Dispersed Crystal Research Articles

Electrospun hybrid microfibers for desiccant cooling/air dehumidification

The aim of this work was to assess the efficiency and suitability of hybrid adsorbent microfibers, produced by the electrospinning technique, in open-cycle adsorption applications, such as desiccant cooling, air dehumidification/humidification and heat storage, requiring high water adsorption capacity and high stability at high relative humidity, up to 80 %. Specifically, silica gel (SG) and magnesium sulfate (MS) as adsorbents and polyacrylonitrile (PAN) as polymer carrier, were used to prepare the hybrid microfibers at different concentrations of adsorbents and tested under isothermal conditions (50 °C) with relative humidity increasing from 0 % to 90 %. Characterization included morphological, structural, and thermal analyses, as well as measurement of ad/desorption isotherms and cyclic hydrothermal stability. The adsorption performances of the SG microfibers were comparable to that of the pure adsorbent: the microfibers with 50 w% silica gel showed a water absorption of 26.1 w% at 80 % relative humidity and T = 50 °C, which was in agreement with the content of SG. Under the same conditions, PAN microfibers with 50 w% MS achieved a water absorption of 42.7 w%. The dispersion of MS crystals in the microfibers improved the stability of the salt to hydration, allowing for a significant enhancement in the adsorption performance of magnesium sulfate.

Influence of dispersion of a new type whole crystals seed on crystallization process and sugar quality

The aim of the work was to study effectiveness of the influence of a new type crystal seed with different microcrystals dispersion on the process of sucrose crystallization and sugar quality. The dispersion of microcrystals of the crystal-forming agent with whole crystals was determined and curves of their differential distribution were presented, which showed the average particle sizes of the “Ester K 01” are 18.2 μm and 46.4 μm. The morphological characteristics were determined of particles of the whole crystals seed and the seed slurry produced at a sugar factory. The duration of massecuite boiling was investigated and a comparative characterization of the quality indicators of the resulting massecuite, mother liquor, and sugar was given depending on the use of the whole crystals seed with different dispersion of microcrystals in comparison with the factory slurry. Microphotographs of sugar crystals in the massecuite were obtained with their size recorded 5, 10 and 20 min after the input of various seeds. The morphology of sugar crystals was studied in the finished massecuite. A comparison is given of the granulometric composition of sugar crystals obtained with crystal-forming agents with different dispersion. It was found based on the results of the study that when using the “Ester K 01” (46.4 μm) in thick juice with high turbidity the corresponding crystals are formed faster in the total amount of the massecuite. It was also found that there is a kind of blocking of the process of adjacent growth of crystals from the particles of impurities of thick juice with high turbidity. This contributes to the formation of more uniform, homogeneous crystals of the correct shape. The results are presented in the article of tests of the whole crystal seed “Ester K 01” (18.2 μm) and “Ester K 01” (46.4 μm) at sugar factories using the method of working on the seed magma and the method of shock crystallization respectively. The dependences were obtained of the average linear size, the amount of sugar of the 0.65 mm fraction, the coefficient of variation and the coefficient of uniformity of sugar crystals on the consumption of the whole crystals seed “Ester K 01” (crystal size 46.4 μm). The regression equation was developed in natural form for the process of sucrose shock crystallization. It was established the rational consumption of the crystal-forming agent “Ester K 01” (crystal size 46.4 μm), which ensures the effective crystallization of sucrose for the process of crystallization by the shock induced method.

Synthesis and evaluation of an environmentally friendly phosphorus-free and nitrogen-free polymer as a scale and corrosion inhibitor

Polyepoxysuccinic acid (PESA) was modified by glycidyl (Gly) to obtain a phosphate-free and nitrogen-free polymer (Gly-PESA), and its scale and corrosion inhibition properties were studied.The effects of Gly-PESA concentration, calcium ion concentration and temperature to scale inhibition performance were studied by static scale inhibition method. The corrosion inhibition performance of Gly-PESA was studied by static weight-loss method. The morphology and structure of calcium scale and steel surface were characterized by spectroscopic and microscopic methods. The scale inhibition efficiency of Gly-PESA for CaCO3 and CaSO4 was 98.06% and 92.6%, respectively. Under the same experimental conditions, the scale inhibition effect of Gly-PESA was obviously better than that of PESA. Gly-PESA could effectively inhibit the growth of CaCO3 and CaSO4 crystals and cause their crystal lattice distortion or crystal dispersion. The corrosion inhibition efficiency of Gly-PESA for carbon steel was 78.17%. The adsorption of Gly-PESA on the surface of the steel test piece followed Langmuir adsorption isotherm, and formed a protective film, which increased the corrosion resistance of the steel test piece, thus effectively protecting the steel test piece. Therefore, Gly-PESA was a green scale and corrosion inhibitor, which solved the problem of environmental pollution.

