TheEEStory.com

1950 was a long time ago in BT research. For example, Feynman in 1963 said Ti could not hardly move so that energy storage in BT was still a mystery. He said the Ba atoms fit loosely, but that they couldn't see how that resulted in high permittivity.

The article appears to be discussing how ferroelectric effects give rise to high permittivity seen with temp change. Feynman states that BT is really ferroelectric despite previous expectations.

The whole discussion of if it's ferroelectric or if the Ti atoms move is irrelevant. There aren't enough electrons in the material to store the energy.

The factor of 8 mentioned by tester is only showing how ferroelectric effect allows Ti to get achieve a high permittivity, not that it stores more energy.

Last edited Wed, 01 Jul 2009, 3:19pm by zawy

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Y_po and EEtom need to continue on this thread :) I BELIEVE it will be there undoing!

Muhahaha Ha!

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Tom - Excellent analysis and great comments.

In your calculations of the energy stored at 350V/um; you got 250J/cc.
When I redid your calculations, I got 1100 J/c.

Can you check your P0? I get 36E-29 (vs your 9E-29)

Another point, If I assume half of the diagonal for the Ti ions to move for maximum polarization, I get 0.875 (3.5A/4A) not 0.75.

Another point, If I assume half of the diagonal for the Ti ions to move for maximum polarization, I get 0.875 (3.5A/4A) not 0.75.

Good assumption. My current theory is poling is intentionally oriented to 111. This is roughly confirmed by DW's "45 degree" statements.

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I received my engineering degree in 1961. There's been a lot of new physics since and I don't think there is a moratorium on new physics as I write.

There's also been a lot of new chemistry as well

EEventually wrote:

Another point, If I assume half of the diagonal for the Ti ions to move for maximum polarization, I get 0.875 (3.5A/4A) not 0.75.

Good assumption. My current theory is poling is intentionally oriented to 111. This is roughly confirmed by DW's "45 degree" statements.

EEv, I don't see how that could work. If I remember correctly, the PET/aluminum patent indicates that poling is done after end cap bonding. Therefore, the applied field will be perpendicular to the plates.

I believe that the morphology of the electrostatic field intrinsic to the unit cell will cause the Ti cation to preferentially shift towards one of the six (oxygen) faces of all the cells in the grain/particle. This shift will impart a dipole moment to the particle that is perpendicular to that face. This in turn will produce a net torque on the lattice that will end with the face of the unit cells (1-0-0) parallel to the plates. Note that this poling step itself implies that each particle is probably a single grain, otherwise the torque behaviour of any particle might be unpredictable, and EEStor needs predictable results.

Seen in this light, I interpreted Weir's comments to mean that all the particles will experience some rotation due to the poling field, and each particle will therefore only rotate a maximum of 45 degrees.

Granted, it's been a while since I read the patent so I might be remembering the process incorrectly...

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ee-tom ORIGINAL CALCULATION wrote:

Arithmetical error and downstream induced errors are highlighted by Technopete

Assume:
qe=Electron charge = 1.6E-19 (SI units)
lattice is 4A =0.4nm = 4E-8cm
Ti ion dynamic charge is +7.5qe.
We get volumetric Ti ion density from
Avogadro's constant * density BatiO3 / molecular no baTiO3 =
6*10E23*6/233 = 1.5*10E22 Ti ions/cc

To verify this we expect one Ti ion per (0.4nm)^3 =
1/(4E-8)^3/cc = 10E24/64= 1.5E22 Ti ions/cc

The max dipole moment per Ti we calculate as:
qe*7.5*0.4*E-9*theta. (SI units) where theta is the fraction of the lattice the Ti ion moves. If the Ti ion moves towards one corner of the lattice cell we have theta=1.5 for translational symmetry. Let us therefore assume theta=0.75 for max dipole moment. Still too large, but it will do. This is equivalent to 3A movement.

qe=1.6*E-19.

So:
P0 = 1.6E-19*0.75*7.5*4E-10 = 9E-29 (SI units)

The polarization density P is:
P = 9E-29 * 1.5E22 (in units of polarization/cc where polarization is SI)
= 1.4E-6

So at 350V/u we have ED (/cc) is
ED = (1/2)E.P = 0.5 * 3.5E8 * 1.4E-6 = 250 J/cc

This is looking more plausible than the previous max value, and comes in a comfortable 1/10 of eestor claimed ED.
...
Perhaps somone could check these calculations!

Kayen wrote:

Tom - Excellent analysis and great comments.

In your calculations of the energy stored at 350V/um; you got 250J/cc.
When I redid your calculations, I got 1100 J/c.

