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학습트랜스크립트
00:00안녕하세요 여러분!
00:06오늘 우리가 살펴볼까요?
00:08Diffusion in solids.
00:10We are talking about solids all the time.
00:13You remember that.
00:15And this diffusion,
00:17in Korean it's called 확산.
00:20Something is moving from one side to the other.
00:24Correct?
00:26In this case,
00:30we do not talk about some kind of molecules moving.
00:34It's the atomic movement.
00:36So,
00:38how atoms move?
00:40How does the diffusion occur?
00:42How atoms move?
00:44Atoms are moving from one side to the other.
00:46How? Why?
00:48Then why they move?
00:50And
00:52So,
00:54why is it important part of processing?
00:56We will have some example here.
01:00Some cars or gears.
01:02How can the rate of diffusion be predicted for some simple cases?
01:08And how does diffusion depend on structure and temperature?
01:12That's what we are going to learn in chapter 5.
01:16So,
01:18where do you see this diffusion?
01:20Where can we find this diffusion?
01:24Like something smells
01:26from outside to inside
01:28or inside to outside.
01:30And if somebody approaches,
01:32we smell
01:34their sometimes fragrance
01:36or sometimes bad scent.
01:38Whatever.
01:40That's diffusion.
01:42So,
01:44we see diffusion everywhere from like
01:48that what I mentioned.
01:50But if we define that one in solid form.
01:54So, here are examples here.
01:56Like
01:58gears,
02:00the case hardened gear.
02:04Right?
02:06Case hardened gear means like
02:08the case
02:10or
02:12the surface part.
02:14And
02:15the
02:16in car or
02:17semiconductor.
02:19So,
02:20we diffuse some elements into
02:22semiconductor
02:24to make the semiconductor from
02:26the pure silicon.
02:27Right?
02:28That's diffusion.
02:30How do they do?
02:32And why do they do?
02:34And
02:36what's happening?
02:38So,
02:40our goals
02:42for this chapter
02:43to define diffusion
02:45and
02:46see its mechanisms
02:48distinguish
02:49steady-state
02:50and non-steady-state diffusion.
02:52That's related to
02:54Fick's Law.
02:55Have you heard about this law?
02:57Fick's Law?
02:58I think you heard this
03:00in
03:01like physics
03:02and chemistry
03:04in
03:05the textbook
03:06when we talk about
03:07the concentration
03:08or
03:09something is changing
03:10from one side to the other,
03:11especially diffusion.
03:13So,
03:14whenever we talk about
03:15diffusion
03:16we will see
03:17this Fick's Law.
03:18And it has
03:19like two
03:20ones.
03:21The first law
03:22and the second law.
03:23What's the difference
03:24between those two?
03:26the first law
03:27is describing
03:29something
03:30which
03:31is related to
03:33only
03:34position.
03:35So,
03:36it doesn't have
03:37any
03:38time
03:39variable.
03:40It only
03:41has
03:42the
03:43position matter.
03:44In that case,
03:45we use
03:46Fick's
03:47first law.
03:48But if
03:49something is changing
03:50depending on
03:51the time,
03:52then we cannot use
03:53that
03:54Fick's Law
03:55because that's not
03:56steady state.
03:57You know,
03:58when we talk about
03:59steady state,
04:00it's
04:01when we look at it,
04:03it looks like it's
04:04not moving at all.
04:05Right?
04:06So, that's
04:07like a steady state.
04:08But if time
04:09depending on the time,
04:10if it's changing,
04:11then something will change
04:14on the surface
04:15on that
04:16object.
04:18So,
04:19we cannot use
04:20that
04:21as
04:22like a
04:23steady state.
04:24For example,
04:25we have
04:26like
04:27the
04:29ink
04:30drop
04:31on the surface
04:32then
04:33in time
04:34that'll diffuse away
04:35to the
04:36solution.
04:37Then
04:38that's not
04:39steady state.
04:40because
04:42we can see
04:43it's moving
04:44and
04:45something's
04:46changing.
04:47Right?
04:48So,
04:49by the end
04:51of this chapter,
04:52you should
04:53and
04:54we should
04:55feel comfortable
04:56using
04:57diffusion equation
04:58fixed
04:59first law
05:00and second law.
05:01And then
05:02also
05:03like
05:04we can
05:05estimate some
05:06time
05:07in some kind
05:08of matter.
05:09and also
05:10depth,
05:11how deep
05:12that elements
05:13can go into
05:14and processing
05:15temperatures
05:16and real
05:17material problem.
05:18So,
05:19we already
05:20talked about this
05:21in the previous
05:22chapters too,
05:23like when we do
05:24carburizing
05:25or carburizing,
05:26then we increase
05:28some temperature
05:29to
05:30penetrate
05:31the carbon
05:32into
05:33iron.
05:34and
05:35that's
05:36interstitial
05:37penetration.
05:38Right?
05:39You should
05:40remember
05:41that.
05:42That's
05:43only
05:44chapter 4
05:45work.
05:46Right?
05:47So,
05:48let's begin
05:49with the practical
05:50example shown
05:51in this picture
05:52here.
05:53shows
05:54a dark
05:55outer.
