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.

Chronic versus acute ingestion of sodium citrate: a randomized placebo controlled cross-over trial for swimming 200 metres in well-trained swimmers age 13-17

A double-blinded, placebo controlled, cross-over design was used to investigate sodium citrate dihydrate (Na-CIT) supplementation improve 200m swimming performance. Ten well-trained, male swimmers (14.9 ± 0.4y; 63.5 ± 4kg) performed four 200m time trials: acute (ACU) supplementation (0.5g/kg), acute placebo (PLC-A), chronic (CHR) (0.1g/kg for 3 days and 0.3g/kg on the 4th day pre-trial), and chronic placebo (PLC-C). Na-CIT was administered 120min pre-trial in solution with 500mL of flavored water; placebo was flavored water. Blood lactate, base excess (BE), bicarbonate, pH, and PCO2 were analyzed at basal, 100min post-ingestion, and 3min post-trial via finger prick. Time, lactate, and rate of perceived exertion were not different between trials. BE and bicarbonate were significantly higher for the ACU and CHR trials compared to placebo. “Responders” improved by 1.03% (P=0.043) and attained significantly higher post-trial lactate concentrations in the ACU versus PLC-A trials and compared to non-responders in the ACU and CHR trials.