48.Rayos X de longitud de onda de 2,63 ... se utilizaron para analizar un cristal. El ngulo de difraccin de primer orden (n-1 en la ecuacin de Bragg) fue 15.55 grados. Cul es la distancia entre planos del cristal, y cul sera el ngulo de segundo orden de difraccin (n = 2)? 48. X rays of wavelength 2.63 were used to analyze a crystal. The angle of first-order diffraction (n 1 in the Bragg equation) was 15.55 degrees. What is the spacing between crystal planes, and what would be the angle for secondorder diffraction (n 2)? 56. El hierro tiene una densidad de 7,86 g/cm3 y se cristaliza en una red cbica bodycentered. Muestran que slo el 68% de una centrada en el cuerpo red est actualmente ocupada por tomos, y determinar la atmica radio de hierro. Iron has a density of 7.86 g/cm3 and crystallizes in a bodycentered cubic lattice. Show that only 68% of a body-centered lattice is actually occupied by atoms, and determine the atomic radius of iron.

El hierro tiene una densidad de 7,86 g/cm3 y se cristaliza en una red cbica bodycentered. Muestran que slo el 68% de una red centrada en el cuerpo es en realidad ocupada por tomos, y determinar el radio atmico del hierro. 76) . The structures of another class of ceramic, high-temperature superconductors are shown in the following figure. a. Determine the formula of each of these four superconductors. b. One of the structural features that appears to be essential for hightemperature superconductivity is the presence of planar sheets of copper and oxygen atoms. As the number of sheets in each unit cell increases, the temperature for the onset of superconductivity increases. Order the four structures from lowest to the highest superconducting temperature. c. Assign oxidation states to Cu in each structure assuming Tl exists as Tl3_. The oxidation states of Ca, Ba, and O are assumed to be _2, _2, and _2, respectively. d. It also appears that copper must display a mixture of oxidation states for a material to exhibit superconductivity. Explain how this occurs in these materials as well as in the superconductor in Exercise 85. Las estructuras de otra clase de cermica, los superconductores de alta temperatura se muestran en la figura siguiente. una. Determinar la frmula de cada uno de estos cuatro superconductores.

b. Una de las caractersticas estructurales que parece ser esencial para la superconductividad de alta temperatura es la presencia de hojas planas de cobre y tomos de oxgeno. Como el nmero de hojas en cada celda unidad aumenta, la temperatura para el inicio de los aumentos de superconductividad. Ordene las cuatro estructuras de menor a mayor temperatura de superconduccin. c. Asigne estados de oxidacin de Cu en cada estructura de TI, suponiendo que existe Tl3_. Los estados de oxidacin de Ca, Ba, y O se supone que son _2, _2, y _2, respectivamente. d. Tambin parece que el cobre debe mostrar una mezcla de estados de oxidacin de un material a exhibir superconductividad. Explica cmo esto ocurre en estos materiales, as como en el superconductor en el ejercicio 85. 104. Use the accompanying phase diagram for carbon to answer the following questions. a. How many triple points are in the phase diagram? b. What phases can coexist at each triple point? c. What happens if graphite is subjected to very high pressures at room temperature? d. If we assume that the density increases with an increase in pressure, which is more dense, graphite or diamond? Utilice el diagrama de fase de acompaamiento para el carbono para responder a las siguientes preguntas. una. Cuntos puntos triples en el diagrama de fase? b. Qu fases pueden coexistir en cada punto triple? c. Lo que sucede si el grafito se somete a presiones muy elevadas a temperatura ambiente? d. Si suponemos que la densidad aumenta con un aumento de la presin, que es ms denso, grafito o diamante?

5.13 Lattice energy: estimates from an electrostatic modelThe lattice energy, _U(0 K), of an ionic compound is the change in internal energy that accompanies the formation of one mole of the solid from its constituent gas-phase ions at 0 K.

For a salt MXn, equation 5.7 defines the reaction, the energy change for which corresponds to the lattice energy. The lattice energy can be estimated by assuming an electrostatic model for the solid state ionic lattice; the ions are considered to be point charges. Later in this chapter,we consider to what extent this approximation is true.

Coulombic attraction within an isolated ion-pairBefore we consider an ionic lattice, let us review the appropriate equation for the change in internal energy when two oppositely charged ions Mz and Xz_ are brought together from infinite separation to form the isolated ion pair, Let the ions carry charges of ze and z_e where e is the electronic charge and z and z_ are integers. The ions attract each other, and energy is released as the ion-pair is formed. The change in internal energy can be estimated from equation 5.9 by considering the Coulombic attraction between the ions. For an isolated ion-pair:

Coulombic interactions in an ionic latticeNow consider a salt MX which has an NaCl lattice. A study of the coordination geometry in Figure 5.15 (remembering that the lattice extends indefinitely) shows that each Mz ion is surrounded by: and so on. The change in Coulombic energy when an Mz ion is brought from infinity to its position in the lattice is given by equation 5.10. The ratio of the charges on the ions is constant for a given type of structure (e.g. 1 for NaCl) and so the series in square brackets in equation 5.10 (which slowly converges and may be summed algebraically) is a function only of the crystal geometry. Similar series can be written for other crystal lattices, but for a particular structure type, the series is independent of jzj, jz_j and r. Erwin Madelung first evaluated such series in 1918, and the values appropriate for various lattice types are Madelung constants, A (see Table 5.4). Equation 5.10 can therefore be written in the more simple form of equation 5.11, in which the lattice energy is estimated in joules per mole of compound.