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# Lec 5. Phase Diagrams and Phase Transitions

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#### Automatisierte Medienanalyse

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you see those lines that are between the between the phases the boundary face is trial phase boundaries at those points usually have coexistence faces like you have liquid and solid phase at the boundary where the arrow is the other the other the part where you have someone curve that's where you have the vapor liquid phase boundary there was a special
about these bands well when you start to heat up a solid and the media as an example we start up a solid was purely self let's water here because we have a specific temperature which melts what happens is you had heat the temperature starts arrive vineyards 0 degrees Celsius even tho you're adding more he temperature persisted this not increase anymore why because now I have an equal between the solid phase in the liquid phase what happens is the sources to convert to a liquid and if you keep on adding heat that's what's going to happen if you keep the temperature constantly stopped leading the keep it as your degree Celsius equilibrium just stay there OK was always going to be a solid or liquid so you keep on reading here is somewhat of a steady curve for the temperature right temperature remains constant until all the solid as converted to liquid after that heating will cause the temperature to rise up again OK so you guys although this 273 . 15 Calvin is the boy is the melting point for water and 373 . 15 Calvin is the boiling point now just sit for his exam 273 and 273 . 15 are not exactly the same OK so we really stresses on these values to make sure the church values that you use your calculations are very accurate of so we basically saying solid and liquid saving happens with the vapor and liquid red you phase boundary where the arrows .period wants us to take place under degrees Celsius temperature stays constant as you're reading until all the liquid converts to a vapor and at that point after all it was vapor temperature starts to rise again OK so that you look at
this you look at the 1st paragraph the notice says that you can actually heaquarters liquid at 285 degrees Celsius that's 185 degrees more than the normal boiling point but then again look at the pressure thousand PSI right so this makes sense "quotation mark that you can keep water liquid at such a height and at such a high temperature yes you're exerting a very strong pressure on right keeping it as something that pressure plays a very important role in the affair in phases the more pressurized something is the more congested as in between vapor and liquid a small equity between the good and solid more solid right the less pressure he exerted more the liquid
over the water the substance starts expand and goes furthermore along the gas that was guest so and I'm going to go back to the triple .period so the travel for the definition eligible .period as you
can see it's kind of like a point at which all the trees in the and his son will call the series of stress you can see from the plot almost 73 280 somewhere there so at this point the substance exists as all 3 exists as a solid basis as a vapor and exist as a liquid is the definition of triple what about the critical point you know is the critical critical point that line kind of disappear the liquid and vapor phase are indistinguishable OK so it so you can have and I went on say
mixture but he can't say if the if the substance is a gas or little so when you put water at 1 atmosphere whereas this year is kind of like the standard pressure writes the pressure the we when the temperature
is between 0 degrees Celsius and 100 degrees Celsius what do I have have a liquid right there is no solid there's no vapor or as you say the more accurate there's not enough Sullivan of vapor that that could account to be so is basically purely liquid below 0 degrees over 100 degrees this paper say exactly these 2 points and I've said this a number of times now exactly as you degree Celsius the liquid or the widow water Kansas mostly liquid and ice and at 100 degrees Celsius in Kansas as both vapor and liquid right
captain but I know you're looking at the phase diagram for if you notice and
if you paid attention and the phase diagram for waters well you notice that ice was existing alike about what 7 phases right she have 7 different phases of solid ice for solid liquid that just infrastructures sitting with common here you have 2 different structures and I think you guys know carbon can exist as graphite can exist as diamond now this kind of that shows you why diamond can be so expensive right I mean look at how much pressure you need to exert on graphite turned into that this is a very expensive procedures but nonetheless people still tend to do it and this he is a very slow process was the catalyst and so there a
number of reasons flooding this process is very expensive and y damages shouldn't OK set again as I said when you
