A metal is evaporated in vacuum from a hot filament. The...

A metal is evaporated in vacuum from a hot filament. The resultant metal atoms are incident upon s qusrtz plste some distance away and form there $B$ thin metallic film, This quartz plate is maintesined at a low temperature so thal. any metal atom incident upen it sticks at its place of impact without further mipration. The metal atoms can be ansumed equslly likely to impinge upon any element of area of the plate. If one considers an clement of substrite sres of gize $b^{x}$ (nhere $b$ is the mete] atorn dismeter), show that the number of metsl atoms piled up on this ares should be distributed approximately according to a Poiason distribution Suppose that one evaporstes enongh metel to form a film of mean thickness corresponding to 6 atomic layers. What frsction of the aubstrate sres is tben not covered by metal at sll? What fraction is covered, respectively, by metal luyers 3 atoms thick and 6 atoms thick?

Key Concepts

Mean Coverage and Atomic Layers

In thin film growth, the mean thickness is expressed in terms of atomic layers, representing the average number of atoms stacked per unit area. When the mean number of deposited atoms corresponds to a certain number of layers, statistical methods can be applied to determine the fraction of the surface covered by various numbers of atomic layers.

Poisson Distribution

This is a probability distribution used to model the number of events (in this case, atom arrivals) occurring within a fixed interval or region when the events happen independently with a constant average rate. In the context of thin film deposition, it helps predict the likelihood of a given number of atoms landing on a specific area of the substrate.

Random Deposition Model

This model assumes that atoms or particles are deposited on a substrate randomly and uniformly, with each atom having an equal probability of landing at any location without subsequent migration or diffusion. This results in a statistical distribution of deposited atoms that can be described by the Poisson distribution.

Surface Area Scaling

By choosing a characteristic area that is comparable to the size of the depositing atom, one creates a natural scale for the deposition process. The area corresponding to a single atom helps to relate the discrete nature of atomic deposition to the continuous probability models, providing the basis for applying the Poisson distribution to the number of atoms deposited per unit area.

Transcript

00:01 This is question 89 from chapter 22 and we have nitanyl, which is a nickel and titanium alloy.

00:07 And the first thing we can do is trying to find the dimensions of the austin type itself.

00:15 Okay, so to find this, it's going to be set up to 2 times the radius of titanium plus 2 times the radius of nickel.

00:31 And they give us the ppms the radius for each so for nickel is going to be two times 145 and for nickel it's 125 so 2 times 125 and this is equal to 540 ppms now this is a cube so we have to use a cube root type thing you have to find x so we have x so we have x 3 is going to be equal to this 540 ppm so this is the dimensions we are trying to find okay so when you solve for that it's going to come out to be 312 ppms or 3 .12 1 2 times 10 to the negative 8 centimeters okay now b is asking to calculate the density of the nittinol based on the austin tight cell parameters.

02:11 So we're going to be using the molar mass.

02:15 I'm going to find the mass of nickel and titanium.

02:19 So i want to do the nickel first.

02:24 It has 47 .87 grams per more of this molar mass.

02:38 And we are going to be dividing that by avogadro's number.

02:45 So 6 .022 times 10 to the 23rd.

03:05 So i wanna add that with doing something with titanium.

03:08 So titanium has 58 .69 grams per mole.

03:27 And once again, i'm gonna divide that by avogadroa's number two.

03:42 And this is gonna come out to be 1 .770 times 10 to the negative 22 grams...