Question
How can the interplanar spacing of a set of Miller planes be calculated in terms of Lattice parameters?
Step 1
Miller indices are typically denoted as (hkl), where h, k, and l are integers that represent the orientation of the planes in the crystal lattice. Show more…
Show all steps
Your feedback will help us improve your experience
Mirza Aslam Beig and 66 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
7. Interplanar spacing. Show that, for an orthogonal lattice with lattice parameters a1, a2, a3, the perpendicular distance between adjacent (hkl) planes is d_hkl = [(h/a1)^2 + (k/a2)^2 + (l/a3)^2]^-1/2 8. Angle between planes. Determine the angle between planes with (h1k1l1) and (h2k2l2) in a cubic system.
Obtain the expression for inter-planar distance between two adjacentplanes of Miller indices hkl in a cubic crystal?
Using the data for silver in Table 3.1, compute the interplanar spacings in nm for the (a) (110) and (b) (221) sets of planes. Table 3.1 Atomic Radii and Crystal Structures for 16 Metals Crystal Structurea Atomic Radiusb (nm) Metal Aluminum FCC 0.1431 Molybdenum BCC 0.1363 Cadmium HCP 0.1490 Nickel FCC 0.1246 Chromium BCC 0.1249 Platinum FCC 0.1387 Cobalt Copper Gold HCP 0.1253 Silver FCC 0.1445 Tantalum BCC 0.1430 Titanium HCP 0.1445 Iron Lead 0.1241 Tungsten BCC 0.1371 FCC 0.1750 Zinc HCP 0.1332 aFCC = face-centered cubic; HCP = hexagonal close-packed; BCC = body-centered cubic To compute the interplanar spacings in nm for the (110) set of planes, we need to find the atomic radius of silver in Table 3.1. The atomic radius of silver is 0.1445 nm. The interplanar spacing for the (110) set of planes can be calculated using the formula: d = a / sqrt(h^2 + k^2 + l^2) where d is the interplanar spacing, a is the lattice constant, and h, k, and l are the Miller indices of the planes. For the (110) set of planes, the Miller indices are h = 1, k = 1, and l = 0. Substituting the values into the formula, we get: d = 0.1445 / sqrt(1^2 + 1^2 + 0^2) d = 0.1445 / sqrt(2) d = 0.1445 / 1.414 d ≈ 0.102 nm Therefore, the interplanar spacing for the (110) set of planes in silver is approximately 0.102 nm. To compute the interplanar spacings in nm for the (221) set of planes, we use the same formula. For the (221) set of planes, the Miller indices are h = 2, k = 2, and l = 1. Substituting the values into the formula, we get: d = 0.1445 / sqrt(2^2 + 2^2 + 1^2) d = 0.1445 / sqrt(9) d = 0.1445 / 3 d ≈ 0.048 nm Therefore, the interplanar spacing for the (221) set of planes in silver is approximately 0.048 nm.
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD