J.Konstapel,Leiden,12-10-2026.

© 2026 J. Konstapel. Quotation with attribution is permitted. Reproduction of the whole requires written permission.

Aanleiding: Delftse microscoop­technologie boekt succes in de vermaarde labs van Harvard, MIT en Google

The perovskite crystal is one of the most versatile structures in materials science. It powers solar cells, ferroelectrics, superconductors and catalysts. This essay examines that structure through the closure rule of the Vacuum.Net theory. Four findings stand out.

First, the perovskite unit cell is an occupation of the trit cube. The chemical formula ABX₃ follows from occupying three of the cube’s four grades. Second, barium titanate passes through all four grades as it cools. The number of variants in each phase matches the number of cells per grade: 1, 6, 12 and 8. Third, the closure rule carries the point symmetry −3m. Perovskites reach exactly this symmetry in their deepest rhombohedral states.

Fourth, and most practical: a ferroelectric perovskite can act as the open wall of a mesh. Its polarisation has three states — positive, zero and negative. This gives a single junction three settings of its asymmetry. The only measured device of this kind has lacked exactly that.

Along the way, the essay corrects one step in an earlier reading of that device. The published curve shows current, not power. At the widest gap, the difference is a factor of more than ten.

2. The net in brief

Picture a fishnet stretched in water. One strand runs everywhere and crosses itself. The strands are under tension. Where strands wind around each other, knots form. These knots are matter. Between the strands lie meshes: openings with a shape and a size. A winding persists only if it returns in phase inside its mesh.

At each crossing, the strand holds one of three values: +1, 0 or −1. This unit is the trit. Three trits form a window. A window is closed when its three values sum to zero, counted modulo 3. An open window carries tension. Only what closes, stays.

Three values in three places give 27 windows. Nine of them close. Three have equal values: (+,+,+), (0,0,0) and (−,−,−). Six have three different values: the six orders of (−, 0, +). The remaining 18 are open.

3. The trit cube

Give each axis of a cube one trit. A value of 0 means the axis plays no part. A value of +1 or −1 means it takes part, with that sign. Each cell (x, y, z) then has a grade: the number of axes that do not read 0.

Grade	Position in the cube	Cells
0	centre	1
1	on the axes	6
2	in the median planes	12
3	at the corners	8

The total is 1 + 6 + 12 + 8 = 27 = 3³.

Apply the closure rule to the cells. A cell closes when x + y + z ≡ 0 (mod 3). Nine cells close. The centre (0,0,0) is one of them. Six plane cells with opposite signs, such as (1, −1, 0), form a hexagon around the centre. The two corners (1,1,1) and (−1,−1,−1) complete the set.

All six axis cells are open; their sum is ±1. Six of the eight corners are open. Six of the twelve plane cells are open.

4. The perovskite cell as an occupation of the trit cube

The ideal perovskite has the formula ABX₃. Its prototype is CaTiO₃. Place the B ion at the origin and take half the cell edge as the unit. The ions then sit on the cells of the trit cube.

Grade	Cells	Occupant	Share per cell	Count	Closed / open
0	1	B	1	1	1 closed
1	6	X	1/2 (shared by 2 cells)	3	6 open
2	12	empty	—	—	6 closed, 6 open
3	8	A	1/8 (shared by 8 cells)	1	2 closed, 6 open

The count gives B₁X₃A₁, which is ABX₃. The perovskite formula is the occupation of grades 0, 1 and 3 of the cube.

Three features follow at once:

• The anion cage stands entirely on open cells. All six X positions have a sum of ±1. The octahedron carries the tension of the cell.
• The rest sits in the middle. B occupies the only closed cell inside the cage.
• The closed hexagon is unoccupied. In the algebra of the cube, the hexagon is the register of rotations: the bivectors, or the quaternion disc. Section 8 returns to this.

5. The fit of the occupant

The A ion sits in the opening between eight octahedra. In the terms of the net, A is the occupant of a mesh. Goldschmidt’s tolerance factor measures how well it fits:

t = (r_A + r_X) / (√2 · (r_B + r_X))

The ideal value is 1. Three titanates illustrate the range, using Shannon radii (O²⁻ 1.40 Å; Ti⁴⁺ 0.605 Å; A in twelvefold coordination):

• SrTiO₃: t = 1.00. The cell is cubic.
• BaTiO₃: t = 1.06. The occupant is too large. The B ion has room and leaves the centre. The crystal becomes ferroelectric.
• CaTiO₃: t = 0.966. The occupant is too small. The octahedra rotate to narrow the mesh. Rotation typically begins near t = 0.97.

