Fee lattice

Figure Bl.21.2. Atomic hard-ball models of stepped and kinked high-Miller-index bulk-temiinated surfaces of simple metals with fee lattices, compared with anfcc(l 11) surface fcc(755) is stepped, while fee...

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

The higher mass fullerenes (C76, Cs4), with multiple isomers of different shapes, also crystallize in the fee structure at room temperature, with an fee lattice constant which is approximately proportional to where n is the number of carbon atoms in the fullerene [53]. 

As examples of the successful application of the PIMC method outlined in Sec. IV D 1, we focus here on studies of crystal properties where either Ar, Ne atoms or N2 molecules occupy sites on an fee lattice. 

FIG. 13 Phase diagram of a vector lattice model for a balanced ternary amphiphilic system in the temperature vs surfactant concentration plane. W -I- O denotes a region of coexistence between oil- and water-rich phases, D a disordered phase, Lj an ordered phase which consists of alternating oil, amphiphile, water, and again amphi-phile sheets, and L/r an incommensurate lamellar phase (not present in mean field calculations). The data points are based on simulations at various system sizes on an fee lattice. (From Matsen and Sullivan [182]. Copyright 1994 APS.)... 

Figure 6.9 B12 Cubo-octahedral cluster as found in MBj2. This Bj2 cluster alternates with M atoms on an fee lattice as in NaCI, the Bj2 cluster replacing Cl.

The detailed structures of P0X4 are unknown. Some properties are in Table 16.5. P0F4 is not well characterized. P0CI4 forms bright-yellow monoclinic crystals which can be melted under an atmosphere of chlorine, and PoBr4 has a fee lattice with aq = 560 pm. These compounds and P0I4 can be made by direct combination of the... 

The fee lattice of the coinage metals has 1 valency electron per atom (d °s ). Admixture with metals further to the right of the periodic table (e.g. Zn) increases the electron concentration in the primary alloy ( -phase) which can be described as an fee solid solution... 

The functions Pcu(c,q) for the fee alloys can be averaged over the concentration c to obtain a probability Pcu(Q) that a Cu atom in any fee alloy will have a charge between q and q+dq. Recall that all of our calculations for fee were carried out with the same lattice constant. We approximate this function by averaging over the five concentrations that we considered, giving equal weight to all of them. It can be seen from the plot of this function in Fig. 5 that the probability is not uniform in q, but has thirteen prominent peeks. Since there are twelve atoms on the nearest-neighbor (nn) shell in a fee lattice, it is reasonable to write Pcu(q) as the sum of conditional probabilities Pcu(ci.q) where ci is the concentration of Cu atoms on the nn-shell. Five of the possible thirteen conditional probabilities are also plotted in... 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

Surprinslngly, we observe an drastic effect of the concentration on the SRO contribution (figure 2) indeed, in PtaV, the maxima are no longer located at a special point of the fee lattice but the (100) intensity is splltted perpendicularly in the (010) direction and presents a saddle point at (100) position. Notice that these two maxima are not located just above Bragg peaks of the ordered state the A B ground state presents Bragg peaks at ( 00) and equivalent positions whereas the SRO maxima peak between ( 00) and (100). 

Furthermore, a hierarchy of the potentials is expected, due to the geometry of the fee lattice. As the second, first and fourth can be reached by two first neighbours steps only and the further neighbours require more steps, we observe, especially with the Pt V set, the corresponding hierarchy Vi >> V2jV3,V4 >> V5,V6," - The fact that we observe this fee hierarchy between the V s and their concentration independence gives us confidence in the model and our procedure. 

We have measured the experimental SRO contribution in PtsV and Pt V alloys. The PtsV SRO displays maxima at (100) positions despite a ground state built with the (1 0) concentration wave. For Pt V, the maxima are not located at special points of the fee lattice. 

The aim of the present study is precisely to investigate the thermodynamical properties of an interface when the bulk transition is of first order. We will consider the case of a binary alloy on the fee lattice which orders according to the LI2 (CuaAu type) structure. 

We have carried out impurity calculations for a zinc atom embedded in a copper matrix. We first perform self consistent band theory calculations on pure Cu and Zn on fee lattices with the lattice constant of pure Cu, 6.76 Bohr radii. This yields Fermi energies, self consistent potentials, scattering matrices, and wave functions for both metals. The Green s function for a system with a Zn atom embedded in a Cu matrix... 

