Phase field modeling and simulation is employed to study the underlying mechanism of enhancing electromechanical properties in single crystals and polycrystals of perovskite-type ferroelectrics around the morphotropic phase boundary (MPB). The findings include: (I) Coherent phase decomposition near MPB in PZT is investigated. It reveals characteristic multidomain microstructures, where nanoscale lamellar domains of tetragonal and rhombohedral phases coexist with well-defined crystallographic orientation relationships and produce coherent diffraction effects. (II) A bridging domain mechanism for explaining the phase coexistence observed around MPBs is presented. It shows that minor domains of metastable phase spontaneously coexist with and bridge major domains of stable phase to reduce total system free energy, which explains the enhanced piezoelectric response around MPBs. (III) We demonstrate a grain size- and composition-dependent behavior of phase coexistence around the MPBs in polycrystals of ferroelectric solid solutions. It shows that grain boundaries impose internal mechanical and electric boundary conditions, which give rise to the grain size effect of phase coexistence, that is, the width of phase coexistence composition range increases with decreasing grain sizes. (IV) The domain size effect is explained by the domain wall broadening mechanism. It shows that, under electric field applied along the nonpolar axis, without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. (V) The control mechanisms of domain configurations and sizes in crystallographically engineered ferroelectric single crystals are investigated. It reveals that highest domain wall densities are obtained with intermediate magnitude of electric field applied along non-polar axis of ferroelectric crystals. (VI) The domain-dependent internal electric field associated with the short-range ordering of charged point defects is demonstrated to stabilize engineered domain microstructure. The internal electric field strength is estimated, which is in agreement with the magnitude evaluated from available experimental data. (VII) The poling-induced piezoelectric anisotropy in untextured ferroelectric ceramics is investigated. It is found that the maximum piezoelectric response in the poled ceramics is obtained along a macroscopic nonpolar direction; and extrinsic contributions from preferred domain wall motions play a dominant role in piezoelectric anisotropy and enhancement in macroscopic nonpolar direction. (VIII) Stress effects on domain microstructure are investigated for the MPB-based ferroelectric polycrystals. It shows that stress alone cannot pole the sample, but can be utilized to reduce the strength of poling electric field. (IX) The effects of compressions on hysteresis loops and domain microstructures of MPB-based ferroelectric polycrystals are investigated. It shows that longitudinal piezoelectric coefficient can be enhanced by compressions, with the best value found when compression is about to initiate the depolarization process. / Ph. D.

Relaxor ferroelectrics have been a subject of intense research owing to their interesting physical properties such as high dielectric constant and giant electro-striction. Unlike the conventional lead based relaxors, the relaxors belonging to Aurivillius family of oxides have received much less attention because of the poor understanding of the origin of the relaxor behavior and high processing temperatures involved. In the present investigations, an attempt has been made to understand the origin of relaxor behavior of the materials belonging to Aurivillius family of oxides. The structure and relaxor behavior of BaBi2Nb2O9 (BBN) has been established via the XRD, electron diffraction and dielectric spectroscopy. The results are compared with that of a normal ferroelectric like SrBi2Nb2O9 belonging to the same family as well with that of a conventional relaxor like PMN. The results indicate that the dielectric behavior of BBN is significantly different from that of the conventional relaxors like BBN with very slow broadening of relaxation times and was attributed to the absence of significant polar ordering. To substantiate the existing understanding, studies have been carried out by adopting different strategies such as B-site and A-site cationic substitutions and texturing of the ceramics. Vanadium doping on B-site was found to decrease the sintering temperatures significantly. Aliovalent La3+ doping was found to affect the dielectric behavior strongly with substantial decrease of the freezing temperature and dielectric constants which shows that the relaxor behavior of BBN is highly sensitive to A-site order-disorder. The (00l) textured ceramic of pure and vanadium doped BBN was fabricated via a simple melt-quenching technique and was found to exhibit a significant dielectric and pyroelectric anisotropy. A new class of relaxor compositions (K0.5La0.5Bi2Nb2O9 & K0.5La0.5Bi2Ta2O9) have been synthesized and characterized. These new compounds exhibited interesting physical properties which are akin to that of the conventional lead based relaxors. The presence of superlattice reflections in the electron diffractin patterns recorded on these compounds establish the presence of polar nano regions of significant size. These relaxor crystallites at nano/micro level embedded in a glass matrix have been found to be very promising from their physical properties view point.