Can you check your P0? I get 36E-29 (vs your 9E-29)

Another point, If I assume half of the diagonal for the Ti ions to move for maximum polarization, I get 0.875 (3.5A/4A) not 0.75.

Tom, Kayen,

Apologies for not checking this sooner.

9E-29 for PO (polarisation per Ti ion) should be 3.6E-28. 9E-29 omitted the multiplier of 4 in 4E-10 for the lattice spacing.

Edit by Technopete 2 August 2009 - Ee-tom's original conclusion of 10% of EESU energy density is correct as the EESU figure comes out around 10,000J/cm3. The ratio in his original post would have been 2.5% rather than 10%

Corrected calculation:-

ee-tom WITH FIRST CORRECTIONS wrote:

Figures corrected by Technopete are highlighted
...
P0 = 1.6E-19*0.75*7.5*4E-10 =3.6E-28 (SI units)

The polarization density P is:
P = 3.6E-28 * 1.5E22 (in units of polarization/cc where polarization is SI)
= 5.6E-4

So at 350V/u we have ED (/cc) is
ED = (1/2)E.P = 0.5 * 3.5E8 * 5.6E-4= 984 J/cc

This ...comes in at 1/10 of eestor claimed ED. Amended by Technopete 2 August 2009 to reflect the true Eestor energy density claim of around 10,000 J/cm3.

This gives an ED of 984 J/cc (call it 1000 J/cc)

Kayen's 1100J/cc is because he has included his factor of 0.875 / 0.75 in his calculation to get 1148 (assumed rounded down to 1100).

10% means that to work, Eestor must have ion movement beyond the unit cell boundaries.

Peter

Last edited Sun, 02 Aug 2009, 5:46pm by Technopete

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Daniel R Plante wrote:

EEventually wrote:

Another point, If I assume half of the diagonal for the Ti ions to move for maximum polarization, I get 0.875 (3.5A/4A) not 0.75.

Good assumption. My current theory is poling is intentionally oriented to 111. This is roughly confirmed by DW's "45 degree" statements.

EEv, I don't see how that could work. If I remember correctly, the PET/aluminum patent indicates that poling is done after end cap bonding. Therefore, the applied field will be perpendicular to the plates.

I believe that the morphology of the electrostatic field intrinsic to the unit cell will cause the Ti cation to preferentially shift towards one of the six (oxygen) faces of all the cells in the grain/particle. This shift will impart a dipole moment to the particle that is perpendicular to that face. This in turn will produce a net torque on the lattice that will end with the face of the unit cells (1-0-0) parallel to the plates. Note that this poling step itself implies that each particle is probably a single grain, otherwise the torque behaviour of any particle might be unpredictable, and EEStor needs predictable results.

Seen in this light, I interpreted Weir's comments to mean that all the particles will experience some rotation due to the poling field, and each particle will therefore only rotate a maximum of 45 degrees.

Granted, it's been a while since I read the patent so I might be remembering the process incorrectly...

Here's the section of the 536 patent:

7466536 wrote:

After completion of the bonding step the aluminum electrode layers at two opposite ends of the multilayer array are connected to one another of the same side after these sides have been abrasively cleaned to expose the aluminum electrodes. A high-conductivity silver-loaded epoxy resin paste with elastomeric characteristic (mechanical shock absorption) is selected to connect the aluminum electrode layers of the multilayer array to the aluminum end caps for attachment by silver-filled epoxy resin.

The completed multilayer components are poled by applying a polarizing electric field across each of the active dielectric layers. Since there layers are electrically parallel within each multilayer array and that these multilayer arrays can be connected in parallel, the applied voltage to accomplish the polarizing electric field can be as high as the working voltage. The components are heated in an oven to at least 180.degree. C. before the polarizing voltage is applied. A temperature of 180.degree. C. and applied voltages of +2000 V and -2000 V for a duration of 5 minutes were utilized in the example of this invention.

You are correct sir. I reread the 2008 patent. Endcaps are on. Now the effect of the field on the particle is with respect to the field strength and distance, right? Particles will still be closest to the plane of the electrode so the endcap contribution to field at the particle is fairly small seeing as the distance between endcaps is comparatively huge.

So then we are left with the notion of which orientation provides the greatest polarization. Correct me if I'm wrong by my understanding is the strongest charge is going to want to go to the strongest unlike charged field. The effect you are looking for would be a preference in bulk, not at the surface.

