 Hello, today we are going to discuss the basic EPR instrumentation, whatever items are used to make an EPR spectrometer. We have seen in earlier lecture that the armour frequency of an electron is given by this, this is the gyromagnetic ratio of electron, this is the magnetic field is the frequency of precession. This gamma E, gyromagnetic ratio gives the frequency in angular frequency unit that is radian per second. If you want frequency normal unit let us say nu E will be gamma E by 2 pi B and we have seen the value of this gamma E by 2 pi is 28.02 gigahertz per tesla. So, you see our typical frequency will be of the order of several gigahertz if the magnetic field is of the order of 1 tesla. So, this frequency comes in the microwave region. So, what do we need to have a spectrometer based on whatever we have understood about the principles of EPR spectroscopy. Let us look at this slide here. We need a source of radiation then we need a sample cell to hold the sample which in this parlance called a cavity. Then we need a magnetic field and also detection system. We also have seen the resonance condition is given as h nu is equal to G E beta E B. This is the G factor, this is both magneton and this is the magnetic field and this is the frequency of resonance. And we have just now said that this frequency comes in the microwave region for typical magnetic field of the order of a tesla. So, here once again to recapitulate our early understanding that we can either vary the frequency and keep the magnetic field constant or vary the magnetic field and keep the frequency constant. Both are possible in principle but in practice it is almost always true that we vary the magnetic field and keep the micro frequency constant. We will see several reasons why that is so. So, we need therefore is fix and vary. So, how will a spectrometer look like a simplest possible and simplest possible spectrometer will look like this. And here we are comparing a normal absorption spectrometer which you must have seen in optical experiment for example, ultraviolet visual spectroscopy, infrared spectroscopy or what not. The source of radiation and the monochromator which chooses a particular frequency then sample cell which is normally called cuvette, radiation goes to this and whatever comes out is measured on detector. Whenever the radiation absorbed by the sample at a given wavelength that change in the signal cinema detector is in a sense spectrum. In that spirit we can think of a simplest EPR spectrometer which will have a source of micro radiation k, radiation comes and falls on a sample which is called sample cell is called cavity and this is kept in a magnetic field north and south and the transmitted radiation is detected by detector. This is all very similar both the cases. Now in case of optical spectrometer we can change the direction of the light we can bend it we can focus it using appropriate optical elements. Let us say you can use lens or mirror we can use any of this optical elements to bring the radiation to the sample and to the detector. But the trouble in EPR spectroscopy is the micro radiation that is used here wavelength of this is pretty long. So, typical lambda for micro is of the order of centimeter. There is a type of spectrometer they normally use as few centimeter wavelength. Now in that case it is very difficult to have an optical element to focus it well is so big that when it goes to any element it gets diffracted very easily. So, you have a source of radiation let us say microwave comes from here but very easily it will go all over. So, compared to again here that I have got the radiation source from an optical element going to the micrometer and this radiation can be easily brought to this sample cell may be with a lens or a banded the mirror. But here the radiation is coming out well very easily gets spread out all over. So, whatever radiation comes out to the sample will be so small that the experiment will be very very difficult to perform. So, the real problem in this micro spectroscopy is how to transmit the microwave. So, for that there are certain tubes which are used to force the microwave to stay inside. So, these tubes which carry microwave are called waveguides. So, here is an example. So, you see the rectangular tube here rectangle across section and the hole here through and through hole if you can see it yeah the hole is seen clearly. So, here the microwave enters here it is forced to stay inside this it does not come out. So, these tubes sometimes it is rectangular it could be also cylindrical these tubes are called waveguide because it guides the radiation inside it. So, whenever we need to bring the radiation from one place to another place I can use different type of this waveguide elements. For example, this is a different length here one is bigger other is smaller. So, you can join these two to make a bigger waveguide and these are their holes here and then this could be screwed appropriately to join. But often we need to bend the microwave radiation in case of optical experiment we use mirror for example, but here you have similarly an arrangement to bend it here bends. So, we can have a microwave which is entering here it can bending in this way. So, that is possible. So, but you see here because rectangular nature the radiation will have certain polarization that is there will be specific orientation of the electric field and magnetic field inside this tube. So, when you want to change the orientation there also tube available which is called the twist here. Here again see the plane of radiation enters here and gets twisted and then because perpendicular to that. Now, naturally the wavelength of the radiation which is going through the tube