And this lecture is on Plato's idealism theory of ideas in continuation with the previous lecture, where we have discussed the contributions of the sophist. And this is in a sense of an ideal passage to discuss Plato, because in between we will see the contributions of Socrates as well, who is supposed to be the first martyr of philosophy. So, this lecture will be trying to address following issues, Plato's idealism and overview. So, we will try to provide an overview, then after that the influences on Plato, those philosophers and philosophical movements, which have influenced Plato, then the relevance of Socrates in this context has to be underlined, because Plato was the disciple of Socrates and the most famous disciple of Socrates. This is in the objects of the sensible world. So, when we discuss Plato's idealism, this distinction is paramount, the distinction between the ideas, the sensible objects, the objects in the sensible world. So, this distinction is primary in Plato's idealism, so this has to be discussed and clarified. And then afterwards we will see the ideal world, because Plato says that the ideas on the one hand is a monist, he says that ideas alone are real, on the other hand he believed in a plurality of ideas. So, he says that ideas constitute a kind of unity, there are plurality of ideas and there is a hierarchy they form in the ideal world. So, the ideal world needs to be discussed to understand this problem, after that the reality of ideas, because according to Plato ideas alone are real. And in this context we have to also mention a very important distinction, a very important dualism which Plato maintains. Plato says that matter is different from ideas or forms or essences. Ideas or forms are the only reality and matter for according to Plato is basically unreal. Then to elucidate and to explains these points further, we will discuss a couple of parables, the first one a couple of analogies, the first one is the famous parable of the cave and the second one is the analogy of vision. With all these things we are trying to understand, explain Plato's idealism. Now, about Plato, Plato was some details about his personal life, his life and he was born in Athens in a noble family in about 427. And he was educated by Catilus who was the disciple of the famous philosopher Heraclitus, who stated that everything in this world is under constant flux. The famous saying that you cannot step into the same river twice is attributed to Heraclitus. Earlier Plato had was educated by this person called Catilus who was himself a disciple of Heraclitus. Then Euclidus is another important thinker who was Plato's teacher once upon a time and who at Plato had studied Parmenides, the philosophy of Parmenides under the guidance of this man who later became a disciple of Socrates along with Plato. Now, let us see, there is a very famous quotation from the history of western philosophy written by Bertrand Russell and this says that Plato and Aristotle were the most influential of all philosophers ancient, medieval or modern and of the two it was Plato who had the greater effect upon subsequent ages. I say this for two reasons, first that Aristotle himself is an outcome of Plato, second that Christian theology and philosophy at any rate until the 13th century was much more platonic than Aristotelian. So, this underlines the importance of Plato as a philosopher in the whole history of western philosophy. So, according to many other historians of philosophy Plato is supposed to be the most important philosopher in the whole of western philosophy. Now, there are certain very preliminary problems which we come across which we encounter when we try to understand Plato's idealism. So, some of them are the problem of universals, what do you mean by a universal? See for example, you have a pen or a computer in front of you, let us take the example of a pen, there are thousands of pens in this world, but there is only one idea of pen, the general idea of pen what do you mean by a pen all of us know there are different types, different colors, different makes, but there is something called a pen what it is. So, that is a universal pen. So, he is concerned about the universal and his theory of ideas precisely deals with the universals and in connection with this problem we will come across another issue, what is the common element in the many particular objects that bear the same name, all these are all these objects we call pen, what is that common element by means of which by virtue of which all of them are understood as pen that is the question here. So, the common element the general features then again what is the relationship between particular and universal. So, there is a universal penness or an essence of pen in what way the ordinary pens which we use to write are related are connected with this universal pen, can we say that there is no universal apart from this particular many philosophers hold that view that is a very significant that is a very important view, but Plato would assert that it is a universal it is a essence which is more important than the particular objects in this universe. Again the next question is what happens to the universals when particular is perish, what happens whether anything happens to the idea of pen if one or two pens in this universe perish that is the question. So, these are some of the preliminary issues which which Plato is concerned as far as his theory of ideas are concerned. And now let us look into some of the subsidiary issues, the first one is the question of method, what should be the method of enquiry, this question an answer to this question we will consider in the next lecture, but this is a very important thing like the question is what should be the method of enquiry, when it comes to as all of us known natural sciences employ a very peculiar method of enquiry. Natural sciences will employ the method of observation, the method of experimentation, so it observes the world what happens to the world and observation rely on sense organs. And for Plato the question of method presupposes something else than the observation method, because he is a philosopher who has proclaimed from the very outset is disbelief in the sensible world, he says that the sensible world is only a copy we will see that subsequently. Can man a were no reality that is another very important philosophical problem, philosophers talk about reality a lot there is a reality, but can man ever know it, if man is unable to know it then why do you bother about it, but if man can know it then you have to tell how man can know it, the methodology has to be devised, so these are some of the questions again what are the different aspects of human reality, human reality can be there are there is a spiritual aspect of it there is an intellectual aspect, there is a sensible aspect, there are several phases of human reality what are they, so these are some of the issues which in general Plato is concerned about or rather we are concerned about when we discuss Plato. Now let us see the thinkers who have influenced Plato, the first and foremost one is Pythagoras who is famously associated with the Pythagorean theorem and who is a mathematician who is a religious person who has a very peculiar religion of his own and, but Plato was influenced by Pythagoras mostly with respect to the mathematical theories he has developed or the respect for mathematics, belief in immortality and other worldiness and the mysticism, mathematics is important because Plato also thought that mathematics is a very important discipline because mathematics involves abstract thinking and for Plato a philosopher a thinker is a person who has the capability of abstract thinking and if you are not able to think in terms of abstract objects you are not qualified to be a philosopher, so Pythagoras is important because mathematics he was a mathematician he was primarily a mathematician and Plato has famously brought it is said that in front of his academy Plato's the school which Plato established it was written that no man ignorant of mathematics should enter, so because he considered mathematics as so important in learning process of a philosopher. The second very important influence is from Parmenides, we have already discussed a little bit of Parmenides in one of the early lectures, Parmenides is a philosopher early great philosopher pre-socatic thinker who believed in the permanence of reality he says that reality must be imperishable, eternal and something which is permanent immovable in order to move something has to be located in space and time and if an object is conditioned by space and time it cannot be real in the philosophical sense of the term. So, this belief in an eternal and timeless reality the unreality of change Plato owes to Parmenides a lot and interestingly the next important influence in Plato is from Heraclitus we have already discussed Heraclitus just a few seconds ago. Heraclitus was a philosopher who says that there is nothing permanent in the sensible world hence do not believe in the senses. So, Plato derives this inside from Heraclitus do not believe in the senses though Heraclitus himself never proclaimed so and now comes the most important the most significant contribution the most significant influence on Plato's intellectual life by none other than Socrates. The great philosopher who was Plato's teacher and Plato was indebted to Socrates for making the ethical problem as the central concern of his philosophy. We can see that even in Plato in Plato's Utopia the state republic the major issue the most important question is what is justice which is an ethical question and when it comes to his metaphysics which we are going to discuss in this lecture the idea of good is at the center it is according to Plato the some important the most important essence the most important idea and every other ideas are under that. So, in one sense we can say that there is only one idea that is the idea of good everything is a derivative of this idea. This is a very important influence from Socrates then again the teleological rather than mechanical explanations of the world which we will find even in Aristotle's philosophy as well and also most importantly the method of dialectics I have mentioned the importance of a method the method to know truth and it is to this method Plato was inducted to Socrates the method of dialectics. Now, a little bit of Socrates we have to mention Socrates was a person who has literally taken philosophy to the marketplace and what I mean by marketplace is taking philosophy to the common man taking philosophy to the places where people from all weeks of life come assemble to do their daily business. So, he you will find Socrates in the marketplace you will find him in a marriage ceremony where he discussing philosophy with his friends and allies practical task of philosophy is according to Socrates to help man to think right in order that they may live right. So, again we can see the emphasis on the ethical issue what is more important is to live the right kind of life and in order to live the right kind of life you have to think in the right manner. So, here again practical task of philosophy is to help people to do that and to know what is good so that one becomes good. So, these and again further questions of knowledge truth and goodness are intimately connected you cannot separate these issues. So, a philosopher is concerned about all these problems about the question of knowledge truth goodness and in that sense logic ethics and aesthetics are all interconnected.  