A cubic metal (radius of hypothetical touching atomic spheres:r=0.77Å) showsplastic deformation by slip along...

A cubic metal (radius of hypothetical touching atomic spheres: r=0.77Å) shows
plastic deformation by slip along the<111>directions. Based on this
information, deduce the planar packing density (atoms/m2) for its densest family
of planes.

Solutions

Expert Solution

Since there is a slip along <111> directtions, it should be a BCC system with a slip {110}, <111>

Therefore, in this case : a x cube root ( 3 ) = 4r

or, a = 4r / cube root (3 )

Substituting the given value of r = 0.77A^o = 0.77 x 10^-10 m we get,

a = 4 x 0.77 x 10^-10 / cube root (3) = 2.14 x 10^-10 m

Now densest planes are {110 } so packing density is -

2 atoms / { a² SQRT (2) } = 2 / [ 2.14 x 10^-10 ]² x 1.4142 = 3 .0883 x 10¹⁹ atoms / m²

or, = 3 x 10¹⁹ atoms / m²

queen_honey_blossom answered 1 year ago

Next > < Previous

Related Solutions

Chromium metal has a metallic atomic radius of 0.200 nm. It shows plastic deformation via slip along the <111> directions.

Defects and Slip Chromium metal has a metallic atomic radius of 0.200 nm. It shows plastic deformation via slip along the <111> directions. a) What is the planar density (atoms/m2) for its densest family of planes? What is the magnitude of the Burgers vector for the dislocations that promote slip in chromium metal? c) A chromium ingot has tensile stress applied at a 25° angle to the slip plane normal and a 63° angle to the slip direction. It experiences...

List the differences between deformation by twinning and deformation by slip in terms of (a) mechanism,...

List the differences between deformation by twinning and deformation by slip in terms of (a) mechanism, (b) condition of occurrence and (c) consequences. Any reasonable answer is accepted. Limit your answer to 25 words for each difference.

1. Listed below are the atomic weight, density, and atomic radius for three hypothetical alloys. For...

1. Listed below are the atomic weight, density, and atomic radius for three hypothetical alloys. For each determine its crystal structure and then justify your determination. Alloy // Atomic weight (g/mol) // Density (g/ cm^3) // Atomic Radius (nm) A // 43.1 // 6.4 // 0.122 B // 184.4 // 12.3 // 0.146 C // 91.6 // 9.6 // 0.137

Consider a single crystal of a cubic metal that is subjected to a tensile stress along...

Consider a single crystal of a cubic metal that is subjected to a tensile stress along the [0 1 2 ] direction. Calculate the Schmidt factor for the following slip systems. In each case sketch the tensile axis as well as the slip plane and slip direction. a) (0 -1 1) [0 1 1] b) (1 0 1) [-1 -1 1] c) (0 1 0) [ -1 0 1 ] d) If the crystal above is subjected to an increasing...

Polonium is the only metal that forms a simple cubic unit cell. The radius of the...

Polonium is the only metal that forms a simple cubic unit cell. The radius of the polonium atom is 1.67 x 10−8 cm. Determine the mass and volume of the unit cell for polonium. An average polonium atom weighs 209 amu. Calculate the density (in g/cm3) of polonium. a) The distance between touching spheres equals twice the sphere radius b) Remember to account for the number of atoms in each unit cell c) 1.00 amu = 1.66 x 10−24 g

What is a slip system and what role does it play in plastic deformation?

--Given Values-- Atomic Radius (nm) = 0.116 FCC Metal = Gold BCC Metal: = Sodium Temperature...

--Given Values-- Atomic Radius (nm) = 0.116 FCC Metal = Gold BCC Metal: = Sodium Temperature ( C ) = 1017 Metal A = Tin Equilibrium Number of Vacancies (m-3) = 6.02E+23 Temperature for Metal A = 369 Metal B = Gallium I need help with 3, 4, 6, 7, 11, 12. Am I entering the notations incorrectly? ) If the atomic radius of a metal is the value shown above and it has the face-centered cubic crystal structure, calculate...

Consider a hypothetical metal that has a density of 12.7 g/cm3, an atomic weight of 135.9...

Consider a hypothetical metal that has a density of 12.7 g/cm3, an atomic weight of 135.9 g/mol, and an atomic radius of 0.129 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, with a and c parameters 0.452 and 0.348 nm, respectively.

Consider a hypothetical metal that has a density of 8.40 g/cm3, an atomic weight of 108.6...

Consider a hypothetical metal that has a density of 8.40 g/cm3, an atomic weight of 108.6 g/mol, and an atomic radius of 0.136 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry; values for the A and C lattice parameters are 0.494 and 0.352, respectively.

The density of aluminum metal is 2.70 g/mL, the atomic mass 26.98 g/mol, the radius of...

The density of aluminum metal is 2.70 g/mL, the atomic mass 26.98 g/mol, the radius of an aluminum atom is 143 picometer and the packing density is 74% theory. Compute Avogardo's number from these data and briefly outline your reasoning/strategy.

Subjects