Welcome back to Mental Health TV. I'm Amy Golding, Director of Psychology for the Workplace Mental Health Institute and I'm here with our CEO Peter Diels. Welcome back. Thank you. And so today we're going to have a chat about some of the things that have been in the news lately. Things related to mental health, psychology, well-being and things that impact all of us in this day and age. So in particular we're going to focus on a topic that is crucial for our mental health and well-being which is the topic of relationships.  So this came about because there's an article out in today at the moment around all of the couples who have separated or divorced recently. So Kevin Costner after 18 years of marriage. Ariana Grande, I mean there were many but I didn't recognize many of them. This is the one that I remember. Ariana Grande after three years. Yes. And then who was the other one? Sofia Vergara, family. After eight years. There's some amounts of time together and people go into a relationship thinking this is going to be forever and no one thinks that at some point they're going to separate. And yet statistically the majority of people that do get married do end up divorcing. So what's going on here? Well actually it's interesting because falling in love is so amazing that I've seen people suffering from schizophrenia fall in love and the schizophrenia was gone for at least three months. Well they were still in the heightened sense of being in love. Well isn't being in love a little bit? Another kind of crazy. Kind of mental illness. Yeah. But it's a good one. It's a one that feels really good. And if you think about the dynamics of falling in love where you're in your best behavior both people are both people feel that they're fantastic because they have the attention of the other person and the other person seems to think that they're fantastic. So that's very addictive. But it feels very good for your self-esteem, for your confidence, you're walking on air. So what happens then after a while that stops being the dynamic? Because if we knew what it takes to keep that dynamic of being in a state where you're making the other person feel amazing and that person is making you feel amazing then you wouldn't have to divorce.  I have a few theories on this. So number one I think in the beginning all of those lovely things you just described also take time and attention and we do that in the beginning but it's a sustainable over time and I think if you see a lot of people get busy with other things in their life they're kind of like alright well I've got to get back to paying attention to my work or family comes along and that becomes a priority and we get distracted and we don't give the same amount of attention and love and all those things that we did in the beginning over the course of time. That's one theory of mine. My life is not used to the same excuse not to do it. Everybody has got 24 hours and recently we went to my uncle and auntie's 50th wedding anniversary. 50 years married. So there's obviously still proof of people lasting a long time in a marriage. That doesn't mean that they're completely happy but they do seem to fall in love again after the years passed. Yes, they fall in love again. So there's something about that that can be regained and yeah time is something important but how much more time costly is a divorce. Especially when you're for kids. It's about making the conscious decisions. You get to do it. But I think one of the things that we start to forget about in relationships after we become familiar is we take for granted this idea that we're making the other person feel good just by us being there. My presence is over there. Look what I have to contribute. And that is a problem because making another person feel good. And notice that I'm using these terms which are not very popular right now.  I'm about me. I am amazing. Amazing. I deserve your attention. That is completely narcissistic. Completely and utterly narcissistic. In order for a relationship, I mean what works with me and you for me is when you give attention to me for no reason but because it's me. Yeah. And that makes me thrive. That's amazing. You know what I think? I was going to say expectations. I think that expectations again are doing generally change over time. In the beginning we go in just kind of discovering and everything's great. So then over time we start to layer on this, well, I expect this from you and I expect that from you. And now we're up to ante instead of coming from that mindset of isn't this person amazing. You have a good point because when we started a relationship, the priority is love always. Love. And when you have love as a standard, your demands of other people get lowered. What happens with time is become afraid for our own well-being, for our own stuff. We become really egotistical. Then fear takes over. Instead of putting love as a standard, fear becomes a standard. Now fear as a standard is ruthless. What if I'm not being respected? Yeah. What if questions? Yes. Yeah. What if I'm not being loved? All that stuff that you just mentioned, but the standards get heightened to a degree, no human being can meet them. Yeah. So the treat is that one, isn't it? In many ways we're trained socially as well to look for perfect. I expect perfection in my partner when that's not realistic. We would all admit that none of us are perfect. And yet sometimes we've got to consciously remind ourselves that this is a person with their flaws, with their faults, but I can still love them anyway. And it's the same thing with friendships too, to be honest. Yeah. That's what friendships are. Actually, I heard a friend recently say that, which I think is very true. She says, if you have somebody that you like and they do something that you don't completely like, you forgive them because you like them. Yeah. And that one you don't like did the same thing. You crucified them because you don't like them. Yeah. So that's loving actually. When you have love for a person, your standards get lower. You don't need them to be perfect. And yet that's the problem in our romantic relationships. We tend to demand more of that person than anybody else in our lives. Instead of that, in psychology we call it that unconditional positive regard, that commitment that you make to say, well, whatever happens, I believe this is a good person. And I want to reveal what I always describe it when I'm talking with clients, that every action you take is a step towards each other or a step away from each other. And which is it going to be? Even if they've done something that is hurtful or isn't perfect, but they haven't disappointed you, it's going to happen. But can you keep taking those steps together towards each other? Yeah. So I mean, we're talking here from three angles here. One is we're expressing psychology and relationship is part of that psychology. The other one is we are therapists. So we've held a lot of marriages and couples stay together. And in some cases, separate. And the other one is we happen to be married and that we come from personal experience. So what would you say there are some of the things from a female perspective that need to happen in relationship to make sure that the relationship is healthy? Everyone will say communication, but it's true. But it needs to be good communication. And I think that that's lacking because no one teaches you anywhere. You know, there's no subject in school saying this is how you do it. Well, how is communicating in a marriage different from communicating normally? Exactly. I think it's more and it's more specific. It's more vulnerable. Like, in order for communication to happen of good quality in a marriage, you have to be make yourself vulnerable. You have to talk about your fears. And that's very hard. Especially for guys because most of the time we're not aware of our fears anyway. And also understanding those differences in communication styles that are going to exist between any two people because we're not the same. So, not just understanding it, but being able to make requests for, you know, this is what works for me. This is what doesn't work for me. Particularly, for example, in the area of conflict where there's been a disagreement about something, how do we communicate in a healthy way around differences of opinion? How do we handle conflict? Conflict can be a healthy thing. If two people you're not going to be exactly the same, it's going to be serious. You have to blow up sometimes. But you have to blow up in love, not blow up in hate. And have those conversations about when we're in that moment, we have the conversation outside of the moment about when we're in one of these moments, what are our rules for fighting? What are our agreements that we won't call names, for example, or if someone needs a timeout, we'll respect that, but we will definitely come back to it. We have a little one in which we remind each other, I'm just fighting as they love you. I still love you. So these things are some of the micro-strategies that you can do. Reminds me what one of our relationship coaches once said to us, focus on the intention, not the words that are being used. What's the intention behind it? That's been very useful. Because when you focus, what are they trying to do here? If they're still fighting with you, they're still fighting for the relationship. So that's a good thing. Even in fighting, they still care.  So while we're still fighting, they still hope. And we also know that whenever there is one of these intense moments, there's always fear underneath. It's come back to what you said earlier. There's always a fear underneath, usually on both sides. So if you can have that empathy for the other person and find that compassion that you have for them in that moment and remind yourself, okay, there's a fear here. That's all it is. This person is afraid of something. And so that kind of immediately softens your perspective on them. And you can... I think oftentimes it takes one person to be the person who can step up in that moment. Sometimes there'll be one person, sometimes there'll be the other. But there needs to be someone who can be the... who can kind of rise above the present moment and do what's needed for the good of the relationship. And sometimes it's me and sometimes it's you. It's not about who's the guy or who's the woman. No, no, no. Sometimes the one that is feeling it, the least as a threat, needs to step up for the relationship. So that's an important difference I've learned over the years. You don't do things for your partner. You do things for the relationship. And as that, the side effect is that your partner gets all these goodies. But that's an important one. Do things for the relationship. So what would you say that some of the common fears would be? Well, I mean the biggest fear I think that people have is, am I going to be abandoned? Am I going to be rejected? Am I not going to be loved and appreciated and seen for me? Am I going to be left behind? I think there's a question always, am I still special to you that people have? Which in the beginning we don't have that question. Of course I'm special. Amazing. Well, we can tell the person all the time that they are demonstrated. We do a number of things. And attention. They get a lot of attention. They get a lot of attention, even hanky-panky. They get a lot of hanky-panky. In fact, that's a good thing to say to people if you are going through a dry spell in your relationship, try having sex every day for a month. Is it the process in therapy? Yeah, there's a process in therapy. It's kind of like a homework past for people. Even if you don't feel it, just commit. Connect every day a little bit. Going to go there. So, good. I'm just interesting. What would you like to know about this topic? Is relationship something important to you? Because I mean, divorces are at an old-time high. We know the impact of divorces not just on the couple, but also on the kids, on the grandparents, on the whole family. And communities. Going back to the celebrity couples that were originally talking about, all of us, I think, have couples in our lives that we think, oh, they're doing really well, they're great, I admire them. And then suddenly when something happens, it can really impact the whole community. And we do see the domino effect, don't we? Somebody gets divorced and then all of a sudden two or three of their friends get divorced. There's that domino effect. There's a group happening, it makes things difficult. So what do you think? What are your thoughts on this subject? Are relationships important to you? Do you think being in love is something worth fighting for and spending the time on or not? This is about you. So I hope you have enjoyed our chat today. Yeah, this is an area of passion of mine, of course, because I've seen how important that can be for people's well-being. So with that, we'll leave you to it. We look forward to reading your comments and keep this conversation alive. Bye now. Look forward to hearing your thoughts. Take care.