This is basically Socrates approach you always believe that the domain of truth is absolutely clear one should be able to understand if at all one understands it it should be understood with absolute clarity and certainty and this truth should be universal and it should be distinguished from confused and vague opinions and thoughts we have we have lot of vague ideas about this world what is happening in this world. But truth as far as truth is concerned it cannot be vague at all it should be absolutely certain and despite diverse opinions there is a common ground of principle people might think differently people might have different beliefs and opinions but there is only one truth and that can be attained that can be achieved with the help of a method employed which is the dialectical method. Ideas and opinions are expressed in propositions and judgments truth can be expressed in the universal judgments which is beyond all doubts and contradictions. It is to arrive at these kind of judgments which with Socrates thought is the primary objective of philosophy and in all his endeavors all his delugs all his conversations with other other philosophers and other thinkers and other people we can see that the approach is to to to get a direct access to truth. And now let us talk about a little bit about Socrates method we will take it up in the subsequent lectures he pretends I mean this is the famous dialectical method of dialectics which we will explain in the next lecture. But primarily what happens is that he pretends not to know any more about the topic of discussion. So, he gets into conversation with other people by raising questions and as and he pretends that he does not know anything about it and he often acts as though he knew less than his opponents. Then he ask questions insist for clear definitions and explanations and in this way the process of dialogue proceeds makes them contradict and this is what happens in this process he makes his opponents or his partner in conversation to contradict himself. And this contradictions will eventually and ultimately expose the confusions the his opponents have in their minds and soon his opponents feel that Socrates is the master of the situation. This is what happens in in the dialect method of dialectic and now we will try to see we will straight away come to Plato we will see the influence of Socrates further when we discuss certain other issues in Plato's philosophy. Now, we will come to the central principle the theory of ideas or theory of forms it is called. What are they what are these forms what are these Platonic ideas which we are talking about. So, here we will see an interesting observation from famous very famous 20th century philosopher Gilbert Ryle. He says Gilbert Ryle says that it originated out of several different and partly independent features of the general ideas or notions that constituted the recurrent themes of dialectical disputations that include definitions standards of measurement and appraisal immutable things timeless truths one of a many intellectual knowledge conceptual certainties and ontology of forms. So, in a sense ideas are derived from all these things there is as I have already mentioned a very straight forward approach to generalize to see the generalizations. And when you take theory of ideas there is a famous observation by Bertrand Russell. Russell says that the theory of ideas is partly logical and partly metaphysical.  Again when it comes to the metaphysical aspect what in reality corresponds to the general word. So, here an ontology of sentences is being envisaged.  So, this corresponding object cannot be a particular object because particular objects are when I talk about a pen which is there in my pocket I am talking about a particular pen, but when I talk about penness it is not there in my pocket it is not there in this world it is somewhere in my mind I can say to some extent. So, but what sort of an entity it is if it is there in the mind what is it status is it just an image shadow. So, these are questions which Plato deals with and Plato would say that they are absolute realities will see that there is a quote from again from Bressel the history of western philosophy it says that the logical part has to do with the meaning of general words. There are many individual names of whom we can truly say this is a cat what do we mean by the word cat obviously something different from each particular cat an animal is a cat it would seem because it participates in a general nature common to all cats. So, this is the central this is the crux of it an animal is a cat it would seem because it participates in a general nature common to all cats. So, this all concept of participation is very important again I start reading something which is not this or that cat, but some kind of universal cat in us this is not born when a particular cat is born and does not die when it dies in fact it is no position in space or time it is eternal this is the logical part of the doctrine. And now when we come to the metaphysical part of the doctrine it says again from Bressel the word cat the word cat means a certain ideal cat the cat created by god and unique particular cats partake of the nature of the cat, but more or less imperfectly it is only owing to this imperfection that there can be many of them the cat is real particular cats are only apparent. So, here you can see the problem of one and many appearance and reality what appears is the many cats what appears is a reality which is a reality of particularities, but what is real reality is always something which is unique there is only one cat in us. And again when you talk about ideas and idealism ideas are objects of the intellect known by reason alone Plato as categorically affirms that they are objects they are objects not of course of this word, but of the intellect known by reason alone they cannot be known through observation through sense experience they can be known only through reason there comes the relevance of mathematics. Mathematics is another discipline where we employ reason not observation and again their objective realities that exist in a world of their own they are not just there in the human mind, but they have a world of their own the objective realities. There are as many ideas that there are common names and every common name designates an idea. So, wherever you find a common name camera or a telephone computer all these are common names. So, the responding to all these there are ideas, but then now we have a problem in what sense these ideas are related to particular objects in what sense the idea of cat is related to cats in this world the idea of computer is related to different types of computers in this world. So, here Socrates Parmenides and Heraclitus are all met what is common to all of them is the man type the essence or idea of man beautiful flower beautiful poem beautiful painting and in all these cases what is common beauty the idea of beauty then again a moving car a moving man a moving cycle motion is the idea. So, common to all these things now when we talk about the knowledge about these ideas we see beautiful things we can say that it is a beautiful flower a beautiful mountain a beautiful house all these are beautiful things and lot of beautiful flowers are only, but what about beautiful as such where is beauty the essence of beauty. So, Plato's philosopher is a person of wisdom who is not bothered about particular beautiful objects in this world, but who is concerned about beauty as such the essence of beauty we see moving body is not the idea of moment where to the generalizations exist do they exist only in the human mind these are some of the questions and when it comes to general ideas they can be approached only through reason I have already mentioned this this cannot be a subject matter of observation that can be understood only by the employment of the intellect by reason. Reason has to be properly trained to see the ideas which are real every one of us all human beings are rational in fact one of the defining features of humanness is rationality procession of rationality if that is the case then why is it that everyone is not a philosopher according to Plato through reason with the employment of reason you can graduate you can understand the essence the world of essence is and thus you can become a philosopher, but everyone is not able to do that why the reason for that is that reason has to be properly trained to see the ideas which are real and when you contrast this world of ideas with the world of senses we can see that the world of senses are constantly fleeting and reality needs to be searched not in the world of senses because the world of senses is the world of change it is the world of destruction it is the world which is never the same the next moment it keeps on changing. So, in a world of complete change nothing is real reality is changeless and eternal. So, one has to search for the eternally changeless reality it needs to be searched in the intelligible world in the intellect and here we can see we will just contrast the sense objects and general ideas the common sensical view is that they are mental copies of the sensible objects as far as general ideas are concerned the common sensically we understand general ideas as copies of sensible objects we see different objects we see a computer for example the computer is a relatively new invention. So, this has not existed from time immemorial so it is a new invention and now all of us have an image of computer in our mind. So, we can logically conclude that the image of computer is being derived from the computer which came into existence only recently, but Plato would disagree with that they depend on the objects this is the common sensical view they are not real, but exist only in the individual mind and they cannot be communicated completely because since it exist only in my mind the ideas in my mind cannot be communicated to you to another person in complete sense of the term. Because to some extent it is mind and Plato's idealism presents an entirely different view it says that ideas are the models or the originals they are not copies of sensible objects, but they are the most original models of reality and individual objects are the copies it is the other way round for common sensical view the objects the ideas are copies of objects, but here for Plato individual objects are copies. But both are thoughts and the eternal objects of these thoughts both are thoughts and the eternal objects of these thoughts are part of that ideas and thoughts of God which no human intelligence can wholly reproduce so these are the differences main different ways in which Plato understands the ideas from the common sensical perspective. The most important point is that for Plato they are absolute realities and the world of objects are copies of these absolute realities and now when it comes to the question of the sensible and the real the real according to Plato and according to the general philosophical assumption it must be more enduring and unchanging it cannot be something which changes quite frequently it has to be more enduring and unchanging and again it must be eternal something which perishes cannot be treated as real or in other words the reality of perishable objects is a minimal reality they do have only a relative reality not absolute reality individual objects and instances may come and go like individual human beings Plato Aristotle all these people have come and they have gone all of us will go one day but manness exist they are not real what the individual objects are not real the individual pens and cats and mountains and human beings and whatever things in this world they are not real because they come and go they perish they are subjected to change the idea is what the individual expresses so but this is what from here he is trying to bring out one important aspect one important thing about the relationship between the objects and the ideas the idea is what the individual expresses so when you have a computer in friend of you an individual computer or a particular computer or a particular pen these objects express the ideas for instance the pen the particular pen expresses the universal idea of penness and the particular computer expresses the universal idea of computer without the idea it expresses the individual cannot exist so Plato puts the relationship the other way round the individual owes its existence to the universal idea it is the universal it is by virtue of its participating in the universal and individual acquires its name and status we call an object a pen because it partakes because it participates in the universal idea of penness we call a man we call an object a man an entity a man because that entity that object partakes or participates in the idea of universal manness the idea is absolute and unlimited sensible objects has something of what the idea is sensible object I repeat sensible object has something of what the idea is so this is that partaking relationship that participation and sensible objects partake of the idea is undivided being it cannot be divided it can it is it is simple in that sense and in contrast the objects of the phenomenal world everything is subjected to change and destruction fleeting and uncertain I have already mentioned it nothing is permanent in this world one cannot step into the same river twice because both the river as well as the person who is stepping down in the river will change so everything is a fleeting reality no absolute reality is the question of absolute reality never comes into picture at all as far as the object of phenomenal world is concerned we have small and big it is a big mountain a small mountain but all these are relative terms a big a tall man is tall in relation with a short man a man who is shorter than him but