05:56Is it
05:57clear to see
05:58like inside
05:59it's quite
06:00brighter,
06:01but outside
06:02is quite
06:03dark.
06:04Dark one.
06:05Dark outer rim.
06:06That's
06:07kind of
06:08case.
06:09That has
06:10been hardened
06:11by diffusing
06:12carbon.
06:13We put
06:14some carbon
06:15and then
06:16increase the temperature
06:17and that'll
06:18diffuse into
06:19the surface
06:20high temperature.
06:21That's
06:22carburizing.
06:23The
06:24increased
06:25carbon content
06:26raises
06:27surface hardness
06:28and well
06:29resistance.
06:30Importantly,
06:31it also
06:32introduces
06:33residual
06:34compressive stresses
06:35near the surface
06:36which can
06:37improve
06:38fatigue
06:39resistance.
06:40Fatigue
06:41resistance.
06:42What's
06:44fatigue
06:45resistance?
06:46We
06:47will
06:48learn about
06:49fatigue
06:50resistance
06:51in the later
06:52chapter.
06:53But briefly
06:54it's related
06:55to
06:56some sort
06:57of
06:58피로도
06:59How
07:00easily
07:01or
07:03how
07:04much
07:05the material
07:06can get
07:07tired
07:08of some
07:09outer force.
07:13So
07:15this
07:16is
07:17diffusion
07:18in the real world
07:19diffusion problem.
07:21Atoms moving from
07:22a carbon rich
07:23environment
07:24outside
07:25to
07:26the steel
07:27and altering
07:28surface composition
07:29and properties.
07:31That's what we are
07:32going to learn.
07:33Like today's theory
07:34this is
07:35whole theory
07:36will
07:37you remember that
07:38what's a theory
07:39and we also learned
07:40about some rule
07:41and hypothesis
07:42something
07:43here
07:44it's a theory
07:45will help you
07:46predict
07:47heat
07:48treatment
07:49temperature
07:50so how
07:51how high we
07:52should go to
07:53do this
07:54kind of
07:55carburizing
07:56or
07:57but the other way
07:58whatever
07:59and how long
08:00how high temperature
08:02and how long
08:03the time
08:04and then
08:05resulting
08:06concentration
08:07profiles
08:08and what's happening
08:09inside
08:10that's what we can see
08:12so let's see
08:15what
08:16what the diffusion
08:17is like
08:18kind of definition
08:19it says
08:20like a mass transport
08:21by atomic
08:22motion
08:23mass transport
08:24if we
08:25focus on
08:26this
08:27only mass transport
08:28then
08:29that'll also
08:30include
08:31some sort of
08:32gas and liquids part
08:33but
08:34atomic motion
08:35but that was also
08:37like gas and leakage part
08:38too
08:39but
08:40this one
08:41more characteristic
08:42to
08:43our purpose
08:44like elements
08:45is moving
08:46from one side
08:47to the other
08:48in the
08:49in the
08:50the solid
08:51metal
08:52solid structure
08:53that's what
08:54we see
08:55right
08:56so
08:57another word
08:58like a diffusion
08:59is the net
09:00transport of matter
09:01caused by
09:02atomic motion
09:04right
09:05in solids
09:06atoms are constantly
09:07vibrating
09:08that's very important
09:09in solids
09:11like in liquids
09:14in gases
09:15they are too
09:16like atoms
09:17are constantly
09:19vibrating
09:20so
09:21it's not only
09:22for the solids
09:23but
09:24this textbook
09:25is mainly
09:26focuses on
09:27the solids
09:29that's why
09:30the textbook says
09:31that way
09:32but
09:33atoms
09:34are constantly
09:35vibrating
09:36unless
09:37we
09:38make the
09:39environment
09:41where
09:42the temperature
09:43is like
09:44absolute zero
09:45in that case
09:46they do not have
09:47any
09:48energy
09:49so
09:50it doesn't move
09:54it doesn't vibrate
09:55they acquire
09:57enough energy
09:58because they have
09:59energy
10:00temperature
10:01then
10:02if that energy
10:03is enough to
10:04jump
10:05from one side
10:06to the other
10:07that's
10:08that's how
10:09this diffusion
10:10occurs
10:11in solid
10:12vacancy
10:13diffusion
10:14and interstitial
10:15diffusion
10:16I think you remember
10:17this vacancy
10:18the word vacancy
10:19and interstitial
10:20I already mentioned
10:22many times
10:23vacancy
10:24is like empty
10:25empty
10:26spot
10:27something
10:28is missing
10:29so when we increase
10:30the temperature
10:31the vacancy
10:32the number
10:33of vacancies
10:34are increasing
10:35you should remember
10:37this
10:38that's very important
10:39to understand
10:40solid material
10:41and also
10:43the interstitial
10:44diffusion
10:45that was
10:46like
10:47a very
10:48small
10:49I'm sorry
10:50this is quite
10:51big element
10:52and then
10:53inside
10:54this
10:55this gap
10:56into
10:57this gap
10:58like
10:59small
11:00carbon
11:01or hydrogen
11:02atoms
11:03can
11:04penetrate
11:05into
11:06the gap
11:07between
11:08the solid
11:09lattice
11:10or
