Mechanical properties of steel 10: dislocations & faults

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Mechanical properties of steel 10: dislocations & faults
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The tenth in a series of lectures given by Professor Bruno de Cooman of the Graduate Institute of Ferrous Technology, POSTECH, South Korea. This particular lecture is a continues on dislocations and their role in steels, but including the concepts of stacking fault energy and dissociation.
Keywords The Graduate Institute of Ferrous Technology (GIFT)
Ship class Rutschung Last
Cardboard (paper product) Sizing Rear-view mirror Cartridge (firearms) Ship class Alcohol proof Ship of the line Noah's Ark Abachi Wire Van
Angle of attack Überschallstaustrahltriebwerk Rear-view mirror Spare part Material Hovercraft
Angle of attack Angle of attack Ford Focus Rear-view mirror Crown (headgear) Alcohol proof Spare part Ship of the line
Lugger Typesetting Steel Schubvektorsteuerung Überschallstaustrahltriebwerk Institut für Raumfahrtsysteme Plane (tool) Spare part Forging Ship of the line Kümpeln Clock face International Space Station Photographic plate Typesetting Mechanic Schubvektorsteuerung Slip (ceramics) Bending (metalworking) Hochseeschlepper Diving suit McDonnell F-101 Voodoo Screw Plane (tool) Ship of the line Engine displacement Screen printing Wachsmalkreide
Typesetting Ballpoint pen Car seat Seeschiff Game Seaplane Cartridge (firearms) Screw Plane (tool) Plane (tool) Forging Ship of the line Firearm
Airbus A300 Lugger Hot working Schubvektorsteuerung Roll forming Screw Commodore MAX Machine Plane (tool) Spare part Kümpeln Firearm Material Enigma machine Clock face Photographic plate Typesetting Steel Tool Buick Century Gemstone Schubvektorsteuerung Ford Transit Chemical substance Outsourcing Crown (headgear) Cartridge (firearms) Screw Narrow gauge railway Mode of transport Plane (tool) Ship of the line
Typesetting Airbus A300 Tool Piping Gemstone Gear Separation process Turning Crown (headgear) Screw Spare part Plane (tool) Forging Kümpeln Engine displacement Material Clock face International Space Station Photographic plate
Typesetting Truck Tool Mechanic Ballpoint pen Stagecoach Schubvektorsteuerung Turning Ship class Cartridge (firearms) Screw Spare part Plane (tool) Forging Book design Satellite
Gentleman Screw
plasma what we're going so far whatever so 1st announcement is about makeup class so it's not about this maker plastics linkups class about this course it's this follows so we we missed the 1 class last week the next week on Tuesday all the ups and have some personal issues to attend so I have to travel to Europe for a few days so what that will do this will group these 2 makeup classes and I suggest to do at this week on Friday after 2 minutes around you want to go to Seoul won't forget it they have to leave later I 3 2 5 I don't think I think there's no English class and that's about the only time I'd like to do it and I don't want to sound postponement much 3 2 5 on Friday but don't tell say to your friends Wyoming on 2 of them but then the other thing but last year when we were meeting last time Houston 2 2 long slide we
were discussing we had seen it an example most out to work calculated how to use the phone peach color
formula the 2 parallel edged his will that we've done it for 2 sparrows screw dislocations and we just finished their I'm going through the Ark of the match for the 2 parallel edge dislocations I'm just and it was toward the end of the class and maybe things were not so clear at that time I so to basically what would we do this we we assume we have 1 dislocations here in the In the origin of the euro according to the access and at the end you consider another dislocation parallel to the edge dislocation and this edge dislocation can have on December the specter has look or basically the look of all look the the same just order can have a different respect in this case if we in both cases considered the 3 cases considered week are direction line direction in the board so you know line direction and the board extra have claimed up here that means the Finnish start right hand convention Burgos factories here this 1 samba dislocation in this case of the the likes to have is pointing downwards of the prospective points to the right but so but so and so this 1 stays here and then we would put this dislocations anywhere in this space right but then so was the core of this is focused hasn't X and Y scored and that's basically what defines its position so and so on so basically that there are some places where the dislocation of interesting places with this location can be and so this is the diagonal here at 45 degrees has been alone if the dislocations is quarter here Friday x is equal to what I obviously the SO X over why is 1 of the anywhere along this line as it is this look news on this side of the diagonal X is necessarily larger than wide so X over why is larger than what goes and in this above the diagonal X over White is smaller than what and and if it's exactly on this line so you have this location it's exactly here well here X over why 0 OK if itself is so in this diagram would you basically do is the position of the dislocation that