White Paper EEStor Phase 8 Analysis

White Paper
March 12, 2018

 

An Analysis of EEStor’s CMBT-glass Phase 8 Tests Results

 

In our Phase 7 white paper, we explained in detail that EEStor’s CMBT-glass is a lead-free relaxor dielectric. In the Phase 8 press release, EEStor disclosed 1.4 watt-hours per liter (Wh/l) energy density in sample 344-2B. EEStor CMBT-glass samples are typically produced by slicing and lapping samples from thicker sintered pucks so the naming convention of the individual samples follows the rule that, in the case of the Phase 8 results, sample 344-1 is the first slice of the “parent” sintered part 344; 344-2 and 344-3 are the second and third slices of sintered part 344. Thus, the dielectric layers tested by Intertek, Radiant Technologies and MRA Laboratories, were formed of the same material under the same sintering conditions and can be looked at together in a near identical grouping to characterize the performance of this particular dielectric. Below, is a polarization to electric field (P-E) plot for slice 1 of sample 344 (344-1) showing typical relaxor behavior.

We would like to highlight a few characteristics of EEStor’s CMBT-glass dielectric as measured early in January 2018.

 

Table N: VDC Parameters for Sample ID: 344-2B
Measured

Calculated

Electrode Shape: Round
Electrode width (mm): 2.94
Dielectric thickness (µm): 32
Voltage DC (V) Capacitance C (nF) Leakage current (nA) Resistance iR (GΩ) Relative permittivity k Electric Field (V/µm) Energy Density (Wh/l) Time Constant (s)
300 1.21 0.4 750 644 9.4 0.07 908
500 0.90 0.5 1000 479 15.6 0.14 900
750 0.74 0.4 1875 394 23.4 0.27 1388
1000 0.61 0.7 1429 325 31.3 0.39 871
1750 0.41 0.8 2188 218 54.7 0.80 897
2750 0.29 1.8 1528 154 85.9 1.40 443

 

Table N from the Phase 8 Intertek Report shows that the internal resistance of the material (in red) at first grows with field, up to a maximum value of near 2.2 tera-ohms at a field of 54.7 V/microns. As the field increases further, the resistance then slowly starts to go down at a linear rate of about 21 giga-ohms per V/micron, to end up at about 1.5 tera-ohms at breakdown.


The internal resistance value is important because it measures how much the material can resist internal leakage. Both the internal resistance and the capacitance contribute to the self-discharging time constant, which is the time it takes for a capacitor to lose ~86.5% of its stored energy.

Also note how the relative permittivity (k) of EEStor’s relaxor dielectric (in green in Table N above) slowly goes down from 644 to 154 as the electric field E grows from 9.4 to 85.9 V/microns. The k diminishes 76% while the field E grows 9.13 times, so the k shrinks slower than the field grows. That’s important because the energy density (ED) of the material is proportional to the k times the square of the field E.

Energy density (ED) =   k   x   E²   /   813175  (with ED in watt-hour/litre, field E in V/micron)

Therefore, if the k is reduced at a lower rate than the square of the field grows, the ED is growing significantly with higher field.

It can be difficult to find some point of comparison between tested samples, considering how most of the parameters vary from one sample to another. One convenient point of comparison are tests at similar electric fields from sample to sample. For instance, it is interesting to compare sample 344-2B (in blue in Table N above) from the Phase 8 Intertek report to the samples 105-7 and 207-2 (in blue in Table M and P below) at similar field values ranging between 23.4 and 23.7 V/microns.