has to enter or in other words the dimension of the waveguide which is here this dimension decides what sort of radiation can be carried by this waveguide. Now, here the wavelength has to be smaller than the lambda by 2 has to fit here. So, any wavelength which is bigger than that cannot enter here and therefore, cannot be carried out by carried by this waveguide. So, for example, I have another waveguide here you can see the dimension of these are this is different from that one. You can see this is a smaller dimension than this one both ways this is narrower than this one here. So, this can carry microwave whose frequency is higher than the frequency that is carried by this one. So, there are certain names given to this various frequency ranges that can be carried in a different type of waveguide. I have given you example of rectangular waveguide, but there are cylindrical waveguide also possible. For this particular one the inner dimension is you see that unit is inches which is very old fashioned because the micro of technology came into being sometime in 1940s. There at the time this unit was very common and that has been containing since then and the frequency that can be carried by this waveguide ranges from about 8 to 12 gigahertz this trigger that we carried here. Here we give a certain later code to different frequencies that this waveguide can carry. Similarly, this one can carry a frequency which is some let us say 15 to 18 gigahertz higher frequencies carried by this one dimension smaller. So, in the next slide gives you various types of micro frequency and what is the later code for them. So, s x k q e w the representative frequencies 3 gigahertz here 9.5 and then other frequency given here. So, this x band which is here this is called x band. This is most popular frequency used in EPR spectroscopy and corresponding magnetic field is kilo gauss 3.4 kilo gauss. So, again in this table you see the various bands of frequencies one can have spectrometer and correspondingly magnetic field of course, be different x band is most popular q band is also popular which works around 35 gigahertz micro frequency and requires a magnetic field of 12 kilo gauss when w band is also available where the micro frequency goes of 95 gigahertz and works around 35 kilo gauss of magnetic field. Once again x band is the most popular frequency. Next is the source of micro radiation most common source of micro radiation is micro oscillator called Pleistron. It is a vacuum tube inside which electrons are made to undergo acceleration and deceleration and a very simplistic way the inside part of the Pleistron looks like this. There is a filament which is heated and it produces electron. Now, there is a cathode here and there is this is called cathode this is called anode and this electrons are accelerated through this anode at a very high positive potential and then there is another electrode here which is called the reflector and this is kept at negative potential with respect to cathode. So, what is happening here electrons are emitted by the filament is accelerated by the positive anode and goes through this and then it is reflected by the negative potential they applied here. So, electrons sort of goes up and comes down this is the motions it has it is of course very simplistic picture nevertheless because of this acceleration and deceleration electron that are experiencing that produces the micro radiation this anode is also called the beam or the resonator. So, the frequency of oscillation here decides the frequency of the micro that comes out to change the frequency one can change the physical distance between this beam and the reflector this gap is changed there. So, that changes the transit time of the electron from here to there and back here that changes the frequency of time period and changes the frequency of oscillation. Also the frequency of oscillation can be changed by changing the reflector voltage if you increase or decrease that will also change the transit time between these two and that can also change the frequency of oscillation. Now, here depending upon the reflector voltage and the beam voltage the output is going to come. Now, the way class turn behaves not all voltages are allowed here in other words the micro will come out for only for certain allowed voltages of the reflector that is decided by the physical dimension of this. So, we can plot the output of the radiation as a function of the frequency. The frequency of the micro can be plotted here is a function of power. Now, the way the class turn behaves it does not give constant output power as a function of frequency usually it looks like this something like this. Now, micro frequency as I said earlier is decided by the physical dimension between these two is also decided by the reflector voltage. So, if I keep the dimension constant keep on varying the reflector voltage the frequency is going to change. So, this axis could as well be written in terms of the reflector voltage. Now, the here you see then that when the reflector voltage is this and this there is no output of micro only when the reflector voltage is sudden allowed value from this to this the micro power comes out. So, this behavior is characteristic of the class turn and you call this figure that is output power as a function of the reflector voltage is called the class turn mode. Now, class turn can have more than one mode what do you mean by that may look like this for the certain range of voltage. Let us say this could be the minus 300 to minus 400 volt that is from here to here just for sake of our understanding that is the micro power from the class turn as this sort of shape when the reflector voltage goes from minus 300 to minus 400 