Hi, I'm PGA Goff professional Brian Haas here for the T tournament sponsored by the VA and the DAV Today we're going to cover the long game. So the top end of your golf bag We're going to cover how you hit your driver compared to how you hit your fairway woods and hybrid One of the big issues that I see in players is that they treat their driver and their fairway woods Exactly the same way and they're really completely different from each other the driver We want to hit in an upward motion. So when when the ball is sitting up on a tee We want to swing up at the ball and get the get the ball in the upward swing That keeps the spin low and allows the driver to create shots that are going to be more More straight and direct toward the target when you hit down at a driver You create more spin which creates more movement in the golf ball left and right when we get to our fairway woods We want to treat those a little bit more like our irons. We want to hit down at those We need the ball to climb up the face. It's not sitting on a tee So it's very important that we we get into a downward motion with that club and and we treat it a little bit more like an iron So when we're teeing up a driver the big thing that we want to look for is that we're getting the ball halfway above the club head So what I didn't do is put a ball in my hand Pull one out here So as we're teeing up that ball We want to make sure that that ball is getting halfway above that club head in the in the tee up position That allows us that the position of the club to come up and hit upward at the ball and In the sense of an iron or or a fairway wood that ball sitting on the ground So if we hit up at a ball that's sitting on the ground that ball is going to roll downward We need to hit downward on the ball which makes the ball climb up the face of the club And that is the biggest difference between a fairway wood and a driver So a lot of players are always asking how do I hit my driver farther? Most players have the capability to hit that ball farther than they currently do and it's typically by length of swing so if a player gets his driver into into a good position in a current position if they maintain that same speed but Carry the driver length as long as they possibly can the farther you take that club head the farther the ball will go So if your driver is currently stopping in in a 45 degree position and we move the club head to a parallel position You will gain speed that's consistent with every club in your bag But mostly players are asking about how do I hit my driver farther? That's a great way to get started So the driver and getting back to swinging up at a driver as opposed to down at a driver You can see I have the the ball teed halfway above my club head And in this case we want to make sure that we get our body in a good tilted position So that we can give ourselves an opportunity to swing up at the ball Because the ball sits on a tee that is our the best benefit we can have so again It's a game of physics and we want to make sure that we're using the physics to our advantage The more I swing up at this ball that's sitting on a tee the less spin i'll get so the less curvature of the ball I will get so in that case i'm going to get that ball halfway above my club head I'm going to get my body tilted back to the to the right side just a little bit So that I can get myself in a position to where my club is going to swing upward toward the ball So get myself set find my target Get myself tilted And then go ahead and swing up through the ball And that's how a driver should be hit The fairway wood on the other hand is is more is played more like an iron It is a downward motion that makes the ball climb up So now we want to get ourselves into a strong position to where we're going to mean Get to our left and lean to our left a little bit through impact So taking a small divot or a brush of the turf is an important aspect of hitting your fairway wood So a lot of players as our speeds get slower A three wood is very difficult to hit So it takes a little bit more high speed to hit a three wood that's in that 15 degree range of loft So a lot of players will need a little bit more loft So it's okay that you play with a call it a four wood or a five wood when we're getting into more 17 18 19 or 20 degrees of loft Everything in those loft categories including a hybrid all need to be hit down at so that the ball will climb up the face So unlike a driver, we want to make sure we get our body to the left a little bit And stand very neutral get the ball just barely forward of center So not too far forward so that we don't hit on top of it We don't want the ball to go down into the ground So we're going to get into a strong position Hold that position to our left and we want the club to come downward and through the ball in that position So again, the the driver is going to be an upswing and your fairway woods are all going to be a downward swing


Meredith Moracovitz and Paolo Neal, yes, we are here because people are missing baseball so much. I thought, why not take a trip down memory lane with your 1998 Yankee squad and play for the NBA? OK, we're pretty good team, that you think, though. Yeah, yeah, that's pretty good that year. How about we play a game called Most Likely? You tell me which teammate is most likely to do the thing that I'm going to ask. So we'll start with Most Likely to pick up the tab at dinner. Let's see, 1998, I'm going to say Derek Jeter. Derek Jeter, really, a young Jeter, really picking up the tab. He wanted to make a footprint, he and Tino and Orhe used to go out a lot and I saw it happen. Now I know you still see Tino, Orhe and Derek probably occasionally. Who would pick up the tab now? Jeet better pick up the tab, you know, we used to play a game, it was funny, you would throw credit cards out there and the waiter would pick one and whoever he picked, you know, you'd kind of sort them like cards so you can have a good day or a bad day. A little credit card roulette, I like it. Right. Who would be most likely on that team to miss the bus? Bernie. That's a no brainer. Bernie could be, Bernie didn't know what city or what time it was, half the time anyway. So yeah, definitely Bernie. I also heard through the grapevine that he liked to take naps as well. So he'd fall asleep during the day before he was supposed to get the bus. Exactly. He'd fall asleep on the bus or five minutes before the game. It's just people have different personalities and different schedules. Bernie was on his own, lead. Pretty remarkable too with such a laid back attitude, the intensity he had and how skilled he was when he was playing, the preparation was so different that I imagine the way you prepared. Yeah. I mean, if you look at, like I said, different personalities, different things, Bernie could be playing the guitar five minutes before he went out for a World Series game or he could walk out after he just struck out and lost the game like nothing happened because he knew he was good enough to, you know, to get it together by tomorrow, which the rest of us would be pulling our hair out, thinking we may never get another hit. Now the Yankees have always been like a family and most baseball teams are. Oftentimes you see kids running around the clubhouse. Who on that 98 team was most likely to have their kiddos in the clubhouse? Pettit had his kids in the clubhouse a lot. I had my kids in the clubhouse a lot.  That's pretty awesome. And I can't imagine being a kid, being around that and able to grow up with that type of atmosphere all the time.  So if the kids were in there, they actually had, you know, conversations. Tim Reigns used to tease my kids. My kids did this day still talk about some of the jokes and the teasing that Tim Reigns did. Oh, that's so cool. How about who was most likely to say something to you when you were on a hot street? Probably Tino. Tino and I used to talk more about hitting than a lot of other players because we were both left-handed and we both faced a lot of the same left-handed pitchers. So we would kind of give each other scouting reports on how they would pitch us. So I had a lot of conversations with Tino about hitting. Who was most likely, if you were going through a little cold period, to say something to you? Don Zimmer. Zim used to tell me all the time, you know, if you don't like this job, I got a concrete guy in Cincinnati, he guarantees I'll give you a job. So Zim always had a way to kind of get under my skin, but he was able to do it just because of his personality and what he was in the scene. Oh my God, that's so funny. How about who is most likely to get a visit from Mr. Steinbrenner? Oh my. Usually, those happen during like a big series. Like if you would go to Boston and it meant a lot, Mr. Steinbrenner would show up. So as far as a meeting, probably the starting pitcher, you know, could have been Clemens, it could have been Yicina, it could have been anybody, but probably the starting pitcher for the night of a big game. Paul, thank you so much for playing along.