Fine-pitch ferroelectric domain gratings are extensively used for generation of light in the visible and near-infrared spectral regions through quasi-phase matched (QPM) frequency conversion. Sub-μm QPM devices enables demonstration of nonlinear optics with counterpropagating waves, a field of nonlinear optics which remains sparsely explored due to the difficulty of fabricatinghigh quality gratings. In recent years, bulk Rb-doped KTiOPO4 (RKTP) has emerged as a highly promising nonlinear materials for fabrication of fine-pitch QPM devices through periodic electric-field poling. RKTP possesses large optical nonlinearity and high resistance to optical damage, while demonstrating improved material homogeneity and lower ionic conductivity than its isomorphs, which are important features for poling. Although fine-pitch QPM gratings, as well as large aperture QPM devices, have been demonstrated, fabrication of sub-μm high quality QPM devices remains a challenge. The primary aim of this research was to develop a reliable method to fabricate high-quality sub-μm periodically poled RKTP crystals (PPRKTP) and exploit them in novel optical applications. For this purpose, a novel poling method was developed. It was based on periodic modulation of the coercive field through ion exchange, where K+ ions are exchanged with Rb+ in the crystal, to modulate the coercive field and the ionic conductivity. This enables periodic poling of higher quality and with shorter period than ever before. High quality PPRKTP with a period of 755 nm were fabricated and used to demonstrate the first cascaded mirrorless optical parametric oscillator (MOPO), as well as the first MOPO pumped by a Q-switched laser. PPRKTP samples for blue light generation were fabricated, and second harmonic generation (SHG) was investigated with a high power 946 nm fiber laser. Up to 2 W of blue power was demonstrated for bulk samples, where the output power was limited by absorption of the SHG, leading to thermal dephasing of the devices. Laser-written waveguides were fabricated in PPRKTP for the first time, and a record high SHG power of 76 mW was obtained. Finally, the high-temperature stability of ferroelectric domain gratings was investigated. This is of utmost importance when a PPRKTP crystal is used as a seed for crystal growth. It was found that for charged domains walls, the domain-wall motion was highly anisotropic with rapid movement in y-direction while only small movements were observed in the x-direction of the crystal. / Ickelinjära ferroelektriska kristaller med artificiella domängitter med perioder av några mikrometer används idag för generering av ljus i de synliga och nära-infraröda våglängdsområdena, genom kvasifasmatchad (QPM) frekvenskonvertering. Med sub-μm QPM domängitter kan man åstadkomma ickelinjära optiska effekter med motpropagerande parametriska ljusvågor. Detta är ett område av den ickelinjära optiken som fortfarande är tämligen outforskat på grund av svårigheten med att tillverka högkvalitativa domängitter.  Under de senaste åren har Rb-dopat KTiOPO4 (RKTP) blivit ett mycket lovande ickelinjärt material för tillverkning av QPM-gitter med mycket korta perioder genom periodisk elektrisk fält polning. RKTP kristallen har en hög optisk ickelinejäritet och den tål höga optiska intensiteter, samtidigt som materialet har bättre materialhomogenitet och lägre jonledningsförmåga än vad dess isomorfa kristaller har. De två senare egenskaperna har visat sig viktiga för att få en lyckad polning. Fastän QPM-gitter med kort periodicitet, liksom QPM-gitter med stor apertur, har demonstrerats, är tillverkningen av högkvalitativa QPM-kristaller med sub-µm perioder fortfarande en utmaning. Det primära syftet med denna avhandling var att utveckla en pålitlig metod för att tillverka högkvalitativa sub-μm periodiskt polade RKTP kristaller (PPRKTP) och utnyttja dem i nya optiska tillämpningar. I detta syfte utvecklades en ny polningsmetod. Den baseras på periodiskt jonutbyte, där K+ joner byts mot Rb+ i kristallen, vilket resulterar i en samtidig modulation av materialets koerciva fält och jonledningsförmåga. Detta möjliggör i sin tur periodisk polning av högre kvalitet och med kortare perioder än någonsin tidigare har uppnåtts. Högkvalitativa PPRKTP kristaller med en period på 755 nm tillverkades och användes för att demonstrera den första kaskaderade spegelfria optiska parametriska oscillatorn (MOPO), liksom den första MOPO processen pumpad av en Q-switchad laser. Vidare utvecklades PPRKTP-kristaller för generering av blått ljus via frekvensdubbling. Dessa utvärderades med hjälp av en högeffekts-fiberlaser vid 