volt. In other words the voltage because more negative than that there is no output also becomes less negative than that there is no output. But it is possible that for same setting of this one I am get another output of this kind very similar this might be let us say minus 150 volt this will minus 250 volt. So, this is very similar where again the voltage because more negative than minus 250 there is no output a less than minus 150 then there is no output this is second mode the another mode here that is a way a class turn gives more than one mode. Now, what normally chooses that mode which gives the maximum power this voltage is maximum that voltage is chosen here for operation of the class turn other than class turn more modern micro source that is being used in the EPR spectrometer is called a solid state device and that is called a gun oscillator this is a solid state device unlike class turn which is actually based on vacuum tube everything in that is happening here is inside a in a vacuum tube this has no such thing as solid state device or electrons are meant to oscillate because of certain gun effect. We do not go into detail but we will only distinguish the behavior of this versus that one important difference is that the gun out oscillator output as a function of frequency is almost constant. So, that way there is a main difference here. Now, here I say the reflector voltage changes the micro frequency to a certain extent here also see my earlier the voltage that applied to the gun oscillator diode that also changes the frequency of the micro. The next item in the spectrometer is the sample holder or the cavity. Now, cavity is a rectangular box or it could be a cylindrical box where the sample is kept but the important function of these is to ensure that the sample sees the magnetic field of the microwave radiation and not the electric field. You have seen earlier that is the magnetic variable transition which is what we observe in EPR spectroscopy. So, micro cavity functions a very important role it ensures that magnetic variable transition is taking place in the sample. In other words sample must see mostly the microwave magnetic field and little or no electric field because micro also can cause electric field transition and that is not what we are trying to look at. So, two designs are given here this is a rectangular cavity and a cylindrical cavity and then there is a hole kept here we call the iris hole and the waveguide can enter allow the microwave to enter here through this hole. That is the way the waveguide is coupled to the rest of the microwave circuit and usually one uses a screw here by inserting the screw at the appropriate depth one can cause a proper matching of the microwave radiation to the cavity as it is shown here this green object is the screw and you can see the hole through which the microwave can enter here. Now, one can have a cavity which looks like this small hole here another small hole here and radiation this is the waveguide radiation enters here goes through this and through this iris goes to the cavity and again goes out here. So, sample could be kept somewhere here this is called a transmission cavity and the cavity we have shown in this picture here is the radiation comes from here goes through this hole and then gets reflected at the back and then goes out again. So, this is called a reflection cavity. So, we will see that reflection cavity is a lot more useful cavity than this one. As I have said earlier the sample must see the maximum of the microwave magnetic field and not the electric field and the way this cavity helps doing that is to form a sudden pattern of the radiation inside this and some places there will be electric field maximum and some other place there will be magnetic field maximum and that is called the mode of the cavity. So, this mode will depend on the dimension of this cavity and also wavelength that enters here. Now, to understand what a mode is it will be good to take example of common microwave device that you almost all of us use and that is the microwave oven the microwave frequency used in a microwave oven is 2.45 gigahertz and the corresponding wavelength is 12.2 centimeter approximately. So, you see this is a really large wavelength comparable to the food stuff that is used there and in microwave oven we cook food or rather we warm food by placing it in the box and that box is sudden as a town table. So, this keeps moving it. So, the whole box is actually cavity that we have here and how does it form a mode. So, here this is the rectangular box which is the microwave oven and if you see carefully usually at the top right corner there is a rectangular sort of element there through which the radiation from the microwave generator enters and it stays inside and this is the rotating plate. Now, for cooking the food it is electric dipole transition that is used there that is most polar molecule the water for example the most polar molecule that absorbs microwave radiation undergoes rotational transition and then very high rotational frequency it causes the heating. So, it is electric dipole transition. So, here to find out where the electric field is maximum one can do a small experiment to remove the rotating plate then keep a very thin layer of let us say pappard for example or some thermal paper which changes its color from white to black when it is hot and then run the microwave oven for some time then what will happen because it is not turning wherever the electric field the maximum at that place the maximum heating will take place and the color of the paper will change or the pappard may become charred. So, here the experiment which is done and reported in this paper given in this here. So, here mode