So, let's get started.

I think the time is already 4.16.

So, am I audible at the back?

Okay, so let's continue what we started looking in the pre-recorded lecture.

We are talking about this electrochemical corrosion measurement techniques and we looked

at potentiodynamic polarization and we also briefly looked at the linear polarization

resistance method to measure the corrosion rates.

Today we will be continuing on that line and introduce you to a new technique.

It is not really new technique for this class that is electrochemical impedance spectroscopy.

So before that, I would need to start with the perspective from an electrical engineering

systems perspective that we have some dynamic system here in corroding reaction.

If you take a beaker of electrolyte and immerse your material, it is in a dynamic steady

state with the cathodic reaction that is happening on the surface, which is usually hydrogen

evolution reaction or the oxygen reduction reaction and the metal dissolution.

So they are always equal to each other.

So it is in a dynamic steady state.

So it can qualify as a system to which we can apply a stimulus and get a response out

of it.

So all these corrosion testing methods that was discussed earlier or whatever we are

going to discuss in this lecture and next couple of lectures is going to be having

a particular stimulus and there should be the you apply it to a corroding system and

you get a response out of it.

For example, if you are applying some potential steps as the input, you are going to get

current transients because when you apply a small step of voltage, it stops corroding

and you stop applying the voltage, it comes back to the steady state.

That is how you get these current transient.

And if you ask, use the potential stat to apply a particular current, if you ask the

system to corrode at a certain rate, if you apply an anodic current, then it will want

to get an anodic net current value.

So if you apply that, the potential needs to change because it cannot attain that current

at OCP.

At OCP, the net current is zero.

But if you are applying a net current, say 5 milliampere centimeter square, it cannot

happen at the OCP.

It needs to go up because usually anodic reaction happens above the open circuit potential.

So if you apply plus 5 milliampere centimeter square current and as a square wave here,

you are going to get something like a response in terms of potential.

And the same goes for this potential ramp.

If you ramp it fast, you are going to get something called as cyclic voltammetry, which

is not used really in corrosion systems because we don't want to go such high, fast scan

rates.

This potential ramp was essentially what we were doing when we did the potentiodynamic

polarization and LPR at a very limited range.

We were applying this potential ramp.

We are going back up and going down here.

This is a typical polarization curve for a material that is undergoing pitting corrosion,

where you are applying a positive potential.

It is corroding and then it initiates here and you come back and it repassivates.

We will discuss about pitting and passivity and pitting corrosion in future lectures,

but this is how the cyclic polarization response will look like.

But the system, also in the systems theory, this input and output needs to be connected

by something called as the transfer function that relates the stimulus to the response.

For example, if you have current and potential that they are usually related by Ohm's law,

there is a resistance.

That's what the polarization resistance method was trying to get to that Ohmic potential

that was there.

But if you apply an alternating current source, what you are going to get is not just in

resistance, you are going to get something called impedance.

The system's impedance is the transfer function that describes the behavior of the system

that can be used to predict the response.

If you know this transfer function, because let's say if E by I is equal to R,

if you know this transfer function, that is the resistance, then you can say, okay, if I will get,

apply a particular current, a particular voltage, I can get I is equal to E by R.

I divide the E value by the resistance and I get the output.

So this can be used if I know this transfer function, I can predict the response of the

system to a particular stimuli.

In corroding systems, we are interested mainly in steady state.

Why we are interested in steady state?

Because in real service conditions, the material is not going with the potential stat.

You cannot, you are not going to be polarizing the material.

It would be at its steady state because as the real service environment is something like this,

there is an electrolyte and you are fully immersed or you just have a piece of metal exposed to

humid air.

So there is no electrical connection, no whatever we do in our experiments is not available.

So we want to see this steady state under its own condition.

We do not want to move away from the OCP.

So what we do is because when we try to move the system out of its steady state,

we are going to induce some changes that are not representative of the service conditions

because you can change the surface, you can change some form, some films that might not be

formed under steady state conditions.

So how do we measure that?

How can we get the steady state response?

There are two things that we may do.

Maybe apply a time varying voltage or current very slowly that you are not pushing the system so

fast.

You are still maintaining a local step quasi steady state at each step.

Or you just apply a very small exciting voltage or current because for example in the linear

polarization resistance method, we were going within a range of 20 millivolts from below and

above the OCP so that we are not altering the surface.

So this technique that I am going to talk about today is called the electrochemical impedance

spectroscopy.

It relies on these two strategies.

I am going to apply this time varying voltage very slowly, but also I am going to not perturb

the system far beyond the equilibrium.

So I am going to apply V as a function of E.

It is a sinusoidal wave what we see in alternating current power source.

And we are going to the magnitude, the amplitude, the RMS, the root mean square value is going to

be only 10 millivolts action from the OCP versus the OCP.

So we are not perturbing the system far from the steady state and also we are applying this

steady state thing at a fixed which is also a function of frequency.

What frequency you are applying this voltage transient.

So what we apply is that we apply a sinusoidal wave like you can say V of V is equal to V0.

If you apply the sinusoidal voltage, this is the amplitude, what we get as an output is.

So it is at the same frequency.

The frequency is not changed.

The current output, the current wave is also at the same frequency as the input voltage,

but it is shifted by, there is a phase shift theta or phi whatever some people

write it as theta, notation does not matter.

So this is what we get in an electrochemical impedance experiments that we apply a voltage

and get a current output.

So how do we do this EIS experiment?

As I said, we apply an AC voltage alternating current voltage with a voltage amplitude V0.

That is usually very small.

You are only out of 10 millivolts not perturbing the system at all because you do not want to

change the surface.

So now we know we applied a current, applied a potential and got a current output.

As I said earlier, like with a simple resistance working on Ohm's law, Ohm's law applies here

but now this potential is also a function of this frequency and

the response is also a function of frequency and what we get output is

impedance that is also a function of the frequency.

So what we do is we do this experiment over a range of frequencies.

Start from probably 10 power minus 2 or minus 3 Hertz and go up to 10 power 5 Hertz.

This is the omega value.

We can change the frequency of the voltage that we are applying, the sinusoidal voltage.

So this impedance Z is a function of the frequency and it is a complex number.

It is not a resistance.

If you see resistance, it is a real number.

But the impedance is a complex number with a real part that is often called as the

resistive part because resistance is also a particular case of impedance.

So the imaginary part is called, often called as the reactance that is usually associated with the

capacitive component of the capacitive and maybe there might be inductance but in corroding

systems we do not see any inductance like response.

So I will come to the point why we are getting this combination of passive elements like

resistor and capacitor because we described the electrochemical interface because we are

looking at the interface.

The interface nature will determine how this impedance is.

Is this impedance going to be fully resistive or is it going to be a complex number like

combination of resistance and capacitance and what not.

So this impedance acts as this transfer function in the frequency domain

connecting the applied stimulus and the response.