946 nm. Upp till 2 W av blått ljus erhölls för bulkkristallerna. Uteffekten begränsades av absorption av det blåa frekvensdubblade ljuset, vilket ledde till urfasning i QPM-gittret p.g.a. termiska effekter. Laserskrivna vågledare tillverkades sedan i PPRKTP för första gången, och en rekordhög effekt på 76 mW erhölls via frekvensdubbling. Slutligen undersöktes stabiliteten hos de periodiskt polade domängitterna vid höga temperaturer. Det är viktigt att domängittrena är stabila när PPRKTP kristallerna används som ympämne för kristalltillväxt. Det visade sig att instabila domänväggar flyttade sig mycket anisotropt, med en snabb rörelse i kristallens y-riktning och en långsam rörelse i kristallens x-riktning. / <p>QC 20170519</p>

The aim of this thesis was to improve the understanding of microstructure in single crystal ferroelectrics. This was achieved through macroscopic testing of Lead Magnesium Niobate – Lead Titanate (PMN-PT) and microscopic observations of Barium Titanate (BT) single crystals. Multi-axial polarization rotation tests on PMN-PT showed a gradual increase in the change in dielectric displacement due to ferroelectric switching as the electric field is applied at increasing angles to the initial polarization direction. A relatively high remnant polarization for loading angle near to 90° suggested that PMN-PT is more polarizable in certain directions. Strains measured in two directions, parallel to the electric field and perpendicular to the electric field, showed a noticeable variation on two opposite faces of the specimen suggesting an effect of local domain configurations on macroscopic behaviour. A micromechanical model gave an insight into the switching systems operating in the crystal during the polarization rotation test. Domain structure in BT was mapped using synchrotron X-ray reflection topography. By making use of the angular separation of the diffracted reflections and specimen rocking, different domain types could be unambiguously identified, along with the relative tilts between adjacent domains. Fine needle domains (width ≈ 10μm) were successfully mapped providing a composite topograph directly comparable with optical micrograph. The domain structure was confirmed using other techniques such as piezoresponse force microscopy and atomic force microscopy/scanning electron microscopy and optical observations on the etched crystal. Results show that combined use of multiple techniques is necessary to gain a consistent interpretation of the microstructure. Finally, domain evolution in BT under compressive mechanical loading was observed in-situ using optical and X-ray diffraction techniques providing a series of images that show ferroelastic transition. The domain configurations influence the switching behaviour and constitutive models that can account for such effects need to be developed. Quantitative and qualitative data presented in this thesis can assist model development and validation.

The increasing miniaturization of electric and mechanical components makes the synthesis and assembly of nanoscale structures an important step in modern technology. Functional materials, such as the ferroelectric perovskites, are vital to the integration and utility value of nanotechnology in the future. In the present work, chemical methods to synthesize one-dimensional (1D) nanostructures of ferroelectric perovskites have been studied. To successfully and controllably make 1D nanostructures by chemical methods it is very important to understand the growth mechanism of these nanostructures, in order to design the structures for use in various applications. For the integration of 1D nanostructures into devices it is also very important to be able to make arrays and large-area designed structures from the building blocks that single nanostructures constitute. As functional materials, it is of course also vital to study the properties of the nanostructures. The characterization of properties of single nanostructures is challenging, but essential to the use of such structures. The aim of this work has been to synthesize high quality single-crystalline 1D nanostructures of ferroelectric perovskites with emphasis on PbTiO3 , to make arrays or hierarchical nanostructures of 1D nanostructures on substrates, to understand the growth mechanisms of the 1D nanostructures, and to investigate the ferroelectric and piezoelectric properties of the 1D nanostructures. In Paper I, a molten salt synthesis route, previously reported to yield BaTiO3 , PbTiO3 and Na2Ti6O13 nanorods, was re-examined in order to elucidate the role of volatile chlorides. A precursor mixture containing