Last time we were talking about a interplay between probability statistics and data science. We said that real world is going to have some underlying model, probability model which we are going to capture. So that is where we try to come up with some probability models and then from the real world we observe some data and we analyze the data and do some statistical analysis on that to get the parameters which will further go and help us improve our probability models. So that was just the interplay but now let us get back to our study of the probability. So I want to really go through quickly because some of this as I said is also covering and now I will not get into any examples, I will just go through this notions. Because of you have any issues, just raise your hand, we will discuss that. I should go beyond her, right? Then I will be just ending repeating the same thing, right? Sir, if you do not move many, for example, like 2, 3, 4, 5, 6, 10, okay, let us see. So maybe I will go now, start, maybe after 10, 15 minutes I will ask you the pace and you can tell me, okay, okay, conditional probability. What is conditional probability? Like let us say you have 2 events and I want to know event happening, one particular event happening after you know that another event has already happened. For example, if you take 2 events E and F and probability of event E, given that F has occurred, we are going to write it as P E given F and this event is defined in this way. Probability E given F is ratio of 2 quantities, the numerator is probability of the intersection between E and F divided by probability of F and naturally this definition going to make sense when probability of F is greater than 0, otherwise this ratio is not defined, right? And also you do not want to condition on an event for which likelihood happening is 0, you want to condition on the things which has some positive probability of happening and based on that you want to see what is the probability of other events, okay? So this makes sense, okay? For example, if you are going to roll a dice, a fair dice and you are interested in 2 events, the first event is outcome is event, the second event is divisible by 3. Now if you want to condition, want to understand, okay, event E, F has happened, what is the probability that event E is going to happen? Now if you have been already told that, see either 3 or F has happened, now what is, which one of them is divisible by 2 and which of them is E 1, like the E 1, that event E will happen only if out of 3 and 6, 6 has happened, right? So if 3 and 6 has happened, you already have a, you know what is the likelihood happening of E now? You know that 2 and 4 are not going to happen, only possibility is 6, now your likelihood has changed about the, whether you are going to see E 1 number or not. So and now onwards, sometimes I will also use this notation instead of saying E intersection F, I may simply write it as E F, okay? That already means that, sorry, that it is going to be simply E and F, that means already E intersection F, okay? Now with this, let us, we will get to the notion of independence of 2 events, we are going to say that 2 events are independent, if occurring of one event does not provide any information about the other event, okay? For example, I have, let us say, if it so happens that probability of E given F is same as probability of E, so you see that probability of E, this is like an unconditional probability and whereas this is conditional. So the conditional probability is same as unconditional, means happening of the event F is not providing improving anything about the probability of E and similarly if this is the case here also, happening of E is not improving anything about my knowledge of F. So whenever this happens in a way like observing, this one event is not providing any information about the other, maybe that means there is some kind of independence in this and that is where the independence comes into picture and what we are going to say formally is based on our conditional probability, that is right, that is the type of here, okay? Okay, now if I go with my conditional probability P E given F, this is equals to P E F divided by P F, right? But if E and F are independent, the left hand side is simply equals to P of E. So what this is going to say is now P of F is simply P of E into P of F. So in a way like our intuition about independence is kind of implying that probability of E and F happening together is equals to the product of probability of E and F. Now that is what we are going to take as a definition of our independence. We are going to say that E and F are independent if probability of their intersection is nothing but the probability of the, sorry, is equals to product of the probability. Now naturally, if the two events does not satisfies this, we are going to say that to be dependent, okay? And one trivial thing we need to observe is whenever we are going to talk about E and F, right? Obviously, we need to assume that this E and F, they are not equals to null set. If one of them is a null set, what happens? So this quantity is going to be null set, if let us say E is a null set, E intersection F is going to be null set, probability of a null set is 0, whereas on the other side also probability of null set is also 0. So this also becomes 0, if this is if let us say E is a null set. But then is let us say if I have E null set and some event F, does null set provides any information about F event F happening or not? It may not provide, right? Like I mean null set here, that means if it is null set, the complement that means omega has happened, F is a part of omega, right? F is a part of omega. So it may provide some information. So but according to this definition, they are independent because both left hand side and right hand side is 0. So that is what when you are going to apply this definition, we will make sure that both of them are not equals to null set. If it is null set, it becomes a little bit a vacuous definition. Okay, now example, I will just look into one example, other I will skip. Let us say we have two dice and we know that in this outcome, there are 36 possibilities and now I am interested in event when the outcome is 6. Now let us say I am interested in two events, event E is like outcome is 6. So these are the possible possibilities. It has to be 6, 1, 5, 5, 1, 2, 4, 4, 2 or 6 can happen or something is wrong here, right? And the second event F is outcome, the first outcome is 4. If the first outcome is 4, I mean 4, 1, 4, 2, 4, 3 all of interest to me. Now what I want to now want to see, I want to understand whether these two events E and F are independent or not. So how to do this? First I want to go and apply my definition. I will compute probability of this intersection. So what is the probability of that intersection? The only thing that is common to E and F is 4, 2. And what is the probability of 4, 2 happening? 1 by 36, right? This is 1 out of 36 possibilities. What is probability of E? E is there are about 5 possibilities E can happen in 4 and out 5 out of 36. And what was P of F? That this is 6 out of 36 probability that is 1 by 6. Now if you look into that 1 by 36 is not equals to the product of these two. So naturally as per our definition E and F are dependent. Now can you think about how does if the outcome is 4, how we can see that whether it will tell me something about whether my outcome is going to be 6. So let us say F has happened. F and happen means my outcome, first outcome is 4. Now does this provide me some information whether my 6 can happen? There is a possibility, right? Like if 4 has happened, now that if 2 comes there is a chance that my I can have some, yeah the sum can be 6. So there is already some dependency here and that is kind of getting implied here. And similarly I will not go into this example you can see that instead of 6 I am interested in sum being 7. And if let us say first outcome forms to be 4, is there a possibility that I can get 6? So now my question is this like if my first outcome is 4 and I mean I mean interested in sum to be 7. So what happens in this case like will I get, if first I have 4 then is there chance that still I am going to get 7? So this 2 events are dependent or independent, but what they are saying, if you are going to look into this what is that probability of intersection this is 1 by 36 and P of E and P of F 1 by 6 1 by 6 that is also 1 by 36. So as per our definition what they are independent, but you are saying that is dependent why is it so? So 4 has happened and now if you 4 has happened you know that there is a chance that if 3 happens my sum can be 7, if 4 did not happen something else has happened. So 4 did not happen means it could be 1, 2, 3, 5 or 6 ok. And now does it still if 4 does not happen can you still say that what is your likelihood of happening 7? It could be same right. So event 4 happening or not it is not improving your knowledge about 7 happening. Now can you just go back and apply the same analogy and see that why this is not true here like now we are concluding that these are independent. Why because 4 happening or not there has the same information about some happening but why that is the case why? Do you all agree if 4 did not happen let us say 6 happen can the sums be 6, 6 no right it cannot be 6 something it has to be greater. So that is the kind of intuition. So often intuition may be not apparent whether looking into the two events whether they are going to be dependent or independent, but we will go with our definition. Definition is easy to verify just compute their intersection and see the probability and see that that probability is equals to the product of the each of