As you can write the response is just the transfer function times the perturbation.

Perturbation was the stimulus.

Similarly, if you get a current response, then this conductivity, the conductance

times the resistance, the voltage, the applied perturbation is the I

because you are applying a DC current, DC voltage.

But if you apply an AC voltage, you are going to get this impedance or this y of

omega that is called as admittance but we will be dealing mainly with the impedance.

We will not talk about admittance anymore.

So as I said, the behavior of these electrochemical systems or corroding systems can be

modeled in an experiment as a combination of these passive elements such as passive

elements in the context of electrical engineering means that one that does not produce power

is a passive element.

So we are not talking about passivity in the context of corrosion.

This is in the terminology that is used in electrical engineering where people call

non-power producing elements in a circuit are called as these passive elements.

So the representative model for this electrical circuit can be determined by

fitting this z of omega to already known response.

We know a resistor has only real component.

If you just have a resistor, z is nothing but R.

There is no imaginary component.

J is the root of minus one and if you had a capacitor, you do not have the resistive part.

There is no real part.

The impedance of a capacitor is fully imaginary.

It is in the imaginary plane where you get this minus.

I do not think it is very clear in the thing z for capacitor.

So, if you have just a pure capacitor, pure capacitor is going to be zero minus j by

omega c.

So, one by omega c is the z minus one by omega c is the z of capacitor.

If you have just a pure capacitor

and if you have an inductor, it is inverse of a capacitor, you get only imaginary component here

too. This is the inductance. C is the capacitance and this is the inductor.

But in corroding systems, we will not see inductance at all.

We usually see because it is due to the nature of the electrochemical interface that resembles

like a capacitor or a combination of capacitor and resistor.

So, we will come to this. We will derive in the example in this class.

By the end of this class, we will derive this parallel combination of resistor and capacitor,

because that is very important in our electrochemical interface, because our electrochemical

interface is neither a pure resistor nor a pure capacitor. It acts more like a leaky capacitor,

where there is a resistance in parallel to this capacitor.

So, this is the plot showing the logarithmic plot showing the magnitude of the impedance

versus the impedance of the capacitor.

The logarithmic plot showing the magnitude of the impedance versus the frequency,

because I said we will be applying during EIS measurements. We apply a range of frequencies

ranging from 10 power minus 2 hertz to 10 power 5 hertz. So, because there is a huge range,

we are scanning through. We always use the logarithmic scale here. And you see a resistor,

it is because resistance has only the real part, it is independent of the frequency.

So, it does not change. You see a constant value of impedance with respect to frequency,

it does not change at all. So, if you see a horizontal line in an impedance plot,

then it means it is a resistor. And the resistor has zero degree phase shift, which means if I

apply a voltage like this, if I apply a V naught, then there is no phase shift. You are going to get

the same phase shift zero for the resistor, because there is no omega t. This is gone.

.

Yeah, in resistive if you just have a pure resistor and apply an AC voltage to that,

you still have this,

there is zero phase shift. So, if you divide by this, this is still a function of time,

because you are applying sinusoidal voltage and getting sinusoidal current, but they are not

shifted by, there is phase shift is zero. The phase shift is zero, if you divide this by this,

you are getting z, but this omega dependent terms will get cancelled and you will just get

the V by I, just the magnitude. Yeah, just similar to Ohm's law. So, resistor, there is no phase

shift. That is why you are getting zero. So, I do not think this is very clear here. So,

the axis here is minus 10 and plus 10 and this is zero. So, even if you change the frequency,

it is not going to respond, because you just have a resistor. So, this is a dummy circuit that I

just have a resistive element and do apply an AC current to it. How I measure the response of

this magnitude of impedance versus the frequency, I do not see any change at all. It is a horizontal

line, because resistance is independent of frequency. But on the other hand, capacitor

always has a slanting line and there is a phase shift. The current leads the voltage by 90 degrees.

There is always this phase shift and because we are plotting the phase shift with respect to the

voltage, it is lagging. Voltage is lagging behind the current by 90 degrees. So,

you usually will see it goes to minus 90. This constant at minus 90. Now the axis is

minus 80 to minus 100 and in between that there is a minus 90. So, the phase shift

is also now independent of the frequency. But the modulus of the

impedance is a function of omega, because modulus of

the frequency is a function of omega. This is the complex number. The modulus of the complex

number is a square plus b square root. But in this capacitance case, I told you this is the

capacitor. So, what I do is, modulus of z is equal to root of 0 square plus minus 1 by omega

whole square. So, what we get is 1 by omega square plus square

and it becomes 2 by omega.

That is why if you plot versus log omega

d, you get an increasing line with a slope of 1. Because for a few capacitors this is the modulus.

Yes, when you have capacitor, it is the characteristic behaviour of capacitor. It shifts the,

it becomes out of phase.

I am not an electrical engineer.

We are using these principles. We know a pure capacitor has 90 degree phase shift.

Probably I can refer some basic textbook and see. But in terms of corrosion class,

I think it is beyond the scope. Why a pure capacitor has minus 90 degree phase shift.

I think it should be associated with the way a capacitor behaves. When you apply voltage

to a capacitor, it charges and discharges. So, I think there is a lag in time between

the time it takes to fully charge the capacitor. So, I think that must be the reason why there is a

lag between the voltage and current. Because you apply voltage and it will not immediately charge.

There is a response time of this capacitor. So, that needs to, it will need to respond in a given

time. Because it accumulates charge and once it is fully charged, it will not further charge

anymore. So, there is some time difference between that. So,

but I will, I can confirm from some basic textbook.

So, let us leave these basic fundamentals, how resistance behaves and the capacitor behaves.

We are interested in the electrochemical interface. So, we said in the first class that

this electrochemical interface behaves like, when we started we were talking about this

Helmholtz model, the double layer and it behaves like a capacitor. But if it were a pure capacitor,

corrosion will not occur. Because if you take a capacitor, you apply voltage. Now it charges,

after charging it remains as such. You cannot, it does not go further. It is not permeable to

charge transfer. Because it is just, both the interface will get charged, both the inner and

outer Helmholtz plane will get charged and nothing will happen. For corrosion to occur, we need

charge transfer to occur. So, we are seeing charge transfer. So, it means that this electrochemical

interface at the, for a corroding system is not a capacitor. So, what is it then?

We have also described the polarization resistance concept. So, then you might think, okay, let us say

the electrochemical interface is a resistor. But the resistor should not be frequency dependent.

But in corrosion we see there is a frequency dependent response. So, it cannot be a pure

resistor also. So, it needs to be something else. So, people have attempted to model this. So,

this is trying to fit the real behavior to an equivalent circuit. So, we are trying to fit it.

It is not there. It is not a capacitor or a resistor. We are trying to fit the behavior of

this electrochemical interface to a combination of some of these electrical elements. We are

using this electrical engineering concepts to understand what is going on at the interface.