barium (or lead) and titaniumwas annealed in the presence of NaCl at 760 °C or 820 °C. The main products were respectively isometric nanocrystalline BaTiO3 and PbTiO3. Nanorods were also detected, but electron diffraction revealed that the composition of the nanorods was respectively BaTi2O5/BaTi5O11 and Na2Ti6O13 for the two different systems, in contradiction to the previous studies. It was shown that NaCl reacted with BaO(PbO) resulting in loss of volatile BaCl2 (PbCl2 ) and formation and preferential growth of titanium oxide-rich nanorods instead of the target phase BaTiO3 (or PbTiO3 ). The molten salt synthesis route may therefore not necessarily yield nanorods of the target ternary oxide as reported previously. In addition, the importance of NaCl(g) for the growth of nanorods below the melting point of NaCl was demonstrated in a special experimental setup, where NaCl and the precursors were physically separated. In Paper II and III, a hydrothermal synthesis method to grow arrays and hierarchical nanostructures of PbTiO3 nanorods and platelets on substrates is presented. Hydrothermal treatment of an amorphous PbTiO3 precursor in the presence of a surfactant and PbTiO3 or SrTiO3 substrates resulted in the growth of PbTiO3 nanorods and platelets aligned in the crystallographic &lt;100&gt; orientations of the SrTiO3 substrates. PbTiO3 nanorods oriented perpendicular to the substrate surface could also be grown directly on the substrate by a modified synthesis method. The hydrothermal method described in Paper II and III was developed on the basis of the method described in Appendices I and II. In Paper IV, a template-assisted method to make PbTiO3 nanotubes is presented. An equimolar Pb-Ti sol was dropped onto porous alumina membranes and penetrated into the channels of the template. Single-phase PbTiO3 perovskite nanotubes were obtained by annealing at 700 °C for 6 h. The nanotubes haddiameters of 200 - 400 nm with a wall thickness of approximately 20 nm. Excess PbO or annealing in a Pb-containing atmosphere was not necessary in order to achieve single phase PbTiO3 nanotubes. The influence of the heating procedure and the sol concentration is discussed. In Paper V, a piezoresponse force microscopy study of single PbTiO3 nanorods is presented. The piezoelectric properties were studied in both vertical and lateral mode. Piezoelectric activity and polarization switching was observed in the vertical mode, demonstrating the ferroelectric nature of the nanorods. The nanorods decomposed after repeated cycling of the dc bias at one spot on the nanorod, which resulted in parts of the nanorod disappearing and/or accumulation of particles on the surface of the nanorod. In Paper VI, a method to contact single nanorods by electron beam induced deposition of platinum is presented. An organometallic compound, (trimethyl)-methylcyclopentadienylplatinum(IV), was used as precursor. A home-made apparatus was constructed for the purpose and was mounted onto a scanning electron microscope. Calculations based on apparatus geometry and molecular flow were used to estimate the deposition time and the height of the deposits. The location and height of the deposits were controlled so that single nanorods could be successfully contacted at the ends of the nanorods. Fabrication of a sample device for piezoresponse force microscopy studies of single nanorods using an axial dc bias setup is described in Appendix IV. A proposed experimental setup for such studies is also presented.

In this thesis the InSb(111), InAs(111) and GaSb(001) surfaces have been studied by means of time- and angle-resolved photoemission spectroscopy based upon the femtosecond laser system. The pump-and-probe technique allows to analyse both electron states in the valence band and normally unpopulated electron states above the valence band, which can be occupied by transiently excited carriers at the optically pumped surface. The life time of excited carriers is analysed by controlling over the time delay between pump and probe pulses. Experimental studies of the InSb(111) surface and comparison with a previously studied InSb(110) surface show electron excitations in the bulk region with a minor surface contribution. Time-resolved experiments of carrier dynamics at the polar InAs(111)A and InAs(111)B surfaces show about the same life time of excited carriers, while no populated states above the valence band maximum have been found at the InAs(111)A due to the charge removal. Surface intergap electron states have been found at the GaSb(001) surface located at ~250 meV above the valence band maximum. Angle-resolved