the events ok fine. Now in collect so often you may have to deal with more than two events maybe you will have to deal with a sequence of events and want to see whether they are independent or not. Now how you are going to check that we are going to extend the definition we had for 2 for the multiple event case and what we are now going to do is if you have this finite set of events even e 2 e 3 up to all the way up to e n. Now we are going to say that they are independent if you take any subset of this n events and if you look into their joint probability that probability should be equals to the product of their individual probability. What we are saying is suppose let us say you have this 1 2 3 up to n and let us take I took some numbers 1 3 and 4 this is the one subset of this right. Now I looked into probability of e 1 intersection of e 3 intersection e 4 this should be equals to probability of e 1 into probability of e 3 and probability of e 4 this should happen. This has now happened on one set one subset of 1 2 3 4 n. But what we are asking is for any subset other subset could be let us say other subset could be 2 5 like that if you take any subset this should happen. Now if you now look into that at least when we want to talk about independence I need at least 2 sets. So when I have only 2 sets I just need to see that whether take them and see their intersection. But now when I have more than 2 there are so many subsets possible and that is what we are doing to do that. So you have to select 2 2 at a time how many possibilities n choose 2 are there you have to take 3 3 how many possibilities n choose 3 are there and at the end all of them. So this will lead to total sum of 2 to the power n and I think there is also minus 1 missing here. So all of you know what is this sum to n choose 0 plus n choose 1 plus n choose 3 like that n choose I if you start from I equals to 0 to n this is equals to 2 to the power n right. So if you just add this I am subtracting n and minus 1 because there is no n choose 0 and n choose 1 term in this ok. And now you see that this is growing like exponentially in n. So if you have more events to check for independence you have to do lot of that combinational things are just exploding. But because of this often most of the times you will be not interested in independence of the hall events but some subset some kind of weaker notion called as pair wise independence. So in this what we are going to do is we take the set of events and look into just to take 2 2 at a time I am only interested in 2 2 and see that their intersection their the probability of their intersection is nothing but the product of their probability if this happens then I am going to say they are pair wise independence. And as you see that in this case I only need to check n choose 2 conditions and it is going to be quadratic in n you can check and often it so happens that obviously it is independent it is implies that pair wise independence but pair wise independence need not in imply that the set of those events are independent.


Welcome to Using Tableau to Visualize Data, part of the research and assessment cycle toolkit project offered by the Association of Research Libraries and made possible by a grant from the U.S. Institute of Museum and Library Services. This presentation, which is part of a module that focuses on organizing and analyzing data, provides a brief introduction about using Tableau for data visualization. We hope the content is useful to library practitioners seeking to conduct assessment projects. At the close of the presentation, you'll find a link to a feedback form. Please let us know what elements were useful to you. This presentation will provide a basic overview of Tableau, what it is, how it can be helpful, and then with some explanations and demonstrations, I'll share some basic steps for connecting data, describe the key features, demonstrate how to create some simple visualizations with filters, and then combine visualizations into interactive dashboards that can be shared with others. If you'd like to follow along with the demonstrations on your own computer, please download the Excel file using Tableau to visualize data that is available with the module materials. You will also need to have Tableau downloaded to your computer. To download a free seven day trial version, visit Tableau.com. Tableau is a data visualization and analysis tool that allows you to easily create interactive visualizations and has a very low learning curve for getting started. Tableau enables you to create dashboards that contain multiple visuals on a single screen. You and your viewers can then apply filters for categorical variables in your data set that allow you to identify trends and nuances in your data. Tableau desktop creator license is needed to take advantage of the full functionality of the Tableau tool. You can try it out for seven days. And there's also a free Tableau app that allows you to create visualizations, though the ability to share your work is limited to doing so on the Tableau public server only. Finally, Tableau allows students to download a 12 month license for free. Tableau allows you to go from a cleaned data source to interactive visualizations. For example, what you see on the left of the screen is a screenshot of an Excel file with library checkout data that was downloaded from Primo, a library integrated system. And there you can create, you can connect your data to Tableau and then create visualizations, such as this dashboard dashboard in a matter of minutes. To use Tableau, you will need to connect to a cleaned data source. If this is a new concept to you, I recommend watching the video video cleaning and organizing data that is part of the same module cleaning and analyzing data in the same training series. In other words, to get started, Tableau requires a connection to a data set rather than being a data set in and of itself. There are many different file types that you can connect to Tableau as shown here on this screen. You can connect to a traditional spreadsheet, statistical file, or a database file such as Excel, SPSS, or Microsoft Access. You can also connect to data that is stored on a server, such as a Microsoft SQL server or a MySQL server. Finally, you can connect to cloud-based data files that may be stored in Box, Dropbox, or Google. In my own work, I most often connect to Excel or Google Sheet files, Google Analytics, or data stored on my organization's MySQL server. For the demonstrations in this video presentation, I'll first connect to an Excel file with library checkout data, create a few visualizations, and then create an interactive dashboard that can be shared with others. Once you connect your data file, you'll see a mirror version of that data source on your screen. You can also connect several files together, so long as they each have a key identifier that can be used to link your files or database tables together. Once you have your data connected, then it's time to open a worksheet and begin creating your first visualization, which requires some familiarity with basic features and terminology specific to Tableau. Visualizations are created in Tableau worksheets. Each visualization will require its own worksheet. The first thing to take note of is the section called Tables. In this area, the fields or the columns in your Excel worksheet are organized into dimensions and measures. Dimensions are most typically qualitative values that are fields that can be used to categorize or segment data. This often includes demographic data, names, dates, or geographic data. Measures contain the numeric quantitative values that can be measured, calculated, aggregated in some way that may result in a sum or an average. Think of the measures as data that can be collected, counted, calculated, or combined in some way to return a single value. In research terminology, you can also think of dimensions as independent variables in measures as your independent variables. So in this screenshot, the dimensions are things like academic year, borrower category, the date, timestamps, etc. The default measure is typically counts. Sometimes Tableau's default sorting of fields into dimensions and measures might be off a little bit, such as the case of the item barcode. Because the barcode came through in a numeric format, Tableau automatically judged it to be a measure or something that we would calculate when in fact it is a dimension, a representation of a specific item that was checked out. This is a simple adjustment. You can simply drag that field up into dimensions and you'll be all set. Every visualization will need at least one measure and either a dimension or a date. The other key features you'll need to create visualizations are rows and columns. You don't always have to have both rows and columns in play at the same time, but you'll need at least one or the other. To get started, you simply drag your fields of interest up into the rows and columns space. If you don't like a particular format, the fields can be easily moved around. The real magic happens in Tableau once you create some simple visualizations and then add filters. In this screenshot, we're looking at a simple visualization of the number of checkouts in the data set that occurred based on a day of week. You can see we use the event date time field and put it into the column section to narrow down the data to day of week. You can also use this same field to select year, quarters, months, weeks, specific dates of a month, hours and more. On the right highlighted in red, you can also see different filters that I added including academic year, term, month, hour and hour category. And then in the upper right corner of