Transformation point

Ytterbium has a bright silvery luster, is soft, malleable, and quite ductile. While the element is fairly stable, it should be kept in closed containers to protect it from air and moisture. Ytterbium is readily attacked and dissolved by dilute and concentrated mineral acids and reacts slowly with water. Ytterbium has three allotropic forms with transformation points at -13oC and 795oC. The beta form is a room-temperature, face-centered, cubic modification, while the... 

Umwandltmgs-produkt, n. transformation prod uct. -punkt, m. transformation point, transition point, -spanntmg,/. (Elec.) transforma-... 

Uwp.,a66rec. (Umwandlungspunkt) transformation point, transition point. 

Allenylcobaloximes, e.g. 26, react with bromotrichloromethane, carbon tetrachloride, trichloroacetonitrile, methyl trichloroacetate and bromoform to afford functionalized terminal alkynes in synthetically useful yields (Scheme 11.10). The nature of the products formed in this transformation points to a y-specific attack of polyhaloethyl radicals to the allenyl group, with either a concerted or a stepwise formation of coba-loxime(II) 27 and the substituted alkyne [62, 63]. Cobalt(II) radical 27 abstracts a bromine atom (from BrCCl3) or a chlorine atom (e.g. from C13CCN), which leads to a regeneration of the chain-carrying radical. It is worth mentioning that the reverse reaction, i.e. the addition of alkyl radicals to stannylmethyl-substituted alkynes, has been applied in the synthesis of, e.g., allenyl-substituted thymidine derivatives [64],... 

Kawata et al. (1979) and Kawata and Ichioka (1980a, 1980b) discuss the convergence of these methods from both linear algebra and Fourier transform points of view. They also introduce a reblurring method that guarantees convergence. We pursue this idea in Section IV.D.3. 

Molten sodium and potassium hydroxides are completely miscible in all proportions, and the f.p. curve has a minimum at 187° with a mixture containing 38 7 atomic percent, of KOH, that is, 48 97 per cent, of KOH by weight. The transformation temp, of the cooling solid alloys furnish a curve similar in form to the f.p. curve, and the solid eutectic has a transformation point at 181°., Mixtures of potassium and rubidium hydroxides are completely miscible, and they give a curve with two maxima-, one rises from the m.p. of potassium hydroxide 360-4° up to 399° with 87 atomic per cent, of KOH, and the other from the m.p. of rubidium hydroxide... 

F. Wallerant found that when mixed crystals are formed with increasing proportions of rubidium nitrate, the transformation point of caesium nitrate was lowered from 161°, until, with 75 per cent, of RbNOa, it reaches 145° the transition... 

To check the phase transformation isotropic -> nematic, the validity of the Clausius Clapeyron equation is examined. It has been shown 38), that within the experimental error the results fulfill Eq. 1 in analogy to the low molar mass l.c. The phase transformation isotropic to l.c. is therefore of first order with two coexisting phases at the transformation point. Optical measurements on the polymers confirm these thermodynamical measurements (refer to 2.3.1.3). 

R, which transforms / into a new function / = Rf, is called a function operator. Equation (3) states that the value of the new function Rf, evaluated at the transformed point x, is the same as the value of the original function / evaluated at the original point x. Equation (3) is of great importance in applications of group theory. It is based (i) on what we understand by a function and (ii) on the invariance of physical properties under symmetry operations. The consequence of (i) and (ii) is that when a symmetry operator acts on configuration space, any function/ is simultaneously transformed into a new function Rf. We now require a prescription for calculating Rf. Under the symmetry operator R, each point P is transformed into P ... 

The second equality states thatf( xy z ) is to become f( yxz ) so that x is to be replaced byy, and v by —x (and z by z) this is done on the third line, which shows that the function dxy is transformed into the function —dxy under the symmetry operator R(n/2 z). Figure 3.6 shows that the value of Rdxy = d xy = —dxy evaluated at the transformed point P has the same numerical value as dxy evaluated at P. Figure 3.6 demonstrates an important result the effect of the function operator R on dxy is just as if the contours of the function had been rotated by R(n/2 z). However, eq. (7) will always supply the correct result for the transformed function, and is especially useful when it is difficult to visualize the rotation of the contours of the function. 

It will be more economical in the first two sections to label the coordinates of a point P by xi x2 x3. Symmetry operations transform points in space so that under a proper or improper rotation A, P(xi x2 x3) is transformed into P (xi x x3 ). The matrix representation of this... 

The displacement by in the first row and fourth column comes from the mirror reflection in the plane at x = 1/4. The A in the second and third rows of the fourth column are the components of the diagonal glide. The location of the transformed point is that marked by a comma (,) and M>+. The MR of the operation (rry A 0 0)[xyz], when the axial glide plane lies at y=lA, is... 

Assessment of the fit By calculating the transformed points Yj = Ryt + t, one can report the deviation in individual atomic positions xt — Yt. Scanning such a list can reveal that certain portions of the selected regions fit well and that others do not. 

Near the solid state transformation points the isobaric temperature coefficients can reach very high values. An example of such behaviour is the temper-... 

The situation is quite different when the Townes-Dailey Equation (IV.6) is applied to substances which change the crystal structure at certain transformation points within the usual range of measurements. Such an example is shown in Fig. IV.2. The effective temperature coefficient la I is fairly high and differs considerably from modification to modification. The consequence is a difference of up to 5 per cent in the calculation of the covalent character from NQR measurements at different temperatures. 

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