Synergistic catalytic degradation of Methotrexate using Ce-based high-entropy metal oxides: Insights from DFT calculations and CWPO performance

Methotrexate (MTX), a widely used anticancer drug, is a refractory organic pollutant posing serious threats to ecosystems and human health. This study focuses on the development of a novel catalyst composed of Ce-based high-entropy metal oxides (NHEMO) supported on nepheline for the catalytic wet peroxide oxidation (CWPO) process, targeting MTX degradation in simulated wastewater. The NHEMO catalyst exhibited a unique high-entropy structure that enhances catalytic performance by facilitating diverse electronic interactions, which was confirmed through X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses showing a well-defined crystal structure and uniform dispersion of metal oxides. Additionally, X-ray photoelectron spectroscopy (XPS) and energy-dispersive X-ray spectroscopy (EDS) revealed a stable metal composition and high oxidation states of active metal sites. At a reaction temperature of 160 °C, with a residence time of 150 s and an oxidation coefficient of 5, the catalyst achieved a MTX removal rate of 93.49 % and a chemical oxygen demand (COD) removal of 99.95 %. Density Functional Theory (DFT) calculations further demonstrated that H2O2 decomposes into both adsorbed (surface-bound) and free (solution-phase) hydroxyl radicals (·OH). These radicals synergistically degrade MTX through both radical and non-radical pathways, ensuring comprehensive pollutant breakdown. The catalyst also showed excellent stability and a very low metal dissolution rate during the reaction, maintaining high catalytic activity after repeated recycling. This catalyst offers high cost-effectiveness, activity, and stability, providing a promising solution for treating refractory organic pollutants in pharmaceutical wastewater.

Capillary flow-MRI of micronized fat crystal dispersions: Effect of shear history on microstructure and flow

Micronized fat crystal (MFC) dispersions are a novel food ingredient enabling more efficient manufacturing of fat-based products as compared to established melt-cool processing. Yet, predicting rheological properties of MFC dispersions, remains a challenge. Here, we demonstrate how a capillary-flow Magnetic Resonance Imaging (MRI) platform provides quantitative measurements of local flow of MFC dispersions, inaccessible by global rheology. The measured 2D 1H MRI velocity maps unveiled a 5-fold velocity enhancement, and corresponding increase in wall slip, upon increasing the pre-shear time within 0–5 h, due to the 14 % increase in thickness of the crystalline nanoplatelets via recrystallization and aggregation of nanoplatelets. In the absence of pre-shearing, MFC dispersions exhibit an unsheared band at the walls of the capillary, likely arising from fouling and migration of thin nanoplatelets. In contrast to FCDs, flow cooperativity could not be observed for MFC dispersions due to the non-fractality of the fat crystal network. These results demonstrate that, by varying the pre-shear duration, the flow-microstructure properties of the MFC dispersions can be altered in a controlled manner. The approach presented here will allow for rapid assessment of shear-history dependence of flow properties of MFC dispersions under industrially relevant flow conditions.

Theoretical and experimental study of plasmon oscillation dispersion in Si and Ge crystals

Plasma fluctuation dispersion has been theoretically and experimentally studied in monocrystal samples of Si (111) and Ge (111). It has been shown that the dispersion depends on crystallographic orientations of materials under study. In this work, the dispersion effects in the CLEE spectra, which manifest themselves in bulk samples of Si and Ge, have been studied. The loss energy electron was studied by the CLEE method upon their reflection from Si(111) and Ge(111) at different angles of incidence of the electron beam on the surface. Calculation of the total electron energy loss with formula (5) shows that the form of the CLEE spectrum of primary electrons depends on the nature and magnitude of the electron density in a given direction and is in satisfactory agreement with the experimental data. Thus, the theoretical and experimental results show that in the case of single-crystalline Si and Ge, with increasing k, the values of the bulk plasma oscillation increase by 2–3 eV.