have 2 phases at when you when you're out of phase boundaries when you have your substance as a liquid and vapor liquid and solid basically what happens is the Sufis there are an equilibrium the atoms or molecules stock to jump from 1 facing the other and ran so visible and trying to say is that the 0 degree boundary not all the solid remains a solid all the liquid remains liquid these Adams stated jump around between the solid and liquid phases at so so we have this experiment that you can use in order to Due to validate that to validate that not everything that's a solid remains a solid everything this liquid remains liquid the which includes food for example you have a certain container that contains liquid water and gas or vapor water right and he somehow introduce G 2 0 so you don't know what the user ID is cheering Sinise at and what you
is when you want to introduce that vapor into the cell and to container at some point the D 2 of April convert into a liquid that you can use mass spectrometry reading use certain lap techniques and you will see that after some time the liquid will contain some G 2 0 OK so really what I wanted to get out of this but this line every year is just that nothing remains the same everything is jumping between the 2 things all the acts but I guess Lussier sentences at all right now and so for some review this might come off as a little or unknown was out to me the 1st time islanders
evaporating cool when you when you're sweating for example when you're running on a hot day sorting is a very that is writing is the cooling process choice some animals can stand the heat so animals don't sweat dry weather they just die out if they don't cool down so what happens basically is and some molecules when you when you have a substance and start to heated up last than 1 of the price someone of what matters is the molecules in the water the water molecules that have high enough energy to break through the barrier and kind of go out into into the atmosphere he just leave the solution to what happens then what happens is all the height the hierarchy the higher energy molecules within the liquid go out so whatever is left in the liquid is actually called there was urgently wants right so and you know office and another container the vapor completely goes out red so there's no chance of the higher energy models to come back in again so the water will be cooler
lower temperatures most molecules do exist at a lower temperature but as you increase the temperature you get some somewhat of a more distributed distributed number of Adams right because that's the curve cutter flattens out is that have more molecules there Towards the higher energy now the shaded region here the Rachida region both the grass are basically the molecules that have enough energy to escape the solution so imagine desire energy molecules escape solution solutions is going to get cool but no but again now you is the last sentence or the 2nd statement in this life-size models may skip from a solid surface too like dry out so this is something I
talked about last there no last week yesterday right when we're talking about the dry how that backtracked advise close 115 degrees out and native 15 degrees Celsius weather well so you guys probably know this fisheries issues do not necessarily have to go from solid to liquid vapor transition can go directly from salt to guess this is something we call some limitation right summation and what it is a compound that is known for doing that understand the role circumstance John Dyson so carbon-dioxide usually for we call a dry ice gone dry eyes because the solidarity goes to the vapor phase it wasn't even doesn't doesn't liquefied doesn't get wet army so these are all the different kinds of
phase transitions that could occur the notice all the more practically irreversible so for sublimation were you go from salt to live together as you have the opposite called that position and if you think about the name deposition makes sense and all the gas molecules are getting deposited on a surface right and Council of melting and freezing you guys already know this to be a transition condensation also assuming you guys already know this so and basically the the statement appeared with says the also liquids have non-zero vapor pressure this is more of an indication that sublimation can actually occur but I don't have a solid phase also can have the so this is a
very close very a problem very close to 1 of the problems in the soulless wonder we did yesterday so tells you that this guy in Wyoming decides
to hang his wet blue jeans outlined in a dry winter day at temperatures you referred to that way below the freezing point of water rights I think I don't know if there a lot but I'm assuming this is lower than the freezing point water the genes 1st freeze but then they dry out so How can we explain this just looking for 1 more sublimation right what happens is the temperature is too low for those with close on 1 and honesty was close and a phrase that so the went close to put them out as you degrees Fahrenheit began a free all the water that was liquid phase detritus
