Questions and Answers of Solid State Materials Chemistry

Use the conductivity of copper given in Table 10.1 to calculate the resistance of a copper wire that is 3 mm in diameter and 20 cm long. Table 10.1 Substance Ag Cu Al Na ReO; Ti La SrMoO; Bi Mn NbN
Show by dimensional analysis that Equation (10.9) gives the proper units (A/m2) for the current density J. Remember 1 A = 1 C/s.Equation (10.9) J = neva = neE
Confirm Equation (10.10) by dimensional analysis in SI units. Remember that 1 A = 1 C/s.Equation (10.10) a=neu
(a) Estimate the carrier mobility μ in Na metal at 300 K via Equation (10.10), using the conductivity of Na in Table 10.2, and the Drude-model assumption that all valence electrons can respond to an
The conductivities and crystal structures of the heavier s-block metals are given in the table below. (a) Calculate the valence-electron concentration n in m−3 and arrange the elements from lowest
Show that at any finite temperature the crystal orbital at the Fermi level will have a 50% probability of being occupied.
At which energy separation from EF is the probability f(E) of an electronic state in a metal being occupied equal to 0.01 at(a) 10 K,(b) 100 K,(c) 300 K,(d) 1000 K.
(a) Within the assumptions of the Drude model, calculate the rms velocity of a valence electron in sodium metal at T = 300 K. (b) Use a quantum-mechanical model to estimate the Fermi velocity of the
What is the temperature dependence of the conductivity for(a) A metal,(b) An intrinsic semiconductor?
Compare electrical properties of copper and nickel. Which has higher carrier concentration? Which has higher carrier mobility? Which has higher conductivity and why?
Calculate the value of f(E) at the conduction-band edge in intrinsic Ge (Eg = 0.7 eV) at 300 K. Assume the Fermi level is located midway between the valence- and conduction-band edges.
Calculate the donor ionization energy and Bohr radius for a donor impurity in InP (the dielectric permittivity εr = 12.1, effective mass m* = 0.07me).
Will the temperature range over which a semiconductor that is in the saturation regime increase or decrease in response to the following changes:(a) The band gap of the semiconductor increases,(b)
In compounds containing lanthanoid ions, the 4f orbitals are sufficiently localized that interactions with orbitals on neighboring atoms can be neglected, hence W ≈ 0. In this limit, the Hubbard U
The perovskite NaOsO3 undergoes a transition from a paramagnetic metal to an antiferromagnetic semiconductor upon cooling below 410 K.(a) What is the electron configuration of osmium in this
Each of the following compounds contains an octahedrally coordinated transition metal ion and behaves as an insulator/semiconductor. Identify each as either a band insulator or a Mott–Hubbard
The images below show a portion of a chain of the conducting polymer polypyrrole, before (top) and after (bottom) oxidative doping. (a) Is the charge carrier formed in this process a polaron,
Consider the electronic structure of graphene. (a) At how many points in the first Brillouin zone do the conduction and valence bands of graphene meet? (b) What is the name given to those points? (c)
Name at least three ways in which the electronic structure and transport properties of graphene differ from a conventional semiconductor.
What percentage ofsingle-walled carbon nanotubesin a typicalsynthesis batch will be semiconducting? Explain your answer.
Consider the circumferential and translational vectors of a potential carbon nanotube shown below. (a) What are the n and m values of the circumferential vector C? (b) Is the T vector shown below a
Consider the unit of a carbon nanotube projected onto a graphene sheet shown below. (a) What are the n and m values of this carbon nanotube? (b) Is this a metallic or semiconducting nanotube? (c)
Tunneling magnetoresistance between two ferromagnetic films oriented parallel and antiparallel was measured to be 0.4, referring to Equation (11.1). Calculate the spin polarization P and the
All atomic magnetic moments in YBaFe2O5 lie along the y axis. Based on Figure 11.3 (in which two chemical unit cells are drawn on the left, four on the right) and information in the text, sketch
YBaMn2O5 has a structure with two crystallo graphically different Mn sites:(a) Determine the oxidation state and orbital occupancies of Mn(1) and Mn(2) in charge ordered YBaMn2O5. (b) The occupation
For each of the following perovskites predict whether there will be a cooperative Jahn–Teller distortion:(a) LaCrO3,(b) LaTiO3,(c) Low-spin LaCoO3,(d) High-spin NdMnO3.