Study on the catalytic performance of Fe in-situ modified small crystallite Silicalite-1 zeolite in Chichibabin condensation reaction

Pyridine and its derivatives, collectively referred to as pyridine bases, are widely used in industries such as pesticides and pharmaceuticals, serving as crucial intermediates in the chemical industry. In recent years, with the development of the pesticide and pharmaceutical industries, the demand for pyridine bases has rapidly increased. The Chichibabin condensation reaction is the most commonly route for industrial production of pyridine bases. Currently, the most used ZSM-5 zeolite catalyst is limited by the instability of its silicon-aluminum framework structure, resulting in a short active reaction cycle (5 h). To address this limitation, this study selected the thermally stable and hydrothermally stable Silicalite-1 zeolite. Polyvinylpyrrolidone (PVP) was employed as a colloidal dispersant and Fe was introduced into the MFI framework through in-situ modification during the hydrothermal synthesis of zeolite. The influence of PVP dosage, template agent dosage, and other crystallization conditions on the crystallinity, pore structure, and acidity of Silicalite-1 zeolite products was investigated using XRD, SEM, TG, and N2 adsorption-desorption measurement. The acidity of Fe-modified Silicalite-1 zeolites was characterized using NH3-TPD, Py-FTIR, FT-IR, and XPS. These results indicated that the introduction of seed crystals effectively reduced the particle size of the zeolite to about 200 nm. Fe-modified Silicalite-1 displayed a disk-like morphology with excellent crystal dispersion. The highest relative crystallinity of the zeolite reached 103% with 15% seed crystal input and 3.75% PVP addition. The Fe-modified Silicalite-1 possessed a significantly enhanced abundance of both Lewis (L) and Brønsted (B) acid sites, resulting in an increase in the initial activity from 66% to 85% for the pyridine bases synthesis through the Chichibabin condensation. Compared to ZSM-5, Fe-modified Silicalite-1 exhibited superior catalytic stability, maintaining the total carbon conversion and pyridine bases yield above 66% and 40%, respectively, over a 15 h reaction period. Furthermore, the strategy proposed in this study, employing polyvinylpyrrolidone as a colloidal stabilizer to modify Silicalite-1 zeolite, could significantly broadened the application prospects of weakly acidic pure silica zeolites in the field of acid catalysis. This approach has demonstrated significant scientific value and industrial potential.

Microwaves induced epitaxial growth of urchin like MIL-53(Al) crystals on ceramic supports

Shaping Metal–Organic Frameworks (MOFs) poses a significant challenge for their widespread application on a large scale. In particular, a precise control over crystal orientation and arrangement on substrates are expected to provide exiting opportunities for novel materials with customized characteristics and enhanced performance in catalysis, gas storage, sensing, optics and electronics. Here we demonstrated for the first time that microwave irradiation can induce well controlled epitaxial growth of urchin-like MIL-53(Al) crystals via the hydrothermal conversion of Atomic Layer Deposition alumina layers on SiC foams. The resulting large, ordered crystals feature specific size, homogeneity, dispersion, and quantity that strongly correlate with the nature of the ceramic support and its ability to absorb microwaves. Furthermore, the supported MIL-53(Al) urchins were considered as templates for generating nanostructured alumina fibers on SiC foams, providing attractive catalyst carriers with high specific surface areas.

Manipulation and applications of ultrafast all-optical switching based on transient absorption and dispersion in KTN crystals.

Potassium tantalate niobate (KTN) represents a noteworthy category of optical crystals known for their superior nonlinear optical properties. In this study, we conducted measurements of femtosecond time-resolved transient absorption (TA) spectra in KTa0.57Nb0.43O3 crystals. Notably, a rapid and pronounced "plateau" phase, ∼1.5 ps in duration, was detected at the onset of the TA kinetics and succeeded by two distinct decay components, exhibiting lifetimes of ∼140 ps and over 10 ns, respectively. We attribute these observations to a decay process involving two-photon absorption, dispersion characteristics, and excited state absorption. Based on this unique TA characteristic of KTN crystals, an all-optical switching strategy was proposed and utilized to measure the ultrafast lasing dynamics of single-crystal CH3NH3PbBr3 nanowires. This polarization-independent TA gate approach offers an adjustable gate width combining ps and ns time scales and introduces a versatile tool for advanced optical applications.

