Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Effect of diurnal cycling temperatures on cardiovascular- ventilatory function in statically-acclimated rainbow trout, Salmo gairdneri

Four groups of rainbow trout, Salmo gairdneri, were acclimated to 2°, 10°, and 18°e, and to a diurnal temperature cycle (100 ± 4°C). To evaluate the influence of cycling temperatures in terms of an immediate as opposed to acclimatory response various ventilatory-cardiovascular rate functions were observed for trout, either acclimated to cycling temperatures or acclimated to constant temperatures and exposed to a diurnal temperature cycle for the first time (10° ± 4°C for trout acclimated to 10°C; 18°+ 4°C for trout acclimated to l8°e). Gill resistance and the cardiac to ventilatory rate ratio were then calculated. Following a post preparatory recovery period of 36 hr, measurements were made over a 48 hour period with the first 24 hours being at constant temperature in the case of statically-acclimated fish followed by 24 hours under cyclic temperature conditions. Trout exhibited marked changes in oxygen consumption (Vo ) with temp- 2 erature both between acclimation groups, and in response to the diurnal temperature cycle. This increase in oxygen uptake appears to have been achieved by adjustment of ventilatory and, to some extent, cardiovascular activity. Trout exhibited significant changes in ventilatory rate (VR), stroke volume (Vsv), and flow (VG) in response to temperature. Marked changes in cardiac rate were also observed. These findings are discussed in relation to their importance in convective oxygen transport via water and blood at the gills and tissues. Trout also exhibited marked changes in pressure waveforms associated with the action of the resp; ratory pumps with temperature. Mean differenti a 1 pressure increased with temperature as did gill resistance and utilization. This data is discussed in relation to its importance in diffusive oxygen transport and the conditions for gas exchange at the gills. With one exception, rainbow trout were able to respond to changes in oxygen demand and availability associated with changes in temperature by means of adjustments in ventilation, and possibly pafusion, and the conditions for gas exchange at the gills. Trout acclimated to 18°C, however, and exposed to high cyclic temperatures, showed signs of the ventilatory and cardiovascular distress problems commonly associated with low circulating levels of oxygen in the blood. It appears these trout were unable to fully meet the oxygen requirements associated with c~ling temperatures above 18°C. These findings were discussed in relation to possible limitations in the cardiovascular-ventilatory response at high temperatures. The response of trout acclimated to cycling temperatures was generally similar to that for trout acclimated to constant temperatures and exposed to cycling temperatures for the first time. This result suggested that both groups of fish may have been acclimated to a similar thermal range, regardless of the acclimation regime employed. Such a phenomenon would allow trout of either acclimation group to respond equally well to the imposed temperature cycle. Rainbow trout showed no evidence of significant diurnal rhythm in any parameters observed at constant temperatures (2°, 10°, and 18° C), and under a 12/12 light-dark photoperiod regime. This was not taken to indicate an absence of circadian rhythms in these trout, but rather a deficiency in the recording methods used in the study.

The effects of temperature on nickel tocicity in goldfish (carassius auratus L.)