you you actually you the X over why ratio so this is the acts of wire ratio and this is the force on dislocation if this is for such accomplished positive you have repulsion if it's negative you have attraction :colon yet so I went into the results that tells you that if you have the same size when you're in the region from 1 2 infinitely for X over 1 so if you're in this region here In this region here but you have a positive force it's kind of repulsive the report the dissipation will however there if I did if I get close enough 2 events diagonal to equal to what I have to export the white 1 yes I see that the the repulsive force gradually decreases and becomes 0 so if the gift the edge dislocations kind of Venice yes I have this 0 for this and then and then I come in a range where the dislocations attract each other the attractiveness of in this region here in this region here there is an attraction this aggression will want to move closer to each other you have to realize that there may be an attractive forces between these 2 yes but this is the case cannot you move up and down so settles glide closer to as close as possible to discuss so right and if they have opposite side which is to reverse the opposite sides the Red region there will always attract in this region there will look and so it began as as it's interesting because it
explains to us why it is that's it issued a foreign material yes and you heated up slightly as so that means you give the dislocations the thermal energy shares they will they will move which respect to each other and for lower low energy dislocation configurations they would in other words they will tend to move let me go back like the other direction it would be so they will tend to
move to situations where the force between them is 0 is very good and that is the principal of the recovery basically so what what what does this craft health you well for instance it tells us that OK so if you have on the same side as the edge dislocations in this region here will be attractive attracted to words this 1 and the anticipation of in this part of the diagram located in this part of space will be repulsed answer so as a consequence of the like signing dislocations will have a tendency to align I like that's go on top of 1 another here's where the force is 0 so it can so that means going to
disappoint X because will exceed the wine and when you have that kind of edge dislocations like this if you have a low angled tilt boundary and this would be friends as the result of a defamation that's followed by recovery and you could see the amount of this focus hasn't diminished but the energy has diminished with the strain energy has diminished but the new refers necessary have different the Burgos factors then In this part of the interaction will be repulsive and in this part of space the interaction will be attractive them so you will tend to see the dislocations of burgers which would different Burgos factories in you an equilibrium configuration it looks like that's today the line along the 45 degree a diagonal to began to minimize the and and so what does this correspondent this corresponds to this point here the other 0 forests .period and I you can have this step aside or you can this is also a little lower energy configuration alternative but when this happens the slow but again stressed the fact is no 1 knows the amount of dislocation doesn't decrease the the same amount of this location but this is not it's not really crystallization what what we're seeing here but if so they know last week I
realized it was moving too
fast Whitmire and
explanations here and I needed to I needed To go
back a little bit because of so so we we yeah remember last week we and we calculated the the energy of dislocation 1 and we are we yeah we noticed that while he had basically the start of the week terrorists the term G B squared divided by then but term where you see this "quotation mark Alpha yes that is basically of tells me that the dislocation energy is a function of whether it's an edge dislocation screw dislocations makes good and then a term that is related to the and how you integrate how you determine the energy basically and I although it's interesting physical problem this calculation by the turns out that the impact of this fact not lot planets and told you this the natural logarithm there at the end of about 5 and a half and it's not very sensitive to do the things we will do with this and then you have a L which is the length of this little longer dislocation is that more energy so and that allowed us to determine To tell you that that of introduced a fact which we call the wine tension is basically the energy per unit length and that's about it said the average of the the orientations if you take the natural logarithm if it goes to 5 etc. But you countless for pie factor this is the energy per unit length of this not so and we knew I told you that this be squared criterion was very important because it that tells you but weather a specific dislocation will change into another dislocation or whether to dislocations will come together and form a new dislocation and we like to talk about this as dislocation reactions obviously they're not reactions the like