Questions and Answers of Solid State Materials Chemistry

Use crystal-field theory to qualitatively predict the energy splitting of the d orbitals for a transition-metal ion linearly coordinated along the z axis.
Predict which of the following pairs will have larger ligand-field splitting (Δoct): (a) [Fe(HO)]+ or [Co(HO)]+, (b) [Co(HO)]+ or [Rh(HO)]+.
A carbon atom has a 1s2 2s2 2p2 electron configuration. The various ways of filling the 2p orbitals lead to 15 microstates that can be grouped into three terms: 1D, 3P, and 1S. (a) Determine the
The UV–visible spectrum of the octahedral complex [Ni(NH2CH2CH2NH2)3]2+ is shown below.(a) Given that ethylenediamine ligand, NH2CH2CH2NH2, is a neutral bidentate ligand (both nitrogen atoms
Which of the two correlation diagrams shown below would be appropriate for tetrahedral [CoCl4]2−? For the applicable correlation diagram, what are the correct term symbols for the lines labeled W,
For which of the following ions is the d-to-d transition spin-forbidden, Laporteforbidden, both or neither: (a) Tetrahedral Co2+, (b) Square-planar Cu2+, (c) Octahedral Mn2+ (high spin), (d)
Tetrathiomolybdate MoS42− is tetrahedral and features a strong t1 → e LMCT absorption at 470 nm. (a) What color would you predict for (NH4)2MoS4? (b) What is the energy in eV of the LMCT
Which semiconductors in Table 7.8 will have colors other than white or black? For each compound in your list predict the approximate color.Table 7.8 Si Ge Elemental semiconductors Bond Band gap
The red pigment vermillion (HgS) is a semiconductor with a band gap of 2.0 eV. It was replaced in the late nineteenth and early twentieth century by CdS1−xSex pigments that are less toxic and more
How do fluorescence and phosphorescence differ from each other in theory and experiment?
The Pr3+ ion has 91 microstates that can be grouped into six terms before spin–orbit coupling is included: 1D, 3F, 1G, 3H, 3P, 1S. (a) What is the electron configuration of Pr3+? (b) What are the
For each of the following phosphors, identify the type of electronic transition responsible for luminescence and predict whether it will show weak, moderate, or strong electron–phonon coupling: (a)
As the difference ΔQ between the equilibrium bond distances of the ground and excited states increases, would you expect the following phosphor characteristics to increase, decrease, or be
The luminescence of AWO4 scheelites (A = Ba, Sr, Ca) shows large variations in thermalquenching behavior. The photoluminescence of CaWO4 only drops by a few percent when heated from 90 K to 270 K,
Orange, red, and near-IR LEDs are often made from GaAs1−xPx solid solutions. For compositions with x < 0.45, a direct band gap is observed, while for larger x the band gap is indirect. Assuming a
The phosphor BaMgAl10O17:Eu2+,Mn2+, whose excitation and emission spectra are shown below, is of interest as a combined blue and green phosphor in plasma-display panels. The Eu2+ ions absorb at 336
CeMgAl11O19:Tb3+ is a green phosphor used in tricolor fluorescent lights.Figure 7.25 Ce+ ions in the host absorb photons from the Hg-plasma discharge with an excitation max- imum near 270 nm and emit
When Ce3+ ions substitute for La3+ in a LaCl3 host, the lowest-energy peak in the photoluminescence excitation spectrum falls at 281 nm, whereas a similar substitution in the double-perovskite host
In thiogallate phosphor, SrGa2S4:Eu2+, Eu2+ substitutes for Sr2+ and is surrounded by a square antiprism of eight sulfide ions. The lowest-energy 5f7 4f65d excitation is centered at ~480 nm, and the
SrS, CaS, and SrSe all crystallize with the cubic rock-salt structure. The emission for SrS:Eu2+ reaches a maximum near 620 nm. By comparison, the emission maximum for CaS:Eu2+ is ~660 nm. (a) What
Derive the Clausius–Mossotti equation for the CGSes system of units.
Use the Clausius–Mossotti expression in Equation (8.13) and Table 8.2 to estimate permittivities of SnO2 (rutile-type, P42/mnm, Z = 2, a = 4.74 Å, c = 3.19 Å), TiO2 (rutile-type, a = 4.59 Å, c =
Why doesthe polarizability of the lanthanoid ions decrease as the atomic numberincreases?
