Diagonal effect/properties

All metallic properties have been lost in these elements, and so charge-lo-size ratios have little meaning. However, the same effects appear in the electronegativities of these elements, which show a strong diagonal effects... 

A rather useful means of discussing the diagonal effect is to appeal to the charge density of the ions of the elements in question, a property that consists of the charge of an ion divided by its volume. The ions of elements that show a diagonal relationship typically have similar charge densities. However, in the case of the boron—sdicon relationship, that option is not even available since these elements do not typically form ions. 

Four relevant properties of elements related to the diagonal effect. 

The elements of the diagonal effect. Lithium and magnesium, beryllium and aluminum, and boron and silicon, each pair diagonally located, have similar properties. 

Our network of interconnected ideas helps us to account for many expected properties of the alkali metals. The hydrides, oxides, hydroxides, and halides of these elements are ionic. The oxides and hydroxides are basic in character. Lithium, although stiU an alkali metal with much in common with its congeners, is certainly a good example of the uniqueness principle. It has much in common with magnesium, as forecast by the diagonal effect. 

The alkaline-earth metals superimposed on the interconnected network of ideas. These include the trends in periodic properties, the acid-base character of metal and nonmetal oxides, trends in standard reduction potentials, (a) the uniqueness principle, (b) the diagonal effect, (c) the inert-pair effect, and (d) the metal-nonmetal line. 

The alkaline-earth metals have many similarities to the alkali metals. In both groups, the lightest element is unique, the second element is intermediate in character, the third, fourth, and fifth elements form a closely allied series, and the sixth element is rare and radioactive. The network helps us account for and predict the properties of both groups. The network components of particular importance are the periodic law, the uniqueness principle, the diagonal effect, and the acid-base character of oxides. The alkaline-earth metals have similar reducing properties, boil and melt at higher temperatures, and are less electropositive and reactive than the alkali metals. 

Chapter 14 sketches nonlinear properties of polymer solutions, some classical and some quite modem. Strange behaviors can arise in polymer solutions because the normal stress differences are nonzero, i.e., the diagonal components of the pressure tensor can be unequal. Memory effect properties, such as stress and strain relaxations, and responses to imposing multiple strains, are noted. Finally we consider very recent developments in the study of nonlinear effects, such as shear banding and nonquiescent relaxation following imposition of a sudden strain. 

Diagonal similarities refer to chemical similarities of Period 2 elements of a certain group to Period 3 elements, one group to the right. This effect is particularly evident toward the left side of the periodic table. One example is the pair, B and Si, which are both metalloids with similar properties. Another example is the pair, Li and Mg. They have similar ionic charge densities and electronegativities their compounds are similar in... 

The operators Fk(t) defined in Eq.(49) are taken as fluctuations based on the idea that at t=0 the initial values of the bath operators are uncertain. Ensemble averages over initial conditions allow for a definite specification of statistical properties. The statistical average of the stochastic forces Fk(t) is calculated over the solvent effective ensemble by taking the trace of the operator product pmFk (this is equivalent to sum over the diagonal matrix elements of this product), so that = Trace(pmFk) is identically zero (Fjk(t)=Fk(t) in this particular case). The non-zero correlation functions of the fluctuations are solvent statistical averages over products of operator forces,... 

Equation (I-l) is the general representation of the dispersion model. The dispersion coefficient is a function of both the fluid properties and the flow situation the former have a major effect at low flow rates, but almost none at high rates. In this general representation, the dispersion coefficient and the fluid velocity are all functions of position. The dispersion coefficient, D, is also in general nonisotropic. In other words, it has different values in different directions. Thus, the coefficient may be represented by a second-order tensor, and if the principal axes are taken to correspond with the coordinate system, the tensor will consist of only diagonal elements. 

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