office problem is a temperature is too low for the solid over the ice to go into melting to go into a liquid and then go to a vapor what happens is that goes into now
honestly they will be comfortable to wear the down very stiff and rigid Fiesta give it a shot a it's a very slow process you can ensure that all that although dry out will just be like .period hard words for the firm yeah so the same happens with the freeze-dried food OK so also you what happens is that water is taken off at low temperatures so that the vote the food doesn't get cooked up until he won actually right but the Texas quite different saying the pets
relative humidity so during the summer day the relative humidity is rather high evaporative cooling is slowed down why is a song about equilibrium if you have a lot of vapor in the air chances are liquid is not identical to the Riverforest vapor phase is kind of saturated especially when you have a lot of presenting the red so don't cool off why is not we have dry weather evaporative cooling is more likely to occur while because you don't have a lot of water in the vapor phase there's no humidity and so I guess this is just a fun fact why you feel hotter when desired limited in what follows you don't sweat as much so even when thrill of unity these really 100 per cent the almost right because 1 figured that vapor and the atmosphere is just dying to total to be no
so yeah well over the fun facts that are going to more men here and this is a very important
equation I suggest you guys do it very well I can tell you that you use the preview from familiar that on the exam so basically I don't know if you guys have heard of the Gibbs free energy but industry energy is basically a function very simple functional and Philippine and OK so it's not only a function of energy is also a function of and show and this gives free energy vis-a-vis function kind of determines whether or not process that spontaneous the called G by the way use negative spontaneous positive not squandered its negative news going from a hot from high energy to low positive lawyers died so that of Jews equal to 0 equilibrium both processes are favorable right so L let's say you you have certain equilibrium between liquid and vapor bread but you can use this equation To be able to determine for example at which is a function of the vapor pressure and the temperature to be able to determine your heat or your energy of vaporization you'll see why this is important show 0 before I go further with the slides if you look at this equation right here you notice it looks like an equation straight line within a useful right your wife your wife is United look natural log you're X is 1 of a intercept negative built a Gerard's useful From simple man you know if you're given a certain number of or certain table of values for WiMAX can determine the slow
hours constant into Germany adult age range soldiers you have this can be done so to make sure that what you're writing I was directed to make sure that you're getting the right result should
always see a straight line the Nagar so hopefully at the so as I said before b you let you why equal to the net a lot of the X the slope is native Dr. HO and finally a intercept right so you plot why verses X you get a certain slope which is made of old age over or no OK this this this is
not this is not supposed to be hard for you guys but now we won't understand where this classes pro-immigration came so
basically the most important assumption he used for this equation dissatisfied this training vapors treating her substance your fluid as an ideal guest Sony say ideal guests with that do things volume of Europe particles is negligible compared to the volume of their container left an and the pain of the thing you should take into account is that you send that the vapor expands much faster or its expands at a higher rate than the liquid and therefore will occupy much larger volume than the liquid so you can consider the liquid volume almost negligible compared to it and you consider the mall and will be in the position is independent of temperature otherwise don't age
is no longer constant began including useful the so this should be
a good does this is this is an exact problem that can come up wrecked the gives you to pressures to temperatures so 2 points on that straight line and he can the about need of a position actually just what I think is a plug-in show kind of question right he gives you a set of values are a set of variables and ask you to solve for 1 of the class spelling regard as you guys this fall for the rate cut off but for it recounts sorrow for the gas customers are right will give you certainly to vaporization To
pressures at 2 different temperatures no so this is practice partner problem Wednesday