another taller a taller man in front of a taller man this tall man becomes short so all these expressions small big beautiful ugly good and bad something which is good today might be a bad tomorrow something which is beautiful today might be treated as ugly tomorrow so there are the world the world of objects the world of sensible objects are that is subjected to constant change and they are relative they cannot be absolute now when it comes to beauty I mean I am taking another more concrete example here the example of beautiful objects because this is one reason is that plaita is also preoccupied with the question of beauty very repeatedly very frequently he takes up this example of beautiful objects so there are beautiful objects in this world and the idea of beauty so about beautiful objects this is from Weber's book which is referred in the end of this lecture as Weber says they are fair today fall tomorrow fair at one place or in one relation or in one point of view or to one person fall under different circumstances and in the judgment of other persons hence everything in the world of phenomenal beauty is relative fleeting and uncertain it reminds me of Shakespeare's famous statement fair is foul and foul is fair in his back both everything fair is foul and foul is fair so the world is completely uncertain this world of uncertainties we are living but when you enter the domain of ideal beauty it is everlasting without beginning and without end without diminution and without digging invariable immutable and absolute it is beautiful in all its relations and from all points of view it is beautiful at all times and in all places and for all persons it is pure and clear and aneloid and therefore transcends the power of imagination so you can see the contrast the one is a domain of unrealities relative entities the other one is everlasting absolute entities now proper ideas what you mean by ideas as Plato says ideas are real beings they are the only real beings and they are more definitely more real than the objects of senses they only true realities they are the only true realities and they alone are real they are the eternal patterns after which the things of sense are made and on the other hand the phenomenal world is constituted of objects have which have only a borrowed existence they are mere copies of the world of ideas they receive their reality from the ideas I have already mentioned all these things only a simple an allegory or a figure of speech they exist not in themselves but as reflections of their ideas they do not have independent existence at all their mere copies their shadows they have no reality other than that which they receive from these ideas and when you talk about the ideal world this is a very important point to be understood what is this real world Plato is talking about what is it constituted I have already mentioned that it is constituted of ideas and there are as many ideas are as there are general terms in this world so we keep on inventing or rather invention is not the right word we keep on discovering new ideas with the discovery of new objects computers were not there earlier but with the discovery of computer we are actually also discovering the idea of computer which eternally exist and Plato says that the domain the world of ideas the world of abstract essences or forms or ideas constitute a hierarchical arrangement they form an hierarchy. So, what sort of a hierarchy as in the sensible world where there is a gradation of beings from the most imperfect to the more and more perfect the ideal world too has a gradation. So, here comes some Plato encounters some difficulties here because he recognizes the plurality of ideas there are a number of ideas plurality of ideas how do they relate themselves with each other. So, he says that there is a hierarchy and once you say that they are relational one ideas related to another both of them become relative then they cannot be absolute in the philosophical sense of the term. So, and also once you say that there is a I mean they are hierarchical there is an idea which is more real than other ideas or there is a gradation the more real on the top and then you come across lesser realities lesser real ideas. So, in that case be it seems that ideas are losing their individuality they are not individual ideas then. So, once you accept that they lose their individuality then how can you claim how can you assert their absolute status this is a question and ideas are joined together by means of other ideas of higher order this is what Plato says these are embraced under other still more exalted ideas and ideas constantly increase in generality and force until we reach the top. So, there is a supreme idea there is an idea the summum bonnum the objective of all ideas the goal of all ideas in a sense we can say the top the last the highest the most powerful idea which according to Plato is the idea of good. So, somewhere you can see that Plato takes us to the question of the to the ethical question and answer to the ethical question which he raised in the beginning of his philosophy. So, that ethical question is what is that ultimate objective of life what is that ultimate objective of philosophical thinking philosophical thinking aims at truth what is that truth and here Plato says that truth and knowledge are identical with good. So, truth consists or knowledge consists in knowing the goodness the idea of good which is the last idea what is that idea of good the only real absolute idea that is the only real absolute idea it comprehends contains or summarizes the entire system of ideas entire system of reality just as the visible universe its copy comprehends contains or summarizes all say creatures in this world ideas of a lower order exist by themselves and as substances only as compared to their visible copies. So, you can compare the absolute status of other ideas say for example, the idea of pen the absolute status of this the idea of motion the idea of beauty any of these ideas you take they have kind of substantial existence only when you compare them with the objects which are their copies, but the higher I mean when you compare them with the highest idea the idea of good they cease to have substantial existence they cease to have substances they are modes of the idea of good. And here again to substantiate this view the hierarchy the creation the hierarchical ordering of ideas Plato says that the ideas or the ideal the ideas in the ideal world exhibit a unity there is a universe of ideas ordered hierarchically a unity and connection of ideas at the expense of the individuality of ideas this is what I mentioned it is always done the unity is established always at the expense of the individuality of these individual ideas they form of a unity of an organism this is what Plato says. So, they leave a common life these ideas have a common life and it is not possible to separate them from each other as they are independent of time and space which are principles of separation. So, this is again very interesting to separate one thing from another you need space and time separations happens at a time and two places, but ideas are independent of space and time. So, no separation can be envisaged as far as ideas are concerned now the important question is the abode of ideas where do they exist they do not exist in the in the physical world they do exist in the mind, but not in the individual mind as a subjective idea they the heavens are their abode this is what Plato says and heaven of course is a symbolic term here and he says that they are housed in an ideal and intelligible place. So, you need an ideal and intelligible place what is it it is the the the abode of intellect the human mind of course, but not the subjective domain of human mind, but the domain which houses the universal rational intellectual aspects. The home of ideas is the idea as such it is not it cannot be housed somewhere else because it is self subsistence. So, the home of idea must be idea as such the idea has no place outside of itself it exist by virtue of itself it exist in the intelligence and it can be known through the intelligence alone. Again the absolute idea of good and all other ideas exist in the mind which is the the abode of the intelligence and they form the very essence of the mind. So, what is the human mind after all Plato would say that the essence of human mind is constituted of these ideas they are latent in the mind we are not conscious them of them probably we are not conscious of them, but they are there and when you when you when you try to understand the relationship between ideas and sensations Plato would say that ideas are not known through sensations you cannot know them through sensations. The senses can access only the external copies of ideas only the images only the shadows can be captured by the the the senses, but the original exist in us he says it is there in the intelligence it is already there in the human mind only thing is you have to discover it or rediscover it sensation only provoke ideas and it does not reduce them when you see you see an individual pen it can only provoke the idea, but it cannot perceive the idea what it perceives the individual pen, but it provokes the universal idea senses are deceptive this is a very basic principle in a Platonic approach to philosophy the highly suspicious about the abilities of senses to to depart knowledge they drag the mind into the world of particularities. So, this is something which we will examine when we discuss the cave analogy of Plato because that beautiful analogy brings out how Plato's idealism the theory of Plato's idealism with the help of certain analogies parables and all that truth can be accessed only through reasoning this is the ultimate conclusion of Plato's idealism can only be known through reasoning and whatever you talk about the material world it is essentially non-being. So, Plato calls that matter is essentially a non-endity the idea becomes a creator of this a cause a will in reference to non-being and thus non-being becomes like being and takes part in the absolute existence of the idea the non-being thus becomes the first matter out of which the idea forms after its own image the most perfect divine and finished visible world possible. So, now there are two things to be discussed which we will reserve for the next lecture the most important thing is the parable of the cave and also the analogy of vision which we are planning to discuss in this lecture which will reserve to the next lecture and what is interesting is that this conception about the previous slide we have discussed ideas and sensations where Plato denies the value of sensation and affirms the importance of ideas as far as ideas are concerned they can be known only through reason and here Plato envisages a method the method is called as I already mentioned the method of dialectic which he derives it develops it derives the basic insides of this method to develop this method from the approaches of Socrates, but later on he develops a lot on this and develops a very consistent philosophical method very influential philosophical method which depends a lot on dialogue conversation which consider other people as important. So, all these things we will reserve for the next lecture now we have discussed in this lecture we have summarized we have given a very basic understanding of what theory of ideas are the points to be remembered as number 1 ideas are absolute realities they are not images number 2 the world of objects the world of particular objects or these particular objects are all copies of the ideal objects they are imitations of the ideal objects they are imperfect imitations of the ideal objects because all copies and all imitations are bound to be imperfect number 3 you can never know ideas through sensations or sense observation you can know ideas only with the employment of reasoning only with the employment of intelligence number 4 the world of senses have to be suspected which is contained in point number 3. So, these are some of the points to be noted, but the most important one is the ideas themselves constitute a unity they themselves constitute a universe where the ideas are hierarchically arranged hierarchically organized on top of all these ideas you will find the idea of good which is a summum bottom to which all other ideas are subjected to. So, in one sense Platonic idealism or Plato's theory of ideas announces the importance of goodness in human life and he says that goodness is the summum bottom the most important idea and all other ideas are subsumed under that. So, in one sense Plato's theory of ideas is a theory of idea of goodness idea of goodness thank you.