your screen, you can also see the show me icon. Clicking on the show me icon opens up a dropdown menu that allows you to see the different types of graphics you can create with your selected dimensions and measures. Options that are grayed out are visualizations that won't work unless you add more or different dimensions or measures. A few of the options that would work nicely to visualize checkouts by day of week formats are on the right side of the screen including text tables, highlight tables, tree maps, pie charts, bar graphs or packed bubbles. So now with that basic overview in mind, let's first take a look at the Excel file we want to visualize to understand what we're working with. So this is the sample Excel file that you can find with your module materials. You can see we have just a few columns or fields we have our date time stamps which include year, month, day, hours, minutes and seconds, our borrower category. Then for the specific items we have a barcode, a title, and a call number, and a format, shelving location. And then finally these final two categories are term and academic year, and those really are associated with the event date time. Just new fields were created by me when I cleaned the data set so that I would be able to filter or organize the data in ways that made sense to me. We'll be connecting our Tableau file to this Excel data file. You don't need to keep your Excel file or your data source open. I just simply wanted to give you a quick peek at what it looks like. So I'm going to go ahead and close this for now. And now I'm going to open up Tableau. And we'll connect to the Library Checkouts Excel file which is very simple to do. This is just the first screen once I open up Tableau. And I'm going to under connect. I'm just simply going to say to a file Microsoft Excel. And now I'm going to find the location where that file is stored. I happen to store mine on the desktop. So I'm just going to click it and say open. And now what you see on the screen is a mirror copy of that Excel file, though we're looking at it in Tableau. So our data files are now connected. Now that the data are connected, let's go ahead and create a simple visualization by clicking on sheet one down here at the bottom of the screen. Take a look at the dimensions and measures. As I said earlier, the item barcode really is a dimension, not a measure. So I'm just going to simply slide that up there up into the dimensions section. So now it's a dimension. So as simple as that. Let's create a bar chart based on checkouts by day of the week. So that's to do that is really quite simple. The first thing I'm going to do is day of the week comes from the date time stamp. So I'm just going to pull this up under columns, just dragging it over. And the default is year, but to change that to other options related to time. I'm just going to click on this downward carrot. And I am going to go slide down here under more, and I'm going to select weekday. So now you see we have weekdays displayed here across the top of our screen. And I'm going to under the measures. They have the little there in green, I'm going to bring up checkout data and slide that under rows. And the actualization that automatically popped into our screen as a line graph. But let's say we wanted that vertical bar chart instead. Under show me the closest thing to the vertical bar chart is the horizontal bars. So let's go ahead and click on that. We can easily, you know, the horizontal bars may perfectly suit your needs but if we wanted them to be vertical bars. So let's go up here to this transpose icon and swap our rows for columns. Just click. And so now we have our days of the week, cross the bottom of the screen and the counts on the vertical axis. So that's looking pretty good. We can increase the font size across all of our tableau work, which I think, you know, the default is always size font size nine, which I always think is a little small. So I'm just going to go to format. And I'm going to format the whole workbook. And I'm going to go to. This is just different. Tableau fonts. I'm going to make the font black. And I'm going to increase the font size to 10. That's just a matter of personal preference. We can change the, if we didn't want to spell off the entire days of the week, we wanted to abbreviate them to save some space. We could simply just right click over any given day of the week at the bottom of the screen and say format. And then over on the left is the format window where it says date Sunday. I'm just going to click and say abbreviation. And so now down on the bottom you see we just have the three day abbreviation. Let's go ahead and give this a meaningful title. So where it says sheet one, I'm just going to double click there and say checkouts by day of week. You can adjust the font if you wish. I'm also down on the bottom I'm going to change that where it says sheet one to day of week also. This is just something that'll help you once you get to the point of creating your dashboards just having some your worksheet tabs to have some names. We can add a couple of filters for good measure. So let's go ahead and do that. Let's, I'm going to click this format. I'm going to close this format box over here on the left, which gets suspect to our tables and dimension. So let's say we wanted to have a filter for year and a filter for month. To do that we're going to use that date time stamp. We're going to click that downward carrot carrot and say show filter. So now you see we have filters here and also shows up over here on the right. And this is on the right is where I'm going to spend most of my time formatting and adjusting. So I'm just going to simply click this downward carrot. I want this to be a dropdown option where my users can pick multiple values. And then I'm just going to edit the title to just be here, just trying to keep things as simple as possible. So it's not to overwhelm our viewers. I'm going to add another filter for month. So I'm going to use that same date time field. And we're just going to add another option for months. This time I'm going to drag date time over into the filter section and select months. And I'm going to say we want the default to just be everything all options.  And then I'm going to show that filter. I'm going to just do some quick modifications to make it look nice. If you want to reorder your filters into a particular order, you just can drag those fields up and down. Let's add two more filters. Let's do the borrower category. And I'm just making it a dropdown list. Maybe I want to adjust this just to be borrower category. And then maybe let's add one final filter for format. And maybe I just wanted to shorten that title as well. So now we have a simple visualization if we want to filter and only look at particular like transactions that happened in 2020 versus 2021. We could do that. We could see what the trends look like for our faculty. Faculty coming in Tuesdays that looks like Tuesdays and Thursdays. If we wanted to look at the seniors, they come in on Mondays and Tuesdays, etc. So we have a simple visualization for checkouts by day of the week. Let's create two more simple little visualizations and then we'll bring them all into a dashboard. This time let's create a visualization based on borrower type and the number of checkouts.  New worksheet. I'm just going to call it borrower type here. Just double clicked and gave it a name. And this time let's create a table that shows the counts of loans to each borrower type and then the percentage of total. So this time I'm not going to worry so much about filters. So long as we have one visualization that has the filters for a set that we want to combine into a dashboard, we only only one of the business needs to have the filters. I'll show you what I mean shortly. So let's work on. Let's give it a table to help us keep track of what we're doing checkouts by borrower type. All right, so let's drag event borrower category to columns like so. Let's drag counts up to rows. And you can see the default here was bar charts don't worry about that quite yet. Let's drag. So we have the counts, but let's try count this checkout count data up here again. And we're going to create, we're going to turn one of these into percent of total so we're going to have a basic count here and we're going to have percent of total for the other. So the second one. We want to change that. So let's just go and click on that downward Carol carrot quick table calculation and percent of total. So now let's go ahead and change this visualization to a simple table. Sometimes tables are are the most optimal. So I went to show me and clicked on the icon that looked like a table. We have a simple table. We have our event borrower categories are percents of total and then the counts. So we're looking pretty good just need to make a few little cosmetic adjustments to aid our viewers make things a little easier for them. The first thing we can do is go to analytics, click on totals, and we're going to add a grand total at the bottom. So now at the bottom you can see that there are 6651 checkouts, and then the percents of total. So each category, the checkouts has a percent of total. If you wanted to change the percent of total and move it over. I'm just clicked on it and dragged it. Just very simple. And maybe I want to change these headers just to shorten up the titles a little I can do that by right clicking and clicking alias. And I'm just going to say count here, just try to minimize some of the visual clutter. And then I'm going to do the same thing right clicking at an alias percent of total. If we wanted to reduce the number of decimal points. We could just hover over one of these figures