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Vanyuwa [196]
3 years ago
15

In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the FCC crystal structure alo

ng the [100] direction.

Engineering
1 answer:
timama [110]3 years ago
6 0

Answer:

The distance between the centers of adjacent atoms for the FCC crystal structure along the [100] is 2R√2

Explanation:

From the image uploaded, a Face centered cubic structure (100) plane, there is one atom at each of the four cube corners, each of which is shared with four adjacent unit cells, while the center atom lies entirely within the unit cell.

In terms of the atomic radius, R, we determine the distance between the centers of adjacent atoms.

Let this distance = AC

the two adjacent sides = AB and BC

AB = a = 2R

BC = a = 2R

Using Pythagoras theorem

AC² = AB² + BC²

AC² = a² + a²

AC² = 2a²

AC = √2a²

AC = a√2

But a = 2R

AC = 2R√2

Therefore,  the distance between the centers of adjacent atoms for the FCC crystal structure along the [100] is 2R√2

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The velocity components u and v in a two-dimensional flow field are given by: u = 4yt ft./s, v = 4xt ft./s, where t is time. Wha
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Answer:

vec(a) = 16 i + 16 j

mag(a) = 22.63 ft/s^2

Explanation:

Given,

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                                       u = 4*y ft/s

                                       v = 4*x ft/s

Find:

What is the time rate of change of the velocity vector V (i.e., the acceleration vector) for a fluid particle at x = 1 ft. and y = 1 ft. at time t = 1 second?

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- The rate of change of velocity is given to be acceleration. We will take derivative of each components of velocity with respect to time t:

                                      a_x = du / dt

                                      a_x = 4*dy/dt

                                      a_y = dv/dt

                                      a_y = 4*dx/dt

- The expressions dx/dt is the velocity component u and dy/dt is the velocity component v:

                                     a_x = 4*(4*y) = 16y

                                     a_y = 4*(4*x) = 16x

- The acceleration vector can be expressed by:

                                     vec(a) = 16y i + 16x j

- Evaluate vector (a) at x = 1 and y = 1:

                                     vec(a) = 16*1 i + 16*1 j = 16 i + 16 j

- The magnitude of acceleration is given by:

                                     mag(a) = sqrt ( a^2_x + a^2_y )

                                     mag(a) = sqrt ( 16^2 + 16^2 )

                                     mag(a) = 22.63 ft/s^2

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Vitrification is usually achieved by heating materials until they liquidize, then cooling the liquid, often rapidly, so that it passes through the glass transition to form a vitrified solid. Certain chemical reactions also result in glasses.

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Explanation:

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