compound as unstable as normal boiling point right so unstable that uses reacted so you're compound is not what it is you want purified by distilling the material introduced pressures so was a 1 purify H 2 0 to the normal boiling point ratio to was 150 . 2 degrees Celsius but this is a very high temperature and you guys on our show to raise it was just a very scary compound so as to it has a lot of explosive rested at very high temperatures so we want to try to purify H 2 0 2 by letting it boil lower temperature how do we do that the saddest thing to biologically do we need a higher pressure lower pressure you want condenses more do want a vaporizer well what is seen as 6 0 West German 1 pressure should be distillate fuel to with want to operate at 30 degrees Celsius so we want a boilers at a very low temperature and the media the the
Delta here vaporization as in Calais programs now I'm assuming incident tell told you guys are not responsible for numbers that much it's probably going to give you the conversion rights so you don't know how converted from galleries to jewels and I'm assuming you guys already know how to convert from grants to 2 moles if you're giving them all the best so this is what we did a converted elderly into
a was to call into jewels and since you have the more Limousin you have the grounds you can determine malls then you plug that into
UCC equation that I notice how he put it This is how I want you to answer your questions on the exam he wants you be doesn't want you to To right out of the equation like so and then rearranged for your value while keeping the other ones as you know as non-numeric terms now he just wants to do right directly set up your problem right directly on the paper and I could probably your numbers just as he did he saves a lot of time so the Senate is the pressure that we have to deal with so you notice that your pressure is almost . 0 1 atmosphere very low compared to what it usually is at high temperatures rise and that makes sense because if you're exerting a very small pressure this substance can boil at a very low temperature right I'm so used early this year for a sexy you guessed they can out of it so never solve the equations
symbolically Davis substitute that when you connect to substitute your number OK so I went for a continued as every anybody having questions so far we can go back as far as you guys want we can go back me and I said at 1st visit again if you guys want to slow
down you guys when we just stay on 1 slice you can take enough not to let me know of a rebel attack I can slow down Is there any slide you guys wish to go back to kind of jewelry all of them relaying going that fast "quotation mark I'm sorry about
that let's In OK thank you so yes locally professor please just going on and on and on this is where it all that means would that's OK OK and that feeling bad number too fast so guys really I want you guys to try to tell me what let me go through the almost done but anyway we have a lot of time and what I can do is I can go back again kind of like gold certain things that you that I went over to foster care so figure will 2 inches a Ohio is therefore has the seller terrible right terrible at anyway so now the the
couple notes that's this is obvious and the beginning lecturer said there when you need to when you when you want to solve our numeric equation on the Primerica although motility 273 . 15 to 273 actually make a difference so what do you want to do is those dreaded numbers till you get to the very end of the war the very last step of the calculations OK so forwards like you would even said that specifically like if you can put all the numbers in the calculator that appear calculator to put all those numbers aren't you go and do that again and leave the 2nd very very last 1 now L you don't have to pay attention to this equation in the class pepperoni region is the only talked about vaporization age of vaporization right now let's say we're converting from solid to liquid there are just some of let's say I want deal a different process less sale
as I want discuss smelting or freeze and use the same building the right these indifferent which 1 fusion or melted basically the same stoppers accepts that so I think that she has she probably know there is immediate problems we have a sublimation experiment going on but instead giving you the ability of sublimation interval to heat of fusion and the building of vaporization now logically speaking sublimation is kind of like taking a shortcut to a two-step process here is a solid 1st convention should 1st melt then after acknowledged to vapor you doing that 1 step as it may be the sum of the 2 right Mason OK now you remember I talked about the Gibbs free energy I said that the gives 300 years basically a measure of how spontaneous
reaction can be as you can see it's a function of Delta H you're invoking and a function of Delta house which is your entropy now we said equilibrium noted use equal to 0 why this book processes have the same relevant disorder or have the same relative and so when the have equilibrium In terms of faces well when have face transition 1 sublimation care where melting is occurring few when infusions occurring liberalization or condensation right so the specific phase transition points on endless generalized more in the case we have an equilibrium what you can do is you can actually solve you can put you can set up the equation as such we can find the temperature equilibrium and find adultery the equilibrium or adult as cynical of right it's a really simple really simple concept and it just goes on are just comes from the fact that Delta G's equal to 0 yes on this
