One of the most striking phenomena in nanoscience is the formation of self-assembled structures. Metal doped TiO₂ nanocrystals (NCs) display varying physiochemical properties based on their composition and structure. For instance, TiO₂ NCs made of a doped core have different photocatalytic properties than that doped core encased with a shell layer. This work discusses the choice of aliovalent Scandium (Sc) dopant in anatase host-lattice and the development of NCs with new core/shell morphology as a function of Sc diffusion and segregation during heat treatment of precipitated precursor from 200 to 1000 °C.

Rietveld's refinement of powder X-ray diffraction patterns [1] confirmed that Sc (with a low dopant ratio of 4 at. %) is incorporated into a TiO₂ lattice at temperatures up to 800 °C. It was found that doping with Sc caused lattice stresses and structural defects (vacancies) due to misfit strain energy resulting from different ionic radii between Sc³⁺ (0.745 Å) and Ti⁴⁺ (0.605 Å). Annealing at 800 °C under air generated segregation of Sc into specific regions of NCs. This phenomenon can be explained by simultaneously diffusion and segregation processes of Sc dopant into a thin shell surrounding the TiO₂ core while maintaining to reduce the energy of the Sc-Ti-O system. To investigate the impact of Sc on the NCs morphology, complementary scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS) were employed.

Figure 1a-b shown the core/shell growth of well-crystallized adjacent NCs. The corresponding FFTs (Fig.1b₁) shown the anatase (101) plane, connected to anatase indexed as (1 0 1), (103) and (112) (Fig.1b₂). The EELS profiles across the grain boundaries (GBs) were acquired to estimate the distribution of Sc dopant. Enrichment of the Sc at the shell near the GBs was observed (Fig.1c-d). The segregation shell was estimated to be on the order of a few nanometres.

Evaluation by STEM and EELS showed that the strain-energy driving process can be responsible for the energetically favored core-shell morphology transformation in Sc doped TiO₂ because of the relaxation of strain during NCs growth. The findings could be beneficial to understand the separated stages of NCs' nucleation and growth.

Zirconia based materials possess a unique set of attractive properties, which are responsible for the many applications in which they are used [1]. Some of these involve the use of thin films, whose properties are highly dependent on synthesis and deposition methods. Major changes in the Zr-O phase diagram, thus in material properties, occur when the crystallite size is reduced down to the nanoscale. A good example is that cubic or tetragonal phases, that have better mechanical properties than the monoclinic phase, can be retained in nanocrystalline zirconia [2,3]. The addition of yttria to zirconia can also lead to the stabilization of the high symmetry phases, producing the well-known yttria stabilized zirconia (YSZ). YSZ is the most widely used electrolyte in solid oxide fuel cells (SOFC) due to its high and pure ionic conductivity above 800 °C. However, such high operation temperatures result in high degradation rate for the SOFC, which increases the cost of this technology. Different strategies have been proposed to lower the SOFC operating temperature, being one appealing approach to employ dense thin-film based electrolytes [4].

For this work we synthetized ZrO₂ and 8YSZ (zirconia stabilized with 8% mol of yttria) by the sol-gel method and deposited thin films by dip-coating on glass substrates. The thin film crystallization process was studied in situ by grazing incidence X-Ray diffraction (GIXRD) at the KMC-2 beamline of the BESSY II synchrotron light source of Berlin by varying temperature between 300 and 800 °C in steps of 20 °C, coupled with electrical measurements using the 2-probe method.

Synthesized thin films have thicknesses between 100 and 200 nm. The in situ study on YSZ, presented as example in Figure 1, allowed us to determine how the nano crystallite size of the thin film evolved from 4 nm at 363 °C to 40 nm at 792 °C. The simultaneously measured resistivity enabled us to correlate temperature dependant transport and structural properties of these films. In both ZrO₂ and YSZ thin films, highly symmetric phases (tetragonal and cubic, respectively) are retained at high temperature and after cooling.