11:11solid
11:12atomic
11:13bonds
11:15okay
11:17and then
11:18the
11:19on
11:20a
11:21macroscopic
11:22scale
11:23we describe
11:24diffusion
11:25by changes
11:26in concentration
11:27over
11:28position
11:29your
11:30position
11:31and
11:32time
11:35into
11:36two important
11:37interdiffusion
11:38here
11:40interdiffusion
11:41and
11:42then
11:43another one
11:44is
11:45like
11:46we will see
11:47that
11:48interstitial
11:49one
11:50but in an alloy
11:51here
11:52atoms
11:53tend to
11:54migrate
11:55from
11:56regions
11:57of high
11:58concentration
11:59to regions
12:00of low
12:01concentration
12:02initially
12:03this way
12:04so
12:05if we take a look
12:06at this
12:07like
12:08what is the
12:09orange colored one
12:10this is high concentration
12:11and
12:12if we take a look
12:13at this
12:14gray
12:15sphere
12:16then
12:17this is high concentration
12:18and
12:19this is low
12:20concentration
12:21so
12:22from regions
12:23of high concentration
12:24to regions
12:25of low concentration
12:26so
12:27this gray
12:28wants to go
12:29to the left side
12:30and then
12:31this orange colored one
12:32wants to go
12:33to the right side
12:34part
12:35that's
12:36what's happening
12:37right
12:38so
12:39let's take a look
12:40at this
12:41interdiffusion
12:43a
12:44classical demonstration
12:45uses
12:46diffusion
12:47couple
12:48like a joint
12:49pure copper
12:50to
12:51pure nickel
12:52let's say
12:53it could be
12:54copper
12:55and nickel
12:56I mentioned
12:57this kind
12:58of couple
12:59many times
13:00they are
13:01located in
13:02transigent metal
13:03series
13:04their sizes
13:05are very similar
13:06to each other
13:07like transition metals
13:08their sizes
13:09are very similar
13:10to each other
13:11because they are
13:12using D orbital
13:13and then
13:14auto orbital
13:15S orbital
13:16P orbitals
13:17are almost the same
13:18right
13:19slightly changing
13:20just one S orbital
13:21can
13:22the
13:23electron in
13:24S orbital
13:25can
13:26join to P orbital
13:27or something
13:28but still
13:29the other orbitals
13:31auto orbitals
13:32are all the same
13:33and then they use
13:34like D orbital
13:35to fill up
13:36the electrons
13:37inside
13:38so
13:39like
13:40copper
13:41and nickel
13:42and
13:43copper
13:44and zinc
13:45they are
13:46a couple
13:47is quite important
13:48to discuss
13:49over
13:50and
13:51initially
13:53we have
13:54a sharp interface
13:55here
13:56sharp interface
13:57100%
13:58copper
13:59on one side
14:00and then
14:01100%
14:02on the other
14:03like nickel
14:04after heat
14:05treatment
14:06we find
14:07graded
14:08alloy region
14:09copper has
14:10diffused into
14:11nickel
14:12and nickel
14:13into
14:14copper
14:15the concentration
14:16profile
14:17is smooth
14:18with a steep
14:19gradient
14:20near the original
14:21interface
14:22like this
14:24this is the
14:25interdiffusion
14:26driven by
14:27concentration gradients
14:28which we will
14:29formalize
14:30with
14:31fixed
14:32law
14:33we will see
14:34that
14:35very shortly
14:36and
14:37another one
14:38is
14:39self-diffusion
14:40in an
14:41elemental
14:42solid
14:43atoms also
14:44migrate
14:45elemental
14:47do you
14:48remember this
14:49one
14:50element
14:51do you remember
14:52the word
14:53element
14:55I was asking
14:56you this
14:57before
14:58an element
14:59what's the
15:00definition of
15:01element
15:02if you see
15:03that in the
15:04periodic table
15:05that's
15:06an element
15:07for example
15:08lithium
15:09sodium
15:10kappa
15:11hydrogen
15:12hydrogen
15:13you see that
15:14in the
15:15periodic table
15:16so they are
15:17they are
15:18element
15:19but
15:21water
15:22you don't see
15:24water
15:25from the
15:26periodic table
15:27or
15:28acetone
15:29or
15:30any
15:31metal
15:32alloy
15:33we don't see
15:34them
15:35in the
15:36periodic table
15:38so
15:39they are not
15:40elements
15:41okay
15:42so
15:43here
15:44if they say
15:45it's an
15:46element
15:47solid
15:48so in the
15:49previous slide
15:50we saw like
15:51copper and
15:52nickel interface
15:53but in this
15:54case
15:55we have like
15:56only copper
15:57or nickel
15:58or
15:59sodium
16:00whatever
16:01so
16:02just
16:03one kind of
16:04element is
16:05existing in
16:06solid form
16:07that's
16:08elemental
16:09solid
16:10in this
16:11case
16:12can we
16:13can we say
16:14something is
16:15moving from
16:16the other
16:17like in the
16:18previous slide
16:19we observed
16:20nickel is
16:21penetrating into
16:22copper side
16:23and then
16:24copper is
16:25also
16:26moving to
16:27the nickel side
16:28so they have