is in a microwave oven what is done here is that the turn table was removed and the thermal paper was kept and the empty oven was run at 360 watt power for 30 seconds without the rotation and with rotation. And here you see there were these 4 places maximum heating took place and no heating in this region. So, in other words the way the electric field was forming mode inside the box is that these 4 places the maximum electric field was there. So, that is also the reason why it has to be rotated otherwise the food in this white region will not get cooked. So, turn table job is to cook the food uniformly. So, when it turns this uniformly whole surface becomes hot you can do the experiment very easily by using pappard for example. Now, this is an empty oven in other words in this language is a empty cavity and shows the mode pattern of electric field. Now if we put a sample here the sample is called load here 100 ml of water was kept here and load is written there. Here again the same experiment was done where the turn table was removed and you see that mode pattern has changed compare once again here empty cavity and these 4 regions have the maximum electric field intensity. Now just place a little bit of water here immediately mode pattern has changed. So, that is the important lesson for us that if you do anything to the cavity whenever you place sample or put some sample to you or solvent this is going to disturb the cavity and change its mode pattern. So, here after placing water again we turn the turn table and then see again informally it is here. So, this shows the electric field from sudden standing over pattern for a reflection cavity this is very important. So, radiation enters here enters here gets reflected this way. So, now if the dimension has sudden particular relationship to the wavelength of this radiation then it can form standing over pattern. So, in that case the radiation will be stored inside it will not come out of that not only that when the standing forms then depending upon the dimension of this certain places there will be electric field which is maximum and other place magnetic field will be of maximum. Now, let us see what sort of mode pattern these cavities have here is a rectangular cavity dimension is given here that let us say a is the this broader dimension of waveguide this is the B is the narrower dimension and C is the longest dimension here and the iris hole and the coupling screw is shown on the left. Now, for this rectangular waveguide radiation enters here gets reflected and comes out of this. Now, if the wavelength has the certain relationship to the dimension here given by this let us say the dimension A this broader surface is approximately equal to half of the wavelength and B is very narrow so that it is less than half the wavelength and C has the exactly twice the half wavelength. In that case standing over pattern will have this sort of mode electric field lines shown here in red lines this will be forming the standing wave such that it will oscillate in this plane A B plane and the value of the electric field is maximum here and here a minimum at the two surfaces and also the centre of the cavity electrical is maximum similarly the magnetic field modes are given in the blue line magnetic field in intensity maximum at the centre and also maximum at the wall and it is very small nearly 0 at the centre here and then this centre here. So, if you know imagine the rectangular box that magnetic field has exactly maximum intensity here and the surface here and the surface there electric field has minimum intensity at the plane here and here and here. Now, this particular mode you can see that how critical it is related to the wavelength of the micro which you are working. So, this mode is called TE102 in this parlance of EPR spectrometer and T it stands for transverse electric the radiation is moving in this direction electric field is orthogonal to that that is oscillation of electric field is perpendicular to the direction that is why it is called transverse electric and then one stands for this there half one half wavelength is this A dimension 0 half wavelength in B dimension B dimension is so narrow that no half wavelength can fit here and C dimension has exactly twice the half wavelength. So, this rectangular cavity is called therefore, transverse electric 102 mode. Now, you see how carefully this is designed and we can easily figure out now where to place the sample you can place the sample right at the centre of the cavity. So, in this two pipes here this can act as a sample holder right the centre of the sample the electric field is 0 and magnetic field is maximum that is exactly what you need for magnetic dipole transition to take place. So, this is the placement for sample this is sample to you have shown here this tube here is the centre similarly here the sample tube is here ok. Other popular cavity is called a cylindrical cavity this is nothing but a small cylinder through which radiation is coupled through on side iris here the electric field lines are circular in nature. Here a maximum electric field is approximately the centre of this and minimum at the centre and the magnetic field lines are shown in this dimension here is the magnetic field lines are maximum at the centre and this two walls and minimum at the here as well as here. Now, this mode is called again TE because electric field lines are orthogonal to the direction of the propagation of the radiation transverse electric field and 0 1 1 stands for that there is 0 half wave length along this circular direction and 1 half wave length is this direction along along the radius and another half wave length is along this vertical direction. So, the mode is TE 0 1 