Muffins

Figure B3.2.3. The muffin-tin spheres in the (110) plane of a zineblende erystal. The niielei are surrounded by spheres of equal size, eovering about 34% of the erystal volume. Uuoeeupied tetrahedral positions are iudieated by erosses. The eouveutioual unit eell is shown at the bottom the erystal direetions are noted.

The LMTO method [58, 79] can be considered to be the linear version of the KKR teclmique. According to official LMTO historians, the method has now reached its third generation [79] the first starting with Andersen in 1975 [58], the second connnonly known as TB-LMTO. In the LMTO approach, the wavefimction is expanded in a basis of so-called muffin-tin orbitals. These orbitals are adapted to the potential by constmcting them from solutions of the radial Scln-ddinger equation so as to fomi a minimal basis set. Interstitial properties are represented by Hankel fiinctions, which means that, in contrast to the LAPW teclmique, the orbitals are localized in real space. The small basis set makes the method fast computationally, yet at the same time it restricts the accuracy. The localization of the basis fiinctions diminishes the quality of the description of the wavefimction in die interstitial region. 

Methfessel M, Rodriguez C O and Andersen O K 1989 Fast full-potential calculations with a converged basis of atom-centered linear muffIn-tIn orbitals structural and dynamic properties of silicon Phys. Rev. B 40 2009-12... 

Waffles, muffins, quick yeast breads, all-purpose flour... 

Bakery Products. Sorbates are used in and/or on yeast-raised and chemically leavened bakery products. The internal use of sorbates in yeast-raised products at one-fourth the amount of calcium—sodium propionate that is normally added provides a shelf life equal to that of propionate without adversely affecting the yeast fermentation. Sorbates added at one-tenth the propionate level reduce the mix time by 30% (126). This internal treatment combined with an external spray of potassium sorbate can provide the same or an increased shelf life of pan breads, hamburger and hot-dog buns, English muffins, brown-and-serve roUs, and tortillas. The total sorbate useful in or on these baked goods ranges from 0.03 wt % for pan breads to 0.5 wt % for tortillas 0.2—0.3 wt % sorbic acid protects chemically leavened yellow and chocolate cakes (127). Emit-pie fillings and icings can be protected with 0.03—0.1 wt % sorbates. 

Many other products belong to the category of yeast-raised bakery foods (6—9). Some that may be cited include various kinds of specialty breads, coffee cakes and danish pastries, bagels, croissants, yeast-raised doughnuts, some types of crackers, English muffins, and roUs. Of the total annual sales of the baking industry, yeast-raised goods constitute about 61%. 

We have used the basis set of the Linear-Muffin-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed the Vosko-Wilk-Nusair parametrization for the exchange-correlation energy density and potential. In conjunction with this we have treated the alloying effects for random and partially ordered phases with a multisublattice generalization of the coherent potential approximation (CPA). 

O.K. Andersen, Z. Pawlowska, and O. Jepsen, Illustration of the linear-muffin-tin-orbital tight-binding representation Compact orbitals and charge density in Si, Phys. Rev. B 34 5253 (1986). 

Most of the present implementations of the CPA on the ab-initio level, both for bulk and surface cases, assume a lattice occupied by atoms with equal radii of Wigner-Seitz (or muffin-tin) spheres. The effect of charge transfer which can seriously influence the alloy energetics is often neglected. Several methods were proposed to account for charge transfer effects in bulk alloys, e.g., the so-called correlated CPA , or the screened-impurity model . The application of these methods to alloy surfaces seems to be rather complicated. 

Theoretical calculations were performed with the linear muffin tin orbital (LMTO) method and the local density approximation for exchange and correlation. This method was used in combination with supercell models containing up to 16 atoms to calculate the DOS. The LMTO calculations are run self consistently and the DOS obtained are combined with the matrix elements for the transitions from initial to final states as described in detail elsewhere (Botton et al., 1996a) according to the method described by Vvedensky (1992). A comparison is also made between spectra calculated for some of the B2 compounds using the Korringa-Kohn-Rostoker (KKR) method. 

B. Wenzien J. Kudrnovsky, V. Drchal and M. Sob, On the calculation of the surface Green s function by the tight-binding linear-muffin tin orbital method, J. Phys. Condens. Matter 1, 9893 (1989). 

I.A. Abrikosov and H.L.Skriver, Self-consistent linear-muffin-tin-orbitals coherent-potential technique for bulk and surfaces calculations Cu-Ni, Ag-Pd, and Au-Pt random alloys, Phys. Rev. B 47, 16 532 (1993). 

The muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

Foulis, D.L., Pettifer, R.F., and Sherwood, P, 1995, The removal of the muffin-tin approximation and use of self-consistent-field electron densities for calculating the K-edge X-ray absorption nearedge structure of chlorine, Europhys. Lett. 29 647. 

Sun, C., and Su, C., 1978, Overlapping muffin tin multiple scattering wave Xo method, Scienta Sinica 21 327. 

Local-density approxmiation (LDA) comparison with GGA Local spm-deasity approxmiation (LSDA) Lmear-muffin-tm orbital (LMTO)... 

You are probably most familiar with Teflon as a nonstick coating for kitchen utensils (Figure 23.2). The slippery surface of Teflon-coated fry pans and muffin tins results from Teflon s extremely low coefficient of friction. 

If financially feasible, suggest the use of commerdally available drug organizers. If the patient cannot afford drug organizers, egg cartons or a muffin tin can be labeled and used as drug organize s. 

Elderberries are used medicinally for catarrh, sore throats, fever and asthma. When cooked with a sweetener into a thick syrup known as a rob they offer the same health benefits. Elderberries are excellent in pies, cobblers, jam, chutney, muffins and puddings. Elderberries are rich in vitamin C, calcium, phosphorus and beta-carotene. The berries may be dried and used in winter. Avoid green, unripe berries. The berries should be cooked before eating, remove the seeds when making jam or wine. Elderberry jam is sometimes served as a alternative to cranberry sauce, accompanying turkey or game. 

Sift together the flour, baking powder and salt. Stir in the elder flowers or berries. Add the remaining ingredients. Fill lightly greased muffin tins 2/3 full and bake in an oven preheated to 400 degrees F. for 25 minutes. 

Weyrich, K.H. (1988) Full-potential linear muffin-tin-orbital method, Phys. Rev., B37, 10269-10282. 

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