chemical reaction writer like mechanical effects right away right so the the best way to to introduce this dissociation we have to talk about SEC Chris because you'll see in a moment in the In BCC crystals like variety like everyday steals we have but we don't get Association of dislocations so necessarily have to talk about SEC IRA or Austin it takes deals but also attic steals if so don't that we look at the start of crystal of crystallography off an edge dislocation or so we have here a guy playing which is which 0 1 1 1 planes in the SEC and then we have drawn here an extra half blame yeah even in that particular crystal structure and and so this extra have places 1 1 all type plane inserted here right and so if right I take my line direction into the screen there's my extra have blamed this is coming from up there so my burgers factor is to the last to conventional OK but that if you do this you have to look at the crystal structure that that 1 1 0 planes they actually stack it's not always the same place Will it actually consists of but quite high tide be Type a Type B a B a B to the stacking of it so when you introduce an extra half playing yes and you want it you don't want to disturb the stacking sequence you actually introduced to players 2 1 1 0 play 10 now what can happen and when it does happen in many uh all Semitic steals what is that these 2 1 1 0 0 planes yes you can see they can move away from each other yes they can move away from each other as as separate edge smaller edge dislocations the smaller edge dislocations and when doing this you will keep the rights stacking sequence yes also 1 wonderful planes above and below the the slip here with we're not talking about the 2nd in this direction because when we do this this will see in a moment that we create stacking fault in the sacking of the 1 1 1 place so so we have when this happens we have now yeah the edge dislocation on this side of the edges look at you this location on this side at this location on this side of and for this particular Berber sector of 8 upon too onto 1 bar 1 0 show you in a moment how this works as these are 2 2 partial steps we get 1 0 6 1 Florida was 1 of 6 to bottom part bar 1 all and the the the fact that we create here is a stacking fault and recalled this seen a moment wide intrinsic spectacles of the 1st mopped up this is an application of the the square criteria because this will only happen if the dislocation the the square of the starting dislocation and the square of the the reaction dislocation if you want this be Square is larger than the 1 square was beaten where will be 1 as this 1 and the Jews is this one's birth respect other so but such let's 1st to this little calculation for a so so with the square criteria and the rights suit again this we're not talking with this situation here Crystal graphics situation does not hold for rejects deals will be ceasing its FCC and so necessarily for also Semitic steals from whichever necessary structure so so this is what we call the Burgers vector of UN disassociated dislocation and this is the Berbers factor of these 2 new dislocation is to new dislocation and this is the reaction it's not we write it like a chemical reaction that it's not a chemical reaction don't think about it as a chemical reaction they upon 2 1 0 bar 1 is upon 6 2 bodies plus upon 6 1 1 part of it so I calculate the whole length of this dislocations basically squared I find it square were too and I made to some of this the length square of this factor in the lengths where of disaffected very very simple and when you have way of assure you the we have to to do here and you find 8 square divided by 3 so this is old . 5 times that of a square and this is 0 . 3 times its present this overseas Alaska that than this and so yes B the dissociation will occur yes on the basis of this Bisbee square criteria OK the but and so what the line to the energy
tells you is that yes on the base of the squared it should happen however when you do this yes and these 2 dislocations are created in between these 2 this you create a stacking fault is greatest spectacle so what do we mean is that the use of the 2nd Fulton and the normal FCC is ABC received using like this will then hold offshore you in a moment how this works out in the crystal but and then there are actually 2 ways in which if you remember this is what we had the 2 extra have planes here I'm going to give this number call this number 1 and number 2 there's the dissociation can go into in principle in 2 ways I can have Warrenton have looks the same except that in this case this kitchen that was here is on their side and to is here and in the other case we get theirs OK and they reversed this we 1st but so depending on that's the way this dissociation occurs yes we will I have as stacking that looks as if we have removed playing or we will have a stacking which looks like we have inserted a plane seat so look like ABC see they be very itself and see a seat that is the stacking you get in a hexagonal In epsilon pirate yes so we call this In the nucleus if you want of HCP Byron but it can also work out differently when you can if you if you insist the association has happened so that the stacking fault looks like you have