Synthesis and characterization of bagasse cellulose-based quaternary ammonium peroxyphosphotungstate and their catalytic properties for cyclohexene oxidation in the absence of any solvent

Bagasse cellulose, an industrial waste byproduct of sugar production, was demonstrated to be a viable solid support for a solid-phase ionic oxidation catalyst enabling organic solvent-free aqueous reaction conditions and facile catalyst recovery. Bagasse cellulose-supported quaternary ammonium peroxyphosphotungstate was synthesized from bagasse cellulose-supported quaternary ammonium chloride, phosphotungstic acid, and hydrogen peroxide. The chemical structure of this material was characterized by SEM, XRD, FT-IR, XPS, and 13C NMR, revealing stability of the cellulose matrix to the catalyst loading conditions and effective dispersion of the acicular catalyst crystals throughout the matrix. High catalytic activity of this synthetic complex was demonstrated in the oxidation of cyclohexene to 1,2-cyclohexanediol with hydrogen peroxide in the absence of solvent. Optimized conditions providing trans-1,2-cyclohexanediol with 86.2 % selectivity were 12 wt% catalyst and 4 mL/g 30 % H2O2 (vs. cyclohexene) at 50 °C for 10 h.

Chitosan/MgO NPs/CQDs bionanocomposite coating: Fabrication, characterization and determination of antimicrobial efficacy

The development of new polymer nanocomposites or antibacterial coatings is crucial in combating drug-resistant infections, particularly bacterial infections. In this study, a new chitosan polymer based nanocomposite reinforced with magnesium oxide nanopowders and carbon quantum dots was fabricated by sol-gel technique and coated on 316 L stainless steel. In order to gaining the optimal amount of components to achieve the maximum antibacterial properties, the effect of concentration of nanocomposite components on its antibacterial properties was investigated. Crystal structure, microstructure, elemental dispersion, size distribution, chemical composition and morphology of nanocomposite and coating were characterized with various analyses. The obtained results exhibited that the carbon quantum dot and magnesium oxide nanopowders were distributed uniformly and without agglomeration in the chitosan matrix and created a uniform coating. The antibacterial properties of the synthesized samples against Staphylococcus aureus bacteria (gram positive) were evaluated using disk diffusion and minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) antibacterial tests. The inhibition growth zone formed around the antibiotic and nanocomposite 25 mg/ml under dark and light was about 32 and 14, 11 mm, respectively. Also, MIC and MBC values for final nanocomposite were 62.5 and 125 μg/ml, respectively.

Mineral trapping of carbon dioxide: Rapid hydrothermal synthesis experiments and carbon sequestration potential of dawsonite

Dawsonite, as a natural CO2 tracing mineral, is intimately associated with CO2 injection and serves as a crucial mineral for geological carbon sequestration. The massive and stable presence of dawsonite in the geological background is a key consideration for CO2 mineralization capture and plays a significant role in identifying CO2 geological burial sites. To investigate the optimal conditions for the rapid synthesis of dawsonite using CO2, we conducted comparative experiments to examine the three primary influencing factors: temperature (100 °C, 120 °C, 140 °C, 160 °C, 180 °C, and 200 °C), pH (8.5, 9, 9.5, 10, and 10.5), and reaction time (6 and 12 h). Through scanning electron microscopy and X-ray diffraction analysis, the optimal conditions for dawsonite synthesis were determined. The experiments revealed that within the pH range of 8.5–10.5 and at temperatures of 100–180 °C, the dawsonite products obtained are consistently pure, which indicates that CO2 can be effectively mineralized and sequestered as dawsonite within these temperature and pH ranges. The synthesis yield increased and then decreased with increasing pH and temperature. At 200 °C, the crystallinity of dawsonite decreased and the content of pseudo-boehmite increased. This suggests that higher temperature conditions are not conducive to the mineralization and sequestration of CO2. Extending the reaction time did not have a significant promoting effect on the quality of the product. The maximum amount of dawsonite synthesis, good dispersion and homogeneity of crystals, and maximum ratio of mineralization of CO2 by dawsonite were achieved at a temperature of 140 °C and a pH of 9.5, indicating that these are the optimal conditions for the hydrothermal synthesis of dawsonite using CO2. Moreover, these are the optimal geological conditions for the mineralization sequestration of CO2 in the form of dawsonite.