experiments showed a strong confinement of this state at the centre of the surface Brillouin zone. A new two dimensional angle-resolved multi-anode analyser for the femtosecond laser photoemission setup has been constructed. The analyser can resolve a cone opening angle of ~1º at a drift distance of ~0.5 m with an energy resolution of ~125 meV. A continuous series of binary system SrTiO3–PbZr0.52Ti0.48O3 has been grown by pulsed laser deposition (PLD) on sapphire substrate with crystalline quality control by x-ray diffraction (XRD). The maximum tunability has been tailored to room temperature, where STO�PZT (71/29) composition shows superior performance. A PbZr0.52Ti0.48O3 thin film pressure sensor has been fabricated by PLD and characterised by XRD and electrical measurements. The piezoelectric constant was found to be ~20 % higher compared to the bulk ceramics. A ferroelectric thin film electro-optical cell Na0.5K0.5NbO3/La0.5Sr0.5CoO3 (NKN/LSCO) on sapphire has been fabricated by PLD. Refractive indices and electro-optical coefficient of the cell were characterised by prism coupling refractometry. The tunability of the PLD fabricated 2 μm slot NKN thin film interdigital capacitor has been found ~23 % at 40 V bias voltage and frequency 1 MHz. / QC 20101015

Die vorliegende Arbeit befasst sich mit dem Einfluss der elektrischen Polarisation auf Eigenschaften freier Träger in ZnO basierten Halbleiterheterostrukturen. Dabei werden insbesondere Transporteigenschaften freier Träger sowie deren Rekombinationsdynamik untersucht. Die Arbeit behandelt vier inhaltliche Schwerpunkte. Der erste Schwerpunkt liegt auf den physikalischen Eigenschaften der verwendeten Materialen, hier wird der Zusammenhang der Bandlücke und der Gitterkonstanten von MgZnO Dünnfilmen und deren Magnesiumgehalt beschrieben. Weiterhin wird die Morphologie solcher Filme diskutiert. Auf unterschiedliche Substrate und Abscheidebedingungen wird dabei detailliert eingegangen. Der zweite Schwerpunkt behandelt die Eigenschaften undotierter und phosphordotierter ZnO und MgZnO Dünnfilme. Die strukturellen, Transport- und Lumineszenzeigenschaften werden hier verglichen und Rückschlüsse auf die Züchtungsbedingungen gezogen. Im dritten Schwerpunkt werden Quanteneffekte an ZnO/MgZnO Grenzflaechen behandelt. Hierbei wird insbesondere auf den Einfluss der elektrischen Polarisation eingegangen. Die Präsenz eines zweidimensionalen Elektronengases wird nachgewiesen, und die notwendigen Bedingungen zur Entstehung des sogenannten qunatum confined Stark-effects werden dargelegt. Insbesondere wird hier auf züchtungsrelevante Parameter eingegangen. Den vierten Schwerpunkt stellen Kopplungsphänomene in ZnO/BaTiO3 Heterostrukturen dar. Dabei werden zuerst die experimentell beobachten Eigenschaften verschiedener Heterostrukturen die auf unterschiedlichen Substraten gezüchtet wurden aufgezeigt. Hier stehen strukturelle und Transporteigenschaften im Vordergrund. Ein Modell zur Beschreibung der Ausbildung von Raumladungszonen in derartigen Heterostrukturen wird eingeführt und zur Beschreibung der experimentellen Ergebnisse angewandt. Die Nutzbarkeit der ferroelektrischen Eigenschaften des Materials BaTiO3 in Kombination mit halbleitendem ZnO wurden untersucht. Hierzu wurden ferroelektrische Feldeffekttransistoren unter Verwendung beider Materialien hergestellt. Die prinzipielle Eignung der Bauelemente als nichtflüchtige Speicherelemente wurde nachgewiesen.

Barium strontium titanate thin film varactors have been widely investigated for the purpose of creating tunable front-ends for RF and microwave systems. There is an abundance of literature observing the capacitance-voltage behavior and methods on improving tunability. However, there is a lack of thorough investigations on the nonlinear behavior, specifically the third order intermodulation distortion, and the parameters that impact it. There is also a research void that needs to be filled for nanoscale barium strontium titanate varactors as nanotechnology becomes increasingly prevalent in the design of RF and microwave components. This work aims to advance the understanding of nonlinear properties of barium strontium titanate varactors. Temperature and voltage impacts on the third order intermodulation distortion products of BST varactors are observed by two-tone measurements. The material properties of the films are correlated with the nonlinear behavior of the varactors. Additionally, size reduction capabilities are shown by fabricating planar barium strontium titanate interdigital varactors with nanoscale size gaps between the electrodes. Modeling techniques are also investigated.