Lanthanoid zirconates Ln2Zr2O7 (Ln = La, Pr, Nd, Sm, Eu) adopt the cubic pyrochlore structure (Fd3m, Z = 8), with cubic unit-cell edge a = 10.80 Å (La), 10.69 Å (Pr), 10.67 Å (Nd), 10.59 Å (Sm),
Use the Clausius–Mossotti expression to estimate the dielectric permittivities of the cubic perovskites BaZrO3 (a = 4.19 Å), KTaO3 (a = 3.99 Å), and SrTiO3 (a = 3.90 Å). Compare your estimates
Identify three characteristics of a relax or ferroelectric that distinguish it from a normal ferroelectric.
Why don’t first-order Jahn–Teller distortions, such as those seen with six-coordinate Cu2+ or Mn3+, typically lead to polar materials?
In each of the following pairs, identify the cation that is more likely to undergo an SOJT distortion. Briefly explain your reasoning. (a) Ti4+ or V4+, (b) Mn3+ or Ta5+, (c) Mo6+ or Zr4+, (d) Sn4+
In a simple cubic perovskite like SrTiO3, all oxygens are equivalent. Each makes two bonds to Ti4+ and four to Sr2+, as shown in a bond graph below.(a) Draw a comparable bond graph for a 1:1 ordered
Isit possible for a cubic materialstructure to be(a) Non-centrosymmetric,(b) Piezoelectric,(c) Pyroelectric?
The resonant frequency of a microwave resonator can be approximated by the relationship: Vo C deavity&r
The perovskite BiInO3 can be prepared using high-pressure synthesis. At room temperature, it has Pna21 space-group symmetry, with an SHG signal 120–140 times that of αquartz. Upon heating, no
BiAlO3 and BiGaO3 can be prepared by high-pressure synthesis. The space group of BiAlO3 is R3c while that of BiGaO3 is Pcca. Based on the symmetry alone, what can you say about the possibility for
PbO adopts the tetragonal litharge structure that can be described as a distorted variant of the CsCl structure:Equation 5.18 b a CsCl structure SOJT distortion litharge structure
The black modification of SnO is isostructural with PbO litharge of the previous problem.(a) The bond-valence parameters for Sn2+–O are R0 = 1.98 Å and B = 0.37 Å. Use Equation (5.18) (dij =
We can approximate the Sn2+ coordination in the hypothetical CsCl-type SnO of the previous problem by an SnHs cube. The point-group symmetry for a cube is m3m (On). In SnHg, the Sn 5s and 5p orbitals
The structure of NH4H2PO4 is closely related to KH2PO4. A projection of the NH4H2PO4 structure (comparable to KH2PO4 in Figure 8.20) is shown below. The lightly shaded phosphate tetrahedra are at z
In 2005, two new polymorphs of BiB3O6 (β- and ϒ-BiB3O6) were synthesized using boric acid as a flux [25]. All three polymorphs adopt closely related monoclinic structures. While a-BiB306 has C2
Determine the crystal system and point-group symmetry from the space-group symbol for each of the following borates. In each case determine the point group and state whether the symmetry permits SHG
For borates with similar orientation of the BO3 groups, the NLO coefficients should roughly scale with the coplanar character and density of the BO3 groups. The following borates have highly coplanar
Are penguins found at the south pole of the Earth’s magnetic field?
What is the orbital angular momentum for an s electron and why?
Convert the Earth’s magnetic field of 0.7 Oe to SI units.
What is the volume magnetization M and what is its SI unit?
Which 3d electron configurations (high- and low-spin where applicable) yield in octahedral ligand field an orbital magnetic moment that is quenched or zero? State the reason in each case.
State whether or not you would expect an orbital contribution to the magnetic moment of NiII in octahedral or tetrahedral coordination. Calculate the spin-only moment μeff.
Determine the spin–orbit coupling ground-state terms 2S+1LJ for isolated Mn4+, Mn3+, and Mn2+. Calculate μeff in Bohr magnetons, with and without an orbital contribution.
Show that, when the orbital momentum is quenched, Equation (9.14) simplifies to the spin-only model.Equation (9.14) Heff = 8J HBVJ(J+1),
Calculate effective and saturated spin-only magnetic moments (in μB) per Cr in NH4Cr(SO4)2•12H2O.
Calculate effective and saturated Russell–Saunderstotal moments (in μB) per high-spin Fe in NH4Fe(SO4)2•12H2O.
For NH4Fe(SO4)2•12H2O: (a) Calculate the molar susceptibility at 298 K. (b) Given that the cubic unit cell has a = 1.243 nm and contains four formula units, convert the molar susceptibility to
Estimate the spin-only dimensionless susceptibility of O2 as an ideal gas at 273.15 K and 100 kPa.