You are asked to synthesize two samples of La0.8Sr0.2MnO3+δ, with δ = 0.1 and 0. At which temperature would you equilibrate the δ = 0.1 composition in ambient O2 atmosphere prior to quenching? How
Into the figure below, sketch the ordered dz2 orbitals of Mn3+ such that their orientation explains the magnetic moments in this La1/3Ca2/3MnO3 layer. Use the principle that follows from the magnetic
Perovskites with partially filled eg orbitals at the octahedrally coordinated atom respond to this impending violation of orbital degeneracy in a variety of ways. In SrFeO3, the eg electrons are
Sketch the Andreev reflection of an electron crossing from a metal into a superconductor in an electric circuit.
Calculate the total valence-electron content z per formula and predict the properties of the following half-Heusler alloys: Z Ferromagnet? sat (in g) Half-metal? Semiconductor? PdMnSb IrMnSb TiNiSn
Sketch the spin-up (majority) and spin-down (minority) orbitals of Co2MnSi around the Fermi energy so that half-metallicity is achieved.
Spin-resolved density of states were obtained by M. Kallmayer et al. [38] on Co2MnSi thin films. The DOS of the minority spin was 24 units, of the majority spin 306 units. Calculate the degree of
Consider the main families of superconducting materials discussed in this chapter: elemental metals, intermetallic compounds, fullerenes, organic conductors, cuprates, and iron pnictides. (a) State
State two properties that distinguish a superconductor from a normal metallic conductor.
Al has Tc = 1.14 K. Assuming it is in the BCS weak-coupling limit, calculate the superconducting gap 2Δ0. Give your answer in J, eV, and cm−1.
Al has a Debye frequency ωD = 5×1013 s−1 (~1670 cm−1) and N(EF)·V' = 0.168. Estimate the superconducting gap 2Δ0.
Sn and Pb have Tc = 3.7 K and 7.2 K respectively. When illuminated with far-IR radiation, they show a marked drop in reflectivity at frequencies of ~10 and ~20 cm−1, respectively. Rationalize these
The table below contains Tc values for different isotopically enriched samples of Sn and Hg. Assuming Tc ∝ M−α , determine α in each case. Give a short explanation of why Tc depends on the
Draw a sketch of the fcc structure of C60. Show the positions of octahedral and tetrahedral holes and state the number of each. Assuming that C60 has a radius of 5 Å, estimate the cubic cell
The table below contains data for the alkali-metal fullerides A3C60. (a) Give a brief explanation for the Tc changes observed in the 0 GPa data. (b) Give a brief explanation for the pressure
RbxCs3−xC60 compounds have Tc = 26.9 K, 32.9 K, and 31.8 K and room-temperature cell parameters a = 14.70 Å, 14.60 Å, and 14.45 Å for x = 0.35, 1.0, and 2.0,respectively. Predict the dependence
Perovskite-related SrBiO3 and Sr0.4K0.6BiO3 can both be prepared at high pressure. SrBiO3 has two BiO6 octahedral sites, one with bond distances of 2 × 2.281, 2 × 2.317, 2 × 2.321 Å and a second
Although the true structure of La2CuO4 is orthorhombic, it can be approximated as tetragonal with space group #139 I4/mmm, unit-cell parameters of a = 3.814 Å and c = 13.15 Å, and crystallo
Depending on the level of oxygen vacancies and temperature, YBa2Cu3O7−δ can be either a (poor) metallic conductor, an antiferromagnetically ordered insulator, or a superconductor. A simplified
A black material A was prepared by heating 0.3978 g of CuO, 0.1480 g of BaCO3, and 1.5069 g of La2O3 to 700 °C under N2 and rapidly cooling to room temperature. A contains 15.79% O by mass and
What is unusual about the superconducting phases Nd2−xCexCuO4 and Sr1−xNdxCuO2?
Write out half equations, the cell reaction, and determine the standard potential of the following cells given standard electrode potentials E(Cu+/Cu) = +0.34 V, E(Sn*/Sn) = -0.14 V, E(Co*/Co) =
In its charged state, a lead–acid battery contains PbO2 and Pb electrodes. The half equations that occur during discharge can be written as below. Give the overall cell equation and estimate E°
The non-rechargeable alkaline battery contains a Zn anode, MnO2 cathode, and KOH electrolyte, with MnO2 present slightly in excess of a 1:2 molar ratio for safety reasons. Propose a balanced equation
Nickel–cadmium batteries rely on the reaction between NiO(OH) and Cd metal with an alkaline electrolyte, with both metals forming hydroxides. Propose a balanced equation for the cell reaction and
Use the Nernst equation to estimate the potential of an electrochemical cell Zn(s)|Zn2+ (c1, aq)||Zn2+(c2, aq)|Zn(s) in which Zn concentrations c1 and c2 are 0.3 M and 0.8 M, respectively.