inserted a seaplane than you have ABC AD normally users have be ABC etc still there CB see they've been you can play in this game if you look here then along this line you have then marriage to not With respect to this day C B B so you have made it 20 what that half of course you don't insert planes and what we have is you shift the crystals you you make a ship so if you do as armed and you can try to do it uh rather easily by just looking at the stacking so you but would you basically looking at here is the stacking of 1 1 1 planes view would allow a 1 1 0 direction and so on you can see we have stacking ABC ABC so what so you see here planes above did this a at it is repeated this 1 is repeated here this 1 is reputed to these positions have names that you can do shift the Princess if we shift now this be this be at to this position here this position so it it comes right over the sea yes I'm just doing 1 shift pushing this like that of course the item is not called the anymore right it's not cold beer because it's it's it's a ball of a atom writes a scholar I call it the Seattle now baby so ABC ABC yes so in fact and then insert anything right at included I just shifted know I shifted my crystal look as if a small partial dislocation had passed right that's what that's basically what I what happens when you have a dislocation past him OK N N and if I on another shift yes No I have this way and I shift aid to this position then aid comes on top of so the name of a not called anymore it's called the 1 because we talk about stacking their rights is of the type stacking the Bisbee becomes C and then we have formed ABC ABC B and you can see that way so the do these different stockings on foreign not because we you actually add another layer of atoms it's just because the shifts you get different shifts whether the partial sorry this way or that way this solution that OK so I but whatever you do yes In between those in between these 2 dislocations you create a stack of Napster and M no what is interesting is that if you start with the same edge dislocation of U 2 partials will not be edge dislocations not pure edges there that that but they will have an edge component is the abroad this factor let's say I have a dislocation lying there and a bird respect like this that but it's you this bungle areas when asked yes it's not 0 it's not entitled over to but I can always the composer in edge component perpendicular to the line and a screw component there's so so when you do this dissociation the 2 partials has edged components and the extra half blames for that and the extra have planes all are coming from the same direction right so if I go back to where we started with this morning I have an edge dislocation at the origin and have another edge dislocation here on the same plane yes so in what regions up in what region are we here we're in this region right In the red region yes and that region is repulsion so when the dislocation dissociate that instantly pushed each other white the the edge components Our repulsive and ends it and then we know from this graph that this repulsion is yours it's always reaped repulsive and so on and so but there's something that limits the distance they travel away from each other and that's the stacking fault because as I have as the pushed away as they pushed each other when we generate a stacking fault him and the energy of the stacking fault it is positive so that means that there will be a sweet spot where they stop moving away from each other 1 they're repulsion energy has it is Is this is equal to the energy yes created bye the state-controlled generated at the 2nd at the end so that we can calculate this right so that's so here to see so
that the force between the 2 dislocations so what would we have as it is basically we're going to calculate the force has so we know this is 1 of the partial dislocations yes and I multiplied with that's it these substance this is as it is if you want to do the sheer which sheer component of dislocation at the origin of this style times basically the peach curler equation for this particular case because as I just apply this to an end we know the distance that there the d away from each other so and and this and this deployed in the only thing I need to plug and which are the 2 the vectors Burgers vectors and I have to make adult products that don't from here and and I find it's G times square divided by 24 times did so again she motherless plays a role and the distance 1 over the distance so far a source of the remoteness of the the closer they are to each other the larger the repulsive forces and and the repulsive force dies it has won over whom I get and this force is balanced by an an attractive force due to the stacking fault energy means that you went when these dislocations justifications to the left and this dislocation moves it is not the British-born moves to the right that I create more and more stacking fault and but in a topic that I'd like to thank all the the this the energy of the stack of false gamma so if this force is equal to stacking faults the Energy Inc for will get this acted equilibrium so the distance at which these 2 partial dislocation stop is given by desk "quotation mark cheap where divide by 24 . 