16:29certain gradient
16:30position
16:31we just observed
16:32that
16:33but what's
16:34happening on
16:35this
16:36elemental
16:37solid part
16:38something
16:39occurs
16:40so
16:41somehow
16:42they
16:43labeled it
16:44some of the
16:45elemental
16:46carbon
16:47copper
16:48can be
16:49c
16:50a
16:51b
16:52d
16:53and then
16:54in time
16:55later
16:56they traced
16:57it
16:58to see
16:59where they
17:00went to
17:01a
17:02is
17:03moving to
17:04this one
17:05a
17:06is moving
17:07to
17:08and
17:09d
17:10b
17:11they all
17:12moved
17:14okay
17:15so
17:16diffusion really
17:17occurs
17:18interdiffusion
17:19leads to
17:20measurable
17:21composition
17:22gradients
17:23self-diffusion
17:24is hard to see
17:25directly
17:26but
17:27it's fundamentally
17:28the same
17:29way
17:30okay
17:31so
17:32i hope
17:33you
17:34it's
17:35it's
17:36not
17:37hard
17:39understanding
17:40this
17:41kind of
17:42the concept
17:43right
17:48okay
17:49how does this
17:50diffusion occur
17:51like a diffusion
17:52mechanism
17:53we mentioned
17:54like a vacancy
17:55vacancy
17:56is quite easy
17:57something is missing
17:59so here
18:00we mentioned that
18:01this is copper
18:02and this is nickel
18:03in the previous
18:04slides
18:05then
18:06the
18:08atoms exchange
18:09with vacancies
18:10actually
18:11atoms jump
18:12from
18:13a normal
18:14lattice
18:15side
18:16to a neighboring
18:17vacancy
18:18this requires
18:19like two conditions
18:20what is what are they
18:21an available vacancy
18:23an available vacancy
18:24and sufficient energy
18:26to break
18:27bonds
18:28this bond
18:29should be break
18:30broken
18:31and moving to
18:32and make a new
18:33bond
18:34in with
18:35the neighboring
18:36atoms
18:37right
18:39so
18:40that's
18:41that's not that difficult
18:43to say that
18:44right
18:45the vacancy concentrations increase
18:47with what
18:48remember that
18:49vacancy
18:50vacancy
18:51how can we increase the number of this vacancy
18:55by what
18:56increasing
18:57temperature
18:58so
19:00when we increase the temperature
19:02then we see more vacancies
19:05then also
19:06it has a higher energy to break themselves
19:09so
19:10when we increase the temperature then this
19:12like a vacancy diffusion occurs
19:14um
19:15more favorably
19:16um
19:17more favorably
19:18correct
19:19correct
19:20so
19:21number of vacancies
19:22and activation energy to exchange
19:25so
19:26activation energy
19:27it
19:28it may not be changing
19:29depending on the
19:30uh
19:31the temperature
19:32they might be still
19:34uh
19:35small changes too
19:36but
19:37uh
19:38when we increase the temperature
19:39they are
19:40like a kinetic energy
19:41itself
19:42is increasing to
19:43uh
19:44overcome that kind of activation energy
19:46correct
19:47so
19:48uh
19:49we will see
19:50they are
19:51exchanged
19:52and
19:54then
19:55it's moving to
19:56the
19:58the other way
20:00so
20:01we can penetrate
20:02into
20:03the deeper
20:04area
20:07that can be
20:08do
20:09doing some simulation
20:10over this
20:11if you go to the
20:12the textbook website
20:13and then
20:14also
20:15you can easily find
20:16this kind of simulation
20:18from
20:19um
20:20everywhere
20:21so
20:22like a
20:23this
20:24this void size
20:25so
20:26crystallized one
20:27and then
20:28it's
20:29it looks like
20:30it's moving
20:31but actually what's moving
20:32the particles are moving
20:34but that's
20:35really happening
20:36for
20:37like electron
20:38and
20:39the whole
20:40the
20:41pairing
20:42and moving
20:43too
20:44right
20:45so
20:46rate of
20:47substitutional
20:48diffusion
20:49depends on
20:50vacancy
20:51concentration
20:52and frequency
20:53of jumping
20:54that's
20:55kind of
20:56kinetic energy
20:57right
20:58so
20:59I
21:00hope you understand
21:02this one
21:03this one
21:04so far
21:05and also
21:06there's
21:07another mechanism
21:08like interstitial
21:09diffusion
21:10that's not
21:11that
21:12you already
21:14know
21:15I think
21:16know about
21:17this one
21:18because I mentioned
21:19interstitial words
21:20so many times
21:21smaller atoms
21:22can diffuse
21:23between atoms
21:24so
21:25they drew
21:26this way
21:27because
21:28they want to show us
21:29the gap
21:30between these elements
21:31are large enough
21:33to penetrate
21:35this small
21:36element
21:38position of
21:40interstitial atoms
21:41before
21:42diffusion
21:43I think
21:44it's already
21:45penetrated
21:46into the
21:47some portion
21:48maybe
21:49it's located
21:50at the top
21:51of this material
21:52and then
21:53it's moving
21:54deeper side
21:56it's moving
21:57like
21:58so