side of the ball the numbers so as I told you so can I go by the previous slide was only so much Oh thank you OK let's see which like you amid all the problem here of the case remember he said that in his
1st lecture I think the 2nd 1 you said that you guys don't have to know the numbers numbers will be given now the gave here was a call the told normal boiling point was is a normal boiling point when there's an oral 1 was the pressure where security is suspended from pressure exceeding should note makes sense he gave you a temperature will give you the temperature recovered to Cal right said always converted just got what else he is giving the other temperature that phone right John in this case is 30 degrees Celsius so these numbers are given even digital tapes is probably most likely going to give you the conversion gave so that's why I always say pay attention to the units goes even if you have no idea what the question asking you if you have no idea what these numbers mean Uganda's again analysis and knowledge need to get what he can tell you you have to calories you have grants you have jewels from I wanted to give me jewels I don't that USA commercial you look at it you resent it out he she was supposed to
cancel what and should be able to transfer yes on the other hand you OK so just to be on the safe side any time in dealing with temperature always convert to Calvin unless otherwise the Russia is seen as another thing with pressure from use on the exam is going to let you know but if he doesn't tell you like I want this and these units are this in these units you don't need to worry about but I know anything very he's very efficient so he would probably tell you what units he wants you to get like how many milliliters of this nominee killer jewels from all you get you know so will give you the units that you need to get eventually if he doesn't this is on the edge of the video camera so on my responsibility if you're not required or he doesn't
ask where some obvious that you need to express your at your answers research community expressed in any nearly 81 but Calvin all that always encounter right yet so anyway to go back to your question so all is given over here along with the conversion that they did up here for the calories the jewels that's all you really need to do to get that answer now I'm assuming we haven't done enough exercises for you guys to know the value of the gas costs and even those bridges is is probably going to give the exact this with all on what manager was eager again get it probably doesn't really matter so let's see this as the normal way it was I at 50 . 2 degrees Celsius right the pressure 1 atmosphere so that's P-1 annuity 1 for example 30 degrees Celsius does he have his duty to write and you will find P so that was happening temperatures temperatures going down right so we said that 1 is 150 3rd right why how do I know this because he's telling you this is the initial temperature 150 is going down the road you want to get out of there OK so basically whatever state for you should be able to tell from the wording of the problem lies north if you can tell from here but if you want to be when you see it doesn't matter remember
is that to happened that at the age of vaporization Red Boiling Point is going to happen for a certain pressure at a temperature a point is a straight line Delta constant right so there is a matter which was UP 1 which was used to you which was repeated as long as there are in this for Red Sea can for example Butcher you're P-1 as 1 atmospheres and UT 1 afterward no OK but that is really a matter yes I all
that's probably a type of because it is he says here it's 3rd the resources OK OK but Loria will go over the slides nests Delta as is your interest in folk and basically a measure of disorder no militants the DOE the G dosage
Gibbs free energy of no questions the Ministry of a don't like melting you know old building is right if you need most of the melding his once-solid still liquid fuel is going to be using together the binding together just the opposite the liquid to stop right now here is that I think there's another type of so Boyle and vaporize are basically the same thing right so I would go with and condense and condensation or vaporization condensation OK so old 1 of these 2 pairs down here has to be different has become such a part docket but only if you understand the concept that's all the support of gay and Noriega analysts said
going back to previous lies Gonna make sure you guys get some good news story not true does Our 2000 rule and this usually
