Scaling pressure-dependent resistivity

Measurements of filtration rates should be repeated at different pressures or different vacuum levels. This gives information on the influence of pressure on the specific cake resistance. The specific resistance of cakes that are difficult to filter is often pressure-dependent. Thus, use of excessive pressure can result in blocking of the cake, causing filtration to stop. In the case of compressible cakes, information is needed over the whole range of pressures being considered for industrial filters since extrapolation of compressibility beyond the experimentally covered region is always risky. The larger the scale of an experimental filter, the less risky predictions based on the experimental data. 

Fig. 9. (a) Scaled resistivity p(T)/p (300 K) vs. T/Tq for YbFe4Sbi2> where Tq is the scaling temperature. Inset shows the pressure dependence of Tq. (b) Scaled resistivity of CeFe4Sbi2 vs. T/Tq. Inset shows pressure dependence of Tq. The room temperature resistivity of both compounds was about 0.8 m cm at ambient pressure (E.D. Bauer et al., 2000). 

Fig. 87. Temperature dependence of the electrical resistivity of TmSeo45Te 55. The pressures at room temperature are (a) 0, (b) 9.7kbar, (c) ll.Okbar, (d) 12,9kbar, (e) IS.Okbar, (f) 17.0kbar. Note the linear scale of the resistivity in the inset. (After Neuenschwander and Wachter (1990a,b.)...

Fig. 10. (a) Temperature-dependent resistivity of CeSn3 at various pressures, (b) Data of part (a) in which the temperature scale has been normalized by a factor Tf, F) which is the inverse square root of the low-temperature T -coefiScient of resistivity. Actual units on the horizontal axis are then (nQcm). ... 

The systematics described for the pressure dependence of resistivity features, e.g., A and T, are consistent with a pressure-induced increase in the characteristic electronic energy scale in Ce-based intermetallics, a result that can be understood if the hybridization between conduction and 4f electrons increases with pressure. As noted by Kadowaki and Woods (1986), there appears to be a universal relationship between Sommerfeld coefficient and A values among anomalous lanthanide and actinide compounds. We will show later that this universality continues to hold at modest pressures as well. Presumably this relationship is valid because it is a ground-state property of the underlying electronic correlations responsible for both y and A. However, it must be remembered that y is a thermodynamically-defined quantity whereas A depends on (anisotropic) electronic... 

On the other hand the Gruneisen parameter Q 22 deduced from the pressure dependence of the resistivity maximum in CeCu2Si2 is substantially smaller than the values 50-80 deduced from low-temperature measurements. It is not clear whether this is an experimental artifact or whether it means that single-energy scaling is not valid. 

Similar anomalies may occur in the large-TK mixed-valent compounds. For example, the bulk modulus of CeBeis shows a downturn below 25 K (fig. 24) that represents a deviation from the Gruneisen prediction and may result from a coherence effect. As mentioned in sect. 2, the resistivity of CePds may be far less pressure dependent below 40 K than above this has been taken as evidence that the coherent Fermi liquid scales differently than the single-ion regime. At present these effects are best taken as tantalizing suggestions, rather than well established effects. 

FIGURE 145 Pressure dependence of resistivity of a-Ce58Ru42 shown using (A) linear scale and (B) logarithmic scale (Sakai et al., 1996). 

Tn = 3.1, 3.8, and 3.7 K are deduced from neutron diffraction experiments on TmSe (with a = 5.7lA) at pressures of 0, 8, and 20 kbar, respectively, by Vettier etal. [12]. Electrical resistivity measurements on nearly stoichiometric TmSe (a = 5.712 A) confirm the preliminary results of [12]. A figure in the paper shows an increase in T from 3.46 Kat ambient pressure to a maximum of -4K at 13 kbar, which corresponds to an initial slope dTN/dp=+0.085 0.010 K/kbar. The inital value of T is reached at approximately the highest applied pressure of 30 kbar, Ribault et al. [13]. Fig. 171 shows the pressure dependence of T for the same sample extended to higher pressures in comparison with the linear change of T as a function of x in TmxSe (for 0.8scaled with the lattice constants, Lapierre et al. [14]. Neutron diffraction measurements on a nearly stoichiometric sample with a = 5.709 A show an increase of Tn= 3.3K at ambient pressure to a maximum value of 3.93(2) K at -15 kbar. This is shown in a figure in the paper, which corresponds to dTN/dp = 0.066(8) K/kbar, Debray etal. [15]. 

Depending on the technical requirements such as corrosion resistance, pressure and temperature stability, industrial scale azo pigment synthesis is carried out in appropriate equipment. Suitable materials include cast iron, stainless steel, steel lined with rubber, acid-proof brick, enamel, synthetic resins supported by glass fiber, and wood. 

Resistive Heating Combined with Reaction Zone. The simplest way to form nitride UFPs on a laboratory scale is to adopt the reactive gas condensation method with a resistive heating evaporator. UFPs of the Fe-N system were synthesized by evaporating iron from a tungsten basket heated to 1600-2300°C in NH gas pressure of 27 kPa (37). Crystalline phases of a-Fe, y-Fe including about 2.5wt% of nitrogen, and y -Fe4N depend on the NH3 gas pressure and the evaporation temperature. 

The third factors to control and keep constant are the gas pressure and superficial gas velocity. This probably will involve gas recirculation with either a small compressor, or through a hollow shaft or some other pumping device. As seen before, the bubble diameter, the mass transfer area, the gas hold-up, and the terminal bubble-rise velocity, all depend on the superficial velocity of the gas and the power input per unit volume. When these are kept constant, the various mass transfer resistances in the pilot plant and in the large unit will be the same, hence the global rate will be conserved. The last factor is the input power to the agitator. As required for mass transfer, the scale-up must be made on the basis of constant power input per unit volume. If turbulent conditions and geometrical similarity prevail, this rule imposes the following relationship ... 

Flows that develop a state that depends only on the local flow quantities, such as the local value of the mean velocity and the flow resistance, are said to be self-similar or self-preserving. This state of flow is present in the turbulent flow regime when sufficiently high Reynolds numbers are achieved. A majority of industrial combustion systems operate in this flow regime. When the scale model and prototype are both operating in the selfsimilar flow regime, they will manifest the same flow patterns and pressure drop coefficient despite different absolute local flow quantities. 

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