Similar calculations were carried out for the single impurity systems, niobium in Cu, vanadium in Cu, cobalt in Cu, titanium in Cu and nickel in Cu. In each of these systems the scattering parameters for the impurity atom (Nb, V, Co, Ti or Ni) were obtained from a self consistent calculation of pure Nb, pure V, pure Co, pure Ti or pure Ni respectively, each one of the impurities assumed on an fee lattice with the pure Cu lattice constant. The intersection between the calculated variation of Q(A) versus A (for each impurity system) with the one describing the charge Qi versus the shift SVi according to eqn.(l) estimates the charge flow from or towards the impurity cell.The results are presented in Table 2 and are compared with those from Ref.lc. A similar approach was also found succesful for the case of a substitutional Cu impurity in a Ni host as shown in Table 2. 

As schematically represented in Fig. 3 the structure can be considered two interpenetrating fee lattices of 8,2(8,2)12 units the 8,2(8,2)12 units of each fee lattice differ only by the 90° rotation of these units. Thus there are eight of these 8,2(8,2)12 units or 1248 8 atoms in the unit cell. The metal atom positions and the location of the remaining 8 atoms in the structure can be pictured in the octant of the cell shown in Fig. 3. Six metal atom sites exist in each octant of the ceil, and these are statistically half-filled. The sites are located 1.27 10 pm (for YB g) inside the cell from the center of each face of an octant one such site is depicted in Fig. 3. The center of each octant is occupied by either a 36- or a 48-8 atom group, which are labeled, respectively, configurations I and II (Fig. 4). Half of the octants contain configuration I, and half contain 11 in a random fashion. ... 

The suppression of C60 crystallite formation in mixed LB films was attempted by mixing C60 and amphiphilic electron donor compounds [259]. Observation of the C60 LB film transferred horizontally by TEM clearly showed 10-40-nm-size crystallites. The diffraction pattern gave an fee lattice with unit cell length 1.410 nm. Examination of the mixed films with arachidic acid by TEM showed extensive crystallite formation. Mixed LB films of three different amphiphilic derivatives of electron donors with C60 were examined. One particular derivative showed very little formation of C60 crystallites when LB films were formed from monolayers of it mixed with C60 in a 1 2 ratio, while two others reduced C60 crystallite formation but did not eliminate it. 

The difference between the fee and hep structure is best seen if one considers the sequence of dose-packed layers. For fee lattices this is the (111) plane (see Figs. 5.1 and 5.3), for hep lattices the (001) plane. The geometry of the atoms in these planes is exactly the same. Both lattices can now be built up by stacking dose-packed layers on top of each other. If one places the atoms of the third layer directly above those of... 

The number of adsorption sites on a surface per unit or area follows straightforwardly from the geometry. Consider, for example, adsorption on a four-fold hollow site on the fee (100) surface. The number of available sites is simply the number of unit cells with area (ja /2) per m, where a is the lattice constant of the fee lattice. Note that the area of the same (100) unit cell on a bee (100) surface is just a, a being again the lattice constant of the bcc lattice. 

From a structural point-of-view the bulk metallic state, that is, fee lattice (with varying densities of defects such as twins and stacking faults) is generally established in gold nanoparticles of about 10 nm diameter and upwards. However, such particles still display many unusual physical properties, primarily as the result of their small size. Shrinking the size of gold particles has an important effect it increases both the relative proportion of surface atoms and of atoms of even lower coordination number, such as edge atoms [49] and these atoms in turn are relatively mobile and reactive. 

Fig. 3. The scheme of the directions toward the nearest missing neighbors, cut by the (001), (201), and (101) planes for an atom of the fee lattice.

Fig. 5, The scheme of the arrangement of atoms around the (111) plane of the fee lattice and around the (0001) plane of the hep lattice. The arrows represent those directions toward the nearest missing neighbors, which are sticking out perpendicularly to a given plane. No other directions are indicated. Only the atoms on edges are reproduced here.

Fig. 20. Variation of the composition of Ni-Al alloy electrodeposits as a function of the applied potential in the 66.7 m/o AlCl3-EtMeImCl melt the Ni(n) concentrations were ( ) 10.0, (+) 25.0, ( ) 35.0, and (x) 50.0 mmol L 1. The dotted line represents the theoretical composition assuming an fee lattice at 40 °C, following the thermodynamic treatment of Moffat [80], Adapted from Pitner et al. [47] by permission of The Electrochemical Society.

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