The sign of (t − 1) acts as a trit. A positive value means the centre gives up its closure. Zero means rest. A negative value means the rotation register absorbs the misfit. All three outcomes are measured. Their reading as one trit is an interpretation.

6. Barium titanate walks the grades

Barium titanate passes three transitions on cooling. It is cubic above 403 K, tetragonal down to 278 K, orthorhombic down to 183 K, and rhombohedral below that. The polarisation in the three polar phases points along [001], [011] and [111].

Count the symmetry-equivalent states per phase:

Phase	Polarisation	Variants	Grade of the cube	Cells
cubic	none	1	0, centre	1
tetragonal	⟨001⟩	6	1, axes	6
orthorhombic	⟨011⟩	12	2, planes	12
rhombohedral	⟨111⟩	8	3, corners	8

The sum is again 27. On cooling, the titanium ion walks from grade 0 through grades 1 and 2 to grade 3. The number of variants per phase equals the number of cells per grade.

Atomistic simulation adds one detail. Locally, the titanium is displaced towards a corner in every phase. The higher phases are averages: over 8 corners for cubic, 4 for tetragonal, 2 for orthorhombic. The rhombohedral phase is the ground state, with three polar components in every cell.

7. The symmetry of the closure rule

Which symmetries of the cube keep the nine closed cells closed? Any permutation of the coordinates keeps x + y + z unchanged: 6 elements. Reversing all signs turns a sum of 0 into 0, and ±3 into ±3 — both closed: 2 elements. Together these give 12 elements. A single sign change breaks closure: (1, −1, 0) becomes (−1, −1, 0), with sum −2. No larger group preserves the closed set.

This group of order 12, built from coordinate permutations and inversion, is the point group −3m. The full symmetry group of the cube has 48 elements. The index is 48 / 12 = 4: there are four ways to choose which body diagonal is the axis of closure.

The closure rule therefore carries the trigonal symmetry of one body diagonal. Perovskites reach exactly this symmetry in their deepest states:

• the rhombohedral ground state of BaTiO₃, space group R3m, whose point group 3m is the polar subgroup of −3m;
• the a⁻a⁻a⁻ rotation pattern of LaAlO₃, space group R-3c, with point group −3m.

The count is exact. That the coincidence is more than a coincidence is a reading.

8. The rotations, and a negative result

When t < 1, the octahedra rotate. Glazer’s notation gives each axis a⁺ (in-phase rotation from layer to layer), a⁻ (out of phase) or a⁰ (none). This alphabet per axis is itself a trit.

The raw sign patterns number 27. Up to a permutation of axes, there are 10 sign types. Magnitudes split these further. Glazer listed 23 tilt systems. Group theory by Howard and Stokes reduced them to 15 distinct space groups.

A natural test is to apply the closure rule to the signs. The closed patterns are a⁰a⁰a⁰, a⁺a⁺a⁺, a⁻a⁻a⁻ and a⁰b⁺c⁻. The most common real pattern, a⁻a⁻c⁺ (the GdFeO₃ type, Pnma), has a sum of −1 and is open.

The closure rule on tilt signs does not predict which rotation patterns occur most often. The test was built for this essay, and it is not part of the theory. “In phase” and “out of phase” describe repetition along an axis, not the value at a crossing. The negative result stands.

9. Where perovskites sit on the two roads

The Vacuum.Net theory names two ways in which the net lets energy pass.

• The mesh passes. An opening with a size lets winding through. The passage depends on the size.
• The knot opens. One closure of a knot gives way, and a winding leaves. Stars open knots; that is what their light is.

A perovskite solar cell lives on the second road, at a distance. It catches windings that the sun has released. It needs light.

A device on the first road needs no light. Its question is how much of what the mesh closes leaves as current.

Perovskites can serve the first road too — not as the cell that catches light, but as the wall of the mesh. Before that, one point about the record of the first road needs setting straight.

10. What has been measured on the open side

10.1 The device

Moddel, Weerakkody, Doroski and Bartusiak (2021) built metal–insulator–metal tunnel junctions with an optical cavity on one side. For the cavity series, the stack was:

• nickel base electrode, 38 nm;
• native nickel oxide, about 1 nm, plus aluminium oxide, 0.9 nm;
• palladium upper electrode, 8.3 nm;
• PMMA cavity, 33, 79, 230 or 1100 nm;
• aluminium mirror, 150 nm.