2 times gap so this stance is the 1 between 2 partials is proportional to 1 over them so if I have a 50 the energy of the stacking fault is very high the this dissociation this will be small if the stacking fault energy is very low the dislocation can be very widely separated such letters because the distance is proportional to 1 over the stacking for energy to the stacking fault energy is large I will have a very small the association is the stacking fault energy is I have a very wide at this location and that has very very important implications just as if the this location the 2nd for the energy is extremely high then there is no this association where does this you know what 1 wonders a you know like and steals issue for wonders when did this century dislocation start to decide we don't associate Woods will will will see but the value for the 2nd called energy where there is no more where you can be sure there won't be any & Associates about 100 Miller chose 4 square meters on can the top that military losses jewels Energy Inc meter square surface antigen there is so what is that while this is an example here writers for instance the top years in Austin at its steel yes but you see these 4 white lines there's so that 2 of the top ones are the 2 partials as belonging to a dislocation of there'd have have to Burma's factors indicated B P 1 partial 1 and BP to partial to yes there is another dislocation sojourn ready so it now Of that the equation we've just seen there is a more sophisticated version of it which takes into account did orientation Of the have and associated disappears that went with the dislocation is badge boss screw for mixed yes but it's basically the same but the idea with those of the distance between the 2 parts of this proportional to 1 over the stacking faults so if you use this equation Is this equation for instance other yes you measure this by experiments until you get the from experiments it's how do I measured as a very simple I measured the distance between these 2 additional cases like this and then I plot this as a function of the fungus so injustice TM work I can the of determine what the Berbers factor instead and I can determined to find what the burgers factories I can see what the line direction as riding exceeded the line direction is here and here it's in this direction so that so can determine yes and as so if new here I can plot all the measurements are made yes these are measurements vision measurements of the values the next year and plot this year and plop this this equation here for different values of the 2nd fault energy and by bisecting the data to don't these calculations in these lines here for that are opting for different spectacle of energies like I can basically determine what the start fault energies approximately when you concede scatter can be quite considerable but the 2nd fault energy for this particular material 18 % manganese steal it around 30 military Willsboro square meters of land so it's good just you can assume that all the dislocations will be dissociated from them 4 of the this location of the 2nd vault Energy Inc there's the spectacle energy is the is determined by tool parameters has then the
1st parameter is composition and the 2nd parameter is temperature but the US To this example he forces fought stainless steel and you know that I am AusNet of vary widely used in many applications and you know that the main allying elements in this but this type of steel and chrome and nickel in Austin and the crow is added to give the steel Aid corrosion resistance and in nickel is added to give the steel the Austin intake structure of not for corrosion and Acromas not added 4 To get they have these 2 elements of different reasons to be added let's put it this way now that they influence the stacking fault energy France's if you look at the number of Steele's knows where you don't vary the nickel content too much 13 to 16 thousand relatively narrow range that's and you plot the stacking fault energy as a function of the the chrome content which varies 13 . 4 per cent you see that there is a decrease in the 2nd so adding Kroll will result in wider stacking faults you look at the the effect of Nicole then you use alloys where you select them so that you have a relatively narrow the range of pro contents of 17 to 19 per cent of Crowley and then you very you plot a stack fault energy as a function of nickel called and so you see that the nickel content increasing will increase a sector that has an effective reducing the stacking fault with the stacking fault energy is strong partly influenced by the but by the these composition why is that and also said the 2nd folded his temperature deep and why is that but what 1st of all Oh maker life's simple might might might 1st saying that people have looked at In metals how do How do stacking faults with 2 stacking faults look like this by looking at what dislocation is on what side of the stacking and they find that the stacking fault is usually what say we called in transit and when we have an intrinsic spectacle it basically means but it looks like we have removed the plane or it's the HCP type stacking fault that prevails in practice OK I'm so basically the study