supports when novices guide their own learning, especially when using the Internet.