The active area was 0.02 ± 0.006 µm². At zero applied voltage, the junctions delivered current. For linear current–voltage curves, the maximum power is |I_sc · V_oc| / 4. For the 33 nm cavity this was 1.4 pW. Thinner cavities gave more current.

The group ran eight tests for artefacts. These covered stability over four hours, scaling with area, scaling in 4×4 arrays, the stage of processing at which current appears, leakage through the cavity, electromagnetic pickup, and two thermoelectric checks. All came out negative. The trends held in over 1000 devices from 21 batches. After six months, output had fallen by less than 10% with PMMA and less than 20% with SiO₂.

The authors call their mechanism conjectural. They expected the energy density of suppressed modes to scale as 1/d³, did not see it, and did not attempt a quantitative fit.

10.2 The numbers per area

1.4 × 10⁻¹² W over 2 × 10⁻¹⁴ m² gives 70 W/m² for one layer at 33 nm. One natural mesh measures (45.6 nm)² = 2.08 × 10⁻¹⁵ m². At 70 W/m², that is 1.46 × 10⁻¹³ W per mesh.

10.3 What has happened since

Maclay (2024) modelled the device using current calculations of vacuum fluctuations in a cavity. Two results bear on it. An ideal cavity raises the mean energy of electrons near the electrode, which would drive current in the opposite direction to the one observed. And that mean energy is nearly independent of cavity size, which contradicts the measured dependence. Maclay concludes that the proposed mechanism does not hold. He does not dispute the measurement.

A 2026 funding proposal for a first independent test reports that, five years on, there have been no independent replications, no public raw data and no experimental critiques. It also names an untested pathway. Palladium on aluminium oxide is the standard construction of a hydrogen sensor. The original artefact list did not test hydrogen.

The record of the open side is therefore one group, one structure, a mechanism its own authors call conjectural, and a theoretical analysis that rejects that mechanism while leaving the data standing.

11. Current, not power: a correction

An earlier reading of the device (Konstapel, 2026b) derived a rule for the mesh. Passage equals one over the open size, 1/L, so the slope on a log-log plot should be −1. The test used Moddel’s Figure 4b and read a slope of −0.9 ± 0.15. The interval contains −1.

Figure 4b, however, plots short-circuit current against cavity thickness — not power.

For a linear junction with resistance R, the open-circuit voltage is V_oc = I_sc · R. The maximum power is then P = I_sc · V_oc / 4 = I_sc² · R / 4. If R does not change with cavity thickness, power scales as the square of current. A current slope of −0.9 becomes a power slope of −1.8.

The effect on the numbers, anchored at 70 W/m² for 33 nm:

Gap	Ratio 33/L	Power if P = 1/L	Power if P = 1/L^1.8	Power if P = 1/L²
33 nm	1	70 W/m²	70 W/m²	70 W/m²
45.6 nm	0.7237	50.7 W/m²	39.1 W/m²	36.7 W/m²
1100 nm	0.0300	2.10 W/m²	0.127 W/m²	0.063 W/m²

At the widest gap, the readings differ by a factor of 2.10 / 0.127 ≈ 16.5.

Two ways forward are consistent:

• The rule concerns current. Then the slope test holds as published, and power runs as 1/L². Passage is charge per unit time through the mesh.
• The rule concerns power. Then the measured current must run as 1/√L, a slope of −0.5. That sits outside −0.9 ± 0.15, and the test fails.

The first is the natural reading. Larson’s ladder gives power as 1/S, but what crosses the junction is charge. The voltage across a fixed resistance adds a second factor of 1/L. On that reading, the earlier figure of about 2 W/m² at 1100 nm becomes about 0.06–0.13 W/m².

Nothing at 33 nm changes. The household estimates built on 70 W/m² at 33 nm stand as they were.

The question is not closed. Resistance varies widely between nominally equal junctions, and the published values are averages over chips. Digitising Figure 4a, which gives the full current–voltage line per thickness, would yield V_oc per thickness and settle the power slope directly.

12. A wall with three states

12.1 What already exists

A ferroelectric tunnel junction is two electrodes separated by a ferroelectric barrier a few unit cells thick. Reversing the polarisation reverses the charge at the two interfaces. This changes the shape of the barrier and with it the tunnelling current. On nanometre-thick BaTiO₃ films, resistance changes by about two orders of magnitude on reversal, on a lateral scale of 20 nm, at room temperature. Asymmetric interfaces are a known requirement for the effect.

These junctions are studied as memories. No published work was found in which a ferroelectric tunnel junction is placed beside a Casimir cavity and measured at zero bias.