Full phonon dispersion along the stacking direction in nanoscale van der Waals materials by picosecond acoustics

Phonon dispersion in crystals determines many important material properties, but its measurement usually requires large-scale facilities and is limited to bulk samples. Here, we demonstrate the measurement of full phonon dispersion along the stacking direction in nanoscale systems by using picosecond acoustics. A heterostructure sample was prepared consisting of layers of hexagonal boron nitride (hBN) sandwiching a thin layer of black phosphorus (BP), within which a strain pulse was generated by photoexcitation and observed with an optical probe in the BP layer. The strain pulse traverses to the few nanometer thick hBN layers, where it propagates to the edge and echoes back, like acoustic waves in Newton’s cradle. The echoes returning to the BP layer provide information on the frequency-dependent time-of-flight and group velocity dispersion of the sample system. The microscopic origin of the photoinduced strain pulse generation and its propagation is revealed from first principles. Phonon frequency combs observed in the Fourier transform spectrum confirm the strain wave round trips and demonstrate the feasibility of determining group velocity dispersion through photoacoustics.

Potential reuse of HMX separated from decommissioned propellants: crystallization and characterization of low-sensitivity HMX

ABSTRACT Herein, in order to increase the purity and improve the performance of HMX crude products (Raw HMX) isolated from decommissioned propellants, a new method to obtain submicron levels using the solvent-anti-solvent process was proposed. Two different morphologies of HMX, regular prismatic vs. spherical-like, were obtained by means of two solvents (DMSO, DMF). Polyethylene glycol-200 (PEG-200) was used to improve the morphology and dispersion of crystals at low saturation and low crystallization temperatures. Various rates of addition of anti-solvent (water) were studied to prevent HMX crystalline transition and effectively increase purity. Furthermore, the aging process was applied to further modify the crystals with controlled particle size distribution The purity of the samples was tested by High Performance Liquid Chromatography (HPLC) spectroscopy, and the purity of the crystallized samples was improved from 95.53% in Raw HMX to over 99%. The thermal decomposition properties were investigated by differential scanning calorimetry (DSC) and the kinetic parameters of the thermal decomposition reaction of the materials were calculated using the Kissinger and Ozawa method. The samples were also tested for impact and friction sensitivity, which was reduced compared to both Raw HMX and industrial HMX, demonstrating that this type of modified HMX recovered from decommissioned propellants is fully reusable.

Conical quasi-phase-matching second harmonic generation in a 2D photonic crystal with hybrid Ewald geometric method

The direction variation of the fundamental wave in the same nonlinear photonic crystal would cause different pattern of harmonics generation. In a 2D/3D crystal with dense reciprocal lattice vectors, there will be large numbers of conical harmonic beams evolving with direction change of the fundamental wave. By rearranging the Ewald sphere and superposing it into the Ewald shell, we have a hybrid Ewald construction. It becomes a simple but useful geometric method to comprehensively depict the distribution of these quasi-phase-matching second harmonics and their conical form evolution. It presents conical second harmonic beams by their related reciprocal lattice vectors and simplifies the beams’ distribution according to spatial arrangement of those reciprocal lattice vectors. It finds that the conical beams will create, annihilate, or get enhanced in specific order when fundamental waves change incident directions. We applied the method on a periodically poled 2D LiTaO3 crystal and all observed phenomena, meet the method’s predictions. In our experiment, we observed that the conical beams distorted along the optic axis of the sample due to anisotropy, which was generally overlooked by earlier researches. The eccentricities of their ring projections suggest a potential auxiliary approach for crystal dispersion measurement.

Advanced control of microstructure in ice cream by agitation and mixing during freezing process

Agitation and mixing play an important role in ensuring the appropriate dispersion of ice crystals, bubbles, and fat globules during the freezing process in ice cream manufacturing. The dispersion determines the internal structure of ice creams and hence, the ice cream quality. To achieve advanced control of the internal structure of ice creams, in this study, the effect of agitation on air entrainment, micronisation of air bubbles, and fat globule agglomeration was investigated using a batch-type freezer with an anchor impeller. Besides, rheological properties of an ice cream sample that was stored in the refrigerator for 24 h after freezing were analysed. In addition to steady agitation, unsteady agitation with a periodical change in the rotation direction was employed. Temperature measurement and flow observation suggested more effective scraping of frozen phase from the cooling surface for unsteady agitation than for steady agitation. Furthermore, air entrainment and fat globule agglomeration during freezing were promoted under unsteady agitation. Consequently, the sample manufactured under unsteady agitation exhibited enhanced thermal robustness compared to that manufactured under steady agitation. Thus, unsteady agitation can be an effective strategy to control the formation of microstructures in ice cream.