In the dissertation AVBVICVII type compounds are analyzed theoretically and experimentally. Theoretical studies were carried out using Density Functional Theory (DFT), along with the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method and the Generalized Gradient Approximation (GGA). For calculations Wien2k and PHONON comp. packages were used. Experimental studies were performed using spectroscopic ellipsometry method and measuring permittivity (electrical capacitance) as a function of temperature. The study discusses AVBVICVII type compounds’ inter-atomic chemical bonding, the electronic structure, optical properties, lattice dynamics, vibrational thermodynamic functions and dielectric properties in the paraelectric, ferroelectric and antiferroelectric phases. / Disertacijoje teoriškai ir eksperimentiškai nagrinėjami AVBVICVII tipo junginiai. Teoriniai tyrimai atlikti naudojantis tankio funkcionalo teorija kartu su pilno potencialo tiesinių padidintų plokščių bangų metodu ir apibendrinto gradiento aproksimacija. Skaičiavimams naudoti Wien2k ir PHONON komp. paketai. Eksperimentiniai tyrimai buvo atliekami naudojantis spektroskopinės elipsometrijos metodais bei matuojant dielektrinės skvarbos (elektrinės talpos) priklausomybes nuo temperatūros. Darbe nagrinėjamas AVBVICVII tipo junginių tarpatominis cheminis ryšys, elektroninė struktūra, optinės savybės, gardelės dinamika, virpesių termodinaminės funkcijos ir dielektriniai pokyčiai paraelektrinėje, feroelektrinėje ir antiferoelektrinėje fazėse.

The aim of doctoral dissertation „Grain Size Effect on Dielectric Properties of Ferroelectrics and Relaxors“ by Maksim Ivanov is to investigate, how grain size of ceramics and powders of a few ferroelectrics and relaxors influences macroscopic dielectric properties. The studied materials are powders of a relaxor PbMg⅓Nb⅔O3 (PMN), ceramics of a relaxor with a spontaneous phase transition PbSc½Nb½O3 (PSN), ceramics of a ferroelectric 0.36BiScO3-0.64PbTiO3, and ceramics of Ba2SnO4, which were compared to a better investigated BaSnO3. Investigations were performed in broad frequency (100 Hz – 55 GHz) and temperature (30 K – 1000 K) ranges. Experimental investigations and modelling showed, that bulk properties of relaxor materials are heavily influenced by polar nanoregions, but they do not fully determine them. Morphology of the material (i.e. grain size of ceramics) determines growth and interactions of the nanoregions, thus influencing bulk properties. Moreover, effective medium approximation can explain evolution of dielectric properties of ferroelectrics and relaxors only if dependence of bulk properties on grain size is known. The most interesting result is, that there exist polar entities in ferroelectrics, which are different from ferroelectric domains and are similar to polar nanoregions in relaxors. Their contribution to dielectric permittivity can be comparable to all other contributions. Dimensions of these entities depend on grain size in accordance with Kittel's law. / Maksimo Ivanovo daktaro disertacijos tema yra “Grūdų dydžio įtaka dielektrinėms feroelektrikų ir relaksorių savybėms”. Šio darbo tikslas yra ištirti, kaip keramikų ar miltelių grūdų dydis įtakoja makroskopiškai stebimas kelių feroelektrikų bei feroelektrinių relaksorių dielektrines savybes. Tirtos medžiagos yra klasikinio relaksoriuas PbMg⅓Nb⅔O3 (PMN) milteliai, relaksoriaus su savaiminiu feroelektriniu faziniu virsmu PbSc½Nb½O3 (PSN) keramikos, feroelektriko 0.36BiScO3-0.64PbTiO3 keramikos, bei Ba2SnO4 keramiką, kuri buvo palyginta su kiek labiau žinoma BaSnO3 keramika. Tyrimai buvo atlikti plačiame dažnių (100 Hz – 55 GHz) bei temperatūrų (30 K – 1000 K) intervaluose. Eksperimentiniai tyrimai bei modeliavimai parodė, kad polinės nanosritys labai stipriai įtakoja tūrines relaksorių savybes, tačiau jų neapsprendžia. Medžiagos morfologija (antai keramikų grūdų dydis) lemia nanosričių augimą bei tarpusavio sąveikas, tokiu būdų įtakojamos tūrinės savybės. Be to, efektyvios terpės aproksimacija gali paaiškinti feroelektrikų ir relaksorių dielektrinių savybių priklausomybę nuo grūdų dydžio tik, jei žinomas sąryšis tarp dydžio ir tūrinių savybių. Įdomiausia yra tai, kad feroelektrikuose yra objektų, kurie nėra feroelektriniai domenai ir yra panašūs į relaksorių polines nanosritis. Jų indėlis į dielektrinę skvarbą gali būti palyginamas su visų kitų procesų (pvz. domenų sienelių ir polinių modų) indėliais. Šių objektų dydis priklauso nuo grūdų dydžio pagal Kittel'io dėsnį.