from looks like this like a little sliver little sliver of Allston inside FCC structure right so if that's the case you can basically the use thermodynamics to calculate the stacking fault energy because you basically have to say well when I create stacking faults I basically transform Austinite into HCP and and that's 1 thing I do and and 2nd I create interfaces I create false tonight the Exelon Byron interfaces this little this is the stacking fault region used to be the Austinite so I transform into epsilon right and so that's 1 thing and then the other thing is here it used to be a gamma gamma interface transformed to demo epsilon interface units here and here OK so and With this we can calculate the this really reaction just using delta G yes the change in free energy From thermodynamics and so and I don't arrive this equation here but the the relation is stacking fault energy is 2 times the of Boehlert surface density 2 kinds the free energy change 4 the reaction in this case commented transformation DeMint to epsilon plus a term related to the surface antigens yes so I have 8 actually very simple formula which if I know this into facial energy value and if I know as I can basically calculate with the stacking fault and useless this term here is is basically got it's molar the surface density of 1 1 1 we should be gameplay modes of course is I'm and and and this is the formerly you just apply this and that and then you get this parameter so easy to to calculate if you have the lattice parameters of your allies going so let's let's let's calculate that showed an example here so what we need is a lattice parameter we need have gatherers number we need a driving force for the government to epsilon transformation that's 200 shows from all it where does this come all this is basically comes from either thermodynamic measurements or from the programs that allow you to look like thermal that allow you to get this this data this thermodynamic data will so busy from the literature review and then the interface energy that's probably 1 of the weakest point in this theory right out of it at 10 military was the square meters but that's a little interface energy and that's which is what we usually use gas for this kind of interfaces the shear modulus there is comes it appears in the form of an across the Burgos factor of the partial dislocations that state upon 2 1 1 2 if you apply this you find them all .period about 15 mm and imports alteration consider stacking fault Energy Inc that's the best equation here I just plugged in although these
these parameters Of course making sure I've got the right dimensions here and I find 32 Miller chose per square meter Clinton for this this particular set of the data so that if I know stacking faults the energy I can determine How much is the separation between 2 screw dislocations that basically this equation right separation for screw dislocations Peter is 0 Florida the edge dislocation his pipe over to all 90 degrees OK and so
I find 3 nanometers for screw dislocation and 7 nanometers for the edge dislocation about double about them so the distance between screw dislocations and edge dislocations is that is different and the edges of it all was widely more widely separated them dislocations fall for this and for the same original burger structure and for the same stacking fault energy of so 2 obviously composition has an effect on free energy because you could have epsilon face and you can a gamma phase but depending on what a lawyer you have you have different free energy and of course the free energy of a phase is temperature dependence the so what would we see instead the effect of the temperature is that the stacking fault energy increases when the temperature when the temperature increases you get less less the dislocation separation is smaller at higher temperatures focus but if analysis led some let's talk about Alpha buyer for Riddick steals what's the problem on which the situation there white white but that they're not but what why did I choose to focus on Austin attic steals when I talked about spectacle for the simple reason that because this stacking fault energy of elsewhere and of 4 Riddick still is huge that's so on an I that I don't know how much power hiatus we so the only way you can actually I guess how high it is by doing by calculating and there's an because it ended with the Austin deals you couldn't you can just experimentally look at with the desperation and determine the stacking fault which have in the BCC I Infotech steals the Sierra for you can never see a separation so you you have to assume it's very high so so with which you can do it and what people do nowadays because of the computational tools we have they will but they will determine what we say the generalized stacking fault energy with basically do they take for instance the bcc lattice and a sheared the lattice yes they shared the lattice yes and they can determine what is the increase of the energy they gaps yes as you shared the lattice and then you can know computationally spoke about their only 2 DFT calculations you can do any shift you walked in and calculate thinks that will of course not be seen in in nature of the experiments so you can do shift