Temporal and spectral signatures of the interaction between ultrashort laser pulses and Bloch surface waves

The resonant excitation of Bloch Surface Waves (BSWs) in dielectric one-dimensional photonic crystals is becoming a realistic photonic solution for surface integration in many domains, from spectroscopy to local field management. Bringing BSWs to ultrafast and nonlinear regimes requires a deep knowledge of the effects that the photonic crystal dispersion and the resonant surface wave excitation have on the ultrashort laser pulses. We report on the experimental evidence of spectral and temporal modifications of the radiation leaving a planar one-dimensional photonic crystal after coupling to BSWs. In such a resonant condition, a characteristic long temporal tail is observed in the outgoing pulses. Observations are performed by employing both frequency-resolved optical gating and field cross-correlation techniques.

Efficient fluoride removal using nano MgO: mechanisms and performance evaluation.

In this study, highly efficient fluoride removal of nano MgO was successfully synthesized using a simple hydrothermal precipitation method. Hexadecyl trimethyl ammonium bromide (CTMAB) was utilized as a surfactant. Its long-chain structure tightly wrapped around the precursor crystal of basic magnesium chloride, inhibiting the growth of precursor crystals, reducing their size, and improving crystal dispersion. This process enhanced the adsorption capacity of nano MgO for fluoride. The adsorption performance of nano MgO on fluoride was investigated. The results indicate that pseudo-second-order kinetics and the Langmuir isotherm model can describe the adsorption behavior for fluoride, with a maximum adsorption capacity of 122.47mg/g. Methods such as XRD, SEM, XPS, and FTIR were employed to study the adsorption mechanisms of the adsorbent. Additionally, factors potentially affecting adsorption performance in practical applications, such as pH and competing ions, were examined. This study enhances our profound understanding of the defluorination effectiveness and mechanisms of nano MgO.

Metabolic mechanism and pharmacological study of albendazole in secondary hepatic alveolar echinococcosis (HAE) model rats.

Albendazole (ABZ) is the primary treatment for alveolar echinococcosis (AE); however, its limited solubility impacts oral bioavailability, affecting therapeutic outcomes. In this study, various ABZ-solubilizing formulations, including albendazole crystal dispersion system (ABZ-CSD), albendazole hydrochloride-hydroxypropyl methylcellulose phthalate composite (TABZ-HCl-H), and albendazole hydroxyethyl sulfonate-hydroxypropyl methylcellulose phthalate composite (TABZ-HES-H), were developed and evaluated. Physicochemical properties as well as liver enzyme activity were analyzed and their pharmacodynamics in an anti-secondary hepatic alveolar echinococcosis (HAE) rat model were investigated. The formulations demonstrated improved solubility, exhibiting enhanced inhibitory effects on microcysts in HAE model rats compared to albendazole tablets. However, altered hepatic drug-metabolizing enzymes in HAE model rats led to increased ABZ levels and reduced ABZ-SO production, potentially elevating drug toxicity. These findings emphasize the importance of dose adjustments in patient administration, considering the impact of alveolar echinococcosis on rat hepatic drug metabolism.

Inverse design of arbitrary non-reciprocal acoustic dispersion in non-local phononic crystals and metamaterials

We present inverse methods to obtain arbitrary non-reciprocal dispersion relations in periodic, multi-degree-of-freedom lattices with non-local interactions. Just as phase-delayed interactions such as local resonance govern the frequency-dependence of a lattice’s dispersion relation, spatially non-local interactions govern the wavenumber dependence of the coefficients of the lattice’s characteristic equation. Thus, the use of fully general non-local interactions can, in principle, specify every branch of the dispersion diagram at every wavenumber. However, calculating a viable set of non-local interactions for a given set of desired dispersion curves is challenging, as there are multiple possible sets of coefficients that yield the same polynomial roots. To solve this problem, we first present a general method to calculate the dispersion relation of multi-degree-of-freedom non-local lattices, showing that non-local interactions create a Fourier series expansion that governs the wavenumber dependence of each matrix element. Next, we present numerical techniques to solve the inverse problem—i.e., given the desired dispersion relation, calculate the required non-local interactions—and discuss the associated computational challenges. Finally, we discuss practical methods to realize non-local interactions leveraging piezoelectric sensors and actuators, and we highlight how non-local interactions can be introduced in unit-cell based finite-element dispersion calculations.