21:59can you guess
22:00which one
22:01has
22:02like
22:03easier way
22:04to
22:05move
22:06the previous one
22:07like a vacancy
22:08what do we need
22:09like
22:10the number of vacancies
22:11is also important
22:12and also
22:13we need
22:14some kind of
22:15kinetic energy
22:16to exchange
22:17the
22:18both of them
22:19but in this case
22:20interstitial diffusion
22:22we don't need
22:24to break
22:25the bond
22:26between
22:27the original
22:28positioned elements
22:29it
22:30just
22:31look
22:32through
22:33the
22:34what is that
22:35the gap
22:36so
22:37more rapid
22:38easier
22:39than
22:40vacancy
22:41diffusion
22:42so
22:45this
22:46what's the example
22:47of this diffusion
22:48remember that
22:49I mentioned
22:50many many many many times
22:51I think you can
22:52write it
22:53in your midterm
22:54exam
22:55the other way
22:56what is it
22:57like a carbon diffusion
22:58in the iron
22:59which
23:00underpins
23:01steel
23:02heat treatments
23:03like
23:04carburizing
23:06okay
23:08let's move to
23:10the slide
23:11this one
23:12that's what we
23:14but in the previous
23:15the slide
23:16the
23:17the case part
23:18was not easy
23:19to see
23:20because
23:21he mentioned
23:22like
23:23the dark
23:24case
23:25diffuse
23:26carbon atoms
23:27into the host
23:28iron atoms
23:29at the surface
23:30an example of
23:31interstitial diffusion
23:32is a case
23:33hardened
23:34gear
23:35so this is
23:36this occurs
23:37through
23:38interstitial diffusion
23:40the iron is quite
23:42big
23:43and
23:44carbon is quite
23:45small
23:46and presence of
23:47carbon atoms
23:48make iron
23:49this steel
23:50harder
23:51iron man
23:53superman
23:54superman
23:55superman has carbon
23:56on the surface
23:57right
23:58and also this is the
24:03another diffusion
24:04one
24:05in the silicon
24:06we have some
24:07from
24:08the
24:09here
24:10like
24:11phosphine
24:12and then
24:13put on
24:14the silicon
24:15surface
24:16and then
24:17increase the temperature
24:18that
24:19goes on
24:20to make
24:21certain
24:22in the case of
24:23P
24:24that's
24:25n-type doping
24:26right
24:27in the case of
24:28aluminum
24:29or boron
24:30that's
24:31P-type doping
24:32so
24:33a lot of
24:34n-type
24:35control
24:36that's
24:37another kind
24:38of
24:39diffusion
24:40processing
24:41you know
24:42semiconductor
24:43is very
24:44important
24:45in the future
24:46so
24:47I
24:48think
24:49we
24:50our
24:51country
24:52still need
24:53a lot
24:54of
24:55semiconductor
24:56expertise
25:00now
25:01finally
25:02we have
25:03some
25:04equation
25:05quantified
25:06diffusion
25:07we define
25:08diffusion
25:09flux
25:10J
25:11whenever
25:12we talk
25:13about
25:14diffusion
25:15flux
25:16some kind
25:17of flux
25:18we always use
25:19J
25:20right
25:21I don't know
25:22why they use
25:23J
25:24but
25:25it's not
25:26the first time
25:27you see
25:28J
25:29for the flux
25:30flux
25:31is
25:32or mass
25:33diffusing
25:34and
25:35then
25:36that's
25:37some
25:38basic
25:39area
25:40in certain
25:41time
25:42so
25:43that's
25:44the
25:45flux
25:46so
25:47officially
25:48like
25:49the mass
25:50or
25:51number of
25:52atoms
25:53crossing
25:54a unit
25:55area
25:56per unit
25:57time
25:58correct
25:59so
26:00mathematically
26:01this can be
26:02defined as
26:03shown here
26:04the
26:05spatial rate
26:06of
26:07change of
26:08concentration
26:09so
26:10we link
26:11this flux
26:12and
26:13gradient
26:14using
26:15fixed
26:16first of
26:17we observed
26:18in
26:19that
26:20vacancy
26:21diffusion
26:22part
26:23steady state
26:24situation
26:25so
26:26that
26:27can be
26:28defined
26:29empirically
26:30this
26:31one
26:32mass
26:33can
26:34be
26:35in
26:36time
26:37so
26:38the
26:39total mass
26:40can be
26:41increasing
26:42in
26:43time
26:44sometimes
26:45right
26:46so
26:47that's
26:48also
26:49important
26:50thing
26:51okay
26:52fixed
26:53first law
26:54times
26:55concentration
26:56change
26:57divided
26:58by
26:59the
27:00position
27:01change
27:02so
27:03I mentioned
27:04that
27:05this
27:06one
27:07like
27:08fixed
27:09first law
27:10is related
27:11to only
27:12position
27:13function
27:14so
27:15we do not
27:16have any
27:17time function
27:18here
27:19right
27:20so
27:21in the case
27:22of
27:23it can
27:24be seen
27:25so
27:26high concentration
27:27here
27:28and low concentration
27:29here
27:30and then it's moving
27:31this could be
27:32like a
27:33metal
27:34what was that
27:35I'm sorry
27:36I
27:37the
27:38some
27:39the
27:40membrane
27:41I'm sorry
27:42the metal membrane
27:43or
27:44any kind of membrane
27:45can do this