Note that in the case of 100, the sequencing vertically is cation-anion-cation. In the case of 111, anions line up with anions and cations line up with cations. While the electrostatic moment for all but the Ti+4 might be small, you have no competition for displacement position at 111 other than the repulsion of the like charges. In either case, the preferential torsion will be toward vertical lines of like charges.

... I could be off my rocker too.

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Oh man here we go again.....

Last edited Fri, 31 Jul 2009, 9:09pm by hoarybat

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"Daniel R Plante" wrote:

EEv, I don't see how that could work. If I remember correctly, the PET/aluminum patent indicates that poling is done after end cap bonding. Therefore, the applied field will be perpendicular to the plates.

I believe that the morphology of the electrostatic field intrinsic to the unit cell will cause the Ti cation to preferentially shift towards one of the six (oxygen) faces of all the cells in the grain/particle. This shift will impart a dipole moment to the particle that is perpendicular to that face. This in turn will produce a net torque on the lattice that will end with the face of the unit cells (1-0-0) parallel to the plates. Note that this poling step itself implies that each particle is probably a single grain, otherwise the torque behaviour of any particle might be unpredictable, and EEStor needs predictable results.

Seen in this light, I interpreted Weir's comments to mean that all the particles will experience some rotation due to the poling field, and each particle will therefore only rotate a maximum of 45 degrees.

Daniel

The correct way to look at the effect of poling is based on the formula:-

dE = -f.dx

where E is energy, f is force and x is distance and dx, dE represent small incremental changes.

Rearranging this:-

f = -dE / dx

This should be interpreted that the force on poling will tend to orient the granule in the direction where the total energy is least. See Feynman lectures volume 2 ("Mainly Electromagnetism and Matter") chapter 10 section 10-5 ("Fields and forces with dielectrics") figure 10-9 and equations 10-30 to 10-32 on the force generated when partially inserting a dielectric sheet between two parallel plates with opposite charge.

Strictly poling is to do with orientation, so one ought to use a 3D angle for the orientation of the granule instead of a distance, but this leads to a very similar formula with exactly the same effect and my maths is not up to 3D angles without looking things up.

For a given (and fixed) charge on the plates of the capacitor, the voltage will be highest when the dielectric constant is lowest. Since a change in energy is proportional to the change in voltage (as the charge on the plates is fixed), then the energy will also be highest when the voltage is highest.

For a given charge on the plates, if the dielectric saturates in one orientation (e.g. [1,0,0]) but not in another (e.g. [1,1,1]) then the voltage and energy will be higher in the direction which saturates and the dielectric constant will be lower. There will be a poling force on the granule to orient it in the direction which does not saturate and therefore has least voltage and energy (and highest dielectric constant).

The poling force will tend to orient the granule in the direction of optimum polarisation which corresponds to the minimum energy and lowest voltage for a given charge, but this implies a maximum capability of storing energy since you can add much more charge to the plates withuot exceeding a given voltage.

Most likely [1,1,1] orientation is optimum. Certainly [1,0,0] orientation results in the Ti ion heading straight for the nucleus of the closest oxygen ion, which is likely to give dielectric saturation earlier than [1,1,1]. [1,1,0] orientation is also a possibility. Both [1,1,0] and [1,1,1] could be interpreted as a 45 degree shift from [1,0,0] orientation in line with DW's audio interview.

Regards,
Peter

Last edited Sat, 01 Aug 2009, 11:08am by Technopete

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Technopete wrote:

"Daniel R Plante" wrote:

EEv, I don't see how that could work. If I remember correctly, the PET/aluminum patent indicates that poling is done after end cap bonding. Therefore, the applied field will be perpendicular to the plates.

I believe that the morphology of the electrostatic field intrinsic to the unit cell will cause the Ti cation to preferentially shift towards one of the six (oxygen) faces of all the cells in the grain/particle. This shift will impart a dipole moment to the particle that is perpendicular to that face. This in turn will produce a net torque on the lattice that will end with the face of the unit cells (1-0-0) parallel to the plates. Note that this poling step itself implies that each particle is probably a single grain, otherwise the torque behaviour of any particle might be unpredictable, and EEStor needs predictable results.

Seen in this light, I interpreted Weir's comments to mean that all the particles will experience some rotation due to the poling field, and each particle will therefore only rotate a maximum of 45 degrees.

Daniel

The correct way to look at the effect of poling is based on the formula:-

dE = -f.dx

where E is energy, f is force and x is distance and dx, dE represent small incremental changes.

Rearranging this:-

f = -dE / dx

This should be interpreted that the force on poling will tend to orient the granule in the direction where the total energy is least. See Feynman lectures volume 2 ("Mainly Electromagnetism and Matter") chapter 10 section 10-5 ("Fields and forces with dielectrics") figure 10-9 and equations 10-30 to 10-32 on the force generated when partially inserting a dielectric sheet between two parallel plates with opposite charge.