12.2 The proposal

Replace the passive insulator of the cavity device with a ferroelectric barrier of the same thickness.

• Thickness. Moddel’s insulator totals about 1.9 nm. Five pseudocubic cells of BaTiO₃ at about 0.40 nm make 2.0 nm. The tunnelling regime is preserved.
• Electrodes. Use an oxide bottom electrode such as SrRuO₃, standard in these junctions, and a thin upper metal that does not take up hydrogen. With no palladium, the hydrogen pathway is closed by construction.
• Cavity. Keep a dielectric spacer and a mirror on the side of the upper electrode, as in the original device.

The polarisation of the barrier has three states. P⁺ points towards the cavity. P⁻ points away. P⁰ has no net polarisation; it can be reached by heating the barrier above its Curie point, or by a twin junction from the same growth run with a paraelectric SrTiO₃ barrier of equal thickness.

In the terms of the net, the polar barrier is the open wall, and its trit sets how the wall returns what the mesh closes. The three states change the asymmetry of one junction without touching its geometry.

12.3 What the design discriminates

Published comparisons are between different devices, where fabrication spread dominates. This design compares one junction with itself.

Observation	Cavity-driven passage	Artefact
Mirror absent, any P	zero current in all three states	current present
Mirror present, P⁺ vs P⁻	currents differ; difference tracks barrier asymmetry	no systematic difference
Mirror present, P⁰	current of the passive device	—
Current over hours at constant temperature	constant	pyroelectric current needs a temperature change; it vanishes
After a polarisation switch	steady value after the switch	depolarisation current decays
In darkness	unchanged	ferroelectric photovoltaic effect
Current against time at fixed bias; frequency dependence	flat	ionic motion of vacancies shows slow drift and low-frequency response
Exposure to hydrogen	unchanged	hydrogen uptake in the electrode

The prediction is fixed before the run. With the mirror present, I_sc(P⁺) ≠ I_sc(P⁻). Without the mirror, both are zero. The theory gives no value for the size of the difference. That size is the open number: the fraction of what the mesh closes that leaves as current.

12.4 The size of the mesh in whole cells

Oxide films grow layer by layer with unit-cell control by pulsed laser deposition, monitored by electron diffraction during growth. In SrTiO₃, one cell measures 0.3905 nm.

Size	Unit cells of SrTiO₃
33 nm (Moddel’s thinnest cavity)	84.5
45.6 nm (the natural unit)	116.8
60–75 nm (a resting gap)	153.6–192.1

An epitaxial spacer adjusts the mesh in steps of 0.39 nm — about 1% of the natural unit. The region around 45.6 nm can therefore be traced cell by cell.

A spacer of high refractive index also separates two readings of the gap. PMMA (n = 1.52) and SiO₂ (n = 1.49), the two spacers Moddel used, differ by only 2%. If the current follows the geometric gap, as the net’s 1/S says, then spacers of very different index at equal thickness should give equal current. If it follows the optical cutoff, which scales with n·L, they should not. A spacer of high index must be transparent across the relevant band; that choice is part of the design.

12.5 Where in the Netherlands

The Dutch groups mapped earlier (Konstapel, 2026d) cover Casimir switching, tunnable cavities, critical fluctuations and membranes. One group is missing from that map: the University of Twente group that grows perovskite oxides with unit-cell control by pulsed laser deposition. In 2025, that group completed a doctoral thesis on ferroelectric gradient films and published a study of barium titanate gradient films. A gradient film has two unlike sides by definition. Together with Groningen, the same group reported room-temperature epitaxy of the halide perovskite α-CH₃NH₃PbI₃.

The two capabilities missing on the open side — mesh size by the cell and a built-in, switchable asymmetry — sit in one laboratory.

13. Why not halide perovskites as filling

Halide perovskites conduct ions as well as electrons. First-principles barriers in CH₃NH₃PbI₃ (Eames et al., 2015) are 0.58 eV for iodide vacancies, 0.84 eV for methylammonium and 2.31 eV for lead. The iodide value agrees with kinetics measured on a working cell.

The order matches the trit cube. X stands on cells that are all open (6 of 6). A stands on corners of which 6 of 8 are open. B stands on the closed centre. With three items, a random order matches with a probability of 1 in 6. This is a correspondence, not a proof.

At 300 K, kT = 0.02585 eV:

• iodide against methylammonium: e^(0.26/0.02585) ≈ 23,000 times more hops;
• iodide against lead: e^(1.73/0.02585) ≈ 10²⁹.