 

Table M : VDC Parameters for Sample ID: 105-7

Measured

Calculated

Electrode Shape: Round
Electrode width (mm): 6.09
Dielectric thickness (µm): 464
Voltage DC (V) Capacitance C (nF) Leakage current (nA) Resistance iR (GΩ) Relative permittivity k Electric Field (V/µm) Energy Density (Wh/l) Time Constant (s)
11000 0.28 4.8 2292 504 23.7 0.35 642

 

Table P: VDC Parameters for Sample ID: 207-2

Measured

Calculated

Electrode Shape: Round
Electrode width (mm): 6.09
Dielectric thickness (µm): 488
Voltage DC (V) Capacitance C (nF) Leakage current (nA) Resistance iR (GΩ) Relative permittivity k Electric Field (V/µm) Energy Density (Wh/l) Time Constant (s)
11500 0.26 14.4 799 492 23.6 0.34 208

 

Different glasses have been used as binders for these three samples. One can see that the glass selected for sample 344-2 resulted in its k being reduced about 20% relative to that of sample 105-7 and 207-2, from 504 and 492, respectively, to 394. But that 20% reduction in k of sample 344-2 came with a 2.12-fold gain in self-discharged time constant over that of 105-7 (1388 vs 642 second) and a 6.67-fold gain over that of 207-2 (1388 vs 208 second). The time constant improvement is a result of the glass of 344-2 having much higher resistivity than that of the two other glass formulations.

As seen above, at comparable fields, the three samples have rather similar relative permittivity (k), though 344-2 value was deliberately made 20% lower to gain significantly in resistivity. However, one can see that the thickness of the sample has a major impact on the maximum field (and therefore, energy density) that a layer can sustain. As Table Q shows (below), by simply reducing the thickness of the layer of the comparable materials from 466 and 488 microns respectively to 32 microns, the breakdown voltage has been increased three times from approximately 30 V/microns to over 90 V/microns. That’s the main factor responsible for the much higher 1.4 watts-hour/litre energy density of sample 344-2.

Table Q: Breakdown voltage

Measured

Calculated
Sample ID Electrode shape Dielectric thickness (µm) Highest DC voltage of stable C (V) Breakdown DC Voltage (V) Highest Field (V/µm)
105-7 Round 464 12500 13000 28.017
207-2 Round 488 14500 15000 30.738
344-2B Round 32 2750 3000 93.750

 

 

A comparison of 344-2B with commercial capacitors1


The fact that the breakdown strength of EEStor layers goes up significantly as their thickness is reduced is common to a larger number of dielectrics, as can be observed in this chart from this glass manufacturers brochure.

The explanation reads, “Furthermore, the breakdown field strength increases substantially with decreasing glass thickness […]. For ultra-thin glasses, the dielectric breakdown strength can show extremely large values. With an alkaline free glass, breakdown strength of 1200 kV/mm has been measured on 12 µm thick samples.”

It remains a focused objective of EEStor to determine what kind of field and ED the CMBT-glass dielectric can sustain as thicknesses between those of sample 344-2 (at 32 microns) and those of Phase 6 CMBT-polymer layers (around 10 microns) are further explored.

Finally, a point of comparison between different samples at similar fields is evident at around 28 volts per micron. In comparing samples 344-2 (in yellow in Table N above) and the Phase 5 epoxy samples tested by a third party last year, the 344-2 sample features a k of 325 at 31.3 V/microns and a k of 394 at 23.4 V/microns. The MRA Laboratories Phase 5 epoxy sample 1 was 76.1 microns thick and measured 1.42 nF of capacitance at 2120 VRMS in AC, for a k of 42.8 at 27.8 VRMS/microns. The linear interpolation of the 344-2 values above giving a k of 355 at 27.8 V/microns show a gain relative permittivity for this CMBT- glass sample of over 8 times at similar field, over the performance of the epoxy CMBT sample of a year ago.

 

LINKS to:

Intertek Phase 8 Report

http://www.eestorcorp.com/march_1_2018-radiant-phase-7.html

http://www.eestorcorp.com/march_1_2018-mra-phase-7.html

 

  1. Am. Ceram. Soc., 92 [8] 1719–1724 (2009) DOI: 10.1111/j.1551-2916.2009.03104.x
Back to Press