Strictly poling is to do with orientation, so one ought to use a 3D angle for the orientation of the granule instead of a distance, but this leads to a very similar formula with exactly the same effect and my maths is not up to 3D angles without looking things up.

For a given (and fixed) charge on the plates of the capacitor, the voltage will be highest when the dielectric constant is lowest. Since a change in energy is proportional to the change in voltage (as the charge on the plates is fixed), then the energy will also be highest when the voltage is highest.

For a given charge on the plates, if the dielectric saturates in one orientation (e.g. [1,0,0]) but not in another (e.g. [1,1,1]) then the voltage and energy will be higher in the direction which saturates and the dielectric constant will be lower. There will be a poling force on the granule to orient it in the direction which does not saturate and therefore has least voltage and energy (and highest dielectric constant).

The poling force will tend to orient the granule in the direction of optimum polarisation which corresponds to the minimum energy and lowest voltage for a given charge, but this implies a maximum capability of storing energy since you can add much more charge to the plates withuot exceeding a given voltage.

Most likely [1,1,1] orientation is optimum. Certainly [1,0,0] orientation results in the Ti ion heading straight for the nucleus of the closest oxygen ion, which is likely to give dielectric saturation earlier than [1,1,1]. [1,1,0] orientation is also a possibility. Both [1,1,0] and [1,1,1] could be interpreted as a 45 degree shift from [1,0,0] orientation in line with DW's audio interview.

Regards,
Peter

Pete, do you have a reference that explains why the Ti cation will experience less resistance to total displacement at 400V/um field strength (+2,000V/-2,000V over 10 um) in the [1-1-1] direction vs the [1-0-0] direction? After studying the bond types, degree and polarity of ionic charges, and the probable resulting differential displacements of those charges intra and inter unit cell, it seems somewhat counter intuitive to me that the contribution to bulk permittivity provided by Ti displacement in the [1-0-0] direction would fall faster than, and ultimately overtake, the drop in contribution to bulk permittivity provided by Ti displacement in the [1-1-1] direction. I don't necessarily disagree, I'm just saying I'm finding it hard to make it add up for me.

On a side note, it looks like the dipole moment manifest by mobile charges in the (doped and probably semiconducting) particle would preferentially migrate to the [1-1-1] direction in the particle (the entire lattice as a whole), but only if the particles are more or less cubic during the poling step. In that case, the resultant space/surface charge at a "corner" of the cubic particle would impart a dipole moment that would result in torque under field that would also orient the lattice in the [1-1-1] direction. My only problem with this is that I can't reconcile how cubic particles with the material volume percentages specified in the patent could possibly rotate past each other - they're just packed in too close together, and if the particles are closer to spherical then there won't be any preferential orientation for space charge, but the volume percentages also won't add up.

I hope you don't mind me taking a phenomenological approach to my explanations. I really don't like getting into the math unless there's no other option.

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Pete gave it to us earlier today.
http://theeestory.com/files/Crystal-chemical_as...

A confirmation of the disorder occurring in all structures of barium titanate, except rhombohedral one, has been additionally obtained from first-principle studies of the phase transitions and electronic structure calculations [ref]. All they indicate that the possible disordered structure of the BaTiO3 crystal corresponds to a presence of eight potential wells along the [111] diagonals of the cube....In high temperatures, the crystal attains the cubic structure when the position of the central cation is an average of the all eight stable locations. The crystal transforms to the paraelectric completely disordered nonpolar state.

Thanks again, Peter for this paper.

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Daniel R Plante wrote:

Pete, do you have a reference that explains why the Ti cation will experience less resistance to total displacement at 400V/um field strength (+2,000V/-2,000V over 10 um) in the [1-1-1] direction vs the [1-0-0] direction? After studying the bond types, degree and polarity of ionic charges, and the probable resulting differential displacements of those charges intra and inter unit cell, it seems somewhat counter intuitive to me that the contribution to bulk permittivity provided by Ti displacement in the [1-0-0] direction would fall faster than, and ultimately overtake, the drop in contribution to bulk permittivity provided by Ti displacement in the [1-1-1] direction. I don't necessarily disagree, I'm just saying I'm finding it hard to make it add up for me.

Daniel,

Sorry, I don't have a reference, and no-one would have an answer unless they had access to a computer and could perform some complex quantum mechanical calculations probably taking weeks to run. So you have to make plausible assumptions.