Write down the half equations that occur at each electrode in the oxygen sensor of Figure 13.17 and state the overall cell equation. Oxygen sensors of this type are used in car engines to monitor the
The table below contains conductivity data for a crystal of NaCl. Comment on the shape of a plot of ln(σT) versus 1/T. Estimate the activation energy for vacancy migration and Schottky defect
AgI is often described as a fast ion conductor. Given that NaCl has around 10−4 carriers per formula unit immediately below its melting point and that conductivities are ≈ 1 S/cm (AgI) and ≈
The table below contains conductivity data for two materials. The melting point of PbF2 is 1103 K.(a) Describe the structure of each material and the origin of the relatively high conductivities.(b)
At high temperature, La2Mo2O9 has a structure closely related to cubic β-SnWO4, which contains WO4 tetrahedra and Sn in a distorted six-coordinate environment. On cooling through 580 °C, a 2a × 3b
The table below lists the in-plane conductivity for graphite and K0.125C at two different temperatures. Comment on these values. Substance Graphite K0.125C (90 K) (S/cm) 1.3x104 1.1106 o(300 K)
The table below lists d spacings of the first four strong diffraction peaks observed in the diffraction patterns of graphite and two Rb intercalation compounds. Note that the graphite interlayer
The structure of the stage-1 KxC intercalate has been reported in space group Fddd with a pseudohexagonal unit cell of a = 4.92 Å, b = 8.51 Å, c = 21.4 Å with K at 0 0 0, C1 at 1 /4 1 /12 1 /8, C2
The Li graphite intercalate has a limiting composition LiC6. Sketch a possible unit cell in 2D and estimate the Li–Li distance assuming a C–C bond length of 1.42 Å.
Calculate the theoretical capacity in A h/kg for the electrode materials: (a) Li metal anode, (b) LiC6 anode, (c) LiTiS2 cathode, (d) LiCoO2 cathode.
For LiC6 calculate the theoretical capacity in A h/kg of carbon.
Assuming densities for LiFePO4, carbon black, and Teflon® to be 3.6, 1.8, and 2.2 g/cm3 respectively, calculate the reduction in volumetric density of a cathode comprising 10 wt% carbon and 5 wt%
Calculate the energy density in W h/kg for the Li/TiS2 cell. Assume an operating voltage of 2 V and that the electrolyte and packaging make up 50% of the mass.
Calculate the energy density in W h/kg for a battery based on a LixC6 anode and a Li1−xCoO2 cathode, operating at an average voltage of 3.6 V. Assume that the electrolyte and casing make up 50% of
The figure below shows E against x at 30 °C for a cell with a spinel-based LixMn2O4 cathode (0 (a) Describe the structure you might expect for a LiMn2O4 spinel. (b) State what can you conclude from
Li1Mn2O4 (a = 8.2495 Å) is cubic, whereas Li2Mn2O4 is tetragonal (a = 5.653 and c = 9.329 Å). Suggest a reason for lower symmetry of Li2Mn2O4. Calculate the volume change upon its formation from
The α-cristobalite polymorph of SiO2 has a tetragonal cell with a = 4.971 Å, b = 6.922 Å, with Si on 2a and O on 4f Wyckoff sites. The Si–O bond length is 1.60 Å and the average O–O distance
Calculate the surface area of(a) A 1 g single crystal of cristobalite (density = 2.3 g/cm3, assume the crystal takes a spherical shape),(b) A uniform powder of spherical crystals each with a diameter
Zeolite A can be described using a 11.9 Å primitive cubic cell with the origin at a β-cage centerin Figure 14.3. From the figure, make a visual estimate of the size of a sphere that would fit
Calculate the number of tetrahedral atoms per nm3 for each zeolite framework type listed in the table below. Name Space group Cell () SOD Imm LTA FAU ANA RHO Pmm Fdm la'd Im m 8.9650 11.919 24.34
The table above contains ideal framework coordinates for different zeolites. Use a package such as vesta (http://jp-minerals.org/vesta/en/) to produce a 3D drawing of each structure. For each example
Assuming that O atoms are in contact and have a radius of 1.35 Å, estimate the pore opening formed by a planar six-, eight-, ten-, and twelve-membered SiO4/2 ring. Note that if the rings are
In NaA, the total void space accessible is approximately 926 Å3. Sorption studies suggest H2O fills a volume ~833 Å3, whereas N2 only fills ~755 Å3. Comment on these observations.