Yes, yes. Here we are going to try to fit different models of this equivalent circuit.

And what is the physically reasonable circuit? You can fit the same data to multiple equivalent

circuits. But we need to be very reasonable in terms of rationalizing what kind of circuit will

best represent my physical system. So, we have seen some resistance component when we applied the DC

current. We saw resistance. So, there is polarization resistance that is there. We know there is a

polarization resistance. And we also know that there is this double layer structure. So,

we also know there is some capacitive behavior to the interface. But what combination? Can we put

capacitor and resistor in series or parallel? What will fit the response? It turns out that the

parallel combination of the resistor and capacitor will closely represent an electrochemical interface,

not completely. I will tell why it might not completely represent. So, coming to that point

again, the better description of this interface is a leaky capacitor. It is a capacitor. It charges

when you apply a potential. But at the same time, it allows charge transfer. It leaks. So,

it allows, there is some path, it gives some electron path to transfer current. So,

there should be a resistor. So, what we, the leaky capacitor is nothing but you have a,

because this capacitive part describes the nature where it charges. If it is in parallel,

it still pass, this can pass electron. Electron cannot pass through like this.

There is a resistor, it can pass through. Here it gets charged. So, whatever electron comes,

it is continued by both of them. Like both these processes occur simultaneously together at the

electrochemical interface. I cannot describe it like this, because capacitor will not allow the

electron to pass through it. Just capacitor will charge itself and charge, stores charge.

And otherwise also not possible, because then there is a potential drop already.

But here it will not charge fully. It might not, if you apply a certain potential,

if you apply like this, it will not reach the applied potential, because there is already

an R drop that is in series and if there is, IR is dropped already, then there is nothing else.

But if you consider solution and the resistance is actually the full system,

you always have the solution resistance also that is in series with this parallel framework,

because there is always this potential drop. As I said, the IR drop can, if you apply a certain

potential, your surface might not reach whatever potential you try to apply in potential stack,

because there is a ohmic, there is a resistance of this electrolyte. So, between the reference

electrode and the electrolyte, there is a finite volume of electrolyte that is there,

that has a finite resistance. So, there will be I into R drop. So, the applied potential will not

be actually seen by the reference electrode. So, this element, this RS.

So, this is the total circuit. If you have just an active metal, there is no other passive layer

or anything. The equivalent circuit that best fits the electrochemical system is this.

We will come to that. So, and this other electrochemical processes, for example, as I said,

I already told about the RS, there is an ionic ion transport resistance, that is RS, there is

ionic current. But if you have a passive oxide layer on this metal surface, that acts as another

capacitor, because there is a charge separation that happens in this oxide film. So, you add

another parallel circuit, two pair of RC with the two resistors together.

Because the passive oxide layer, there is also charge separation there. So, it behaves like a

capacitor. And it also allows certain charge transfer to happen. So, it is also a leaky

capacitor. So, you have two leaky capacitors in series with the solution resistance,

you get the full equivalent circuit. We can keep building this equivalent circuit for

more and more complex structures with multiple layers of oxide, with multiple resistances and

multiple capacitors.

That is far, far away from where corrosion is occurring. This dielectric breakdown of these

oxides can happen probably at one or two volts versus your OCP, two, three volt. That is not

realistic service condition for any of the metals. So, yes, there is dielectric breakdown that can

happen at very high potential. If you go beyond that potential, it will break down.

Yes, because for corrosion to occur, you need to allow charge to pass, because metal becomes

metal ion releasing this electron. So, it needs charge to pass. So, it needs to be leaky. It

cannot be just a capacitor. If it was just a capacitor, it will not transfer any charge and

you will not get corrosion at all. But we see corrosion happen. So, it is like reverse thing.

We are observing certain things. What phenomena can explain. So, I am trying to fit, I am not

saying this interface is a capacitor or a combination of capacitor and resistor. It behaves like a

combination of capacitor and resistor. So, we exploit that theory and apply. Maybe it is

much more complex than a simple combination of a capacitor and resistor. But with this,

I can model the response. Then I can construct for this entire circuit, I can construct an

equivalent Z, the impedance. Now, I can predict if my potential is going to shift to a certain

value, what will be the response of the current. So, this transfer function gives me the

predictive capacity, how my system will respond to the stimulus. So, this is the circuit I drew.

This faradik resistance due to the dissolution, there is a charge transfer. This metal becomes

a metal ion. The charge transfer has a resistance. That is what this Rp is. That is the polarization

resistance. This Rp is a charge transfer resistance. People also call it as Rct sometimes,

not Rp. Rp is also called in the East sometimes in the Uttarakhand as Rct, charge transfer resistance.

Rs is solution resistance. That is outside the interface.

Yes, that has a resistance. There is ion. If the ion needs to move through an electrolyte,

this electrolyte is also a conductor. It is an ionic conductor. Ion moves through it.

There is an ionic current. There is some resistance to this ion motion. That is Rs.

Let me clarify.

So, let us consider an interface and there is electrolyte here.

This surface, there is a double layer.

It is a double layer structure which we saw on the interface.

It moves through the electrolyte. A very small angstrom layer.

So, there is ion. Let us say it is pure ion. It needs to cross this barrier layer to come into the solution.

So, this process has a certain resistance to cross this double layer. That is Rp.

And then this ion will move in this electrolyte. That resistance is Rs. So, that is outside,

that is ionic current flow resistance that is outside this interface. So, that is happening in

the solution. That is what Rs is. Solution resistance. This is polarization resistance.

Yes, there is capacitor here. There is a negative charge that is built on here and positive charge

built over here. There is, this is a parallel plate of conductor. Metal is a conductor and this

electrolyte is also a conductor. There is two parallel plates of conductor separated by

dielectric medium. This is a capacitor.

If corrosion is happening, there is always charge transfer.

Corrosion cannot happen without a charge transfer.

Now, if you put this, immerse this piece of metal, immediately it will corrode. So, it is,

you are not going to see any pure capacitive behaviour in the material. Because pure capacitor

does not allow any charge to pass. A leaky capacitor will allow it. The leaky in nature

is coming from this resistive nature. It is not a pure capacitor. That is why we

like to call it as a leaky capacitor. So, if you have modeled this equivalent circuit,

then you know the R value. Then you can use this Stern-Gerri equation that was described in the

last lecture recording. And if you divide by Rp, you can get the I-corr. You do not need to do

any polarization. Just do this EIS, try to get this Rp model to a circuit, try to find this Rp value,

you get the I-corr. Do you measure its elementing in like Rp minimum?

So, you get this response. Let me go back to, yeah, here, what we do is,

that I will come, how we will measure that. I have not come to the part where we measure this Rp.

So, by fitting this behaviour, behaviour, whatever I am telling is, whatever you measure.