right click. Save format. Now over here under format font, we could click fields. Select percent of total. It's a percentage. And we want to reduce that to one. If you so right now all of the different borrower category types are listed alphabetically. If you, if there were some particular fields that you just didn't really want to see you could like maybe retirees or cooperative borrowers, you could just right click on any of those. And you could select exclude which is going to exclude them from the entire analysis of this biz, or you could hide them. So if you exclude them, the number, numbers in the totals will be reduced by that. If you're in that data set, or if you hide them, the totals remain the same to just start aren't shown on your screen. I'm going to just go ahead and remove a couple of these that are perhaps of less interest. If you wanted to reorder the names of these fields, maybe you want it to be like this, the freshman, sophomore, juniors, seniors, let's see, let's do grad students, faculty and staff. And then maybe you're a little less interested in some of these other ones I'm going to go ahead and exclude the friends of the library borrowers. I'm going to actually move up early college and distance learning students. So I feel pretty good about that. Let's create one simple last visualization. I'm going to click one last time on new worksheet. Time. Let's do formats. Let's create a packed bubble chart related to format. Very, very easy to do. We are just going to drag up item format to columns counts under rows. Now let's go over to show me and select packed bubbles. Here you can see just gives you read relative sizes so you can see that we have way more books that were checked out compared to visual materials, and this little orange circle is music so not too many checkouts related to music. And I'm just going to say checkouts by item format. So now we have three visualizations. I'm just going to click on labels under marks. I'm going to click on label and say show mark label. And with that in mind, perhaps we don't need this vertical axis anymore. I'm just going to say the select show header. Again, I'm just trying to minimize as much visual clutter as possible. So I'm just hiding some of these things that are maybe obvious and we don't need to have labels for them. Let's return back to our slides for just a moment or two. Once you have a few visualizations that you think make sense to be displayed together on a single screen, you can then create a dashboard. Kind of like the dashboard in your car so you can see multiple things at once. On this slide, you can see I created six different visualizations. Six was more than I wanted to look at it a single time on a dashboard so I elected to create two dashboards I would only be looking at one dashboard at a time. Both of these dashboards are in the same tableau file just will be displayed differently upon clicks. You can set the dashboard so that the filters will apply to all of the visualizations that are displayed. And creating the dashboard and adjusting the filter settings is very simple and I'll show you how. So I'm going to return back to our tableau file. And this time I'm going to select the icon at the bottom of the screen that kind of looks like a window pane that says new dashboard and over on the left. These are the three different worksheets that we have to choose from if we had more worksheets that we created, we could select those that were of interest to us. So I'm just going to over on the left under sheets, I'm just going to drag each sheet over into the active pane. And then we can rearrange as we feel make sense to us. So here I have the day of the week displayed in bars I have the checkouts by borrower type down here in the left, and then I have the formats. I'm actually quite satisfied with that but if I wanted to move things around I certainly could. I could just clicking or clicking on this little visual and just moving it over, or I could move it up, etc. I could create a little separation borders between each of the visuals, so they don't all appear to run together. It's a matter of personal taste I'm just going to do that by clicking on each visual at a time. Then on the left I'm going to select layout and add a border. Maybe I wanted to add a background color. This kind of gives it again a little more visual separation and doing the same thing for each of these other visual visualizations. One more time. And then I can this one already if you wanted to this one already fits the width here and the height.  We can do the same for bubbles and our table. This, this little legend goes to this visual so I'm actually going to slide this over so that things will be kind of side by side with each other. And I want this legend to be more in line with this particular visualization. So I'm going to add a little empty space here. Just going to go to dashboard. Down towards the bottom and going to select blank. And I just added a big blank space. A couple of last things right now the filters only apply to this bar chart. We want them to apply to everything on our screen. So I'm just going to make some simple adjustments here for each filter. I'm going to select the downward carrot, say apply to worksheets. It says right now only this worksheet. But we want to have them apply to all worksheets on the dashboard. So activating the filter downward carrot, apply to worksheets, selected worksheets and all on dashboard. Two more times. So now you can just check things I like to check every filter to make sure I haven't missed anything. So here, nothing is selected. If we wanted 2020 to be selected, or all, this is what we want to be happening. So maybe we want to just see what happened in December or November or maybe everything. We want to look at behavior for particular groups. We could do that. You can see faculty mostly are checking out books. Whereas seniors is a little more balanced here between books and visual materials. And then format, if we just want to look at behavior, comparative behavior for books or music, let's see who checks out the music. Mostly staff or visual materials that could be we have a lot of DVDs, for example. So now we have a nice tiny little dashboard. If you wanted to take a look to see how that would display when it's published, you could go to window and select presentation mode. That eliminates all of the Tableau creation clutter. Everything still works. I'm just going to escape. And then if you wanted to publish it so that it could be shared with others, you could publish it depending upon your preferences. I'm going to return back to the slides to finish up the presentation. Once you feel pretty confident about how things look and work, then it's time to share your dashboards with others so they too can interact with your data. Once you publish your data, and if you want to make any adjustments, you can always go back and make those adjustments republish and then reshare. There are four primary ways that you can share your Tableau dashboards. The most popular and easiest thing to do is publish to Tableau public under your profile. If you do this, be sure your visualization visualizations don't include personally identifiable or sensitive data. Posting to Tableau public will give you a URL that you can share so that anyone you wish may interact with the dashboard. You can put many of our libraries dashboards on Tableau public and then share the link with the entire library team or those who who may find it beneficial so they can explore the nuances in the data on their own. If you don't want to make your dashboard publicly available, you can share access to colleagues who may have a Tableau viewer license. Tableau viewer license carries a monthly fee but allows you to easily share visualization files with select others who have that license. Our library dean and associate deans have Tableau viewer licenses and I often share internal budget dashboards or things related to personnel to those select individuals. I often share a full Tableau workbook files with others to have Tableau creator licenses so they can work on the same files. In this case, you both need to have the creator license to interact with and edit the files. And finally, many organizations pay for a Tableau server. This is the most secure option for organizations. An institution's server will most likely be password protected and may be limited to senior administrators and assessment and data analysts. Costs for the servers is dependent upon core licensing agreements. So to recap Tableau is a wonderful tool for creating visualizations that allow you to create and share interactive visualizations with others. Using visualizations and dashboards with easy to use filters facilitates data exploration in important and nuanced ways. For Tableau to work, it will require a connection to a data source. This could be as simple as an Excel or Google Sheets file or a statistical data file or data that's stored on a server. Visualizations will require both a dimension or a date time field and a measure. Several visualizations can be combined into a single dashboard so you can see the data displayed in several ways at a single time. And then filters can be adjusted so that they apply to all of your visualizations on a single dashboard. And remember, there are many ways that your dashboards can be shared with the most common being via Tableau public, which enables you to share a simple link that anyone can use to interact with your data. And does not require a license. Thank you for viewing this presentation on using Tableau to visualize data. Please use the link provided to complete a feedback form for the usefulness of this information for your purposes. Thank you.