1. So, this is the cylindrical cavity here again the best place to place the sample for if your experiment is the centre of this here magnetic field is maximum and electric field is minimum that is the way I have shown here sample placement is this centre of the cylindrical cavity. So, both for rectinal cavity or a cylindrical cavity only one particular frequency can form the standing wave inside this. Therefore, it cannot have a variable frequency appear experiment. In fact, this is the single most important reason why the p p s spectrometers are always constructed to work in a fixed frequency mode this is the reason. How well does a cavity store microwave inside there is a quantitative way of stating that in order to understand that let us guess how the deflection of microwave from a cavity depends on the frequency of the microwave reflected power. So, cavity could be a rectangular cavity or a cylindrical cavity let us say we have coupled the microwave and the frequency of the resonant frequency of the cavity and the microwave they are matching either here or here. So, for that condition correction let us say we have coupled the microwave to this cavity or this cavity and the frequency of the microwave matches with the characteristic frequency of the cavity. So, at that time the cavity supposed to store the microwave without reflection at least the reflection should be minimum. So, let us say at the characteristic frequency of the cavity nu 0 let us say this is the reflection here. So, as the frequency of the microwave changes either this way or that way power is going to be reflected from the cavity. So, this will be somewhere here and here see if we keep imagining that as the deviation of the microwave frequency is higher and higher from the characteristic frequency of the cavity the reflection will be more. Of course, we have to keep the input power of the cavity constant. So, the shape of the curve will be something like this. So, when the microwave frequency is very far from the cavity return frequency the power that is reflected will be totally the input power that goes inside. So, this is the input power totally power gets reflected. So, here the quality of the cavity or how well it stores the microwave inside it without reflection is measured in terms of the narrowness of this profile. So, if I call this delta nu then this quality of the cavity it is universally called the Q value Q of Q stands for quality obviously is defined to be this nu 0 by delta nu. So, with this definition it is obvious that the narrower the cavity higher will be the Q value. So, the Q value is a quantity measure of the quality of the cavity is shows how well the micro power is stored how well it is stored. So, if it is narrower then I say that it is better cavity why is that. So, in this slide I have shown this reflection profile of a cavity for 2 different Q values. So, this shows the response of 2 different cavities the red one is sharper and the pink one is broader. So, delta nu for this is smaller than the pink one. So, as the Q is defined to be equal to nu 0 by delta nu this cavity with the red profile is sharper and higher is the Q higher is the sensitivity should be apparent from here. So, this is the place where the cavity is matched with the micro frequency. So, well that there is a reflexes minimum 0 percent and maximum when it is further the maximum away from the nu 0. Now, if there is any disturbance in the cavity or change in the characteristic property of the cavity then for a small change this pink cavity for a small change the reflection from the cavity will be much larger for the red profile than the pink profile back to this for a very small change in this frequency the red is going to reflect a lot more than the pink one. So, any signal which depends on the reflection for the cavity will be more with the cavity has very sharper response. So, that way the sensitivity comes into the instrument. The Q is also defined in this way that is how much power other how much energy is stored in the cavity divided by energy dissipated per cycle. So, the higher the Q the lesser the amount of energy that is lost per cycle. So, it is stores energy much more efficiently if the Q is high. So, these two are actually equivalent definition. So, in a spectrometer the one which has a higher Q that cavity can store energy less than cavity more efficiently. So, the spectrometer also become sensitive because any small disturbance in the cavity because of the absorption of microwave the reflection for the cavity will be correspondingly higher if the cavity is Q is also higher. Now, here these two are reflection cavity and I also said in earlier that this sort transmission cavities were also used early days by the Q of transmission cavities are much much lower than Q one can get for in reflection cavity. Therefore, this is not a very sensitive cavity and therefore, these are not used anymore. Reflection cavities have much higher Q even between these two this is the rectangular cavity and this is the cylindrical cavity Q of cylindrical cavity is about two times higher than this one about two times rectangular cavity. So, the spectrometer that uses a cylindrical cavity will be about two times more sensitive than a spectrometer that uses a rectangular cavity. Let us summarize now what we have discussed in this class. Today we have discussed the following topics the source of microwave need for waveguides and how it restricts the fixed frequency experiment. Then we talked about the role of cavity and the Q value and its importance. We will continue our discussion on the other components of an EPR spectrometer and see how that EPR spectrometer looks like afterwards in the subsequent lecture that is it.