that and you can determine for every position every lattice mismatch basically what the energies and if you do that but for instance this is for the sheer on on the a Heublein officers were Shearer on a 1 of the 1 0 playing and this is for sheer also won 1 0 plane that this share is a long 1 1 1 direction and this 1 is long but to edge direction and you see I had told you a hundred million jewels per square meter that's kind of how I already this goes up you know thousand 500 so these stacking fault energies in bcc Irish destined for its huge so you we never see a dissociation In the C Byron and forensic steals and that is very essential property of the BCC apparent as we will see in a moment but you can do the same for the SEC says and just I we want to introduce a Soviet Union you plop the energy that you create when you shift a crystal In but part of the crystal aim 1 1 2 direction yes and you compute the the energy as a function of the position and so on when you do this when you do this so Francis I shift this be atom here 2 the right now as it was the 1st I see that when I create the 2nd fall 2 years this be out of here the world will go to a position where it's on top of the uh with words shifted gears when it comes In between us and a symmetric position it is difficult to see that this kind of but equally separated from the east to the atoms that's a slight this has a slightly higher energy we call this the energy of the unstable stacking fault and then when we continue to shift the yes it becomes a sea stacking playing the that and that has a cracked slightly higher energy and that's the intrinsic stacking fault stable stacking fault and you can see that the structure here is HEP crystal the new keeping sliver of each of the material in the FCC material and then if I would continue to push this see atom to the right it would now face this atom I would have an ace 8 conditions that's a very high energy energy situation very high energy and and that of course I get an increase in the stacking fault and and as I continue the energy will decrease so it's a new concept that people are using instead of just the stacking fault energy which is this when they used the generalized stacking fault energy which allows you to for instance consider this this because the way the dislocations will dissociated disassociate will required to go through this unstable stacking faults situation that more details later perhaps if we get that far 4 In fact so we will I need this a little bit in and in the future but but I just want to make sure by introduces some of
concept In which is very widely used as to the described the dislocations in the FCC Austin steals and BCC sporadic states have and I so you know that both these crystal structures have BCC and pubic units sounds but it's very very inconvenient to use CU unit sells to describe the this locations instead we use these geometrical but shapes here this is a a he draw this tricky drop and and this is the wrong I don't he dropped don't occur means 12 12 faces but not the 1st let's do it perhaps this a picture he dropped as and when when we use the stature he dropped to just enough to work with dislocations and SEC crystals which would call it the Thomson debt-ridden because that's the guy who just the I proposed the use of this system and it's very useful so basically where does this detector he drawn I fit in the FCC unit well here because of the CDU itself and then I put the 1 of the corners of the country in the origin and this is what I had OK so you can see them going from here to here what is what is the but this a factor that I go for instance from this atom which I call it to this item which are called the this time the suspects this Hawaii and of this and the atoms of the unit sales are here is the itself and so has at the level higher I have this afternoon here and I have this afternoon there was a book so the the detector he drawled as seen from busy direction it is it's like this and this life here that this is not paying respect respected the satellite called the answers and its distract Americans so this factor here what is it there's while we know that this is the length of the suspension all 1 all right and this length here to do this this year that is the 1 both were so from here to here it is the state upon too 1 of them all and from here to here is based on for 1 thing OK so this specter here is the some of this factor and this factor so it's it's the sum of it's a sum of on 2 only 1 this factor and this factor is the negative of the factor of it's a over to minus 1 home so 2 minus 1 all so a the vector 80 B is equal to this to some of these 2 factors date forward to minus 1 1 of OK but so basically have etc. he draws where all the edges yes all Burgers vector and the associated with so I'm going to ship subsidies would be .period state this has been so if I go as I said from day to this this vector here is Over to 1 of our 1 1 of the solutions yeah we so now we do another thing at this point here is called .period this plane here it is crystal graphically 1 1 1 but we also call it the ABC playing the peacefully this factor here is upon to bar 1 1 0 0 weakened call it that way but we also call it the baby vector so with the