Q065 - Physics For Engineers And Scientists - Solutions
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# Question 65 - Problems - Chapter 1¶

## Problem:¶

Some crystal can be polished at an angle to produce sharp "Atomic Steps" (see fig. below).

## Question:¶

a) Wat angle $\theta$ should be chosen to produce a step every 5 atoms?

b) What angle to produce a step every 10 atoms?

c) How many atoms will there be along a step if a crystal is polished as flat as is normal practical. (usualy arround 0.10°)

We assume that the atoms are spherical.

## Solution:¶

Since the atoms are spherical we can use the ratio without having to know the dimensions.

$$\theta =\textrm{atan}\left(\frac{\textrm{upright}\;\textrm{side}}{\textrm{lying}\;\textrm{side}}\right)$$

In [1]:
# Calculations
import numpy as np
from astropy import units as u
from astropy.coordinates import Angle

step = 5
Theta = Angle(angle, u.degree)
print(f'The angle for a step of {step} atoms is {Theta.dms.d:.0f}° {Theta.dms.m:.0f}\' {Theta.dms.s:.2f}\"' )

step = 10

The angle for a step of 5 atoms is 11° 18' 35.76"