So, in electric cells energy is used to force electrons in the opposite direction that they would normally go, so in the non-spontaneous redox direction, the electrons going in the opposite direction. What it means is that things would normally oxidize, ions had reduced and things that are normally reduced would then oxidize. So we're forcing the electrons in the opposite direction. We can use electrolysis for a few things, we can use it to plate metals onto other metals, or metals onto anything that conducts electricity. We can make active metals from their ions, and we can also make gases from liquids, for example. You can use electrolysis to break up water into hydrogen and oxygen, and that tells us where the name comes from. So, electro for electricity, lysic, lysis is breaking, so breaking using electricity. So here's an example of electrolytic cell. So we've got a copper sulfate solution down the bottom here, two copper electrodes, and we've got a source of electrons being forced in the other way, so this is a battery up here. So we're forcing the electrons in this direction over here, so we're forcing them over to this electrode, and at that electrode we're getting copper ions from the solution plating onto the copper electrode that's in the solution. So because we've got the ions being reduced to copper, so the copper ions are being reduced to copper, that's happening at the cathode, so cathode is where reduction happens. And because we're pushing the electrons over here, we've got a lot of electrons on this electrode, that's giving it a negative charge. If we have a look at what's happening at the other electrode, so this is going to be the anode, copper from the rod is being oxidized to copper ions. So the copper is being oxidized to copper ions there, sitting in solution, and then some of those copper ions will be reduced onto the copper rod. You could use this to plate something in copper, so rather than having a copper rod in here, you could have a graphite sheet, a graphite rod. You could have another metal, so you could have a key, and you could code that key in copper for example. Here's another example, so here we have making sodium. So here you have a molten sodium mix, so this is just sold as being heated up. It has to be molten, not a solution, because the solution won't work. You'd reduce water rather than the sodium. So at the cathode again, we're getting a reduction. The sodium ions from the melts are being reduced to liquid sodium. The liquid sodium would go up in this case because it's less dense than the salt, so you could collect it at the top over here. And the chloride ions over here would be oxidized, so their oxidation is lost. The chloride ions lose their electrons and you make chlorine gas. So chlorine gas would be bubbling up over here. So this is how you make active metals from their salt. So you can use this to make sodium, potassium, lithium, and so on. Some things to remember from those diagrams we saw. In electrolytic cell, the anode is always the side of oxidation, and the cathode is always the side of reduction. That's the same for electrolytic or galvanic cells. What changes though is the science. So because we're forcing electrons in the opposite direction, what would normally be anode negative oxidation if a galvanic cell becomes anode positive oxidation. And over the other side, what would normally be cathode positive reduction becomes cathode negative reduction. So you can still use your mnemonics from the galvanics to help you remember, but you just have to remember that the charge changes over. So in an electrolytic cell, the charge is reversed compared to the galvanic cell.


So far, I have discussed with you various components of a spectrometer starting from beam tailoring at the reactor to detectors but neutron being a spin half magnetic nuclear particle The few more important parameters are the neutron polarization for some experiments and the capability to flip the neutron spin because often in Magnetic neutron scattering we need to polarize the beam of neutrons and Then use it for scattering experiments and sometimes even analyze the polarization of the reflected beam So in this lecture, I will introduce you to neutron polarization and Very briefly about spin flippers because these designs can be intricate and elaborate and if you get In details, then we might not be able to reach the target of neutron diffraction So I will be briefly discussing spin flippers and neutron polarizers Now we know that neutron is a spin half particle a Magnet with minus one point nine one nuclear magneton Which is of course the nuclear moment is much lesser than what we have for electron nearly two thousand times weaker but it's a tiny magnet which can penetrate deep and Sometimes for many magnetic studies We need to polarize the neutron beam That means with respect to some direction the neutron beam will either have plus of spin or minus of spin and Also for such experiments often we need to Flip the polarization of the neutron beam from plus half to minus half or vice versa. So so far The point that I've discussed direction. Yes we get the Direction defined using various kinds of collimeters in pile collimeters as well as solar collimeters We get the energy of the beam defined using monochromators If we want a broad beam then using velocity selectors or even sometimes using filtered neutron beams So direction energy how they have to be defined we have discussed now comes the polarization polarization can be done By various means using drag diffraction from a magnetized crystal using super mirror reflection and also presently a very novel Polarizer called helium-3 transmission polarizer are used in some few Advanced neutron sources. So I will give brief introduction to these techniques Now it is I will prefer to start with an expression for Bragg diffraction from magnetic crystal the derivation of this expression is long So I'll skip that but I will Give you the expression for intensity of the Bragg reflection which has got nuclear part magnetic part and Various terms as I defined So if there is a K is a unit vector along the Momentum transfer and if mu Is the unit vector along the magnetic moment in general? I can consider this Happening from a plane sample then Q is a vector Q is a vector which basically if I take out the component of Mu That is along the K direction then I get this u vector once I define the vector then the Bragg intensity is given as Fn square Plus Q square if m square plus 2 Fn Fn P dot P dot Q P is the polarization of the neutron now this expression. I will explain you term by term So I am talking about a sample. Let me just Try to give us so which is a crystalline sample crystalline sample Which also has got magnetic moments and these magnetic moments are aligned And I am Carrying out a Bragg diffraction from this sample now here the term Fn is the nuclear scattering amplitude Which I had defined earlier to you which was actually It was a coherent scattering length to do by IQ dot rj if you remember The counter part of it is a magnetic scattering amplitude. So that also looks so here you can see this is the Nuclear scattering amplitude which is BJ times to the power IQ dot rj that Q I have replaced it with a G which is a which is a reciprocal lattice vector and then twice pi hx plus ky per cell z is Fn square and There is a thermal term. There's a Debye-Waller factor which I discussed earlier that because of the atom Oscillating around its mean position you have a reduction in the Bragg intensity and That reduction is given by a to the power minus To W where it is W is basically earlier I had discussed it is sigma square q square by sigma is a root mean square displacement similarly Apart from this constant terms which you can just accept for the timing point five G is the London splitting factor J is the angular moment of the nucleus total J value of the nucleus it is same Except for a F which is the magnetic form factor and rest of it is same. So we have very similar terms So there are terms which are square of this and there's an interference term. So this has got This is nuclear term This is the magnetic term and this is the interference term Where P is the polarization of the neutron and q is the vector which are defined just now so now this is the expression of Bragg intensity coming from a certain plane of a crystal with magnetic moment at the sides when we write this We can see now Q is this in case the Q is if the magnetic moment is in plane Then you can see that mu dot K will be zero Then Q is equal to minus mu which is the I mean the unit vector. So Q square Q square is equal to one and Q is equal to plus or minus one When I have in plane The magnetization vector is in plane in that case you see I have got several cases P dot Q can be plus one or minus one and then I Is equal to If n square Plus if m square Q square equal to one I have put plus 2 fn if m fn fm and P dot Q P is the polarization of the Neutron beam. So this is what I wrote I have put Q square equal to one because I have assumed that the magnetization is in plane in that case please note that if polarization Please note that this P is not the P vector. Let me make it capital P. I'm sorry Just make it capital P. So that he did not get confused This is capital P capital P This is not the vector here and this is also capital P This is also capital P so now You can see when Q is one when the the Neutron If it is plus half this P will be one. Let us say P will be one and When it is opposite To the magnetization of the sample it will be minus one in that case when P is plus one I is equal to intensity is equal to fn plus fn Square so this is when the nuclear form factor or nuclear scattering amplitude interferes constructively With the magnetic scattering amplitude when P is minus one That same is equal to fn Minus fm So