use of the the advantages you'll wonder why will want to move and make things confusing and using a B instead of just using the crystal ball you can you can use whatever you want basically but this is shorter than than that "quotation mark that's basically why people use this much more it's like it's also gives you shorthand notation often dislocation all right and then the there are other the important point is another important point on the you're on the phone on the year Thompson detritus of if I take .period be here yes when I connected wait this point here so I basically take the diagonal yes it will intersect my triangle here in a special point which I call .period Delta and I can do this for all the other plants for instance if I'd I be I'd do the same I like connect With the diagonal the point the atom to on the diagonal diagonal direction I find .period data and why is that important so I have to be point here in the Middle East Delta the bonds of basically but this is .period Dean if I let down the normal normal on this plane from .period but I explained Delta but the interesting thing is that these vectors here yeah but actually the vectors for the partial dislocation doing so if I can see that France's this vector I
can be created by the sum of 80 Delta Delta B right so baby they don't most dealt B and of course these vectors here have crystallographic notations equivalent the 2 this is shown here so this ABC this Delta here as tool of the Delta Eighty Delta these are the leading the corresponding moral Crystal graphic notations for these factors they upon 6 minus 1 2 minds was the upon 6 2 minus 1 and minus 1 can and then of course there is 1 in this direction also the state concentrated the Thomson Tetra is something for SEC metals and alloys right so if you're working on for erratic still so you don't need all of this because the slip planes and Burgos factors are different and that's why this is for gamma Byron what else are and for forensic steals a configurations of the the light planes has and the burger structures are different it's 1 thing and the 2nd thing is as already said there are no partial dislocations yes there no equivalents in the delta Delta the type of factors so how does it work there In a they succeed Crystal the the delight planes a 1 1 for now I don't know how much you know about the the formation seed crystals with new maybe you you've had some classes about this in the past and and and people say Well you know yes it's 1 1 0 but it's also 1 1 2 when it can be 1 1 2 3 is a truck to at this stage I worry about it will talk about this in more detail but for for all practical purposes in steals again instead 1 1 0 you should consider 1 1 0 as the like can but that it it will go back into although details as as we continue soaked up to what we do in this case will we do the same thing as we did for the Thompson drove which is what to Thompson Tetra drove this is basically just cut out a shape which is bound by the same place all the possible slip planes in the crystal structure to what we do is we do the same thing now for recent and we cut out the subplots yes and we find to something similar where do the surfaces are slip planes the faces of and the the edges are Burgers vector yes to hear the shape shapes will but more complex and that's so we have the various factors in here 1 1 all types of planes so far the yield as you can see that so can you see you see this square this square but as of this year new looking down 1 of the few direction likened x-direction right from the if if I am myself so I know know there's another few directions restricted to the said the symmetry of of the crystal balls so N did you see the hexagon this is Mexico yeah OK so in 1 direction is to queue the cube hexagonal is accused have a hexagonal symmetry that's in 1 1 1 directions right so the aim and so you can see here when when you see that the hexagonal shape these majors also are parallel in the same direction to Andes a 1 1 1 and indeed 1 1 1 directions and so what it basically means is that our such planes are 1 0 0 planes and hour slipped directions of Burgers vectors are the upon to the infant also in this case by April 2 1 1 1 direction from 10 right so if I have about it the drawing this way so 1 of the so for instance itself the most of them are right to be so that here this year's it's 1 of the could be 1 1 all playing against let's saying and so we have made a dislocation with this Burgers factor so but if I have a move here the dislocation loop instance like this this part here will be a screw dislocations is also screw dislocation and this part here will be it's type this is the bird perspective so that's what would we have in the case of the the PCC no dissociation and you will see that's about all I'm going to stop here this is that that will lead to very different behaviors In a from mechanical point of view I think it will stop here yeah let's let's stop hero of talk about this on on Thursday we don't have to worry about this for
the quiz the other for the guys who came in late Friday we have makeup Friday at 3 to 5 years yes and dumb just 3 to 5 dependent on Thursday morning grows as usual


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