Q1. Diamond Structure The diamond structure shown below is NOT a Bravais lattice. It can be...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Q1. Diamond Structure The diamond structure shown below is NOT a Bravais lattice. It can be viewed as two inter- penetrating FCC lattices: Points represented by black balls form an FCC lattice while those represented by white balls form another FCC lattice. The two lattices are displaced along the body diagonal of the cubic cell by one quarter the length of the diagonal. Show that the angle between any two of the lines (bonds) joining a site of the diamond lattice to its four nearest neighbors is arccos(-1/3) = 109°28′. (3 marks) Q2. Miller Indices for Planes In the diagram below, draw all the lines with Miller indices (34) that intersect with the interval AB (including the endpoints A and B). Count the number of these lines and find the distance between neighbouring lines (assuming the lattice is a cubic lattice with lattice constant a). (3 marks) a₂ a₁ A B Q3. Relation Between [hkl] and (hkl) (a) In a simple cubic Bravais lattice, a set of primitive lattice vectors are given by a₁ = aê, a₂ = aŷ and a3 = až. Is the direction with Miller indices [hkl] always perpendicular to the lattice planes with Miller indices (hkl) for any possible values of h, k and l? Show details of your reasoning. (2 marks) (b) Answer the same question if the lattice is BCC and the set of primitive lattice vectors are given by a₁ = (-âî + ŷ + ê), ā₂ = ½ (î − ŷ + 2) and ã3 = (2+ŷ − 2). Show details of your reasoning. (2 marks) Q1. Diamond Structure The diamond structure shown below is NOT a Bravais lattice. It can be viewed as two inter- penetrating FCC lattices: Points represented by black balls form an FCC lattice while those represented by white balls form another FCC lattice. The two lattices are displaced along the body diagonal of the cubic cell by one quarter the length of the diagonal. Show that the angle between any two of the lines (bonds) joining a site of the diamond lattice to its four nearest neighbors is arccos(-1/3) = 109°28′. (3 marks) Q2. Miller Indices for Planes In the diagram below, draw all the lines with Miller indices (34) that intersect with the interval AB (including the endpoints A and B). Count the number of these lines and find the distance between neighbouring lines (assuming the lattice is a cubic lattice with lattice constant a). (3 marks) a₂ a₁ A B Q3. Relation Between [hkl] and (hkl) (a) In a simple cubic Bravais lattice, a set of primitive lattice vectors are given by a₁ = aê, a₂ = aŷ and a3 = až. Is the direction with Miller indices [hkl] always perpendicular to the lattice planes with Miller indices (hkl) for any possible values of h, k and l? Show details of your reasoning. (2 marks) (b) Answer the same question if the lattice is BCC and the set of primitive lattice vectors are given by a₁ = (-âî + ŷ + ê), ā₂ = ½ (î − ŷ + 2) and ã3 = (2+ŷ − 2). Show details of your reasoning. (2 marks)
Expert Answer:
Answer rating: 100% (QA)
Question 1 Question 2 Miller indices are used to specify directions and planes in lattices and cryst... View the full answer
Related Book For
Statistics For Business And Economics
ISBN: 9780132745659
8th Edition
Authors: Paul Newbold, William Carlson, Betty Thorne
Posted Date:
Students also viewed these law questions
-
The Triple Bottom Line can be viewed as a three-legged stool in that each element must be present or, if one or more elements are removed, then the entire structure collapses. To what extent do you...
-
The budgeted income statement can be viewed as the apex of budgeting. Explain this statement.
-
The Internet of Things (loT) can be viewed as an emerging concept and technology in the modern world. Specifically, it comprises of a network of interrelated dig2tal and mechanical machines and...
-
Which statement about the pass-by-reference is NOT true? a.Every time you pass a reference variable to a method, you also pass the object referred by the refenerece variable to the method. b.In the...
-
An industry currently has 100 firms, all of which have fixed costs of $16 and average variable cost as follows: Quantity Average Variable Cost 1............ $1 2.............2 3.............3...
-
Find F(f(x)) for f(x) = xe -x if x > 0, f(x) = 0 if x < 0, by (9) and formula 5 in Table III (with α = 1). Consider xe -x and e -x . f(w) = F(f) f(x) (1 if -b < x
-
What electronic information is discoverable?
-
Examine the following pairs of puts, which differ only by exercise price. Determine whether either of them violates the rules regarding relationships between American options that differ only by...
-
Please answer Trillo, a resident of Quezon City, died on June 5, 2019 with the following data: Property acquired by Trillo before marriage Property acquired by his wife before marriage Family house...
-
Imagine that the perfectly competitive market described in Chapter 7, Problem S1, was transformed into a pure monopoly. (What were formerly independent small firms are now production units owned by...
-
iii. Prove that in determining lattice parameters, the greater the diffraction angle the greater the accuracy Calculate Bragg angle at which electrons accelerated from rest through a potential...
-
What are some reasons you can think of for a company using a predetermined overhead rate? Based on your work experience, what are some factors that should be considered for direct material, direct...
-
Cost overruns and extraordinary spending by healthcare organizations harms the sustainability of the healthcare organization. Through activity-based costing (ABC), the healthcare industry is working...
-
5. For the polynomial P(x) = x - 12x + 4x + 15, two zeroes, are -1 and 3. The other two zeroes are?
-
Post a description of at least three specific policies, initiatives, or programs that you think would reduce child poverty/homelessness or ameliorate its consequences. Explain briefly what each would...
-
Using the Trade Stats Express page and response to the following questions: What are the leading U.S. exports and imports in terms of value? Which trading partners are most important to the United...
-
On December 31, 2026, when the market rate was 8%, West End Corp. issued $6,000,000, 11%, 5-year bonds. Interest is payable semiannually on June 30 and December 31. The bonds were issued for...
-
Conduct a VRIO analysis by ranking Husson University (in Maine) business school in terms of the following six dimensions relative to the top three rival schools. If you were the dean with a limited...
-
Of a random sample of 172 elementary school educators, 118 said that parental support was the most important source of a child's success. Test the hypothesis that parental support is the most...
-
An experiment was carried out to test the effects on yields of five varieties of corn and five types of fertilizer. For each variety-fertilizer combination, six plots were used and the yields...
-
A business school placement director wants to estimate the mean annual salaries 5 years after students graduate. A random sample of 25 such graduates found a sample mean of $42,740 and a sample...
-
Find the fundamental frequency of longitudinal vibration of the tapered bar shown in Fig. 8.41, using Rayleigh's method with the mode shape \[U(x)=c_{1} \sin \frac{\pi x}{2 l}\] The mass per unit...
-
Approximate the fundamental frequency of a rectangular membrane supported along all the edges by using Rayleigh's method with \[W(x, y)=c_{1} x y(x-a)(y-b)\] \[V=\frac{P}{2}...
-
The root mean square value of a signal \(x(t), x_{\mathrm{rms}}\), is defined as \[x_{\mathrm{rms}}=\left\{\lim _{T ightarrow \infty} \frac{1}{T} \int_{0}^{T} x^{2}(t) d t ight\}^{1 / 2}\] Using this...
Study smarter with the SolutionInn App