Superconductors expel a magnetic field from their bulk. In liquid N2, 102.5 mg of a YBa2Cu3O6.9 powder of apparent density 3000 kg/m3 was placed into the center of a miniature induction coil (a
Calculate the effective and saturated, spin-only, ge = 2, paramagnetic moments per high-spin Mn in La 0.5 Sr 0.5 MnO3.
Calculate the effective paramagnetic moment per magnetic atom in DyCrO3.
Mass susceptibility of Sr2MnMoO6 (molar mass 422.114 g/mol) was measured as a function of temperature, from which the Curie constant, Cm, was obtained by leastsquares fitting as Cm = 1.306×10−4m3
The molar susceptibility χmol of the Prussian-blue CsFe[Cr(CN)6] Curie paramagnet is 0.0163 emu/mol at 300 K and 0.0094 emu/mol at 200 K (CGSem). Using the CGSem formula μeff = 2.828√C in Bohr
Calculate the value with which you divide molar magnetization Mmol in emu/mol in order to get the amount of Bohr magnetons per mole.
Reciprocal mass susceptibility Xmfor (NH4)2Fe(SO4)2 6HO (molar mass 392.139 g/ mol) at T = 100 K, 200 K, and 300 K was measured in a weak field as 1037000kg/m, 2075000 kg/m, and 3112000 kg/m,
Reciprocal mass susceptibilities Xm for CoO at T = 400 K, 500 K, and 600 K in a weak field are 2.000106, 2.315106, and 2.635106 kg/m, respectively. Plot 3, and fit T versus Xm. Assuming a spin-only
What is the percentage of magnetic saturation in an S = ½ paramagnet at 10 K under a field of magnetic induction 1T?
Estimate the magnetic induction BW and the intensity HW of the Weiss field for a spinonly material of S = ½ that orders ferromagnetically at 300 K. How does BW (in teslas) compare with fields
Predict the type of magnetic coupling for the following materials assuming localized electrons: (a) VO with the NaCl-type structure, (b) LaCrO3 with the perovskite structure, (c) the hypothetical
Predict the type of cooperative magnetism in CrCl3 having 90° interactions.
α-MnS and MnO adopt the rock-salt structure. The Néel temperature of 130K for αMnS is higher than 117 K observed for MnO despite the fact that the Mn2+ ions are much farther apart in α-MnS.
Data suggest that the majority-spin 3d sub-band of Co is full. If so, how many electrons are in the delocalized 4s band, given the saturated ferromagnetic moment of 1.751 μB per Co and g factor for
Transport measurements show Fe has 0.95 electrons in the delocalized s band. Given a ferromagnetic moment of 2.22 μB per Fe and g factor 2.094, determine the filling in the spin-polarized d
Would you expect Au4V to be ferromagnetic?
A sample of C60 has 1 mass ppm of Fe impurity. When heated at 700 °C under pressure, C60 is converted to a carbon polymer and iron to Fe3C. Estimate the mass magnetization in J/(T kg) (≡ A m2 /kg)
Derive the formula for the maximum energy product of an ideal ferromagnet in Figure 9.24.Figure 9.24 MH hysteresis loop for ideal hard ferromagnet M -Ha given that M = Mremanent Mat +H in T in Am- B
The spinel MnFe2O4has a saturated moment independent of x. Explain why. = [(Mn+)-(Fe+),Jet[(Fe+)1-x/2(Mn+)/2]2ct04
Which of the following garnets is not diamagnetic: Ca3 TeZn3012, Y3FFe3O12, Mg3Al2Si3O12, NaCaZnV3012?
What is the saturation magnetization, Msat, in Bohr magnetons per formula unit of ferrimagnetic Y3Fe5O12 and Gd3Fe5O12 with Gd3+ in 4f7 5s2 p6 configuration?
The so-called Cu6 ring (cluster) magnet has six Cu2+ coordination octahedra sharing opposite edges of two oxygens. Which type of magnetism would you expect?
The structure of Y(O, F)2+δ materials can be described in terms of a YX slab based on a square grid of anions alternating with a hexagonal anion grid as shown in Figure 2.16. Figure 2.16 (a)
Write down the dissolution reaction of ZrO2 in Cr2O3 and state how the solid solubility will depend on pO2 : (a) About the point of integer structure, (b) About the point of integer valence.