then they are in opposite acting opposite to each other and They are destroy destroying each other or interfering destructively. I must mention here one thing when I am talking about Magnetic thing there is one F came form factor. Now if you remember Earlier when I discussed Nuclear scattering at that time I said that the nuclear scattering potential is a delta function and the delta function Does not have any drop as a function of Q because it is at R equal to 0 a delta function and whose Fourier transform is one all over Q space Now for magnetism. I cannot say the same thing to understand this fact that Tiny nucleus of femtometa size is here, but the magnetism comes from unpaired electrons Unpaired electrons Electrons so you have nickel Hobart Iron these are 3d elements or you have rare earth switcher 4f or 6f that means the these shells Are basically not filled and that's why I can consider it as a shell classically in which you have a Magnetic moment, but now Delta function is Fourier transform as a function of Q is One everywhere acceptable, but this shell But this has got a finite subscending of the order of angstrom and This falls even faster than the Form factor I calculated for x-rays For an atom because then you consider the whole sphere here. It's a shell. So it will fall fast It will fall fast. So that's why the magnetic peaks or magnetic contribution goes at lower Q's Lower Q's because At high Q at high Q Hi Q the Magnetic form factor form factor Factor Falls Rapidly, please remember this You will get back to this point when he come to actual magnetic neutron diffraction So now after explaining this thing that sample magnetized in plane and Q is equal to minus mu Q square equal to 1 that gives me If the polarization is parallel to Q p dot Q is 1 I have Fn plus fm square constants apart They boost each other and they add up the form factor the magnetic scattering amplitudes when the neutron has opposite polarization in that case they Don't add up But the magnetic part gets subtracted from the nuclear part. So the picture is somewhat like this. This is the Scattering vector perpendicular to the plane. This is the planes which are reflecting the neutrons Not just the external planes of a crystal, but they are the reflecting planes Now if magnetization is in plane, then you have two cases either plus or minus half and they are Intensities are different because one is fn plus fm square other is fn minus fm square Now I have to look for a reflection like we know that in crystallographic Perlens we talk about 1 1 0 1 0 0 2 2 0 reflections So if I get a reflection for which Fn is almost equal to fm then the beauty is that fn minus fm is 0 and Fn plus fm is 2 fn. So we have only one polarization. So in that case This are the planes of The crystal The neutron comes they are magnetizing plane With plus or minus polarization with respect to the magnetization But because fn is equal to fm So the down part goes to 0 and then the back reflected beam has it is polarized This is a Crystallographic polar crystal polarizer the black diffracted neutron is polarized and we can use this polarized beam for further experiment so So this is what I want to say that the high polarization is possible in black reflected beam and the polarization efficiency is defined as i plus minus i minus plus is the Reflected intensity of the up neutron minus is the reflected intensity of the down neutrons and this is given by 2 fn fm Fn square plus fm square or when fn is equal to fm the polarization efficiency will be 1 often it is not exactly same, but they are close and Historically Fe3O4 2 2 0 was the first reflection used for polarization The polarization efficiency was not too high. It was 95 percent FCC cobalt gives very good polarization But I must mention that this is cobalt is COO should be small. This is not Carbon carbon net. This is CO Sorry for this. It's a cobalt cobalt It's cobalt. This cobalt 92 percent and iron for 8 percent Alloy it gives 2 to 2 0 0 plane gives very high efficiency But the issue is that cobalt is a strong neutron absorber. So we lose intensity in absorption At present the Heusler along which is Cu2MNAL and Iron silicon Fe3Si are two materials They have a very similar characteristics as polarizers in both of them the 1 1 1 reflections are matched means Fn is nearly equal to fm and these are used as Neutron polarizing monochromatase. So these neutron Here we not only choose the polarization depending on the Bragg angle We also choose the lambda. So it monochromatizes So these monochromatizes plus polarizer So Heusler alloy is used in one of the magnetic neutron diffractometers at Dhruva So this is about Crystal polarizers where the monochromatization as well as polarization takes place Next I will discuss with you about Mirror-based polarizers. But before that I want to bring to notice one thing Suppose we are doing diffraction from a magnetized sample that means apart from crystallographic long range order There is magnetic long range order. We shall come to later when I deal with specific examples Then using this expression These expressions Fn plus fm square and fn minus fm square when you add them up because the beam is Unpolarized so half the neutrons are coming with up Spin with respect to the sample magnetization half of them are coming with minus of Orientation with respect to the sample and the intensity is half of i plus plus i minus From those expressions and their fn square plus fm square. So even for an unpolarized beam we can find out fm square through fitting processes and we can find out the magnetic structure with an unpolarized beam for a magnetically aligned samples and This is used I would say most of the time this has been used and I will discuss it under the Heading of diffraction from crystallographic samples just diffraction Plus diffraction to find out magnetic structures. Now I talk about mirror based Some neutron polarizers. So one can define refractive it takes of a medium for neutrons. So far we have been talking about the atomic structure of the medium when you talked about Neutron diffraction, but at a much lower Q If I do think of Q Which is of the ordinary say 0.1 angstrom inverse Then twice pi by Q max, let us say twice pi by Q max is about 6 by 0.1 60 angstrom. So for such a low Q scattering experiment the medium does not come as a medium comprising atoms and molecules, but as a uniform medium the way you see the medium in case of light So then in this case We can define the refractive index of a medium for neutron in terms of me if it is a non magnetic sample and I'm talking about unpolarized neutron beam then n is given as 1 minus lambda square by pi Rho into B coherent where lambda is the wavelength of the neutron Rho is the number density of the scatterer and B coherent is the coherent scattering length density in this case you can see for Rho some values of Rho B coherent n is less than 1 n is less than 1 you can write n equal to 1 minus delta Where delta is of the order of 10 to the power minus 6 per most materials materials in case of neutrons that means You can say it is 0.999999 It's that close. This means that since n is less than 1 Comparing it with our experience with light rays traveling from a denser medium to a rarer medium here the any medium having refractive index less than 1 behaves like a Lighter medium with respect to air or vacuum because its refractive index is less than 1 So in case of optics, we know that total internal reflection takes place In case of neutron for most materials total external reflection will take place and since n is given by So for large B coherent large density, this n will be more different from 1 this delta value will increase and that means Our total external reflection will take place up to a larger angle So in general if I say a refractivity profile as a function of q or Theta because q is equal to 4 pi by lambda sin theta Just like life. So reflected intensity up to certain point It will be 1 because total external reflection Takes place and then beyond that critical angle the intensity starts falling So this is a typical reflectivity curve of a medium. So in brief that means neutron Allows the lower especially the long wavelength neutrons or rather low q Scattering experiments or that means at grazing incidence the medium behaves like an isotopic medium of a given row B coherent and Total external reflection takes place so I Have just shown you the Experimental data from a silicon wafer and then In the silicon wafer you can see up to the critical angle the reflectivity is 1 and then it falls actually When I go to large q value that falls as 1 by q to the power 4 known as Fresnel Reflectivity, but that come that comes later, but the fact is that I have a critical angle up to which the Medium reflects neutron totally now Reflectivity is less than 1 if there is a magnetized medium then Similar to what I did in case of Bragg scattering now Apart from be coherent For a magnetic medium. We also have a magnetic scattering length, which is be magnetic and now this be magnetic depending on the magnetization direction with respect to the Neutrons pin can either be plus be coherent or be Minus it can be either be coherent plus be magnetic or be coherent minus be magnetic So refractive indices are different for two different spins of neutron So that means now this angle they draw which I drew here So now I can have two different critical angles For plus for minus this is very interesting and you can see that if I go Beyond this angle one Spin component gets reflected the other spin component doesn't get reflected interesting So I will stop now and Then I will continue with the same thing Well introduced to the now it is for a single medium. I'll talk to about neutron super mirror polarizers What are super mirrors? These are beyond mirrors. I will discuss in the next module