So, far in the first two modules, we have looked at the synthetic approaches to materials. In the first module, we have extensively seen all the chemical synthetic roots which are potential for making materials and module 2. We have worked on the various aspects of thin films, how different materials, inorganic materials can be made. The third module, we will be discussing some of very crucial characterization tools that are inevitable for materials chemistry. And materials chemistry and material synthesis is never adventure without use of proper characterization tools. And therefore, in this module, I am going to highlight about diffraction methods, microscopic methods, spectroscopic methods and thermal analysis methods which can be used as a tool to characterize materials. And I have specially singled out x-ray diffraction measurements as a very important tool which stands very different to other characterization tools. Main reason, there are other characterization methods which are post-synthetic approaches. You make a material and then you try to characterize after you have processed it. But x-ray diffraction is a material not just to characterize what you have synthesized, but during the synthesis itself, it is used as a characterization tool much to the tune of infrared spectroscopy or NMR spectroscopy which is actually used in any chemistry lab to map your synthetic strategy.  And therefore, I have coined this x-ray diffraction method as a tool to track your synthesis rather than even characterizing the material. And as you would see here, there are different cartoons that I have given in this opening slide. Any material which is crystalline will actually give very beautiful diffraction spots. And this is a particular SEM image which shows a well-ordered crystal lattice. And each spot in this gives you an idea about how the atoms are arranged in a crystal lattice. As you can see here very clearly, this is nothing but a FCC pattern. Each spot in this diffraction pattern talks about a definite arrangement of atoms in a lattice. And that is what you see in this cartoon that there are different planes which has a preferential occupation of a particular atom. And they are periodic in fashion. And how do we go about analyzing and getting different informations about this atomic arrangement or order in a lattice? We have x-ray diffraction as a tool not just in terms of a pattern like this. But we can also try to map it as a wave because x-ray diffraction is nothing but bending of waves. And therefore, when x-ray hits a particular lattice and if it is ordered there will be bending of waves. And this bending of waves can be either constructive or destructive. If it is a constructive interference then you will see a x-ray peak. And if it is a destructive interference you will see no peak. Therefore a constructive interference will give you a x-ray diffraction pattern not necessarily a spot pattern but a diffraction pattern which is more like a wave. So you can easily understand which material or which element gives what sort of a pattern. So this cartoon shows here one of the latest versions of a diffractometer which can be used for getting a x-ray pattern of a particular material. So let us go progressively in this talk to understand what sort of information I can get about x-rays about a lattice or about a material that I am synthesizing. So XRD when I say that means powder x-ray diffraction principally because we are going to deal more with the powder patterns. And XRD can be used first for phase composition of a sample. So when I am starting with say A plus B giving C then your A and B will actually have a characteristic pattern. And as you are heating during the thermal process C is getting formed and we do not know whether C is complete or still some remnant of A and B is present. Therefore you can talk about phase composition and this can also be quantified. So it is a quantitative phase analysis which determines the relative amounts of phases. Sometimes we might start with A plus B we are expecting C but actually it can give C prime or C double prime which are some secondary phases which are not needed and therefore it is easy for us to map even those phases. And then more importantly when we want to analyze and understand what set of a crystal pattern that comes when two samples are heated together what is the nature of crystal symmetry of the third pattern that is the product then you talk in terms of unit cell parameters and what is the lattice symmetry. And we can quantify all this indexing the peak position and we can also look at the lattice parameters that can vary as a function of the substituent ions composition. So different things we can try to harvest from this simple x-ray pattern allowing doping solid solutions strains etc. And this is a big list not only we look at the cell symmetry we also look at the macro strain in a lattice and how we can correlate the strain induced by the crystallites or induced by this poly crystals and we can correlate that to some physical property like resistivity or magnetism or so on. And then we can also look at epitaxy texture or orientation if we are going to make the material in thin film form. Suppose I have a solgial root as we have seen earlier and then I am going to make thin film how can I look at the texture whether it is growing epitaxially or whether it is growing in a oriented way. As I had shown you in the previous modules a chemical approach to thin film is quite different from a physical root to make thin films and we are talking about a very high degree of epitaxy or order growth and in such case how we can use x-ray for mapping that and also other information like peak broadening that can tell us about crystallite size, micro strain and so on. So we will try to revisit some of these aspects as we go through this lecture and I am going to show at least one example of each of this that we are trying to discuss in this talk. Now let us look at the diffractometer in the first place and see what are all the crucial elements in a diffractometer because all these are going to affect our x-ray studies one x-ray tube and the source of x-rays. So what is that to do with my x-ray analysis because the target that you are going to choose will also change the pattern that you are getting. Suppose I use a particular target for producing x-rays and you shift the target then the x-ray pattern will totally be different. So I need to know the goniometer that is the assembly to get this x-rays and then the sample and the sample holder because that is a very essential. Sometimes I will mount the sample but not get any pattern at all principally because the alignment is not correct and then receiving side optics because when you try to use some x-rays then sometimes the target can also show some reflections therefore you need to filter off stray radiations to get the right pattern. So you are talking about receiving side optics and then the detector that counts the number of rays scattered by the sample which gives you a pattern. So all these are essential components and this is a assembly of target and this is how it is chemically defined. Suppose you have x-ray tube which is sealed tube then you can operate the source between 1.8 to 3 kilowatt but if you are going to have a tube or the target which has a rotating anode that is x-ray tube then you can improve on the flux by increasing the operating voltage to 9 to 18 kilowatts. Why is that so? Because when you look here cathode rays are generated from a filament usually it is a tungsten filament that is actually striking on an anode in this case we are talking about copper and x-rays produced and x-ray is actually taken through these windows which are beryllium windows and this is the way x-ray is tapped out. Now when you are heating it continuously x-ray is produced as a result the whole of your target can melt because of continuous bombardment as a result at the rear side you actually have a cooling system and without this cooling system your target will melt down therefore you need a very good chilling unit to cool your anode that is your source for the target but to bring down this melting effects or heating effect apart from using a cooler you can also rotate the target so that it does not really gets localized. So if you are going to do that then you can improve on the wattage so you can play around between 9 to 18 kilowatts. So this is a perfect assembly and we can also see that in a real picture this is how a target looks like and these are your windows and this is a evacuation as you see this is a vacuum sealed therefore this is typically the x-ray target that you are using in a typical diffractometer. Now when you are using a target there are several things that are happening therefore you need to know which ray x-ray you are trying to use. So the wave length of x-ray is determined by the anode of the x-ray source and the typical chemical process that is happening inbound electron is actually knocking out and this is the case that is ejected and therefore some of the outer electrons are actually coming back to the k-shell and that is where the x-ray is produced because x-ray photon is coming out. So the process is actually listed in this cartoon you can actually have a k-beta radiation coming from a x-ray source and that is nothing but the transition from m level to k level or you can have k alpha radiation which is from l to k and within k alpha also you have k alpha 1, k alpha 2 and that is actually seen in the typical x-ray mapping as you would see here for molybdenum alpha copper you can single out the k alpha and k beta. Beta always comes on the left side of the k alpha peak that is higher energy radiation but if you look at the intensity k beta will be slightly lesser compared to k alpha therefore k alpha is the most preferred radiation that you would use. So in any x-ray analysis you would say you have to specify what is your target you can mention this as copper k alpha that means you are talking about a copper a source and this is the radiation that you are using to analyze your material which has a specific lambda and this lambda is unique of the particular target but what happens is that you also get k alpha 2 and k beta or the stray radiations that keep coming therefore you need a required optics and other alignment to block all this extra stuff so that you get a monochromatic source that is called k alpha. So those are essentially part of the assembly of your x-ray diffractometer as you see here this is your x-ray and from x-ray you are actually getting the monochromatic x-ray beam to your sample and then these are the scattered radiation diaphragm which will filter all the unnecessary ones then you have the k beta filter and this is your detector which will finally sense the x-ray the reflection that is coming and what is the principle here you have this measuring circle which will actually go 120 degrees and as the sample angle is changing at different atomic planes you will have the diffraction coming and therefore the measuring angle is typically theta 2 theta combination so your x-ray is incident over the sample at a distance theta or angle theta and then you are getting the diffraction at an angle 2 theta so that is