Crystals body-centered cubic

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

The conventional unit cell of a body-centered cubic crystal (bcc) consists of the eight corners of a cube and the point in the center. Describe the structures of the (100), (111), and (110) planes. 

Hard blue-white metal body-centered cubic crystal density 7.19 g/cm melts at 1,875°C vaporizes at 2,199°C electrical resistivity at 20°C, 12.9 microhm-cm magnetic susceptibility at 20°C, 3.6x10 emu standard electrode potential 0.71 V (oxidation state 0 to -i-3). 

Soft silvery metal body-centered cubic crystal lattice density 5.24 g/cm melts at 822°C vaporizes at 1,596°C electrical resistivity 81 microhm-cm reacts with water soluble in liquid ammonia. 

Silvery-white, soft maUeable metal exists in two aUotropic forms an alpha hexagonal from and a beta form that has body-centered cubic crystal structure the alpha allotrope converts to beta modification at 868°C paramagnetic density 7.004 g/cm compressibility 3.0x10 cm /kg melts at 1024°C vaporizes at 3027°C vapor pressure 400 torr at 2870°C electrical resistivity 65x10 ohm-cm (as measured on polycrystalline wire at 25°C) Young s modulus 3.79xl0 ii dynes/cm2 Poisson s ratio 0.306 thermal neutron cross section 46 barns. 

Grayish, soft metal with a white luster on polished surfaces ductile and very malleable at room temperature also highly ductile at cryogenic temperatures body-centered cubic crystals density 8.66 g/cm at 20°C melts at 2,468+10°C vaporizes at 5,127°C electrical resistivity 13.2 microhm-cm at 20°C becomes superconducting at 9.15K thermal neutron-capture cross section 1.1 barns insoluble in water insoluble in hydrochloric acid, nitric acid and aquaregia soluble in hydrofluoric acid soluble in fused alkah hydroxide. 

Silvery-white metal body-centered cubic crystals ductile soft and very hght (the fourth lightest metaUic element) Mobs hardness 0.3 density 1.522 g/cm3 at 18°C melts at 39.3°C density of the liquid metal 1.472 g/mL at 39°C vaporizes at 689°C producing a blue vapor vapor pressure 1 torr at 294°C and 10 torr at 387°C electrical resistivity 11.6 microhm-cm at 0°C and 13.1 mirohm-cm at 25°C viscosity 0.484 centipoise at 100°C magnetic susceptibility 0.09x10 cgs units at 18°C thermal neutron absorption cross section 0.73 barns reacts violently with water... 

The type of crystalline structure that is formed depends on the concentration of the particles as well as the magnitude of the Debye-Hiickel thickness. For large Debye-Hiickel thicknesses a body-centered cubic crystal is formed, whereas for smaller values a face-centered cubic crystal is preferred. An example of the latter observed experimentally in a dispersion of latex spheres is shown in Figure 13.3. Note that this crystallization phenomenon is analogous to crystallization of simple atomic fluids, as is evident from Figure 13.3a, which shows the coexistence of a crystal with a liquidlike structure. 

In order to understand and interpret the many details that can be observed, it is necessary to examine how the metal atoms can arrange themselves on a spherical surface. The best way to do this is to make a model of a body-centered cubic crystal, such as tungsten, whose surface is as close to a mathematical sphere as the size of its atoms permits. We have constructed such a model in which marbles represent tungsten atoms. The radius of curvature of the model is 25 atom (or marble) diameters. This is 40 to 100 times smaller than the metal points used in the microscope but does not change any of the essential features which we wish to bring out. 