So, what you will measure, I will show you in next couple of slides.

So, then from what you measure, you fit it to a circuit. And if you know how to fit it to a

circuit, there is this double layer capacitor and this charge transfer resistance and the

solution resistance. You can calculate all these things from experimental. These are experimental

parameters. But you need to fit it to a circuit first. If you fit it to a circuit, then you can

get this Rp value. What do you mean?

Different material means you will have some series of this parallel capacitor resistor combination.

Because each interface is going to behave like a capacitor. But each interface also needs to

transfer charge. So, you will get these kinds of things, this block, imagine this block.

This block will be repeated in series.

If you have a ceramic material on the reference electrode and the reference electrode is already

there, then you would not have the same circuit for it, right?

It will be different circuit. Different material will have. But the nature of the circuit will be

same. By element what do you mean?

The solution resistance is going to be constant.

You have a single electrolyte. There is nothing over it. There is a metal that is facing this

electrolyte. This interface is just modeled by this. This can be modeled by this circuit.

But if you have another layer, you coated something. You coated, let us say,

I should say it is some alumina, ceramic coating, something or zirconia, whatever.

This is CDL of the metal with metal ceramic interface. Because there is charge separation here

also. There will be charge separation. So, this double layer and charge need to transfer through

this interface also. There is this behavior. In addition, this interface is also going to be,

this is what is in the contact with the electrolyte. You add another one.

This value will be different. This C of this interface and this charge transfer of this coating

solution. This is coating solution.

You will see different response. I will come to that. Be patient.

No, it is just we are fitting it to behave. There is no order.

Because this is a model circuit. This is not a real circuit that is there. But we can make

dummy cells and check what is the response of this particular cell. It will mimic what is

happening in the corroding system. But where? Here. So, if you have a model circuit,

so if you have this kind of coating or a passive film, then using this capacitor

and using the dielectric constant of this medium, we can assess. Because this is going to be a

capacitor. There is a new capacitor that has come to charge separation here. There is a capacitance

here. That capacitance, if you know that capacitance, we can model fit to a circuit with

this capacitance and know the value of capacitor, then you can use this permittivity

constants and the area. You know the area that was exposed. Then you can measure even

estimate the thickness of what is the coating. But you need to fit it to a circuit first.

So, now we need to use this analysis method to analyze what the impedance value is. Because

we are interested in this magnitude of the impedance and the phase shift. So, how do we

measure all these things? Because if you take the total z, it is a combination of the solution

resistance z and there is a parallel combination of capacitor and resistor. So, then you can

write use this parallel circuit law from probably high school and you can use this combination.

The total z as the resistive and the reactive component. Reactive component is either

capacitive or inductive thing. But we are not worried about inductor here. We are only talking

about capacitor.

So, you can play around with your algebra and use this complex conjugate, multiply with it and you

can split the resistor. This Rp can be separated, Rs, Rp and you can get this kind of thing. So,

the of R parallel to C, this is the total impedance of the component that was there just

this part, this circuit. This part of the circuit has a real part that is R by this 1 plus omega

square R square C square minus this imaginary part. Now you add this Rs to it. Rs is already there

and you can measure Rp by just knowing the real part. This is just algebraic manipulation.

So, now you get this. The total impedance is Rs plus this Rp by this factor here and

the imaginary part. This is the reactive part.

So, if you substitute omega is equal to zero, you apply DC current, what will be the response?

You will get Rp plus Rs because this term will go to zero, this omega is going to zero and this

1 plus zero is also zero. So, that will go to full zero and if that becomes zero, it becomes Rp plus Rs.

That is what will happen if you apply a DC current. There is no capacitive behaviour. You cannot see the capacitive behaviour.

Still, electrochemical interface is a capacitor that is getting charged, but you will not see it

because the omega is zero. So, you can understand why in DC current we are not seeing any capacitive

response, why in LPR method we did not see any capacitive component. It is still a capacitor,

but we are not observing the capacitor because it is not, we cannot apply a DC current to a capacitor.

It just becomes as if it is not there. Probably you can consider this part, this circuit was,

this part was open. There is no connection here. So, when omega is zero, it becomes as if there is no connection there.

But mostly graphical analysis is, okay, yeah, omega approaches zero, the C becomes open.

That is what I said and the total Z becomes Rp plus Rs.

And if you short it, if you connect these two things together,

if you connect the positive and negative terminals together, this entire component will vanish.

You will just see the solution resistance. If you apply an infinite frequency, then you will measure

only the solution resistance. You will not see any capacitive or resistive behaviour.

Yeah, and just you can also numerically substitute infinite and see what happens to this equation.

This term will go to zero again. This term will also be zero and you will get only Rs.

Coming to the plot, what do we measure? We have two ways to measure this.

Okay, this is again repetition of what I said earlier in the first part of the slide.

But we represent this data by two methods. One is called this Bode plot. It is a Bode plot.

It is a pair of plots. So, two plots together. We have this log of magnitude of Z.

We calculated what was Z, but we can know the magnitude of Z. The potential stat can tell us

what is the total impedance and the magnitude of the impedance. And there is frequency.

Log scale, as I told you earlier, at high frequency, you are seeing only Rs.

But very high, very low frequency. So, you know what is the value of Rs from this plot.

And you know what is Rp plus Rs. If we subtract that, we will get Rp.

And how do I measure this line as the, where there is a mixed capacitor in this frequency range,

there is a mixed capacitor and in intermediate frequencies, we get this mixed behavior. There

is both resistive and the reactive component can be seen. And now you know that for a capacitor,

of a capacitor, you know this, but how can I measure? So, I take, let us make,

we want to calculate C. So, C is nothing but, but we fix this at 1 Hz. When there is 1 Hz

frequency, then whatever magnitude of resistance I am getting, that is the capacitor. So,

I can estimate the capacitance, the double layer capacitance also from this plot by

extrapolating this to a line where the frequency becomes 1 Hz. And then I can just say the

magnitude of the entire resistance is coming from the capacitor. Just a mathematical manipulation.

There is another interesting plot. That is, you plot the real component of the resistance,

the impedance versus the imaginary component of the impedance. And you get something like a

semicircle. It is called as a Nyquist plot. This body plot also has another, I said the body plot

comes in two, it is a pair of plots. There is theta. Usually you plot it from 0 to minus 90.

The limit is lower, limit is minus 90 and the upper limit is 0. What we have until this,

the 0, because there is no phase shift for a resistor. And

between this region it goes down, minus 90 ideally because of this pure capacitor behavior.

But usually we do not see minus 90 degree at all in the plot. Even though pure capacitor should

have shown minus 90, that is because there is some deviation from this capacitor behavior.

That means it is mixed. It will not be 90. In this region it is not 90, it is something like,

you can go to minus 80, something like that, minus 70. And it gradually varies because there is

also some variation, the lateral variation of capacitor of the interface. Double layer is not

constant capacitance. There is distribution of this capacitor with different time constants and

stuff. The time constant is just the way how long it would take me to fully charge this capacitor.