It's not clear what you mean by:-

Daniel R Plante wrote:

the contribution to bulk permittivity provided by Ti displacement in the [1-0-0] direction would fall faster than, and ultimately overtake, the drop in contribution to bulk permittivity provided by Ti displacement in the [1-1-1] direction.

so forgive me if I'm repeating something you understand already, though others may find a clearer exposition useful, and if it is clearer than my original attempt then any flaws will be more apparent.

The explanation using the Feynman logic may not have been very clear. The term "maximum energy" can be interpreted two ways and it is very important to distinguish between them.

1 Maximum and minimum energy relative to granule orientation during poling

This is the tendency of the granule to be oriented during poling in the direction which gives the minimum energy given a fixed charge on the electrodes.

It is only a plausible assumption that the [1,1,1] direction provides more Ti ion movement before dielectric saturation kicks in, but if it is true then for a fixed electrode charge the force will tend to orient the granule in this direction

Using the wikipedia "Ionic radii" topic nominal figures, then in the [1,0,0] direction you have (Ti4+ is 0.60A + oxygen2- is 1.40A) x 2 = 4.00A which is the lattice spacing. This isn't really surprising as it is this distance which sets the lattice spacing. So as soon as the Ti4+ ion moves then you are going to be compressing the lattice or at least subjecting it to significant distortion. If you manage to compress the Ti-O distance much you are going to have overlap of the core electron shells of both ions quite quickly.

If you work out the ionic radii in the [1,1,1] case then the ring of three oxygens from the faces making up a corner of the cell touch too, and, as for [1,0,0] any Ti ion movement will cause overlap of the nominal ionic radii. However, if you view the crystal from the [1,1,1] direction you can see that there is at least a gap between the three oxygens, and that it does not require very much overlap of the outer electron shells of Ti and oxygen to allow the Ti ion to move in this direction. Further, it appears that you can move the Ti ion until it hits the Ba ion with a lower likelihood of there being any overlap of the core electron shells of Ti4+ and O2- (certainly a much lower likelihood than for the [1,0,0] orientation).

The above represents a qualitative argument as to why dielectric saturation would probably set in sooner in the [1,0,0] direction.

Supporting evidence comes from the fact that the "normal" regular cubic paralectric structure is generally postulated to be just a time average of a cubic external box with the Ti ion flitting between the 8 lowest energy positions which are all displaced towards the corners, while the actual centre of the cell is a higher energy position for the Ti ion at which it is never found, or at least never found stationery there. This seems to be known as a "disordered" state and apparently spreads the x-ray diffraction lines which makes it more difficult to work out what is going on in BaTiO3 (which is a wonderful material with lots of great properties and I love it).

If you accept that dielectric saturation occurs later with [1,1,1] then a displacement in this direction will be the lowest energy configuration as it minimises the voltage with a given charge (normal capacitative effect). You have to take a fixed charge to calculate this energy (for the poling orientation), if for no other reason than that is what Feynman does in his example. His suggestion is that this approach very much simplifies the force calculations compared with what would otherwise be a very complex calculation of forces in dielectrics.

During poling probably the CMBT granule starts off spherical and as a single crystal with no defects so all cells in one granule are aligned the same way, with different granules having independent and random orientations.

Poling definitely rotates the granule (as DW said so). Maybe this happens pretty quickly while the granule is still spherical (and thus more easilly rotated) and the rest of the poling time causes the granule to change shape. I'm just guessing on the change of shape, unless you know of any real evidence for it, though it again looks plausible it would happen after the granule had rotated as it seems to be more difficult to accomplish.

Once the granule is poled to [1,1,1] (assuming that is the orientation and not [1,1,0]) then after cooling it will stay fixed in that position, particularly since charging of the capacitor will tend to produce an orientation force in that same direction again. In any case the granule should not rotate when it is cold.

2 Maximum energy density during use as a capacitor

Though the [1,1,1] orientation probably has minimum energy for a given charge, it is also the orientation which gives you the maximum possible stored energy density as it keeps the voltage lower for a given energy stored (higher limit for dielectric saturation helps this), so you hit the CMBT breakdown voltage at a higher energy (because you can pile in more charge on the plates for a given voltage). Further, the increased scope for movement means that you can increase polarisation more before hitting dielectric saturation caused by the overlap of electron shells resisting further movement too strongly.

Ee-tom and I disagree somewhat on the maximum possible Ti ion movement in the [1,1,1] direction, though the true answer is that neither of us knows for sure.

Comments and refinements welcome.

Regards,
Peter

Last edited Sat, 01 Aug 2009, 7:56pm by Technopete

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