27:46kind of thing
27:47so
27:48on the left side
27:49or
27:50one side
27:51high concentration
27:52and
27:53the other side
27:54low concentration
27:55they have
27:56the
27:57gradient
27:58like this
27:59so
28:00that
28:01the
28:02negative sign
28:03here
28:04indicates
28:05diffusion
28:06proceeds down
28:07the concentration
28:08gradient
28:09from
28:10high to
28:11low concentration
28:12and
28:13steady state
28:14does not change
28:15with time
28:16that's quite important
28:17the profile is
28:18what
28:19stationary
28:20so
28:21consider a
28:22thin
28:23metal membrane
28:24here
28:25and
28:26the gas can
28:27penetrate
28:28from one side
28:29to the other
28:30right
28:31so
28:32in that case
28:33we see
28:34steady state
28:35in that way
28:36eventually
28:37the concentration
28:38profile becomes
28:39linear
28:40linear
28:41across
28:42the thickness
28:43and the same
28:44amount
28:45enters from one side
28:46and leaves
28:47from the other
28:48and
28:51this magnitude
28:52of D
28:53reflects
28:54how easily
28:55atoms move
28:56so
28:57guess
28:58what
28:59interstitial
29:00diffusion
29:01like
29:02carbon
29:03ferrite
29:04is typically
29:05much faster
29:06than
29:07vacancy
29:08self-diffusion
29:09is it
29:11correct
29:12so
29:13we
29:14expect
29:15high D value
29:16for
29:17interstitial
29:18diffusion
29:19but
29:20relatively
29:21low value
29:22for
29:23vacancy
29:24mechanism diffusion
29:25so
29:26atom size
29:27matters
29:28smaller atoms
29:30squeeze through
29:31faster
29:32and
29:33crystal structure
29:34matters too
29:35because
29:36that's
29:37site
29:38connectivity
29:39and
29:40barrier
29:41heights
29:42so
29:43when we
29:44have
29:45higher
29:46packing
29:47density
29:48then
29:49it's not
29:50easy
29:51to
29:52penetrate
29:53through
29:54them
29:55so
29:56if
29:57we
29:58have
29:59simple
30:00cubic
30:01and
30:02body
30:03centered
30:04cubic
30:05body
30:06centered
30:07cubic
30:08but
30:09face centered
30:10cubic
30:11and
30:12like
30:13hexagonal
30:14close
30:15packing
30:16their
30:17packing density
30:18is quite high
30:19that means
30:20they do not
30:21let
30:22the smaller
30:23particle
30:24into
30:25themselves
30:26it may
30:27occur
30:28it may
30:29still occur
30:30with
30:31a higher
30:32rate
30:33one
30:34but
30:35slower
30:36rate
30:37I'm
30:38not saying
30:39it's not
30:40completely
30:41prohibited
30:42it's
30:43still
30:44going that
30:45way
30:46but
30:47slower
30:48way
30:49correct
30:50so
30:54that's
30:55concentration
30:56change
30:57and
30:58distance
30:59changes
31:00and
31:01here
31:02example
31:03example
31:04example
31:05is quite
31:06important
31:07clothing
31:08this one
31:09we
31:10at the end
31:11of this
31:12chapter slide
31:13then
31:14we will talk
31:15about this
31:16chemical
31:17protective
31:18clothing
31:19that's
31:20kind of
31:21it's not a
31:22solid
31:23but
31:24it
31:25it
31:26treats
31:27as
31:28a
31:29as
31:30possible
31:31so
31:32methylene
31:33chloride
31:34is a
31:35common
31:36ingredient
31:37on the
31:38paint
31:39removers
31:40it's
31:41very
31:42volatile
31:43and
31:44harmful
31:45chemical
31:46besides
31:47being
31:48an
31:49irritant
31:50what's
31:51the meaning
31:52of
31:53irritant
31:54it's
31:55irritating
31:56same
31:57word
31:58protective
31:59gloves
32:00when using
32:01this
32:02paint
32:03remover
32:04protective
32:05gloves
32:06should be
32:07one
32:08we should
32:09wear
32:10the
32:11chemical
32:12protective
32:13clothing
32:14when you
32:15do the
32:16experiments
32:17and
32:18so
32:19that should
32:20protect us
32:21so
32:22when we
32:23use
32:24especially
32:25like
32:26gloves
32:27to
32:28protect
32:29from
32:30the
32:31chemicals
32:32because
32:33when
32:34we
32:35have
32:36two
32:37gloves
32:38that
32:39can be
32:40used
32:41as
32:42a
32:43buffer
32:44area
32:45so
32:46once
32:47the
32:48fluorine
32:49compound
32:50that
32:51gas
32:52can
32:53penetrate
32:54through
32:55the
32:56next glove
32:57they
32:58can
32:59be
33:00adsorbed
33:01on the
33:02surface
33:03but
33:04it
33:05takes
33:06much
33:07much
33:08longer
33:09time
33:10to
33:11penetrate
33:12into
33:13the
33:14second glove
33:15so
33:16butyl
33:17rubber
33:18gloves
33:190.04 cm
33:20thick
33:21you
33:22can
33:23have
33:24thicker
33:25one
33:26in
33:27household
33:28if
33:29you
33:30do
33:31dishes
33:32then
33:33that glove
33:34is
33:35much
33:36thicker
33:37and
33:38also
33:39when
33:40we
33:41do
33:42some
33:43very
33:44cold
33:45one
33:46or
33:47highly
33:48aggressive
33:49material
33:50and
33:51what is
33:52the
33:53diffusive
33:54flux
33:55of
33:56methylene