Slow ionic currents and hysteresis can imitate a steady signal. A halide perovskite as the cavity filling or barrier would bury the effect sought. Oxides carry vacancies on their X sites too. This is why the ionic test belongs in the table of Section 12.3.

14. What it means in practice

If the open side yields a number, the arithmetic is short. At 70 W/m² for one layer at 33 nm, a household using 3,000 kWh of electricity a year draws an average of 3,000 / 8,766 h = 0.342 kW. That needs 342 / 70 = 4.9 m² of one layer, or 0.049 m² of a hundred layers if layers add.

Each of those conditions is open: that the current is real, that layers add, and that the coupling survives in other materials. A structure that passes continuously, in any place, would sit in the house rather than at the end of a grid. Whether that happens depends on one fraction, measurable in one junction with three states.

15. Status

Counted here

• ABX₃ as the occupation of grades 0, 1 and 3 of the trit cube.
• The anion cage entirely on open cells.
• The grade counts 1/6/12/8 set beside the variant counts of BaTiO₃.
• The closure group −3m of order 12, index 4.
• The power slope of −1.8 from a current slope of −0.9, and the table of Section 11.
• Unit-cell counts of 84.5, 116.8 and 153.6–192.1.
• Hop ratios of 23,000 and 10²⁹.

Measured, from sources

• Tolerance factors and their three outcomes.
• The phase sequence of BaTiO₃ with 6/12/8 variants.
• The 23 → 15 rotation systems.
• Moddel’s stack, 1.4 pW at 33 nm, eight artefact tests, 1000 devices, ageing.
• Maclay’s analysis.
• Tunnelling electroresistance in BaTiO₃ junctions.
• Ion migration barriers in CH₃NH₃PbI₃.

Read

• A as the occupant of a mesh.
• (t − 1) as a trit.
• The trigonal ground states as the symmetry of closure.
• The polar barrier as the open wall.

Negative

• The closure rule on Glazer tilt signs does not predict rotation frequency.

Open

• The power slope of Moddel’s device, from Figure 4a.
• Whether the current follows the geometric or the optical gap size.
• The fraction of what the mesh closes that leaves as current.
• Why grade 2 stays empty in perovskites.

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Annotated References

The net

*Konstapel, J. (2026a). From Quaternions to Vacuum.Net: Mapping Four Theories onto Cl(3). Constable Research, Leiden, 2 October 2026.*
https://constable.blog/2026/10/02/russell-larson-clerk-maxwell-and-the-vacuum-net-theory-on-the-clifford-algebra-of-apace/
Why read? The trit cube, its 27 cells by grade, and the nine closed cells as disc and axis. Sections 2 and 3 of this essay rest on it. Reading advice: Sections 4 and 5.

Konstapel, J. (2026b). Applied Vacuum Theory, Part Four: Energy as Passage, third edition. Constable Research, Leiden, 27 September 2026.
https://constable.blog/wp-content/uploads/def2Applied-Vacuum-Theory-Part-Four-Energy-as-Passage-The-Step-from-Mesh-to-Output-1.pdf
Why read? The rule from mesh to output and its test against Moddel’s curve. Section 11 corrects one step of it. Reading advice: the section on the test, beside Section 11 above.

Konstapel, J. (2026c). The Vacuum.Net Theory. Constable Research, Leiden, 28 September 2026.
https://constable.blog/wp-content/uploads/vdefThe-Vacuum.Net-Theory.pdf
Why read? The five axioms, the natural units and the two roads: the mesh that passes and the knot that opens.

Konstapel, J. (2026d). The Dutch Vacuum Landscape. Constable Research, Leiden, 6 October 2026.
https://constable.blog/wp-content/uploads/The-Dutch-Vacuum-Landscape-Where-the-Net-Theory-Meets-the-Groups-That-Measure-and-Switch-the-Vacuum-in-the-Netherlands.pdf
Why read? The Dutch groups that work on the quantities the mesh needs. Section 12.5 adds one.

Larson, D. B. (1959). The Structure of the Physical Universe. Portland: North Pacific Publishers.
Why read? The ladder of space and time on which power is 1/S. Reading advice: the chapters on the natural units only.

The device and its record

Moddel, G., Weerakkody, A., Doroski, D., and Bartusiak, D. (2021). “Optical-Cavity-Induced Current.” Symmetry 13, 517.
https://www.mdpi.com/2073-8994/13/3/517
Why read? The only measured device of its kind, with its stack, eight artefact tests and its own caution about mechanism. Reading advice: Table 1 for every layer; Figure 4a, not only 4b, for the power slope; Section 3.2 for the tests.