Although it is widely assumed that temperature affects pollutant toxicity, few studies have actually investigated this relationship. Moreover, such research as has been done has involved constant temperatures; circumstances which are rarely, if ever, actually experienced by north temperate, littoral zone cyprinid species. To investigate the effects of temperature regime on nickel toxicity in goldfish (Carassius auratus L.), 96- and 240-h LCSO values for the heavy metal pollutant, nickel (NiCI2.6H20), were initially determined at 2DoC (22.8 mg/L and 14.7 mg/L in artificially softened water). Constant temperature bioassays at 10°C, 20°C and 30°C were conducted at each of 0, 240-h and 96-h LCSO nickel concentrations for 240 hours. In order to determine the effects of temperature variation during nickel exposure it was imperative that the effects of a single temperature change be investigated before addressing more complex regimes. Single temperature changes of + 10°C or -10°C were imposed at rates of 2°C/h following exposures of between 24 hand 216 h. The effects of a single temperature change on mortality, and duration of toxicant exposure at high and low temperatures were evaluated. The effects of fluctuating temperatures during exposure were investigated through two regimes. The first set of bioassays imposed a sinewave diurnal cycle temperature (20.±.1DOC) throughout the 10 day exposure to 240-h LeSO Ni. The second set of investigations approximated cyprinid movement through the littoral zone by imposing directionally random temperature changes (±2°C at 2-h intervals), between extremes of 10° and 30°C, at 240-h LC50 Ni. Body size (i.e., total length, fork length, and weight) and exposure time were recorded for all fish mortalities. Cumulative mortality curves under constant temperature regimes indicated significantly higher mortality as temperature and nickel concentration were increased. At 1DOC no significant differences in mortality curves were evident in relation to low and high nickel test concentrations (Le., 16 mg/L and 20 mg/L). However at 20°C and 30°C significantly higher mortality was experienced in animals exposed to 20 mg/L Ni. Mortality at constant 10°C was significantly lower than at 30°C with 16 mg/L and was significantly loWer than each of 2DoC and 39°C tanks at 20 mg/L Ni exposure. A single temperature shift from 20°C to 1DoC resulted in a significant decrease in mortality rate and conversely, a single temperature shift from 20°C to 30°C resulted in a significant increase in mortality rate. Rates of mortality recorded during these single temperature shift assays were significantly different from mortality rates obtained under constant temperature assay conditions. Increased Ni exposure duration at higher temperatures resulted in highest mortality. Diurnally cycling temperature bioassays produced cumulative mortality curves approximating constant 20°C curves, with increased mortality evident after peaks in the temperature cycle. Randomly fluctuating temperature regime mortality curves also resembled constant 20°C tanks with mortalities after high temperature exposures (25°C - 30°C). Some test animals survived in all assays with the exception of the 30°C assays, with highest survival associated with low temperature and low Ni concentration. Post-exposure mortality occurred most frequently in individuals which had experienced high Ni concentrations and high temperatures during assays. Additional temperature stress imposed 2 - 12 weeks post exposure resulted in a single death out of 116 individuals suggesting that survivors are capable of surviving subsequent temperature stresses. These investigations suggest that temperature significantly and markedly affects acute nickel toxicity under both constant and fluctuating temperature regimes and plays a role in post exposure mortality and subsequent stress response.

Thermoacclimatory variations in the activities of enzymes implicated in ion transport in the rainbow trout, salmo gairdneri

Two groups of rainbow trout were acclimated to 20 , 100 , and 18 o C. Plasma sodium, potassium, and chloride levels were determined for both. One group was employed in the estimation of branchial and renal (Na+-K+)-stimulated, (HC0 3-)-stimulated, and CMg++)-dependent ATPase activities, while the other was used in the measurement of carbonic anhydrase activity in the blood, gill and kidney. Assays were conducted using two incubation temperature schemes. One provided for incubation of all preparations at a common temperature of 2S oC, a value equivalent to the upper incipient lethal level for this species. In the other procedure the preparations were incubated at the appropriate acclimation temperature of the sampled fish. Trout were able to maintain plasma sodium and chloride levels essentially constant over the temperature range employed. The different incubation temperature protocols produced different levels of activity, and, in some cases, contrary trends with respect to acclimation temperature. This information was discussed in relation to previous work on gill and kidney. The standing-gradient flow hypothesis was discussed with reference to the structure of the chloride cell, known thermallyinduced changes in ion uptake, and the enzyme activities obtained in this study. Modifications of the model of gill lon uptake suggested by Maetz (1971) were proposed; high and low temperature models resulting. In short, ion transport at the gill at low temperatures appears to involve sodium and chloride 2 uptake by heteroionic exchange mechanisms working in association w.lth ca.rbonlc anhydrase. G.l ll ( Na + -K + ) -ATPase and erythrocyte carbonic anhydrase seem to provide the supplemental uptake required at higher temperatures. It appears that the kidney is prominent in ion transport at low temperatures while the gill is more important at high temperatures. 3 Linear regression analyses involving weight, plasma ion levels, and enzyme activities indicated several trends, the most significant being the interrelationship observed between plasma sodium and chloride. This, and other data obtained in the study was considered in light of the theory that a link exists between plasma sodium and chloride regulatory mechanisms.

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.