Under certain conditions, a zeolite with the ZSM-5 framework and formula NaAlSi23O48 (A) can be synthesized. In the presence of (CH3CH2CH2)4NOH it is possible to prepare a material (B) with an
A mixture of Si(OCH3)4, (CH3)4NOH(aq), and Al(OCH2CH2CH3)3 was heated to drive off alcohol, resulting in a clear solution. This solution was heated at 130 °C in a sealed autoclave for 8 days. The
Haag and co-workers measured the cracking rate of n-hexane by HZSM-5 relative to a high-surface-area catalyst under identical experimental conditions. The dependence of the rate on the Al:Si ratio
When dimethylbenzenes (xylenes) are passed over acidic zeolites (HZSM-5 that contains 10-rings and HY that contains larger 12-rings), two processes can occur: isomerization to different mixtures of
The first peak in the powder diffraction pattern of a mesoporous MCM material with 30 Å pores recorded with a wavelength λ of 1.54 Å is at 2.2° 2θ. Estimate the thickness of the silica walls. A
Crystallographers have a rough “rule of thumb” that non-H atoms occupy around 18 Å3 in many crystal structures. Based on this assumption, estimate the percent pore space in the tpdc MOF on the
Consider the PtS net listed in Table 1.6. The dehydrated form of MOF-11 has composition Cu2(ATC) where ATC is 1,3,5,7-adamantane tetracarboxylate and contains a Cu paddle-wheel unit analogous to the
Consider a heterogeneous enantioselective catalyst based on a catalytically active metal center attached to a MOF linker.(a) How would you expect the reaction rate to compare to the equivalent
Using Zacharisen’s rules, explain why SiO2 forms a glass and MgO does not.
Explain why Zachariasen’s rules suggest that Al2O3 will not form a glass but aluminosilicates with typical compositions of 11–16 mole percent (mol%) Al2O3, 52–60 mol% SiO2, and 9–11 mol% K2O
Consider a glass of composition (M2O)x(SiO2)1−x, where M2O is an alkali-metal oxide. State the fraction of non-bridging oxygen and the ratio of non-bridging oxygen to silicon.
A sodium-silicate glass contains 25 mol% Na2O. Calculate its O:Si ratio and derive a formula for the composition of a glass with the same O:Si ratio yet with Na2O and CaO as the network modifiers
The glass core of an optical fiber has an index of refraction 1.64. The index of refraction of the cladding is 1.50.(a) What is the maximum angle a light ray can make with the wall of the core if it
Calculate the maximum angle a light ray can make in internal reflection with the wall of the core in an optical fiber made with SiO2 cladding (n2 = 1.609) and a core with a 1% higher refractive index.
Yellow light of the Na doublet with a wavelength of 589.3±0.3 nm and frequency of 5.09×1014 Hz in vacuum enters Fe2O3 that has a refractive index of 3.00. Calculate the speed, wavelength, and
Prove that Equation (15.6) reduces to the Lorenz–Lorentz equation (15.4) in the case of purely ionic bonding.Equation (15.6)Equation (15.4) a = 4x + (n - 1) Va 4 3 -Zeo (1)
Use the Anderson–Eggleton relationship to calculate the refractive index of the mineral orthoclase (KAlSi3O8) with a unit-cell volume 720.4 Å3 containing four formula units. The cation
Calculate the refractive index using the Gladstone–Dale approach for orthoclase of Problem 15.9 using the chemical refractivities from Table 15.1. Compare the result with that of Problem
Given the density of 2.655 g/cm3 of an SiO2 glass, estimate Va in Å3 per formula unit. Use the refractive index of 1.547 to calculate the polarization with the Lorentz–Lorenz equation
Calculate the percentage transmission for a 0.1 dB/km and 0.001 dB/km optic fiber after 1 km.
A layered material with approximate composition PbNbS3 was found to have a very similar X-ray-diffraction pattern to that of Sn1.17NbS3.17. Single-crystal studies revealed that the PbS portion could
The following examples of phase transitions are discussed either in this chapter or in other parts of the book. In each case, would you describe the transition as reconstructive, displacive, or
What is the wavelength (in nm), frequency (in s−1), and color of a photon with an energy of 3.60×10−19 J? What is its energy in eV?
What color would a material be if it absorbed (a) Red light, (b) Blue and green light, (c) Yellow light, (d) Green light, (e) Green and yellow light?
Classify each of the following pigments or gemstones as idiochromatic or allochromatic: (a) Cobalt blue, CoAl2O4, (b) Emerald, Be3Al2(SiO3)6:Cr3+, (c) Yellow ochre, FeOOH.

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