why it is popularly called in powder x-ray diffraction as 2 theta scan so when you say 2 theta scan we are talking about this incident beam which is making an angle theta and then this is measured at 2 theta therefore we measure always as 2 theta scans and that is what we see here. Now as you see here there are spectral contamination in the diffraction patterns so one need to be very careful about those peaks which will actually merge with your peaks so if you are using this x-ray diffractometer you have to be very careful mainly with this k alpha 1 k alpha 2 this is a doublet almost always present and it is very expensive to filter this k alpha 2 but actually k alpha 2 and k alpha 1 they will not be split very much in the lower angles as you can see here this is the split here but at 47 degrees you do not see the splitting much but when you go to higher angles you see the splitting much more clearly for k alpha 1 and k alpha 2 so you got to be careful about the contribution that is coming from k alpha why this is also coming since we are using tungsten filament as the source sometimes on over burning the tungsten lines can also come in the diffractometer therefore we should be very careful to filter off the contributions coming from both k beta of that of the target and also the contribution coming from tungsten filament so this can come as a spectral contaminant in your diffraction patterns and before we go more into the details or the basics of x-ray diffraction I want to tell that in today's diffractometers different targets can be used or x-ray source can be used more popular is copper anode and then we have cobalt anode chromium anode and molybdenum anodes and each of this have a particular k alpha which is to be used in our calculations and we have so far in most of our characterization have used Bearden's data which gives you the k alpha value but in 1997 we have Holzer who has brought about refinements in this data with the much better optics and much better analysis analytical tools that are available therefore these are the refinement datas so typically when we talk about copper k alpha 1 we usually say 1.5405 but you can see here in the fourth and fifth decimal places they do change these are all needed for read well analysis or for more precise analysis of measurements so we need to have this in mind that there are different sources which can be used and I will also tell in one of the slides which anode or which target we need to use copper or cobalt depending on the nature of the sample so it is not always required that you should use only copper we can gamble with other targets typically a diffractometer looks like this this is one of the older version of the diffractometers there are more than six companies which are producing such extra diffractometers this is just to give you an idea how involved this procedure can be and I will also show some of the other ones present generation ones which are much more simpler but with different facilities that are available in a single diffractometer so as you see here this is your x-ray tube that is tower through which x-ray is produced and your sample holder is here mounted here and then you have the receiving slit and your detector and this is all connected to x-ray recorded therefore you can actually get present generation diffractometers not only have a x-ray x-ray machine but they also have computer to record your data so this is the assembly of a diffractometer and the brooker is another company which brings different versions of this x-ray diffractometer there are several versions of diffractometers that are available we have powder we have single crystal only for studying single crystals and presently we also have those which are dedicated use for thin films because the settings for studying thin film patterns are different from powder therefore you need such precise assembly so these are some of the different versions and I will be mostly talking to you about powder diffraction and as you see in this cartoon here you can have tungsten molybdenum copper cobalt iron chromium titanium all this k alphas or L alpha is listed here but what I want to stress here is that if you have iron for example iron k alpha is used for ferrous samples where the iron fluorescence would cause a very high background or you can also use cobalt for ferrous compounds so if I am working with iron oxide or if I am working with ferrite based samples the fluorescence will be very high therefore it is not advisable to use a copper k alpha in those conditions for ferrous samples you always use only cobalt or iron k alpha which is highly recommended but copper is ideal for most diffraction examinations and for thin film analysis also so therefore copper is almost used in many of the laboratories and then you also have molybdenum when low absorption is decided that is with single crystal experiments it is always molybdenum that is usually used and this is again the rear view image of the target that I have been mentioning to you this is copper k alpha target which is used in the instrument and today the version of x-ray diffractometer is much different from the earlier ones as you can see here this is the output that you would get for a typical powder XRD pattern for a complex material and you can see so many peaks are there and it could be as simple as three or four peaks in this whole spectra if it is a highly crystalline and cubic pattern. So, just by looking at a typical 2 theta scan you can guess what sort of crystal symmetry that you are looking for more the patterns more complex the symmetry and therefore just looking at this you can say this should be a monoclinic or a triclinic symmetry. So, number of peaks can also give a quantitative information about what sort of system you are working with and you see there are several menu driven interactive softwares available which can generate the atomic position it can give you the lattice parameter lattice dimension everything can be mapped inside to because such softwares are also available. So, it is very fascinating to use a x-ray diffractometer principally to understand what is the system that you are working with. Now let us go into some of the basics of diffraction and see if I am going to use a x-ray machine what are all the informations that I can look for. Number one as you know we are now looking at a theta 2 theta scan. So, this is what I mean by a 2 theta scan. So, once I get 2 theta values what do I do how do I go from there. So, we have to first understand the basic expression that governs our analysis is nothing but Bragg's law which is n lambda is equal to 2 d sin theta. Now what is this n lambda is equal to 2 d sin theta n in powder x-ray diffraction experiments we always take n to be integer which is 1 because we are looking at the first order reflection n is 1 and the lambda is nothing but your wavelength of your target and this is 2 d sin theta that is actually coming from here this is d and this is your sin theta and this is your sin theta. So, this is actually 2 d sin theta. So, this is what we are measuring. So, n lambda is equal to 2 d sin theta and using this expression we can try to find the interplanar spacing that is nothing but your d this interplanar spacing between 2 adjacent atomic arrangements can be mapped because I know n and I know lambda and I can also know theta from the 2 theta value. So, if I have a peak like this and I have some patterns like this and this is your 2 theta scan this will give me 2 theta value and from there I can find out theta. So, this is how we go about it and first let me start with the featureless curve because this is in reality this is how it is because this is nothing but a x-ray diffraction pattern of glass. Glass is amorphous therefore there is no long range ordering and if you see only a big hump at low angles then that is a very clear indication that it is amorphous in nature. You would not see anything these are all spikes these are not peaks these are spikes. Therefore, what you see here is a featureless noisy curve and that says that it is the material is amorphous or glassy. Now, if you go for single crystal or poly crystals this is how it is if it is a ordered lattice like this then I would get a very sharp pattern as sharp as this and this is for a highly oriented system. So, the peak width or the crystallinity of a particular pattern will be reflected by the shape and size of the x-ray peak. Now, if these lattices are broken into poly crystals as small small crystals then we are actually breaking the long range order and therefore this peak now splits or broadens into this fashion and this B is nothing but your full width at half maxima which gives you idea about the peak broadening and therefore peak broadening has a consequence directly to the size and also shape of your poly crystals. If they are very fine then broadening will become more. So, we are talking about going from a bulk to a very small dimension and typically for that matter nano sized powders will either be amorphous in nature or it will have a very broad peak like this and when there is a broadening you should understand broadening necessarily does not mean it has to be very low sized crystallized or nano sized broadening can also come from several other instrumental problems also. Therefore, we need to be careful where is the origin for this peak broadening. Suppose one peak shows a broad one and the other peak in the same spectrum is showing a thin one then it is not due to the sample but it is due to some alignment problem. But if the sample is truly amorphous or nano in size then all the peaks that are appearing in the pattern will have same broadening then you can be sure that this is truly coming from a nano sized powder. Now what informations we can get number one we can get information about T. T is nothing but the thickness of your crystallite. This is the crystallite that I am talking about and what is the dimension of this crystallite because crystallites are made of very small lattices and therefore I can map what is T. T is given by K into lambda by B cos theta B where K is nothing but a constant that depends on crystallite shape. This is actually taken to be 0.89 and the contribution comes from both broadening and from other factors related to the shape of the crystallite. Lambda we know B is nothing but full width at half maxima so you can actually map your broadening and you can also measure the height and take the full width at the half maxima then that becomes your B and theta B you know that is your bragg angle so you can get T. If T is equal to 20 nanometer then you are saying that your crystallite size is as small as 20 nanometer. So peak broadening is defined by sharers formula which is a very potential information that you can achieve.  