CHROMIUM. [CAS 7440-47-3[. Chemical element, symbol Cr. at. nil. 24. at. wi. 51.996, periodic table group 6. mp 1837- 1877°C. bp 2672 C, density 7.2 g/cm. Elemental chromium has a body-centered cubic crystal structure The metal is silver-white with a slight gray-blue tinge, very hard (9.0 on the Mohs scale), capable of taking a brilliant polish, not appreciably ductile or malleable. The element is not aflected by air or HyO al ordinary temperatures, but when heated above 200°C, chromic oxide CryOt is formed. There tire four stable isotopes f0Cr. and, Cr through wCr. Fuur radioactive isotopes have been identihed, all with comparatively short half-lives 4 Cr. Jl,Cr. 1 Cr. and 5Cr, The element was first identified by Vauquelin in 1797. 

EUROPIUM. [CAS 7440-53-11. Chemical clement symbol Hit. at no 63. al. wt. 151.96, sixth in the Lanthanide Series in the periodic table, nip 822 C. bp 1529 C. density 5.245 g/cm1 20 C). Elemental europium has u body-centered cubic crystal structure at 25"C. The pure metallic europium... 

IRON. [CAS 7439-89-6). Chemical element symbol He. at. no, 26. al. l. 55.847. periodic table group 8 (transition metals), mp 1.535 C. bp approximately 2.750IC. density 7.874 g/cm3 for the pure solid i20 Ci 7.92 for a single crystal of a-iron. Iron has a body-centered cubic crystal structure (a-iron). 

POTASSIUM. [CAS 7440-09-7]. Chemical element, symbol K, at, no. 19, at. wt. 39.098, periodic table group 1 (alkali metals i, mp 63,3cC, bp 760°C. density 0.86 g/cm3 (20°C). Elemental potassium has a body-centered cubic crystal structure. Potassium is a silver-white metal, can be readily molded, and cut by a knife, oxidizes instantly on exposure to air, and reacts violently with H2O, yielding potassium hydroxide and hydrogen gas, which burns spontaneously in air with a violet flame due to volatilized potassium element, is preserved under kerosene, burns in air at a red heat with a violet flame. Discovered by Davy in 1807. 

RUBIDIUM. [CAS 7440-17-7J. Chemical element symbol Rb, at. no. 37, at, wl, 85,468, periodic table group 1. iup 38.9°C, bp 686cC, density 1.53 g/cm3 (20°C). Elemental rubidium has a body-centered cubic crystal structure. 

URANIUM. [CAS 7440-61-1], Chemical element symbol. U, at. no. 92, at. wt, 238,03, periodic table group (Actinides), mp 1,131 to i. 33°C, bp 3,818°C, density 18.9 g/cm3 (20UC). Uranium metal is found in three allotropic forms (1) alpha phase, stable below 668°C, orthorhombic (2) beta phase, existing between 668 and 774°C. tetragonal and (3) gamma phase, above 774°C, body-centered cubic crystal structure. The gamma phase behaves most nearly that of a true metal. The alpha phase has several nonmetallic features in its crystallography. The beta phase is brittle. See also Chemical Elements. 

Use nine 2-in.-diameter balls and eight toothpicks to form three layers of a body-centered cubic crystal, as illustrated in Figure 4.6 (the top layer is the same as the bottom layer). Put the layers together like a sandwich. Draw a picture of this atomic crystalline solid. 

PROBLEM 7.4.4. For a monoatomic cubic crystal consisting of spherical atoms packed as close as possible, given the choices of a simple cubic crystal (SCC atom at cell edges only this structure is rarely used in nature, but is found in a-Po), a body-centered cubic crystal (BCC, atom at comers and at center of body), and a face-centered cubic crystal (FCC body at face comers and at face centers), show that the density is largest (or the void volume is smallest) for the FCC structure (see Fig. 7.12). In particular, show that the packing density of spheres is (a) 52% in a simple cubic cell (b) 68% for a body-centered cell (c) 71% for a face-centered cubic cell. 

That is, among the pure iron forms, only ferrite (a, bcc) is magnetic. This is intriguing, as the 5-Fe form also exhibits a body-centered cubic crystal structure. This must indicate that in addition to the simple 3D arrangement of lattice iron atoms, their individual magnetic dipoles must also be suitably aligned in order to yield a particular magnetic behavior. 