applies to liquids who tend to tend to you to usually like tend to act little ideal right example water doesn't apply because you have a lot of hard money must put it this way 2 diamonds rule applies to molecules were what was to come of technically don't do hydrogen because their molecules that don't relatively interact with each other very much remembered as 1 of the things about ideal gas right floats molecules or interact with each other so a liquid and the gas I want basically distorted faces right the solid is the only ordered fate but a wire P find a water glass a glass of water on the on the table to get irritating if I do that 1st solitaire for ice ice justices said that it was right so the ball this order only differences was condensed the other 1 is not candidates brain so at the entropy of vaporization is basically the same for a lot of molecules and don't have a lot of interaction between each other because basically if you go because you remember vaporizes has gone from liquid to solid was from liquid to a vapor so when we're saying that the book disordered right at so 0 the only thing that's really changing is well the instead of being condensed it being knocked and that's right so and this is usually very similar in the case of all those years when trying to get at it that 2 towers role tells you is that the entropy of vaporization for most molecules of most types of compounds is relatively recent because the only thing that's changing his how convinced that is and how can this is not going to be right which is a very similar phenomena for most molecules and usually the value for that more entropy is 87 . 5 jewels from all Patel for most molecules at that specific pressure and add the normal 1 .period OK so really all you really need to get out of this life you need to understand is that unless hydrogen bonding is involved and here of course to do an approximation I was a
negative exactly 7 . 5 less hydrogen bonding is involved unless the interaction between these molecules is Strong the entropy OK so all Chile has complied yeah exactly so the heat of vaporization is what's different about the interview so always saying basically since both of them on this water the interviews goes insane because the interviews only measure of disorder right is that is the energy of vaporization changes between 1 compound to be so this is a good practice problem
to understand from the prior of the that have the Mets so the passing defined the normal boiling point of hydrogen sulfide and of Oregon knowing the envelope is a vaporization or 80 . 6 and 6 . 4 jewels from all right now I remember always said Agee's equal to 0 which happens for most face transitions or equilibrium you can relate the temperature to the envelope into the entropy right the boiled for example is equal to Delta age while or over Delta 1 come here hasn't is defined teaboy levers alternates work what do doing well we need the entropy right but since we said we made that assumption according to 2 dollars rower ruled that the disorder or the chain's orders which are the same for both so you consider Delta S for these molecules to to be were dealt a severe position so I'm really stressing on this is just the belt as the vaporization you consider to be a constant so for both of them as 87 . 5 spot them into the equation and HHS that you make sure you're temperatures in Calvin you saw the way you should be able to find makes sense yes only a unified yes OK thank you sir show real good no so far .period as you as they give us the true values down here if you had the kind of different they're not so they're very close but in exactly the same as Western approximations go we get all exactly the reason fall OK no this was
what I was talking about so as far
as you guys need to know as long as there is a new Latin bonding 2 does not allow applies why those waters a live for example water decided Bonn any molecule with H F and it is basically also but was still a jet molecules are also divided among anything that has an energy but also those of my right you should know so we know a hydrogen bond is a strong type of intermolecular forces and so it does is it makes the liquid a little more ordered than it's supposed to be a and therefore doesn't 2 dollars apply for no so this order is destructive going to the vapor pressure where there is no hydrogen but With these liquids or with with things that actually do bonding the water takes a while to get disrupted so notice how how large the entropy of vaporization for what it's 100 jewels for Calvin promote as compared to 87 . 5 it's not very low so it would likewise be higher for that show hydrogen bomb OK the easy thing to understand is that shouldn't be too 2 terrible too difficult
these are loaded on this site no this sadly Nunavut OK because it is a regular at the mall and remember that this is the more that's all it is not clear is that the children killed so is this a difference in the unity between the all of us a call between Anthony and helping somebody tell me why where the difference between a review of what from the wall into the units can help you determine what is different is something I said in the previous slide in real life so was the international jewel from all right with you Jules you know where to look for power it's not exactly unit entered the important thing for you guys that's why wouldn't we multiplied by the temperature in the delta G quit because Delta geology it's free energy as an entity so when you multiplier entropy and is going to go back and come back here he was