So this is how you go about doing this but word of caution you can resort to sharers formula only if your crystallite size is less than 100 nanometers or 1000 angstrom if it is more it is not good to correlate your X-ray broadening to crystallite size which is not needed because broadening as I told you can come from strain can come from the instrument and also come from size therefore peak broadening can be very very deceptive therefore we should know what we are looking for. So k depends on T and B and this can be evaluated within 20 to 30 percent accuracy at the best. Now when we look at the data analysis we are looking at the plot data that is 2 theta versus counts that is the principle data that you will get and from there you would define what is the bragg angle that is 2 theta so you can get theta then you can calculate D and you can from D you can calculate A and also you can apply sharers formula to the peaks. So these are the basic steps that you would choose when you are handling any data. Now sharers example we can let us take the case of this 400 refraction that is coming from gold foil which appears at 98.25 degrees then we can calculate the crystallite size in that case using the formula which gives you approximately the dimension of your crystallite size to be 120 nanometer and from there you can actually also calculate your B if you know the crystallite size we can try to see the peak broadening but peak broadening is a direct measure of the peak distance itself. We can also take the other example of calculating your interplanar spacing and this is the bragg example that we can talk about. Let us take the small peak that is 38.3 which is index to 111 reflection for gold foil and how do we go about your lambda is known that is from copper and theta is known so your theta will be 38.3 over 2 so your interplanar spacing for your 38.3 will be 2.35 angstrom. So this is how you assign the peak similarly we can do it for 44.5 degrees 64.7 degrees and you can index a pattern. Now crystalline materials are characterized by the orderly periodic arrangement of atoms therefore when the sample is actually rotating you can see that several planes will come into diffraction. So this is one plane and this is one plane specially these two planes are characterized as two zero zero planes this will have exactly half the interplanar spacing as that of your one one zero. So if you have one zero zero plane it will be exactly half of that will be your two zero zero plane. Similarly when the lattice rotates you can bring other planes also into focus for example this is the way you can visualize a two zero zero two two zero plane and this can also give you a particular reflection. So the unit cell is basic repeating unit and parallel planes of atoms intersect the unit cell and are used to define the directions and distances and how do we map this by knowing the lattice parameter we can actually index this to some miller indices as one one one or one zero zero and so on. So these are called miller indices which we can try to index based on the minimum details that we get from your X-ray diffraction pattern. So the atoms in a crystal are in a periodic array and therefore we can try to use this diffraction to understand the long range ordering or the short end ordering that is available or that is present in the crystal lattice. Here is a cartoon that I want to highlight to you this is X-ray diffraction pattern which gives you idea about the different phases of a single material that is present. For example you take the case of T I O 2 and T I O 2 can actually be present in three different phases anatase and rutile which is more predominant and you also have a brocade phase. Now if you take a X-ray map you would see depending on the phases that are present you can also see different patterns that are emerging and the red ones are predominantly the rutile pattern and anatase pattern comes out as green and then the blue ones are indicative of brocade phase. What you should be careful here is that within a short range all these phases are overlapping. So if you are not precisely measuring then you might confuse one phase for the other. So you need to have some idea about all the phases that are possible which will help you in identifying what sort of phases are present. For example even today the greatest challenge for you to understand is the challenge in T I O 2 to crystallize in a preferred symmetry. For example rutile but what happens anatase comes as a major impurity phase. So chemical approaches are there which are used to stabilize only the rutile phase. So the complex can become more confusing if we do not know what are all the different phases that can be present in your given sample. Now we will look in the other few slides how to index or understand what is the repeating x-ray peak and from that what sort of information that I can get. We will see this in the next two slides. Take for example this x-ray pattern where you only see two patterns that are present. In such case what information you can achieve is important. As you would see here this particular peak refers to 1 0 0 and this particular peak refers to 2 0 0. So in that case only those repeating peaks you will get whereas the other miller indices or other crystal planes like 1 1 0 1 1 1 and 2 1 0 these are all absent in this particular reflection. So just by looking at it you can easily trace that when the several peaks are missing only few peaks are represented in your x-ray scan. You can say those belong to a particular class of hkl reflections. So you call this as 1 0 0 when you put within this inverted brackets then you say that this belongs to H 0 0 type of planes. So you will get only 1 0 0 2 0 0 3 0 0 this also talks about the orientation or the texture of your growth. Now if you look for poly crystals for example then in polycrystalline patterns you would get all the reflections 1 0 0 as you see here 1 1 0 1 1 1 2 0 0 all the peaks of different crystal planes are present which you can get in a polycrystalline sample against a single crystal. So in single crystal you would get only a preferred miller indices reflection whereas in polycrystalline sample you will get all the patterns emerging in picture. Now in the earlier days before we got this x y recorder or as you see in present generation everything is appearing on a computer screen in earlier days it was mostly obtained as a photography. So you would see x-ray patterns coming out as a pattern like this and these are nothing but these lines represent the Debye ring or Debye cone which is coming out as a intersection of your detector on this cone which is appearing as this sort of rings. So with respect to the sample these rings can be measured and each of this ring will give you a particular d value interplanar spacing and if you see here the intensity of this also tells which reflection is going to be at its maximum. For example this is a darker shade compared to these peaks therefore they we can say that these peaks are highly intense compared to the other ones. So this peak for example is intense but this peak is less intense so it comes out like this. So this is the way it was mapped and we can also try to measure the distance from the dark spot. So each of this distance can be evaluated using this formula as S 1 or S 2. S 1, S 2 is nothing but the turn it makes with respect to the incoming x-ray. So if you can measure S 1 based on the distance then you can generate the value theta and if you know the value theta then you can calculate for sine square then you can calculate for case kind of sine square theta and from there you can get your Miller indices and also your lattice parameter. So this is the earlier version by which x-ray diffractions were made and those were available only as a photographic film. So you need to make take a x-ray photograph and then you should develop and calculate the distance from the central spot and that is how you measure the interplanar spacings. But today this is all simplified and you can get everything in a single fashion. Just one or two comments about sample preparation it is not always the problem of the x-ray diffractor meter when you do not see anything. Therefore powder preparation is a very very important protocol when you try to look for a very decent x-ray diffraction pattern. Therefore an ideal powder sample preparation means it has to the different orientations should be smooth and equally distributed. If the crystallize in the sample are very large there will not be a smooth distribution of crystal. Therefore there will be too much of noise coming into picture and larger crystallize size and non-random crystallite they can also affect the peak intensity to a larger fashion. So we need to be very careful about how we orient the sample, how we prepare the sample. If the crystallize in the powder sample have plate or needle shape for example. If those are the morphology then you are sure to get a very confusing x-ray pattern and it can be very difficult to get them adopt to random orientations. So you need to look for a top loading where you can press the powder into a holder and somehow try to make a very continuous spread so that you do not miss out on the reflection. So when we have particles with different morphology it becomes increasingly important how you prepare the sample. So we need to go through that and it should also be densely packed therefore care should be taken how you pack the sample and we should also make sure that the samples are ground nicely if you are looking for a polycrystalline one you cannot just take from the furnace and mount it because when you heat any sample at 900 degrees you are actually looking at samples with 100 micron or so. So you got to bring it down so that it is somewhere in the 10 micron range so the diffraction can be uniform. And also you should understand that low angles you can the spread of your beam has to be this big at very low angles whereas at very high angles it can be very small. Therefore when you spread the sample we should make sure that at all angles the incident radiation is falling exactly on the sample and not elsewhere. So these things we need to bear in mind. And just want to mention to you some of the relevance of this XRD analysis as I am progressively mentioning in this lecture there are different ways of using X-rays for characterizing your sample. Strength of the XRD is it is non-destructive quantitative measurements can be made texture can be used limitation is that it cannot identify amorphous materials. So it grows goes really blank therefore we do not have a potential way to characterize amorphous material and your spot size has to be of the order of 50 micron and you do not get any information on the depth profile. So you just get whatever is on the surface you get that. Now there are also several areas where X-ray diffraction has come into prominence relevant industries who use this analysis are from medical to electronic to several range of industries which are using this as a fundamental tool to characterize the sample. I am going to talk in the next few minutes about some specific examples how we can understand X-ray and always X-ray goes in combination with some physical property where you can try to map some reasonable conclusions. For example take the case of cobalt chromium alloy this is a alloy which is a shape memory alloy and this is used in variety of applications including biomedical applications. Question is are structural transitions induced by magnetic transitions because magnetic transition and structural transition can go hand in hand and we can see if you try to prepare cobalt chromium compounds and this is for a 300 degree C anneal because the