As an example, we calculate F hkl) for a body-centered cubic crystal containing two atoms (e.g., CsCl) that are located in the unit cell at 0,0,0 and respectively. Equation (3.27) now becomes... 

Show that the side of the unit cell for a body-centered cubic crystal is 2.31 times the radius of the atoms in the crystal. 

Documentation exists in the literature as to the observation of anomalies in the temperature dependence of some physical properties of vanadium in the range 175-325 K. Although the anomaly was attributed by different workers to an antiferromagnetic transition, a small distortion of the body-centered cubic crystal structure, and impurities, Finkel et al. ( ) recently ascribed the anomaly to a second order phase transition at 230 K. Using low temperature x-ray diffraction techniques in the study of a single crystal of vanadium, Finkel et al. observed a decrease in crystal lattice symmetry form body-centered cubic (T > 230... 

Ferrite is essentially pure iron with a body-centered cubic crystal stracture. Ferrite forms from austenite at about 1675°F (915°C), as the austenite cools from a normalizing heat treatment. Because ferrite does not contain enough carbon to permit the formation of martensite, it is not hardenable by heat treatment. The most common truly ferritic steel is Type 405 SS, a ferritic stainless steel. The generic term ferritic steel often refers to carbon or low-alloy steels that contain other phases in addition to ferrite. Such steels are usually hardenable by heat treatment. Ferritic steels become brittle at low temperatures. This phenomenon is reversible, that is, the steels regain their former toughness after being warmed up. Ferritic steels are also susceptible to hydrogen embrittlement. 

Body-centered cubic crystal lattice d 5,244 mp 826°, Sol in liq ammonia. Shows two reduction potentials —0,710 and —2.510 v. (referred to a normal calomel electrode) Noddack, Brukl, Angew. Chem. 50, 362 (1937) gives two definite series of salts one in which the metal Is bivalent, and another in which it is trivalent. 

White malleable metal tarnishes in air has three crystal-line forms the a-modification, hexagonal crystals stable at ordinary temp, d 6.17 the 0-form, obtained on heating the a -form at 350% face-centered cubic crystals, d 6.19 the high temp >-form, exists above 868% body-centered cubic crystals, d 5,98. The metal melts at 920 . E°(aq) La3 /La — 2,52 V (calc). Very active dec water slowly in the cold, more readily on heating. Readily attacked by mineral acids not attacked by cold coned H SO, Burns in air at about... 

Light gray or white lustrous powder, fused hard lumps or body-centered cubic crystals not tarnished in air and not appreciably affected by moisture at ordinary temp, mp 1917°. d18 6.11. Sp heat (20-100°) 0.]2 cal/g/°C. Electrical resistivity 24.8 microhms/cm. Inso] in water. Not attacked by hot or cold hydrochloric add, by cold sulfuric acid. Reacts with hot sulfuric acid, hydrofluoric acid, nitric acid, aqua regia. Not attacked by bromine water, or by aq alkalies. The metal precipitates gold, silver and platinum from their salts reduces mercuric salts to mercurous, ferric salts to ferrous,... 

The solid solution of carbon in the body-centered cubic crystal structure of iron. The phase is stable at low temperatures and also, in some ferritic steels, at temperatures close to the melting temperature, when it is called 5-feirite. 

In the patent by Hill, an aUoy of titanium containing 13 wt%vanadium, 11 wt% chromium and 3 wt% aluminum was developed as a hydrogen transport membrane material [12]. In this alloy, the crystal structure of titanium, which is normally hexagonal below 1153 K (880 °C), is stabilized in its high-temperature body centered cubic allotropic form. The body centered cubic crystal lattice is preferred for hydrogen transport. This titanium alloy was found to have hydrogen permeability superior to that of pure palladium in the range 300-450 °C (573-723 K)... 

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