That is the time constant. So I might have, within the surface, this part might have a different

capacitance than this part. So that can lead to some variation in the behavior.

Coming to this Nyquist plot, what it plots. So what we are plotting is at different frequency,

you are plotting this is the imaginary component and the real component. At different frequencies

you are plotting. In this, if you go to this length from here, here,

this is the magnitude. Magnitude is the length from each point in this Nyquist plot to the origin,

that the length of this plot is the modulus of z. The modulus of impedance is the length of

each point, distance of each point from the origin. And this theta, this is the phase angle.

The angle between this plane and here, that gives the theta phase difference. So in the same plot

we got the modulus as well as theta. Each frequency you have both real component and imaginary

component. You just plot it on this plane. This is a complex plane. So this is minus,

because it is the imaginary part is negative, we saw that. So you plot negative of that so that

you can see it like a positive curve. Take a negative. So you plot it in this plane.

And at omega 4, the real part was fully real. Even in omega 1, you have a mixture of both

resistive and capacitive behavior. So each data point represents z of w at each frequency. The x

axis gives the real component. The y axis gives the imaginary component.

No, this is each point corresponds to a different frequency.

You sample more frequencies. You check at different frequencies. Measure the z.

You can apply whatever frequency you can apply in the potentiostat.

You can fix the frequency in the potentiostat while you are setting up the EIS experiment.

You can say, okay, scan this kind of potential. And usually most modern tools gives you both

Nyquist and the body plot. In some cases, body plot is more straightforward. You can see a lot of

things directly. You see this resistive behavior. I always felt body plot is more comfortable to

use than this Nyquist plot. But I will say what are the advantages of Nyquist plot because

right now when you look at it, it seems like Nyquist plot is useless.

But Nyquist plot also has some use when if you are comparing two materials,

they have only subtle differences. They are not different by because that is an algorithmic scale.

So if the difference is not that much, you will not see difference between two

microstructures or you want to measure impact of different passivation treatment.

If the resistance, the magnitude difference is not that much, this plot might be like this.

You will not see any difference at all. If the changes are subtle, the differences are small,

then you do not see it at all in body plot. I will tell you in what cases this body plot

might be more useful than. But intuitively speaking, body plot is more intuitive plot.

Can you explain how we can obtain the Nyquist plot?

The same data is represented in two ways.

Can you explain how we can obtain the Nyquist plot?

I do not understand the question. Because in the same data, you can represent this data either

like modulus of the impedance versus the log of frequency or you split it into real and

imaginary component, do not take any modulus at all. Just put this real and imaginary component

taken at different frequencies on this plane. You will get the Nyquist plot. So Nyquist plot

and body plot are same data seen in different ways.

They are comparable because they are the same.

Both you mean you can generate body plot and Nyquist plot from the same data. So I do not

understand the need to. Both are same. This is same data. If you have 10,

you can say it is 5 plus 5 or 2 plus 8, it is 10. Because it is same data. It is not different.

Same measurement, same experiment, same data. You represent it. In Nyquist plot, you plot the real

versus imaginary component of this impedance. In body plot, you plot the modulus of impedance

versus the frequency. So the frequency is explicit x-axis. In here it is not explicit.

That is a disadvantage. So I understand Nyquist plot is not very intuitive to

see. But they are same data plotted in two different ways.

I need a board.

So, you have this line again.

So, at the starting point at the lowest value you get the RS.

You can also interpret RS because you know that this resistive part is real, fully real.

There is no imaginary component.

So there are two intersecting points of this aqueous plot.

One is RS.

You can, this will now become useful.

This is RS and this is RP plus RS because we know resistor is purely real.

There is no imaginary part in the resistor.

So we can measure that.

It has to start from zero, it can start from any position right?

No, because this is just the real value.

So real part need not be zero.

The weight needs to be zero to start from.

Need not start from the origin.

Here it is zero.

Both zero, nothing, no response.

That is not there.

Even it.

Now this is again makes sense because distance of a point from the origin, it gives the magnitude.

This is Z.

This is also Z.

This is also Z.

Different frequencies.

And at very high frequencies you are going to get this.

Very low frequencies you are going to get this.

Can't be negative?

Can't be negative.

It cannot be negative.

Resistor cannot be negative.

We have the modulus and the resistance.

Yeah, the modulus is positive.

And if you are considering the real part as resistor, resistance cannot be negative.

Physically also it will not make sense.

If there is a negative resistor, it means it is pushing electrons somehow instead of stopping it.

So you can measure this.

Now you can know Rp and Rs.

And you know what was the maximum omega that you applied.

And this omega max.

Omega max is the point at which this plot is maximum.

Not the maximum frequency you applied.

Or the omega at which the theta is maximum.

Yeah, theta is maximum for a pure capacitor.

So theta max or omega max.

This omega max is Rp times CDM.

You know Rp from this part.

So that's CDM.

So the effect of Rs is clearly seen here because if this plot shifts again, then Rs is increased.

Yeah.

So you can see that the Rp is increasing.

So this is the Rp.

So this is the Rp.

So this is the Rp.

So this is the Rp.

So this is the Rp.

So this is the Rp.

So this is the Rp.

And Rs is increased.

So you can clearly see the Rs here.

And again the disadvantages.

Omega does not appear directly in this plot.

Sometimes like the data is swamping.

Like there is a lot of data.

You are going to do it in linear scale.

So if there are multiple circuits that might be there.

If there is a low impedance component.

If you have a surface film that is not very protective.

Form some small layer that has very low impedance.

You will not see that.

You will think as if there is only one semicircle.

But there might be.

You can fit it through a two semicircle.

There might be thing you might miss it out.

It is actually a combination of two circuits.

There is one high impedance component.

And one low impedance component.

The low impedance component will not be seen.

It will be masked entirely by this high impedance component.

I will show you what happens.

Next.

Yes.

If you have an inductor or something.

Not in corrosion.

Not in corrosion.

But AIS is used in several other fields too.

So you might see non semicircular behaviour.

Even here it is not a perfect semicircle.

It is a compressed semicircle.

If you have a low impedance component.

You can put it in the low impedance component.

And then put it in the high impedance component.

Or like this RS is shifted.

It is only because of the high impedance component.

No, it is because.

RS.

Go L by A.

Now if you get closer RS will go down.

But RS is also dependent on the resistivity.

We change electrolyte RS will change.

RS will change.

If you get closer.

Then it will also change.

Yes.

Okay.

Next.

This plot.

Like I explained earlier.

But it is again repeated in the slide.

That is RS at.

Lower.

RS at higher frequency.

Because as omega tends to zero.

Only the real part survives.

So you get RP plus RS.

At low frequencies.