ash prepared compound shows X-ray amorphous nature and because of X-ray amorphous nature you see this low angle big broadening or hump and if this hump is present at low angles you can be sure that it is just crystallizing and when you heat it only to 300 you can see this HCP phase is crystallizing out in your cobalt chromium sample and if you heat it at 900 degree C you can see different phases coming into picture in this case it is HCP plus FCC that is coming and in this case it is purely HCP HCP and at chromium 40 percent you are getting a FCC phase and this seems to be going hand in hand with the phase diagram that is predicted. But what we see here is that for all the 300 degree sintered samples which is HCP there are certain peaks which are showing a nearly anti ferromagnetic interactions or competing anti ferromagnetic interaction for example this 20 and 30 percent compared to a clear ferromagnetic loop but in this case all are HCP but when you try to heat this to 900 degree C when in this case if it is FCC here HCP plus FCC and in both this cases HCP you can see that there is a different change in the magnetization and so we can directly correlate which phase is responsible for the anti ferromagnetic coupling which phase is giving you a ferromagnetic signal all this can go hand in hand when you try to map your X-ray diffraction pattern. So this becomes very useful to understand how the magnetic transformations affect the structural disorders and how the structural impurities can alter the magnetic signature. So a competing interaction between AFM and ferromagnetism in this cobalt chromium is actually linked to the structural changes that are happening. This is another example that I want to quote which is a cobalt silver and this is nothing but a granular alloy because if you try to put silver into cobalt or cobalt into silver, silver is crystallizing in FCC, cobalt will not actually form alloy rather it is a immiscible alloy and in this what happens cobalt actually forms a cluster like this and therefore it is called a granular magneto resistance system where cobalt does not spread and get mixed with silver rather it isolates in into cobalt nanoparticles. So there can be correlation between the cobalt clusters and the way they orient can affect the electrical conductivity also. So this is actually used as a granular MR system or magneto resistance system this is the ash prepared alloy this is alloy that is sinned annealed at 600 you can see that it is getting crystallized and the ash prepared alloy clearly shows the presence of both cobalt and silver and when you annealed it is actually transforming into a poly crystal. Now what you see here is this is silver and in silver when you try to put cobalt as of this is the X-ray pattern as a function of the atom percent of cobalt and you can clearly see even up to 90 percent atom percent of cobalt that is doped only FCC silver phase is present. What it means is that cobalt even though you dump it with 10 percent the crystallites grow but they are remaining in a amorphous form and all that you can see is only the FCC phase the HCP phase of cobalt does not come into picture but when you annealed the sample of the ash prepared compound then you can see that the cobalt phase is emerging out which means cobalt is crystallizing from a amorphous phase to this one. So you can directly make a correlation between the sort of crystallization process that is going on with any other physical properties and if you actually map this peak which is true for silver and this peak which you are seeing for cobalt now as you see here this 30 peak clearly shows a change in the full with that half maxima and the position as a function of cobalt and this can have a tremendous influence on the properties of this silver cobalt nano alloys. Here again you see for the 600 annealed sample the peak position changes and the full with that half maxima also changes and therefore there is a way to actually interpret the peak broadening. So in this case the peak broadening can come from two situation one is due to strain induced broadening or one is due to crystallized size. Crystallized size is what we get from Schrader's formula where you calculate the peak broadening but one should also understand the peak broadening comes from strain which is nothing but delta 2 theta which is given as 2 theta 2 epsilon tan theta where epsilon is nothing but your strain micro strain and therefore you can actually correlate that strain to the grain size and you can see here very clearly that with the maximum strain is there when the crystallized size it has is at its minimum. So when the crystallized when you go down in the nanometer range what you are inducing is a macro strain which will also affect your MR property and that is what we try to see from this measurements we can actually try to map the dependence of this micro strain to coercivity and to MR also. Another example of cobalt platinum alloy which actually shows this sort of decorations when you try to synthesize you as you see the ash prepared one shows a TM pattern like this but as you show the TM beam it gets crystallized in no time and the ash prepared compounds are clearly showing a amorphous phase but with increasing amount of platinum you can see this hexagonal phase coming for the ash prepared alloy but when you try to heat it at 900 degree C you can see a FCC phase that is forming. What you would expect this to be a HCP is actually getting into a FCC phase even for a platinum 0% composition which means metastable phases can be stabilized when they are nano in size and this can be easily mapped through a high temperature X-ray diffraction. So this is a very unique facility that is available the X-ray diffractometer has a platform which can be used for sintering and where you can easily map a FCC to FCT transformation that is happening this you can clearly see in this peak which is building up as you are heating inside to this is not taken out and then recorded as you are heating you can do a isothermal X-ray and you can see how the phase transformations are occurring and you can see how clearly this FCT peaks are coming this peaks are nothing but the peaks of platinum foil which is used for spreading your stuff but the regions that are of interest is the peak that is growing along this 201 and 112 which clearly shows that a FCC to FCT transformation is occurring and also we can use this for mapping the Teflon or PTFE polymeric films which you can deposit using PED and as you can see here this is for a room temperature deposited film and this is for a 100 degree deposited film 300 degree deposited and at 500 degree annealed film you can see that the peak is lost and we can also make correlations with the SEM pattern which I will skip for now and then I will also show another example where you can try to see how you can track different things that are happening this is alloy where if you take starting materials like cobalt and iron you can end up in a sonochemical process alloy which is stable even at room temperature on oxidation gives a cobalt ferrite. So this can go hand in hand with other experimental techniques which clearly gives you idea about the alloy formation which is actually reported for the first time. Another point that I want to emphasize before I close is that we need to be very careful about the X-ray patterns that we are producing I have rounded it here in this cartoon as log plot because when you try to do single crystal studies if you do it at linear intensity you would see only the peak of silicon being very huge and the system peak will almost be absent. Therefore if you want to really map the epitaxy then you need to plot it in log scale instead of linear intensity only then you will see the comparable values for example here is a situation I have deposited a luteatium oxide on silicon or on YSZ. So in that case very close to the silicon substrate reflection you would see luteatium oxide and YSZ reflections coming. If this is the way it shows then you can say that it is epitaxially growing but then that is not enough because you also see in the log scale several small peaks which are coming. These are not commensurate to your 1 1 1 0 0 peak which are showing 1 0 3 4 4 0 therefore we can although a very impressive TEM is there then you have to understand that it is showing some polycrystalline feature and it is not totally a epitaxy therefore this is very important and the other thing that will also tell whether it is a real epitaxy is nothing but your rocking curve each of this curve we can try to do a rocking curve mode which will give you idea about the width of this rocking curve will tell how good the texture or growth of this films are. So rocking curve is one important accessory in thin films for you to map whether you are growing a textured film and also this is another example where I am trying to code for a organic molecule how this patterns can give useful information in linear intensity versus log intensity scale you can see how the same pattern changes but what is the advantage you can easily map whether any impurity ion is there therefore whenever we record any x-ray pattern we should always look at the log intensity scale to see whether any minute impurities are there for example in this case these are very small peaks does not come into prominence but in a log intensity these are projected much easier therefore we can see whether any secondary phase can come out. Another important one I may not be able to cover in this lecture but then certainly I will be able to cover in future lectures is the phi scan which is used for mapping the orientation or textured growth of your thin film samples. Suppose I have a peak at 38.6 degrees then I can try to see whether it is texturally growing in a single crystal substrate for which phi scan is used I will come to this in the subsequent one and there are other examples also which I may have to skip for want of time in this lecture but just want to tell you that there are three things that are fundamentally used using x-rays one is x-ray radiography in medical applications but x-ray fluorescence is also another avenue where you can quantitatively get to know what how many metals are there or what is the composition of the metal using the same x-ray technique apart from the x-ray crystallography. So as I pointed out to you there are several x-ray powder diffraction features that becomes useful and in this lecture I have basically covered few things to bring it to your focus one is about how this whole thing works and the two important laws that can be verified that is Schroeder formula and Bragg's law the information that you get out of it and try to understand how your crystals are growing and I have told you about how we can use inside to hide temperature diffraction in measurements can be made to understand the phase transition and also the strain effects that can be correlated to other properties and in thin films I also try to show one passing example of how we can map the epitaxial growth. So in the next few lectures we will also look the applications of this x-ray in perspective with other case studies and not only that we will be looking at other spectroscopic tools in this particular module.


