Chromium calculation

The total density of states for chromium, calculated by Rath and Callaway (1973), using the technique discussed in Section 2-Ei. The Fermi energy for chromium, at six electrons per atom, is indicated, [After Rath and Callaway, 1973,]... 

To give a feeling for orders of magnitude, Table 4.2 lists some selected potential parameters for chromium calculated from the entries in Table 4.1 by means of (3.50,4.7,8,14). We shall return to them when we consider volume derivatives in Sect.4.5. 

The width of molecular weight distribution (MWD) is usually represented by the ratio of the weight—average and the number—average molecular weights, MJM. In iadustry, MWD is often represented by the value of the melt flow ratio (MER), which is calculated as a ratio of two melt indexes measured at two melt pressures that differ by a factor of 10. Most commodity-grade LLDPE resias have a narrow MWD, with the MJM ratios of 2.5—4.5 and MER values in the 20—35 range. However, LLDPE resias produced with chromium oxide-based catalysts have a broad MWD, with M.Jof 10—35 and MER of 80-200. 

Such significant increase of accuracy may be explained on the base of analysis of the numerical values of the theoretical correction coefficients and calculated for 1, , and for analytical pai ameter lQ.j,yipj.j,jj- Changing from lines intensities for the ratios of analytical element line intensity to the intensity of the line most effecting the result of analytical element (chromium in this case) measurement enables the decreases of the error 5 or even 10 times practically to the level of statistics of the count rate. In case of chromium the influencing elements will be titanium, tungsten or molybdenum. 

For metal compounds, the calculation of the reportable concentration and treatment efficiency is based on the weight ot the parent metal, not on the weight of the metal compounds Metals are not destroyed, only physically removed or chemically converted from one form into another. The treatment efficiency reported represents only physical removal of the parent metal from the wastestream, not the percent chemical conversion of the metal compound. If a listed treatment method converts but does not remove a metal (e.g., chromium reduction), the method must be reported, but the treatment efficiency must be reported as zero. 

CALCULATION OF THE ELECTRONIC STRUCTURE OF ANTIFERROMAGNETIC CHROMIUM WITH A SINUSOIDAL SPIN DENSITY WAVE BY THE METHOD OF DIRAC FUNCTION LINEAR COMBINATION... 

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

The points shown in these graphs have been calculated by the present authors from the original data they are averages for the three soils Nos. 58, 63 and 64 in the American paper. There were only single samples of carbon steel and of 2% Cr steel, but there were three 5% Cr steels, the results of which have been averaged. Some of the chromium steels also contained about 0.5% Mo. 

Now in the case of chromium carbide separation from the steel, three possible crystal structures may be taken up, those of CrjC, (or CrjsCJ, Cr7C3 and CrjCj. It is necessary first to calculate the free energies of formation of the compounds from pure chromium and carbon. The results are ... 

Mukherjee studied the gas phase equilibria and the kinetics of the possible chemical reactions in the pack-chromising of iron by the iodide process. One conclusion was that iodine-etching of the iron preceded chromis-ing also, not unexpectedly, the initial rate of chromising was controlled by transport of chromium iodide. Neiri and Vandenbulcke calculated, for the Al-Ni-Cr-Fe system, the partial pressures of chlorides and mixed chlorides in equilibrium with various alloys and phases, and so developed for pack aluminising a model of gaseous transport, solid-state transport, and equilibria at interfaces. 

Standardise the ammonium iron(II) sulphate solution against the 0.02/Vf potassium dichromate, using /V-phenylanthranilic add as indicator. Calculate the volume of the iron(II) solution which was oxidised by the dichromate originating from the chromium salt, and from this the percentage of chromium in the sample. 

But similar calculations do not fare as well in other atoms. Consider the case of the chromium atom for example.9... 

The calculation of C according to (6) shows (95) that if the catalyst splitting results in the formation of catalyst pellets about 1000 A in size, then even under the most unfavorable conditions (the concentration of the active centers is equal to the total chromium content in the catalyst, 2r2 = ) the diffusional restriction on the primary particle level is negligible. 

In Hogan (69) it was supposed that in a highly active catalyst containing 0.01% of chromium all the chromium ions act as active centers. According to this it was calculated that in the catalyst containing 1% of chromium on silica the number of propagation centers reached 10% of the supported chromium. 

Relaxation experiments. Use the relaxation times for the equilibrium shown to calculate the forward and reverse rate constants. The values are expressed in terms of the total concentration of chromium(VI), or [Cr(VI)]i = [HCrOj] + 2[Cr202 ] ... 

Calculate the atomic radius of each of the following elements from the data given (a) silver, fee structure, density 10.500 g-cm 3 (b) chromium, bcc structure, density 7.190 g-cm-3. 

The role of coordinated ethylene is evidenced by the recent ab initio calculation performed by Espelid and Borve [121-123], who have shown that ethylene may coordinate in two different ways to the reduced Cr(II) species, either as a molecular complex or covalently bound to chromium. At longer Cr-C distances (2.36-2.38 A) an ethylene-chromium zr-complex forms, in which the four d electrons of chromium remain high-spin coupled and the coordination interaction is characterized by donation from ethylene to chromium. Cr(II) species in a pseudo-tetrahedral geometry may adsorb up to two equivalents of ethylene. In the case of a pseudo-octahedral Cr(II) site a third ethylene molecule can also be present. The monoethylene complex on the pseudo-tetrahedral Cr(II) site was also found to undergo a transformation to covalently bound complex, characterized by shorter Cr-C distances (about... 

The total heat requirement is thus around 599.98 kj, which is about 548.81 kj more than the heat available from the reaction. This calculation, however, does not take into account the inevitable heat losses due to the nonadiabatic conditions in the reactor. An estimate of these heat losses can be made by considering the industrial practice for aluminothermic chromium metal production. The charge is preheated to about 500 °C before loading into the aluminothermic crucible. This operation adds about 96.65 kj (i.e., 48.9 cal deg-1 475) of heat to the system. It, therefore, appears that around 41.84 kj (96.65 kj - 54.81 kj) of heat is lost due to radiation and convection for every mole of chromium sesquioxide reduced to the metal by the aluminothermic process. 

The melting points of chromium (1857 °C) and of manganese (1244 °C) are considerably lower than that of alumina. The heat requirement in respect of the reactions leading to the formation of these metals was calculated by considering alumina melting as the objective. The objective changes when aluminothermy is applied to the production of the refractory metals niobium and tantalum. Niobium melts at 2468 °C and tantalum at 3020 °C. Thus, when these metals are the products, the heat requirements for reaching temperatures in excess of 2500 °C and 3050 °C have to be calculated. 

The theoretical amount of sulfurous acid required to reduce a given amount of chromium can be calculated from the above equation. The actual amount of sulfurous acid required to treat a wastewater will be greater than this because other compounds and ions present in the wastewater may consume some of the acid. Primary among these is dissolved oxygen, which oxidizes sulfurous acid to sulfuric acid according to the following reaction ... 

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