And high frequencies.

It becomes short circuited.

And you get only the solution resistance.

The effect of frequency is.

Very clearly seen.

And.

We can also see multiple time constant.

Time constant is nothing but for an RC circuit.

It is just RC.

The product of R and C is the time constant.

That is the response time.

We can see that multiple time constant.

What will happen.

So.

I will show you two.

Nyquist plot and Bode plot.

For this.

This dummy circuit.

I have a.

560 ohm resistance.

In parallel with 100 micro farad capacitor.

And there is another.

This can be possible.

When there is.

A film or.

Surface coating.

You can get this kind of layer.

That one layer.

Is having a lower RC value.

The product of R and C.

Is 10 power minus 6 in this case.

This particular.

RC combination.

For the.

Left hand side.

RC combination.

The RC.

The time constant is high.

Here.

You clearly see there are two.

Time constant behavior.

You can clearly see in the Bode plot.

It can clearly see.

Differences in large changes in.

RC value.

Because the resistor.

The resistance is so low.

And the capacitor is also so low.

That I can get this.

Smaller resistance is also captured.

This corresponds to this 10 ohm.

And this corresponds to this.

560 ohm.

I can clearly see.

Multiple circuit elements.

And multiple time constants.

Very clearly from the Bode plot.

If you see the Nyquist plot.

It.

Appears as if it is business as usual.

And the only single plot is seen.

You can't say there is.

Two elements.

From the Nyquist plot.

If you just see the Nyquist plot.

You will not know.

We need to see Bode plot for this.

Okay.

Can you say there are two.

Elements from here.

If you can say probably.

You can write a paper out of it.

Yes.

There is a semicircle.

But there are two.

There is a surface layer. You cannot say there is a surface layer.

Or not from the Nyquist plot.

Because you only see one semicircle.

Where is two semicircle?

Do you see two semicircle?

If you see.

If you saw two semicircle. Then you can say.

Okay. There are two things.

Okay. There is two interfaces at least there.

In the material.

I don't think you will see it.

Obviously.

If one is quite bigger.

This intensity is quite big.

Yeah. You cannot see it. It is not obvious.

That's what I am saying.

Yeah. Zoom in.

But it is easier to see in Bode plot.

No. But.

Really like. If you zoom in.

You might see.

Yes.

At initial values.

But you will not see the other value.

If you zoom in and show that data alone.

You will not know the existence of this data.

The bigger data.

Yes.

You can see.

But.

If you see one part of this circuit.

You cannot see the other part of the circuit.

The full picture will not be visible.

When one oversees.

It just swarms the data.

Because of the linear scale and stuff.

Here because of this logarithmic scale.

You can clearly see.

Large differences.

Now.

You changed it.

The resistance is comparable now.

The RC values are comparable.

Okay. Here also there is two orders of magnitude difference.

But two orders of magnitude difference.

Can still be seen by the next spot.

But it is too low.

For the logarithmic scale to see.

You do not see.

Big difference in the log scale.

Because of the log scale.

On both axis.

There is.

Both.

The frequency and the.

Impedance axis is logarithmic.

So you cannot see.

If the changes are.

Together.

If the RC values are comparable.

Are within two orders of magnitude.

Beyond three orders of magnitude difference.

Between two different.

Circuit elements.

You cannot see in the Nyquist plot.

Now the Nyquist plot is showing.

Two serving circles.

Now the Nyquist plot is useful.

You see where.

Body can be useful and Nyquist can be useful.

Can be little.

Changed because.

What kind of thing is happening at your interface.

That is why we always need to plot these both plots.

So.

To be on safer side.

We can see everything.

Happening together.

Mostly in.

If you see publications.

They will give you both body and Nyquist plot.

From an examination standpoint.

You might be.

Interested in.

Knowing the difference between body and Nyquist plot.

Maybe it will be convoluted.

Because it is a masters level course.

Not directly ask.

Between Nyquist and body plot will not appear in exam.

So.

You can be the circuit elements can be determined.

Either by this graphical analysis.

Or splitting this real component.

And you can also do this numerical analysis.

We can.

Get this raw data.

And fit it to a circuit.

Ask the software.

To a circuit whichever it likes.

But we need to be careful.

It can introduce non physical.

Elements into the system.

If it thinks ok maybe I will fit an inductor here.

Can fit it.

Yeah.

You just do this measurement.

And ask it to fit it.

Fit to some circuit.

You get body plot and Nyquist plot out of the software.

The measurement.

And you ask it to fit to a circuit.

So you get the data first and then fit to a circuit.

That is what happened.

But when I was explaining.

I started from the circuit elements.

And then went to this data plot.

But in actual reality.

You do this measurement.

And then try to fit it to a circuit.

And determine these individual values of CDL.

But a good fit.

Does not mean.

The model is correct.

You can torture this thing.

To tell whatever you want.

But.

That is you need to justify.

Whatever element you are going to introduce into this system.

You need to justify yourself.

Ok.

Whether is this physical or not.

To the reviewer as well.

To yourself as well.

You just ask your conscience.

Whether I can put this.

Because lot of people have actually put an inductor.

In an EIS fit.

And said.

Oh I am seeing an inductor behaviour.

In a corrosion circuit.

No.

It is a non trivial measurement technique.

But very useful.

Very powerful.

You are not even playing very large potential.

Or something.

But it can give you a lot of insights.

Into what is happening at the interface.

But while it is useful.

You can also use it.

That is what this slide says.

A physical explanation is needed.

If there is no physical explanation in your circuit.

However R square may be 0.99.

Or even 1.

Does not matter.

So now it is fitting this data.

This log Z.

Here.

The fit is good.

Like what is the fit.

And you see the logic.

And you see the logic.

And you see the logic.

Like what is the fit.

And you see the numbers.

Bigger screen.

No.

No.

No.

What is R square.

R square something.

R3 is not what you are supposed to be explaining.

What is the R square of the fit.

The merit of the fit.

Right.

Right.

Okay leave it.

But you can see that the curve is not fully fitting.

The curve.

It is fitting okay actually.

But not completely.

Then what can I do.

The space angle.

Sometimes.

It is not able to fit at higher frequencies.

Like hemicircle.

Cannot fit to a clear hemicircle.

The space angle does not reach a sharp peak.

But rather a broad peak.

But rather a broad peak.

Then there is some problem with the circuit.

But we cannot give more physical interpretation of the circuit.

We have to leave it there.

Because you overfit it.

That will not be physical representation of the system.

Good fit means.

Like.

Like.

Like.

Like.

Like.

Like.

Like.

Like.

Like.

Like.

Like.

But I know.

I know I have a knowledge of this metal.

It is going to passivate.

That should be to passive behaviour.

And if I fit it.

And I am getting only 90 percent fit.

That is fine.

Because I cannot.

I know what is happening in the system physically.

So I can be confidential.

