Calculate the Atomic Packing Factor (APF) for the diamond crystal structure?

Q: the volume of BCC unit cell when the atomic radius is 0.662 nm is

A: Given data: The atomic radius, R=0.662 nm. Write the expression to calculate the side of the cell.…

Q: The unit cell for tin (sn) has tetragonal symmetry, with a and c lattice parameters of 0.583 and…

A: Unit cell: The smallest group of atoms that defines the overall symmetry of the crystal is known as…

Q: Q : (i) Prove that the atomic packing factor (APF) for the BCC crystal structure is 0.68. (ii) Prove…

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Q: Molybdenum has an atomic radius of 0.145nm. The volume of its cubic unit cell is 0.0375 nm3 . What…

A: The data given is,  The volume of the cubic unit cell, V = 0.0375 nm3 The atomic radius of the…

Q: ketch the lattice planes in cubic crystal using Miller indices for (-200), (-1-20) and (302) planes

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Q: What are all the planes in {101} family of an orthorhombic lattice?

A: Solution:

Q: 8. In an ideal hexagonal closed packed system, if the atomic radius of the atom was 0.254 nm, write…

A: Given data, The given lattice is hexagonal closed packed(HCP). r = Radius of the atom = 0.254 nm To…

Q: A) Lithium crystallizes in the body-center cubic structure with an edge length of 350.9 pm.…

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Q: What is the atomic packing factor or packing factor of a crystal structure with one complete atom of…

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Q: Calculate the atomic packing factor for a material with body centred cubic structure.

A: Given: Body Centred Cubic structure

Q: Scandium (Sc) has the Face-Centered Cubic (FCC) crystal structure. The edge length is a = 0.452 nm.…

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Q: In terms of its atomic structure, quartz can be described as silicon-oxygen tetrahedral molecules…

A: we are to discuss on the nature of quartz

Q: The density of BCC iron is 7.882g/cm3 and the lattice parameter is 0.2866nm when hydrogen atoms are…

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Q: For a metal that has the body-centered cubic crystal structure (BCC);  a)Draw the BCC unit cell  b)…

A: (a) BCC - Body Centered Cubic:  Unit cell of BCC crystal structure consists of 8 corner atoms and 1…

Q: Prove that the atomic packing factor (APF) for the BCC crystal structure is 0.68.

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Q: HCP crystals have a higher atomic packing factor than BCC crystals. Is this true or false?

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Q: Represents a body-centered cubic structure, calculating the number of atoms contained in a unit cell…

A: In Body centered cubic structure, one atom present at each corner of the cube and one atom at center…

Q: Q2. Find Atomic packing factor for Simple Cubic, Body Centered Cubic, Face centered Cubic and…

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Q: Sketch an fcc lattice unit cell (lattice constant = 5 Å) with a monoatomic basis, and calculate the…

A: There are 8 corner atoms and 6 face-cent atoms in FCCAtoms in the diagonal of the face are in…

Q: bic crystal, draw any three (3) parallel planes and determine their miller indices.

A: To draw three parallel planes and determine their miller indices.

Q: Compute the density of Zinc, where the atomic radius of Zn=1.453×10-8 and atomic weight =72.4 g/mol…

A: For BCC  structure :-          4r=3ar=radius of atom a=length of unit cell now…

Q: Beryllium with a crystalline structure HCP lattice constant c / a = 1.568 and the radius of the atom…

A: Unit cell: The unit cell is the smallest part of the lattice which repeats multiple times to form a…

Q: Iron has a BCC crystal structure with an atomic radius of 1.241Å. Calculate the interplanar spacing…

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Q: 9. Calculate the planar atomic density for the (100), (110) and (111) planes for a BCC (body…

A: Planar density is given as - Densityρ =Number of atomsArea of plane

Q: How many atoms constitute one unit cell of a face centered cubic crystal?

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Q: If a single crystal material has a Young's Modulus of 100 MPa in the [100] direction, and a Young's…

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Q: (b) Copper crystallises as FCC (face centred cubic). Given that the atomic radius and mass of a…

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Q: Calculate the atomic densities of the directions [100], [111] and [110] in a face centered cubic…

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Q: Given that molybdenum (Mo) with atomic weight 95.94 g/mol and density 10.2 g/cm3 assumes a…

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Q: If the atomic radius of a metal that has the facecentered cubic crystal structure is 0.137…

A: In face centered cubic structure one atom is located at the center of the faces of cube

Q: If the atomic radius of a metal that has the facecentered cubic crystal is 0.137 nm , calculate the…

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Q: The crystalline density of polypropyleneis 0.946 g>cm3, and its amorphous densityis 0.855…

A: Given data as per questionDensity of polypropylene = 0.946 g/cm3amorphous density = 0.855 g/cm3

Q: An atom crystallizes in FCC crystal lattice and has a density of 10 g/ cm 3 with unit cell edge…

A: Given,           Density (ρ) = 10 g/cm3          Edge length (a) = 100pm = 100×10-10 cm = 10-8 cm…

Q: a) For a material having BCC crystal cell structure, write the expressions for Linear atomic density…

A: Linear atomic density for the (1,0,0) direction is calculated as follows: Number of atom is 1.…

Q: Derive the dimension ratio c/a for regular HCP crystal. Please do not use the atomic packing factor

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Q: Vanadium has the Body-Centered Cubic (BCC) crystal structure. The edge length "a" of the unit cell…

A: It is given that Vanadium at room temperature of 20°C is having a BCC structure. In a BCC structure,…

Q: discuss how the crystal structure effect mechanical and electrical and physical and thermal…

A: How the crystal structure effect : Mechanical, Electrical, Physical, Thermal properties.   Crystal…

Q: In an ideal hexagonal closed packed system, if the atomic radius of the atom was 0.112 nm, write…

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Q: HCP crystals have a higher atomic packing factor than BCC crystals. Explain either way.

A: Given question: HCP crystals have s higher atomic packing factor than BCC crystals. Explain either…

Q: Calculate the planar atomic density of (110) for diamond structure.

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Q: If the atomic radius of a metal that has the face centered cubic crystal is 0.137 nm , calculate the…

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Q: calculate the planar density atoms per square millimeter for the following crystal planes in body…

A: No of atoms in plane = 2 Area of plane = √2 a2 Density = atoms/area 1 nm = 10-6 mm

Q: Calculate the volume in cubic nanometers of the titanium crystal structure unit cell. Lattice…

A: A titanium crystal will be in the shape HCP (Hexagonal close packed) at room temperature or at…

Q: What are the indices for the direction represented by the vector that has been drawn within a unit…

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Q: For some reason 0.68 is not accepted as the answer.

A: Atomic radii are -  The volume of the sphere is –

Q: uestion Six: For an FCC crystal: calculate the density of atoms (atoms/a where a is the lattice…

A: here the radius of the atom is given a  For the FCC crystal structure, the planar density for the…

Q: Calculate the radius of a palladium (Pd) atom, given that Pd has an FCC crystal structure, a density…

A: Given data: Density of palladium, ρ = 12.0 g/cm3. Atomic weight, A = 106.4 g/mol. The number of…

Q: If the atomic radius for Pb- 0.175nm and the crystal structure is FCC, calculate the atoms numbers…

A: Calculated number of Atom in unit cell. And relation between atomic radius and lattice constant and…

Q: A/An is formed when an extra atom or ion is inserted into the crystal structure at a normally…

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Q: Draw the crystal atomic directions with following Miller indices. {011}, {110}, {012}. {123}, {222}.

A: Given Atomic direction  To find Crystal atomic direction

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.