The equilibrium constant in Equation (3.5) for oxidation of the oxygen vacancy inEquation (3.5) YBaCu3O7-5 YBaCu3O7-8 at 500 C is Kvox = 55 bar. (a) State the equilibrium composition of at 500 C in a
Derive the simplified expression for gross oxygen non stoichiometry in NdBaFe2O5+δ as a function of pO2 assuming that Fe3+ defines the point of integer valence.
Water flows from a 0.2 cm2 hose at 6 kg per minute. State the mass, volume, mole, and molecule flux of H2O in SI units.
Calculate the mass flux of carbon under steady-state diffusion through a steel plate separating carbon-rich and carbon-poor gases at 700 °C if subsequent analysis gives carbon concentrations of 1
An oxygen-permeable YBa2Cu3O7−δ membrane 1 cm thick operates at 700 °C between pressurized air at 11 bar and pure O2 at 1 bar. The steady-state O2 gas production is 0.84 mL at atmospheric
Consider a random 1D walk of n equal steps of length λ originating at zero.(a) What is the probability of deviating by 4λ from the origin in 4 steps? (b) Construct a table of probabilities of
Calculate the jump frequency of interstitial carbon in bcc iron at 800 °C, assuming a vibration frequency v = 10 s and an activation energy for hopping A*Gm 62 kJ/mol. On average, every x-th carbon
Assume that bcc iron at 1800 K has a fraction of vacant Fe sites of 0.0001, an Fe atom vibration frequency v = 10 s and an activation energy for hopping A Gm = 29 kJ/ mol. What is the jump frequency
Calculate the self-diffusion coefficient of Fe in Problem 3.22, given the unit-cell parameter a = 2.87 Å.Problem 3.22Assume that bcc iron at 1800 K has a fraction of vacant Fe sites of 0.0001, an Fe
Given the diffusivity DC = 10−10 m2/s for interstitial carbon in bcc iron at 800 °C of a= = 103 S-) 2.87 , estimate the activation energy A Gm for hopping of the C atoms (v= via interstitial sites.
The self-diffusion coefficient in Al (fcc; a = 4.05 Å) at 600 K is DAI= 2x10-16 m/s. -1 S Assuming an atomic vibration frequency v= 4103 s and an activation energy for hopping A* Gm = 58 kJ/mol,
Verify the statement that pdirλ2 = ℓ2/6 = a2/Nn, in which the distance a is the unit-cell edge, ℓ the actual jump length, λ its projection onto the unit cell edge direction, and Nn is the
Calculate the self-diffusion coefficient in the primitive cubic α-Po (Figure 1.23;Figure 1.23 3.36 ) at 500 K via vacancy mechanism, assuming 0.001 vacant sites, v = 10 s, A Gm = 36 kJ/mol. Estimate
Calculate the self-diffusion coefficient of α-Po along the direction of the cell edge (Figure 1.23; a = 3.36 Å) at 500 K via an interstitial mechanism with full availability of interstitial
A single crystal of fcc iron (a = 3.6468 Å) having a few ppm of interstitial carbon is kept at 1000 °C and isolated from its surroundings.(a) State the probability of a vibration of C becoming a
Confirm by dimensional analysis in SI that multiplying Equation (3.23) with the charge qi yields mobility.Equation (3.23) D kT 0 q7c
A rectangle of calcium-stabilized zirconia Zro.85 Cao.150 1.85 (a = 5.13 ) is covered with porous platinum electrodes on its opposite faces, heated to 1100 C in air, and an electrical conductivity of
Assuming that oxide-ion conductivity of YBaCu3O7-8 at 500 C in air is (vo") = 10-S/m and the ionic transference number (vo") = 106, what is the total electrical conductivity?
Calculate the enhancement factor DO/Dh • for Equation (3.34).Equation (3.34) Do 1 + D 4c Dr. Ch 4cv Ch
Use Equation (3.34) to generalize the value of the limiting ambipolar enhancement for DA of a neutral atom A, the flux of which consists of a flux of a z-charged ionic defect and a much faster flux
Figure 3.2 suggests that oxidative non stoichiometry of NiO at high temperature is achieved via formation of nickel vacancies and holes. The following data have been measured [5, 6] at 1100 °C in
Set up the equation for the temperature dependence of DCr in oxidized Cr2O3 where chromium vacancies dominate.
Check that of Equation (3.39) is dimensionless.Equation (3.39) u = (v/2)/Dt
A steel blade has been nitridized by exposure to flowing NH3 at 700 °C for 1 hour. The hardened layer, estimated from the penetration depth √Dτ of the nitrogen atoms, is 20 μm. In what time

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