dealt a choice the Belfast saucily announced can practice for you but as jewels for Calvin multiplied by temperature will turn during his the 1st energy turn but thank you In yes you you from is the president
of the repression and the vaporization changes since different so well however how the different from what we and the interview recently that the energy combines 2 different factors a quarter of the year process the spontaneous announced that there are 2 things that regional West company right something the government ordered more from the threat if you put himself you some pepper over right over to shake it up you don't have a way of solemnly at that Reagan and wine is lost workdays have always work that build as the measure work now until the end of the measure energy rates there you different hair was something has higher energy it's less stable responding if anybody else Eraserhead previous raise it higher OK so are we doing here such this is a good day this is a good way of
demonstrating how hydrogen-bonding disrupts the trend so you notice that they have a really high boiling point right molecules that tend to have higher hydrogen bonding find a harder time breaking apart when he did not know this is a question you there is no such negative in terms of election negativity flooring is more to negative than oxygen is more attractive than nitrogen right why is a show at a higher boiling point the hydrogen fluoride new show yes it has lost more opportune to do hydrogen wrecked has 2 items to appearance has more chance of doing hydrogen-bonding pressure and so help wholesalers mortality exact and this is something I guess you guys already knows what that decreasing the mall matters also use a decrease in the morning
,comma scissors importing you guys should know as at the time look at no cost is decreasing in the Moallem as does not fly as you can see there's not quite the things that hydrogen bomb talking for ordinary molecule right
preconceived can should so when you start doing a real thank you Brokers so can't assembly tell me why methane does not follow that age funding trend is but for items I think it might do a lot of money why anybody you Bloomberg exactly
so carbon is not allocated enough 2 polarized its borders are enough for it to do a hydrogen bomb so I guess these are a couple of things you guys should know before you go into the exam condensed phases are far
more complex than Gaza's Gaza-Egypt study the legal entity condensed matter that's because they take much of it at so you know that according to their phase diagram 2 phases can coexist but only at a certain point right so far given pressure you need a given temperature for 2 phases to exist and I'm going to go over that again now we do not yet have a good theory to be able to predict for example the water should freeze at 20 273 . 15 Calvin at 1 atmosphere how do we do that or how do we get this the experiment now I the 4th bullet .period guide tells you the important thing that you should know about extra diffraction use why do we have to refrain from would simply because it determines the structure of the solids because we said that solids that tend to crystallize tend to crystallize certain structures it's important for application purposes to understand why would not understand why but understand how this all of crystal it's important to know why irony forms a bodies in cu structure led by sodium chloride as somewhat of a face and give structure again last point and I guess you guys should notice like on your hand the U.S. sales was the smallest unit in a crystal was said since then the book .period above solid as a regular periodic arrays so it's basically a set of keys repeating units right so the whole 3 lattice is basically is made up of copies of those of that specific itself still has that helpful why would I wanna know this well because it means that you can isolate a single unit cell just knowing how itself looks like this knowing so and is doing all kinds of information problems out that you can generalize
it and terminal and Ward general and a general idea about how the crystal looks like for the properties about this OK so but I'm going to go back to some slides that I feel I need to be should go over more and there very democratic so if you guys choose or there's something specific you wonder goal for please feel free to tell me OK so as long as we're all OK the slide and like to go back to the top there is very OK with that no but there are no aureus the that's about
Körpertemperatur
Substrat <Boden>
Quellgebiet
Alkoholgehalt
Übergangsmetall
Chemische Forschung
Wasser
Konkrement <Innere Medizin>
Klinisches Experiment
Computeranimation
Druckbelastung
Klebeeffekt
Phasengleichgewicht
Sense
Körpertemperatur
Alkoholgehalt
Wasser
Körpertemperatur
Druckausgleich
Computeranimation
Wasser
Umwandlungstemperatur
Schubspannung
Periodate
Computeranimation
Gasflasche
Druckbelastung