Let's go to everybody Chris from jassescasebreaks.com doing our 2019 2020 Fnini Mosaic basketball hobby pack random team number 369 This is the last filler that we need for our 22 23 origins basketball random team number 2 We're giving away 10 spots at the very very end So two randomizers this first randomizer will be for the pack itself our fresh dice are our names from Eric down to Qinghua with the last hot mother. Thank you sir. Thanks everyone and our teams. So we'll roll this dice for both those randomizers Good luck. Thanks again, everyone six and two eight times. Let's do it one two three four five six seven and eight eighth and final time with Mark down to Brian and eight times for our teams one two three four five six seven and eight eighth and final time Chagra bowls down to the spurts All right, so I got our first half here. No trade windows and it's just a filler So we're in a rock and roll mark with the bowls all over with the Lakers Craig with the Cavs Rosario with the Pacers Brian with the pistons and Raptors Brian with the T wolves Tanner with the Kings Brian with the Suns Eric with the heat Nicole with the Jazz Qinghua with the Grizzlies last spot mojo there Chris T with the Knicks Josh with the Mavs Brian with the Celtics Colin with the Wizards Ryan with the Bucks Colin with the Blazers Tanner with the Nets Chris with the Hawks Ryan with the Nuggets Josh with the Sixers Ryan with the Thunder Chris with the Pelicans Ryan with the Hornets Chris with the Magic Dan with the Quippers Brian with the Warriors Eric for the Rockets and Brian with the Spurs Let's get this alphabetized Let's print And let's rip which switch screens here real quick while we print one pack 1920 hobby Six boxes of origins right after this origins is a fun one Some sweet patches first our piece for these kids to see if we can grab In this pack. Let's grab those names and give 10 spots away 369 Chris with the Hawks and the Colin with the Wizards All right, Jared Culver Silver rookie the Zion rookie there's Garland rookie and Bruno Fernando There's Garland rookie going to Craig and the Cavs and the Zion rookie Going to the pelicans and Chris T All right, that's our pack. Let's switch scenes and let's do the fun stuff here 10 names Given up scrub our names here Fresh dice our fresh list All right, and we'll roll this dice so it's a 1 to 10 get in 11 30. Thanks for trying appreciate you getting in But let's do it three and four seven times Are looking for the heat so we are so are we seven times good luck one two three four five Six and seven seventh and final time. Good luck folks So at 11 is Brian Brian down to Brian. Thanks again y'all. Let's see There are some multiples of some of these names here. Let's see who gets in So at 10 is Brian rice Brian nice. You got in Dan gets in Brian gets in Chris T gets in Josh Smith gets in Brian gets in once again Mark L gets in Ryan there we go. I didn't get you in there Ryan gets in Ryan with one more spot and Eric At the top our 10 names here Grab our sheet real quick. There we go Right here So these 10 names here I'll put you into this origins checklist And when we come back our next video will be a six box half case break of 2022 2223 orange the basketball. Thanks again justice case breaks calm. Bye


Hello and welcome to the session. In this session we are going to discuss conditional and biconditional statements and we will also discuss the inverse, converse and contrapositive of conditional statements. Let us start with the definition of conditional statements. The statements which are written in if then form are called conditional statements. If p and q are two given statements, then conditional statement will be written in the form if p then q. A conditional statement has two parts, hypothesis and conclusion. The clause followed by if is called the hypothesis and the clause followed by then is called the conclusion. The conditional statement is denoted by or and is read as p implies q. For example, we have a statement, an angle whose measure is less than 90 degree is an acute angle. Let us rewrite this equation in the if then form if the measure of an angle is less than 90 degree then it is an acute angle. Here the hypothesis is the measure of an angle is less than 90 degree and the conclusion is it is an acute angle. Now let us find the truth value of the conditional statement. In the conditional statement if p then q, p is the hypothesis and q is the conclusion. So here if p is true and q is false then p implies q is false. If p is false q is true then p implies q is true. If p is true q is true then p implies q is also true and if p is false q is false then p implies q is also true. For a given conditional statement we can write its inverse, its converse and contra-positive. Let us now discuss inverse of a conditional statement. If we negate both the hypothesis and the conclusion and rewrite it in the if then form then the new statement formed is called the inverse of conditional statement. The inverse of a conditional statement is denoted by not p implies not q. Let us continue with the earlier example. If the measure of an angle is less than 90 degree then it is an acute angle. Now we will write its inverse. As we know to write the negation of a statement we use the word not so its inverse will be If the measure of an angle is not less than 90 degree then it is not an acute angle. Now let us discuss the converse of a conditional statement. If we exchange the hypothesis and the conclusion in the if then statement then the new statement formed is called the converse of the conditional statement. The converse of a conditional statement is denoted by q implies p. For example the converse of the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle is given by if an angle is acute then its measure is less than 90 degree. Now let us discuss the contra-positive of a conditional statement. If we negate both the hypothesis and the conclusion of the converse of the conditional statement and rewrite in the if then form then the new statement so formed is called the contra-positive of the conditional statement. The contra-positive of a conditional statement is denoted by not q implies not p. We have the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle. The converse of this conditional statement is if an angle is acute then its measure will be less than 90 degree. So its contra-positive will be if an angle is not acute then its measure will not be less than 90 degree. Now we come to biconditional statements. A biconditional statement is formed by joining the conditional statement and its converse using words if and only if. It is a conjunction of conditional statement p implies q and its converse q implies p so it is denoted by p implies q and q implies p or we can simply write it as this or this which is read as p if and only if q. We have the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle. Its converse is if an angle is acute then its measure will be less than 90 degree. Now we write the biconditional statement using if and only if. An angle is an acute angle if and only if its measure is less than 90 degree. If both conditional and converse statements are true then the biconditional statement is also true. So the biconditional statement an angle is an acute angle if and only if its measure is less than 90 degree is a true statement. With this we complete our session. Hope you enjoyed the session.