Maclay, G. J. (2024). “Modeling Electronic Devices with a Casimir Cavity.” Physics 6, 1124–1131.
Why read? The one theoretical analysis of the device. It rejects the proposed mechanism and leaves the data standing. It shows why the open side still lacks a model.

“Electric Field and Voltage Fluctuations in the Casimir Effect” (2021). arXiv:2112.14285.
https://arxiv.org/abs/2112.14285
Why read? An estimate of whether cavity-modified fluctuations are large enough to matter for the junction current.

Manifund (2026). “First independent test of the Casimir cavity vacuum energy claim.”
https://manifund.org/projects/first-independent-test-of-the-casimir-cavity-vacuum-energy-claim
Why read? The state of replication in 2026 and the hydrogen pathway in palladium electrodes. Its same-junction protocol is the mechanical cousin of Section 12.

Casimir, H. B. G. (1948). “On the attraction between two perfectly conducting plates.” Proceedings KNAW 51, 793.
Why read? The two-wall opening in its original form. Three pages.

Perovskite structure

Goldschmidt, V. M. (1926). “Die Gesetze der Krystallochemie.” Die Naturwissenschaften 14, 477–485.
Why read? The origin of the tolerance factor: the fit of an occupant to its opening.

Shannon, R. D. (1976). “Revised effective ionic radii.” Acta Crystallographica A 32, 751–767.
Why read? The radii used in Section 5. The tolerance factor shifts by about ±0.03 between radius sets; this table fixes one set.

Glazer, A. M. (1972). “The classification of tilted octahedra in perovskites.” Acta Crystallographica B 28, 3384–3392.
Why read? The trit alphabet of rotations — a⁺, a⁻ and a⁰ — and the 23 tilt systems.

Howard, C. J., and Stokes, H. T. (1998). “Group-theoretical analysis of octahedral tilting in perovskites.” Acta Crystallographica B 54, 782–789.
Why read? The reduction to 15 space groups and their hierarchy. Section 8 tests the closure rule against this list.

“Atomistic Description for Temperature-Driven Phase Transitions in BaTiO₃” (2016), arXiv:1601.02031; and “Thermodynamics and dielectric response of BaTiO₃ by data-driven modeling” (2021), arXiv:2111.05129.
https://arxiv.org/abs/1601.02031 · https://arxiv.org/abs/2111.05129
Why read? The 6, 12 and 8 equivalent minima of the polar phases, and the local displacement towards a corner in every phase. Section 6 rests on these counts.

Ferroelectric junctions

Zhuravlev, M. Y., Sabirianov, R. F., Jaswal, S. S., and Tsymbal, E. Y. (2005). “Giant electroresistance in ferroelectric tunnel junctions.” Physical Review Letters 94, 246802.
Why read? The prediction that polarisation reversal changes tunnelling through a ferroelectric barrier.

Velev, J. P., et al. (2007). “Effect of ferroelectricity on electron transport in Pt/BaTiO₃/Pt tunnel junctions.” Physical Review Letters 98, 137201.
Why read? The first-principles mechanism in the material proposed here.

Gruverman, A., et al. (2009). “Tunneling electroresistance effect in ferroelectric tunnel junctions at the nanoscale.” Nano Letters 9, 3539–3543.
Why read? The measured change of about two orders of magnitude on 20 nm, at room temperature, in thin BaTiO₃.

Koster, G., Rijnders, G., Blank, D. H. A., et al. University of Twente, publications on pulsed laser deposition of perovskite oxides.
https://people.utwente.nl/g.koster
Why read? Unit-cell growth control, ferroelectric gradient films and room-temperature halide perovskite epitaxy: the capabilities Section 12 needs.

Halide perovskites

Eames, C., Frost, J. M., Barnes, P. R. F., O’Regan, B. C., Walsh, A., and Islam, M. S. (2015). “Ionic transport in hybrid lead iodide perovskite solar cells.” Nature Communications 6, 7497.
Why read? The barriers of 0.58, 0.84 and 2.31 eV. Section 13 rests on them.

Hoke, E. T., et al. (2015). “Reversible photo-induced trap formation in mixed-halide hybrid perovskites for photovoltaics.” Chemical Science 6, 613–617.
Why read? Light sorts the open X sites into iodide-rich and bromide-rich domains, which reverse in the dark. It shows how mobile the open sites are under tension.