33:57chloride
33:58through
33:59the glove
34:00data
34:01that's
34:02our
34:03given
34:04and
34:05do
34:06the math
34:07that's
34:08very
34:09simple
34:10equation
34:11and
34:12then
34:13we
34:14put
34:15the
34:16numbers
34:17there
34:18data
34:19whatever
34:20see
34:21then
34:22the
34:25flux
34:26can be
34:27calculated
34:30so
34:31that's
34:32negative
34:33fifth
34:34very small
34:35amount
34:36of
34:37methylene chloride
34:38will
34:39penetrate
34:40through
34:41the
34:42gloves
34:43per second
34:44but
34:45that's
34:46per second
34:47so
34:48if
34:49you
34:50are
34:51exposed
34:52to
34:53that
34:54kind of
34:55condition
34:56for a long
34:57time
34:58finally
34:59that will
35:00penetrate into
35:01your skin
35:02so you have to
35:03replace the
35:04gloves
35:05open
35:06depending on
35:07what kind of
35:08chemical you are
35:09treating
35:10or using
35:11and
35:12diffusion
35:13is related to
35:14temperature
35:15then
35:16the number of
35:17vacancies
35:18are
35:19increasing
35:20and also
35:21the
35:22atom of
35:23interest
35:24has higher
35:25kinetic energy
35:26and also
35:27if it's
35:28small
35:29that high
35:30kinetic energy
35:31can
35:32be used
35:33to
35:34easy
35:35penetration
35:36through
35:37the
35:38solid
35:39lattice
35:40so
35:41here
35:42d
35:43equal
35:44d
35:450
35:46it's
35:47related to
35:48this kind
35:49of
35:50function
35:51so
35:52the diffusion
35:53coefficient
35:54at a certain
35:55temperature
35:56and then
35:57this is the
35:58original value
35:59maybe 25
36:00degrees celsius
36:01something
36:02we calculate
36:03it
36:04and then
36:05depending on
36:06the temperature
36:07like Arrhenius equation
36:08right
36:09Arrhenius form
36:10this
36:11kind of
36:12thing
36:15so
36:16here
36:17d
36:18has been
36:19tablized
36:21tablized
36:22in
36:23in many
36:24textbooks
36:25and also
36:26d values
36:27and
36:28temperature
36:29that high temperature
36:30high d value
36:32that's
36:33correct
36:34right
36:35then
36:36see
36:39this is
36:40quite low value
36:41and this is
36:42quite high value
36:43see
36:46that's
36:47negative
36:48fourteenth
36:49and eighth
36:50so
36:51that's
36:52much
36:53much
36:54like a
36:55low scale
36:56and also
36:57the gap is
36:58quite large
36:59so
37:00that's
37:01here
37:02we can
37:03see
37:04interstitial
37:05d value
37:06is
37:07much greater
37:08than
37:09substitutional
37:10d
37:11i think
37:12you can understand
37:13this one
37:14with an easy
37:15way
37:16because i mentioned
37:17them like
37:18many many many many
37:19many times
37:20so
37:22here
37:23an example
37:24the
37:25they are
37:26doing
37:27some
37:28diffusion coefficient
37:29and different
37:30temperature
37:31temperature
37:32so
37:33they are using
37:34the
37:35thing
37:36here
37:37here
37:38and you follow
37:39the things
37:40and also
37:41the
37:42you can find
37:43more questions
37:44in the textbook
37:45sample test
37:49and then
37:50do the calculation
37:52here
37:53remember
37:54that
37:55you
37:56you
37:57want to
37:58bring
37:59your
38:00scientific
38:01calculator
38:02with you
38:03for
38:04the midterm
38:05exam
38:06okay
38:07and
38:08that's
38:09steady state
38:10what
38:11it's not related
38:12to
38:13time
38:14but here
38:15non-steady state
38:16so
38:17we have
38:18like a
38:19time variable
38:20we have
38:21to
38:22use
38:23like a
38:24fixed
38:25second law
38:26not the
38:27first law
38:28so
38:29the equation
38:30looks quite
38:31different
38:32but you
38:33remember
38:34this
38:35when do you use
38:36like a fixed
38:37first law
38:38time is not
38:39depending
38:40time is not
38:41a variable
38:42but when we
38:43have a time
38:44as a variable
38:45then
38:46we should come
38:47to this fixed
38:48second law
38:49if it
38:50when
38:51time is
38:52flowing
38:53if it
38:54doesn't change
38:55the phase
38:56then we don't have to
38:57consider that time
38:58as a variable
38:59right
39:00and this
39:01vmse
39:02so you can go
39:03to the
39:04textbook
39:05website
39:06to see
39:07some
39:08simulation
39:09I think
39:10they have a better page
39:11by now
39:12I guess
39:13and
39:14non-steady state
39:15diffusion
39:16so
39:17they
39:18we have a bar
39:19and then
39:20the
39:21surface
39:22concentration
39:23cesium
39:24here
39:26whatever
39:29the
39:30it's not a
39:32cesium
39:33it's like a
39:34surface
39:35concentration
39:36of carbon
39:37and then
39:38high concentration
39:39and low concentration
39:40inside
39:41and
39:42they are still
39:43like a
39:44entering
39:45into this
39:46material
39:47so at the very beginning
39:48it has a
39:49low concentration
39:50but