But some cases when you do not know what is happening physically then it is a problem.

Ich weiß nicht, wo man eine Linie mit einem guten und einem schlechten Fett schenkt.

Wenn man keine physischen Reasons hat, dann wird man auch keine Reasons haben, auch wenn es eine star-square ist.

Jede Entscheidung, die man macht, jeden Element, den man in der Strecke betrachtet, muss von Reasons gestaltet werden.

Es gibt eine andere Sache, die die Menschen benutzen.

Die Kapazität ist nicht ein Kapazitor, sondern ein konstantes Fass-Element.

Es ist ein mathematisches Konstrukt, es ist kein reales Kompressor-Element.

Ein konstantes Fass-Element ist ein mathematisches Konstrukt, das an der Kapazität nicht gut fit ist.

Wenn man die Kapazität nicht gut fit ist, hat man diese Funktion.

Das ist die Funktion, die wir nutzen, um diese Daten zu fitten.

Wenn man einen Kapazitor benutzt, dann benutzt man diese Daten.

Für einen Kapazitor, den wir gesehen haben, ist es wie minus J über Omega C.

Anstatt davon benutzt man diese Funktion, um es zu fitten.

Wie kommt dieses Element aus?

Wenn man nur den RC-Zirkus benutzt, dann ist dieser Punkt vermisst.

Aber wenn man den CPE benutzt, dann ist das Daten besser fit.

Aber kann man CPE-Behavior benutzen?

Das ist immer so.

CPE, was es physisch bedeutet, ist so.

Die Reaktion von Reaktionen auf der Fläche ist auf der locallyen Ebene anders,

in verschiedenen Teilen der Fläche.

Also gibt es laterale Verschleißungen von multiple Kapazitoren mit verschiedenen Zeitkonstanzen.

Es gibt verschiedene Resistenzen, weil die Reaktionrate nicht unibundlich ist.

Es gibt Heterogenen auf der Fläche, verschiedene Teile der Fläche können reagieren.

Das ist der Grund für das CPE-Behavior.

CPE ist eine mathematische Funktion, es ist kein echter Zirkus-Element.

Aber CPE kommt aus diesen Varianten.

Oder durch die Dünnheit eines Films, wird ein Veränder in dem Kapazitor.

Wenn man diese physischen Wünsche hat, dann weiß man, dass bestimmte Dinge passiert sind.

Man hat ein ACM, TEM und hat einige Heterogenen gesehen.

Jetzt kann man sagen, dass man sich mit einem CPE-Behavior befinden kann.

Denn physisch weiß ich aus anderen Techniken, dass ich es benutzen kann.

Nein, nein, statt einem Kapazitor verwendest du den Kapazitor mit dem CPE.

Denn Kapazitor befindet sich nicht richtig.

Denn im Kapazitor befindet sich nur ein Kapazitor im Parallel mit einem einzigen Resistor.

Aber es kann viele Kapazitor und Resistenzen geben.

In vielen Fällen würde es passieren, dass man CPE benutzt.

Ja, meistens benutzen wir CPE für gute Strecke.

Aber um zu lernen, werde ich nicht mit CPE anfangen.

Aber ich habe auch gesagt, was CPE ist.

Wenn du CPE siehst, dann musst du verstehen, warum es kam.

CPE ist eine mathematische Funktion, nicht ein physisches Thema.

Man kann einen äquivalenten Kapazitor benutzen.

Wenn du jemanden fragst, ob er den Charges Transfer von der Kapazität weiß,

kann ich diesen äquivalenten Kapazitor von der CPE Funktion verwenden.

Und wir können ihn fixieren.

Es gibt einen Papier, der von Mansfielden ausgesprochen wurde.

Er ist derjenige, der den Charges Transfer von Mansfielden ausgesprochen hat.

Ihr könnt also das Papier überprüfen.

Und wenn ihr Fragen habt, dann können wir das überprüfen.

Ein weiteres Beispiel, ihr könnt die Lösungresistenzen auch beitragen.

Alles von der CPE-Förderung durch die mathematische Manipulation.

So sieht das so aus.

Was wir hier sehen, ist, dass die CPE-Förderung,

das ist nicht eine Zusatzkontrolle,

sondern ein CPE-Element.

In diesem Papier, das sie an den Charges Transfer nennen,

ist es RCT.

Sie nennen es nicht RP.

Hier gibt es ein Beispiel, das ihr referieren könnt.

Das ist ein Beispiel, das wir in der Kapazität sehen.

Ist es Regen?

So, andere äquivalente Zirkus,

die ihr in parallel haben könnt,

gibt es zwei inneren und äußeren Läder.

Die können ihr mit diesen RC-Zirkus befinden.

Und ihr könnt die Nyquist-Plats plotten.

Ihr habt verschiedene Zeitkonstanzen.

Es gibt 150 und 100.000.

So, trotzdem könnt ihr in der Nyquist-Plats plotten sehen,

dass es zwei kleine Zirkus gibt.

Aber wenn es kleiner wird als diese, nein.

Okay.

Jetzt ist es ein noch mehr komplexes System.

Wenn ihr einen Poure und einen Film habt,

hat dieser Poure eine Resistenzversorgung.

Und wenn ihr einen Poure-Solventschluss habt,

dann ist es ein sehr komplexes System.

Und wenn die Resistenz-Reaktionen

an dieser Interfere statt dem Poure passieren,

dann gibt es eine metallische Elektrolyte-Interfere,

die diesen Randal-Zirkus-Behavior hat.

Und das, was in parallel mit dem Kapazitator ist,

weil es ein Film im Rest des Materiales ist,

und ihr nehmt einen Kapazitator hier,

und es gibt eine Resolution-Resistenz hier.

Also, die Zirkus-Behäfte werden kompliziert.

Aber hier kann ich erklären, warum ich einen Kapazitator hier nehm.

Weil es ein Film gibt,

wo es ein Doppellayer, ein Oxide-Film oder ein Polymer-Kotting gibt.

Ich weiß das, das ist warum ich einen Kapazitator in parallel nehm.

Und es gibt eine Resolution-Resistenz des Poures.

Es gibt eine Resolution im Poure, das hat eine Resistenz.

Da ist noch ein RSI, den ihr in die Hand nehmt.

Und ich habe auch diesen bar-aktiven Metall-Elektrolyt-Interface.

Dann nehm ich einen anderen Kapazitator und Resistenz in parallel.

Jetzt nehm ich diese.

Das ist, was die Slide sagt.

Man kann diesen realen Kapazitator und Resistenz verarbeiten,

und versucht, 2EAS auf dieser Dumme Seite zu machen,

und die Daten zu vergleichen, die ihr aus eurem experimentale Metallsystem measured,

und dann vergleichen.

Versuchen, wie viel ihr könnt.

Wir können es nicht erklären. Dann müssen Sie es im Papier schreiben.