Körpertemperatur
Mischen
Alkoholgehalt
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Druckausgleich
Computeranimation
Diamant
Kohlenstofffaser
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Fettglasur
Computeranimation
Druckbelastung
Chemische Struktur
Graphit
Graphit
Chemischer Prozess
Diamant
Single electron transfer
Molekulardynamik
Wasser
Ordnungszahl
Computeranimation
Stockfisch
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Oberflächenchemie
Molekül
Containment <Gentechnologie>
Atom
Chemischer Prozess
Insel
Zelle
Tiermodell
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Ausschwitzen
Molekül
Salzsprengung
Trocknung
Wasser
Containment <Gentechnologie>
Massenspektrometrie
Chemischer Prozess
Lösung
Computeranimation
Tiermodell
Körpertemperatur
Oberflächenchemie
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Chemische Forschung
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Teststreifen
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Desublimation
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Gen
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Bukett <Wein>
Erstarrung
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Bukett <Wein>
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Molvolumen
Chemische Forschung
Computeranimation
Erdrutsch
Druckbelastung
Klebeeffekt
Körpertemperatur
Gibbs-Energie
Elektronegativität
Mannose
Selbstentzündung
Funktionelle Gruppe
Chemischer Prozess
Altern
Chemische Forschung
Ringspannung
Computeranimation
Altern
Körpertemperatur
Oktanzahl
Schmerz
Nanopartikel
Einschluss
Containment <Gentechnologie>
Boyle-Mariotte-Gesetz
Computeranimation
Druckbelastung
Single electron transfer
Herzfrequenzvariabilität
Wasserfall
Körpertemperatur
Oktanzahl
Druckausgleich
Computeranimation
Substrat <Boden>
Tieftemperaturtechnik
Chemische Forschung
Druckausgleich
Chemische Verbindungen
Computeranimation
Heizöl S
Sieden
Druckbelastung
Körpertemperatur
Alkoholgehalt
Chromosomenkondensation
Disproportionierung
Reaktionsführung
Explosion
Chemische Verbindungen
Druckbelastung
Chemische Forschung
Reaktionsführung
Explosion
Disproportionierung
Computeranimation
Konvertierung
Edelstein
Druckbelastung
Substitutionsreaktion
Sieden
Körpertemperatur
Methyliodid
Tieftemperaturtechnik
Druckausgleich
Computeranimation
Druckbelastung
Zitronensaft
Gold
Einschluss
Computeranimation
Erdrutsch
Azokupplung
Motilität
Auftauen
Altern
Gibbs-Energie
Gangart <Erzlagerstätte>
Bildungsenthalpie
Chemische Forschung
Zellfusion
Zellfusion
Chemischer Prozess
Konkrement <Innere Medizin>
Computeranimation
Reaktionsführung
Chemische Forschung
Körpertemperatur
Thylakoid
Computeranimation
Erdrutsch
Klebeeffekt
Auftauen
Körpertemperatur
Übergangsmetall
Guanosin
Übergangsmetall
Abschrecken
Chromosomenkondensation
Funktionelle Gruppe
Chemischer Prozess
Chemische Forschung
Druckausgleich
Computeranimation
Konvertierung
Edelstein
Druckbelastung
Sense
Körpertemperatur
Alkoholgehalt
Chemische Verbindungen
Disproportionierung
Explosion
Reaktionsführung
Druckbelastung
Altern
Körpertemperatur
Alkoholgehalt
Chemische Forschung
Fleischerin
Druckausgleich
Einschluss
Computeranimation
Konvertierung
Edelstein
Setzen <Verfahrenstechnik>
Chemische Forschung
Körpertemperatur
Einschluss
Computeranimation
Erdrutsch
Klebeeffekt
Dosis
Gibbs-Energie
Krankheit
Übergangsmetall
Chromosomenkondensation
Mas <Biochemie>
Molvolumen
Hydrierung
Natronwasserglas
Setzen <Verfahrenstechnik>
Bildungsentropie
Wasser
Fettglasur
Chemische Verbindungen
Boyle-Mariotte-Gesetz
Computeranimation
Brillenglas
Edelstein
Krankheit
Härteprüfung
Molekül
Wasserstoffbrückenbindung
Molekül
Diamant
Wasser
Einschluss
Chemische Verbindungen
Computeranimation
Edelstein
Altern
Schwefelwasserstoff
Wasserfall
Wasserstoff
Sense
Körpertemperatur
Übergangsmetall
Kettenlänge <Makromolekül>
Krankheit
Molekül
Wasserstoffbrückenbindung
Wasser
Blitzschlagsyndrom
Hydrierung
Setzen <Verfahrenstechnik>
Bildungsentropie
Wasser
Computeranimation
Edelstein
Ionenbindung
Wasserstoff
Chemische Bindung
Bildungsentropie
Molekül
Wasserstoffbrückenbindung
Potenz <Homöopathie>
Seltenerdverbindungen
Chemische Forschung
Körpertemperatur
Computeranimation
Erdrutsch
Edelstein
Klebeeffekt
Körpertemperatur
Gibbs-Energie
Übergangszustand
Übergangsmetall
Delta
Aktives Zentrum
Sonnenschutzmittel
Wasser
Methan
Hydrierung
Fluorwasserstoff
Oktanzahl
Ammoniak
Chemische Forschung
Körpertemperatur
Unterdrückung <Homöopathie>
Druckausgleich
Stickstoff
Computeranimation
Wasserstoff
Sterblichkeit
Elektronegativität
Homogenisieren
Molekül
Funktionelle Gruppe
Wasserstoffbrückenbindung
Chemischer Prozess
Sauerstoffverbindungen
Methanisierung
Altern
Wasser
Methan
Hydrierung
Wasserstoff
Assembly
Ammoniak
Molekül
Chemische Forschung
Funktionelle Gruppe
Körpertemperatur
Computeranimation
Hydrierung
Single electron transfer
Natriumchlorid
Kohlenstofffaser
Wasser
Körpertemperatur
Druckausgleich
Periodsäure
Gasphase
Computeranimation
Druckbelastung
Azokupplung
Kristall
Chemische Struktur
Bukett <Wein>
Körpertemperatur
Thermoformen
Microarray
Sammler <Technik>
Kondensat
Atom
Kristall
Chemische Eigenschaft
Abbruchreaktion
Erdrutsch