39:51the concentration
39:52will increase
39:53in time
39:55so in this case
39:57we have to use
39:58non-steady state
40:00diffusion
40:01that's
40:02this kind of equation
40:03so
40:05I mentioned that
40:06this kind of solution
40:07will be given
40:08if needed
40:09for your test
40:10or
40:13in real
40:14experimental part
40:16you don't have to remember
40:17this kind of equation
40:18all the time
40:19right
40:20in our
40:21brain
40:22it is enough to
40:24keep that in mind
40:25like
40:26the high temperature
40:27will increase
40:29the
40:30atom movement
40:32inside
40:33the solid
40:34or wherever
40:35and that will increase
40:37the vacancy
40:38sides too
40:39but if you
40:40are interested
40:41in like
40:42quantitative calculation
40:43you can come over
40:44to this textbook
40:45or
40:46improve the equation
40:47in
40:48in
40:49publish the article
40:50by somebody else
40:52so
40:53here
40:54we put
40:55this
40:56we need
40:57some error function
40:58that's
40:59given in
41:00table
41:015.1
41:02so you can
41:03if you have
41:04these values
41:05are
41:06determined
41:07then this error function
41:08value
41:09can be used
41:10to
41:11get
41:12this
41:13right-side value
41:14so
41:15there is
41:16some example
41:17here
41:18FCC
41:19face-centered
41:20cubic
41:21ion-carbon alloy
41:22initially containing
41:23some value
41:24is
41:25carburizing
41:26at an elevated
41:27temperature
41:28in an atmosphere
41:29that gives
41:30surface-carbon
41:31concentration
41:32constant
41:331.0
41:34weight
41:35percent
41:36so in
41:37some time
41:38here
41:39the time
41:40is kind of
41:41variable
41:42so
41:43okay
41:44it's not
41:45steady-state
41:46diffusion
41:47it's non-state
41:48state
41:49diffusion
41:50so
41:51this
41:52is the equation
41:53we
41:54have
41:55in the previous slide
41:56and then
41:57we can
41:58put the numbers
41:59and
42:00time
42:01value
42:02here
42:03and then
42:05the surface
42:06concentration of
42:07carbon
42:081.08%
42:09if
42:11the
42:17error function
42:18is not
42:19given
42:20in the table
42:21then
42:22we can
42:23simply
42:24guess
42:25where
42:26that
42:27g
42:28could
42:29be
42:30in
42:31the table
42:32if
42:33that
42:34error function
42:35value
42:36where that Z could be located so that Z value can give us more information about
42:45this way so we can calculate the D from the error function okay
42:56for limited time I I don't know I want you to solve this kind of problem in your midterm
43:09exam but if you do just once that is enough to do the same thing so in the
43:21temperature it's it's a one more like a flipped one so depending on that the
43:27temperature and you can simply calculate the value this is the last one in the
43:38previous is not the sample test we have learned some chemical protective
43:44clothing the the distance and then also that's like a steady state value so it's
43:55asking time value to how long does it then could the gloves be used before
44:02methylene chloride reaches the hand so data is here we do some calculation for
44:18minute so if we have that kind of condition you're putting your gloves are
44:26protecting you from the chemical only for four minutes but if you do not use
44:36that kind of chemicals and you don't have to worry about that much but most likely
44:41in our experimental lab we do not directly handle any chemicals with with gloves
44:50right I know we are handling that the the chemical containing the bottles or some
44:58other the beakers but in that case we do not expect those chemicals are
45:07contaminated they on the outside if that's contaminated we have to clean them
45:12first so we don't we don't need to panic or worry about the this short time for your
45:22experimental condition but if you do something like this in your future company then you have
45:30to wear like two sets or multiple sets and also you have to replace them quite open to avoid
45:39any kind of accidents okay that's that's almost it for this whole chapter and then summary so I I hope you
45:56remember that like a diffusion faster for open crystal structures and materials with
46:04secondary bonding so weaker bond smaller diffusion atoms lower density
46:11material diffusion slower close packed structures materials with a covalent
46:18bonding that's easy not easy to pass through right larger diffusion atoms the
46:26higher density materials I think you understood both most of them without any
46:33difficulties right okay thank you for taking this course and then this is the end of
46:43chapter 5
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