Das ist das Beste, was ich mit expla- nablem Elementen machen kann.

Wenn ich einen besseren Fit haben muss, muss ich eine unerklärbare Elemente hinzu-

ich weiß nicht, was das ist.

Aber Sie müssen eine Erklärung haben, denn wir wissen, dass man bestimmte Dinge nur in einer bestimmten Weise macht.

Wenn man eine Komponente hat, die man an der Komponente schützt,

dann muss man die Komponente nicht verwenden.

Man kann die Komponente nicht verwenden.

Ich kann noch etwas anderes hinzunehmen.

Okay, ich will noch einen anderen Kapazitator geben.

Aber wenn ich nicht verstehe, was da passiert ist,

kann ich noch einen anderen Kapazitator hinzunehmen.

Ja, Erfahrung.

Ja, Sie werden besser mit Zeit.

Ja, Sie sollten das Material von anderen Gründen wissen.

Das kann Ihnen helfen, zu sagen, was passiert ist.

Ja, ich komme zurück.

Es ist eine komplizierte Technik, aber in den meisten Fällen sehr nützlich.

Vielleicht kommt AI mit einem besseren Fit, aber es ist nicht intelligent genug,

um physische Elemente zu erzählen.

Wenn es intelligent genug wird, müssen wir vielleicht nicht mehr über AIS-Fits überdenken.

Wir haben in der Ende die Konzentration polarisierter Elemente gesprochen.

Es kann eine Masse-Transport-Limitation sein.

Wenn es eine Masse-Transport-Limitation ist,

dann brauchen wir einen anderen mathematischen Konstrukt,

einen Warburg-Element, der parallel mit dieser polarisierten Resistenz in der Serie gesetzt wird.

Das bedeutet, dass diese Masse-Transport-Limitation,

wenn Sie diesen Warburg-Element haben,

werden die Nyquist-Plots so werden.

Es gibt keine Semicirkel mehr.

Sie werden wie eine Semicirkel gehen,

aber wenn die Masse-Transport-Limitation aufgetreten ist,

werden Sie so werden,

mit einer erhöhten Frequenz.

Wenn die Theta 45° wird,

und der echte Komponent die imaginäre Komponente equaliert,

dann wird es das Warburg-Element genannt.

Es ist ein mathematisches Konstrukt.

Für ein Warburg-Element,

z.D., ist diese Funktion,

dass es eine entsprechende Parameter gibt,

A und B,

sie haben beide echte und imaginäre Komponenten.

Es geht nicht so runter.

Nein, es geht nicht so runter.

Es geht so runter.

Es kommt nicht runter.

Es kommt nicht runter.

Es kommt runter, weil es eine Masse-Transport-Limitation gibt.

Wenn etwas auf der Fläche passiert,

oder wenn wir eine ORR auf der Fläche haben,

oder wenn es eine excessiv metalische Dissolution gibt,

und es nicht ausfügt,

dann wird es ein Salzfilm.

Wenn Sie eine polarisierte Kurve haben,

wenn Sie diese Art von Behinderungen sehen,

das ist ein konstruktives Konstrukt,

das sich als potentielles Independenten macht,

dann bekommen Sie diese Masse-Transport-Limitation.

So, ja, Sie haben gefragt, wie ich weiß, ob die Funktion validiert ist.

Du musst dir etwas über die Causality sagen.

Wenn du keine Causation für diese Verschwindung sagen kannst,

dann kann ich diesen Komponenten nicht benutzen.

Diese Impedanz muss kontinuierlich und finitiv sein,

über eine komplette Frequenzreinigkeit.

Du solltest keine infinite Impedanz irgendwo bekommen.

Wenn du eine infinite Impedanz hast, dann machst du einen Fehler.

Dein Verschwindung ist nicht wert.

Und das System muss stabil sein.

Wenn du diesen IC-Kurrenten nicht mehr verbreiten und

noch immer die Modelle des OCPs verbreiten,

dann wird es stabiler.

Wenn es nicht stabil ist, dann wird es nicht stabiler.

Wenn das OCPs während der Messung verändern,

dann weißt du nicht, was du verbreiten wirst.

Wenn das OCPs nicht konstant sind,

wenn ich das OCPs nicht sehr gut kenne,

dann ist es weg.

Weil du 10 mV versus OCPs sagst,

aber das OCPs selbst verändert sich während der Messung.

Diese Messung, weil wir über eine Frequenzreinigkeit verbreiten,

kann sehr lange dauern.

Für diese 3-4 Stunden Verschwindung.

Wir wollen es stabil sein.

Es sollte linear sein.

Die Sign-Wave sollte in einer anderen Sign-Wave resultieren.

Die Antwort ist keine Sign-Wave.

Wir sind wieder in Problem.

Denn wenn Sign etwas anderes wird,

dann werden wir die Frequenz, die wir mit diesem

Framework verbreiten, nicht verwendet.

Wenn wir eine Sign-Wave verbreiten,

dann sollten wir eine Sign-Wave outputen.

Wir wollen eine Sign-Wave verbreiten,

denn sie sind einfach mathematisch zu handeln.

Die Leute haben EAS auf verschiedene Probleme verbreitet,

wie ein kleines Stahl, eine sehr einfache Anwendung,

ein paar verkleidete Stehlen, Korrosion-Inhibitor,

vielleicht werden sie auf der Stahlversorgung ausgesorgt.

Denn wenn man einen guten Inhibitor hat,

dann wenn man einen Inhibitor zu Elektrolyte gibt,

dann reduziert man die Polarisierungsresistenz

durch Absorption oder eine Veränderung der Stahlkarte.

Dann kann man EAS anstehen, was ein Inhibitor tut,

wie gut es inhaltet.

Wir können auch EAS-Techniken nutzen,

um zu tun, dass die Elektrolyte mit einer hohen Resistenz sind.

Warum? Weil, wenn ich eine große Polarisierung mache,

wenn ich große Stahlkarten habe,

dann, wenn die Resistenz so hoch ist,

dann wird die Erdbeutung so groß,

dass ich keine PDP oder Potentiodynamische Polarisierung

oder andere Maßnahmen machen kann.

Ich muss also auf eine hohe Versorgung der Stahlkarte betreiben.

Ich muss EAS für diese hohen Elektrolyte nutzen.

Dann können wir EAS-Korrosion-Mechanismen illustrieren.

Die Passivfilm-Breitdauer kann sich beantworten.

Man kann sehen, wie weit die Passivfilm-Effekte

und so weiter sind.

Das ist wieder nicht trivial.

Es ist kein triviales Method.

Es braucht viel考量.

Man muss sehr vorsichtig sein.

Man muss sehr sensibel sein.

Man braucht einen guten Ampulier,

der die Frequenzen über eine Range kontrolliert

und die Bezüge von Messungen macht.

Das war's für heute.