Gas sensing is primarily considered as a surface property of materials. The surface structure however depends to a large extent on bulk crystal structure. Knowledge of surface structure in combination with the knowledge of bulk crystal structure is thus helpful in improved understanding of the surface properties of materials. In the present work, vanadium doped tin oxide samples Sn_1-xV_xO₂ (x= 0, 0.304 and 0.343) have been synthesized by simple precipitation methods. All samples have exhibited ppm level ammonia sensing property. Doped samples have been found to be more sensitive to ppm level ammonia in air in comparison to pristine SnO₂. In order to understand the enhancement in ammonia sensing property due to vanadium doping, all samples have been characterized extensively by X-ray diffraction and X-ray photoelectron spectroscopy. Bulk crystal structures of the samples have been established by Rietveld refinements [1] using high quality powder X-ray diffraction data with the aid of the computer program Jana2006 [2]. Surface electronic structures of the samples have been determined by X-ray photoelectron spectroscopy. Analysis of surface electronic states and crystal structures has revealed a direct correlation between surface electron deficiencies and sensing responses. Based on this correlation a model mechanism has been proposed which explains the enhancement in ammonia sensing property of vanadium doped samples in comparison to pure SnO₂ [3].

Figure 1. Schematic of the mechanism for enhancement in gas sensing property

Nirman Chakraborty would like to thank DST INSPIRE (IF170810) for his research fellowship.

Graphene nanopowders and carbon nanotubes (CNTs) are widely synthesized and used to design new electromagnetic interferences (EMI) shielding materials to avoid of the electromagnetic pollution, which increases sharply with unavoidable development of electronics technology [1-2]. EMI can be defined as conducted and/or radiated electromagnetic signals emitted by electrical circuits which, under operation, perturb proper operation of surrounding electrical equipment or cause radiative damage to living/biological species. More generally, electromagnetic shielding is also defined as the prevention of the propagation of electric and magnetic waves from one region to another by using conducting or magnetic materials. The shielding can be achieved by minimizing the signal passing through a system either by reflection of the wave or by absorption and dissipation of the radiation power inside the material [3]. In the present study, the state-of-the-art research was realized in design and characterization of polymer/carbon based composites as nanostructured EMI shielding materials. The newly designed nanographene/CNT doped polymer gels were applied on the fabric substrates (ST, SG, etc. coded) by using spray coating method. The measurements (to determine electromagnetic shielding effectiveness) were performed according to ASTM D4935-10[4]. The prepared materials (before and after the coating) were also structurally investigated in molecular, nanoscopic and microscopic scales by using several complementary experimental (FTIR, WAXS, SAXS, SEM) methods. The obtained form factors which are related to core-shell cylinder and fractal models were used in nanoscale SAXS analyses (Fig.1) to characterize the morphologies, sizes and distributions. Graphen and CNT doping with percentage of 4% shows the comparative results for the layered coatings and EMI Shielding. Mono/multi layer applications of the newly designed nanomaterials on fabrics were also investigated to develope EMI shielding effectiveness. Multilayered topologies are commonly used as liners for all enclosures in which reflection, absorption of waves has to be minimized. The focused studies were increasing the surface area of the nanoparticles and reaching the stabilized monodispersed morphologies and arbitrarily oriented uniform distributions. So the nanoparticle doped polymer matrix coated nanomaterials may behave such as conductive networks against to incident signals. As increasing reflectivity and absorbance results may cause better shielding efficiency. Figure 1. Shielding Effectiveness of 4% Graphene and 4% CNT doped nanocomposite coating layers (Top), 3D, ab-initio structure (DAMMIN) model for %4 CN-ST sample, fitting curve and PDDs (Bottom)

As a result of the study, it was obtained that ellipsoidal fractal units come together to form larger and more compact core-shell oblate shaped nano aggregations. It was also shown that, the size, shape, and distribution-controlled synthesizing processes may be useful and possible to increase electromagnetic shielding effectiveness in the manner of absorption and reflection.

The aspect ratio of the graphene/CNT to polymer is a major parameter and is determinant for the studied samples. Graphene doping is respectively more efficient than that of CNT. The dispersion method is another important factor and must preserve the high aspect ratio of the doped nanomaterials as much as possible within the polymer. Especially, multilayer applications on fabric substrate make reasonably higher shielding effect because of the better surface coverage. With the further experimental works, more efficient results can be obtained with respect to metal doping inside the polymer, in the manner of corrosion, weight load, flexibility and easy application.

TiO₂ fibers were prepared through electrospinning of polymethyl methacrylate (PMMA) and Titanium isopropoxide (TIP) solution followed by calcination of fibers in air at 500 ºC. CTAB protected Palladium nanoparticles prepared through reduction method were successfully adsorbed on the TiO₂ nanofibers. Combined studies of X-ray diffraction (XRD), Scanning electron microscope (SEM) and Transmission electron microscope (TEM), indicated that the synthesized Pd/TiO₂ was anatase phase. BET indicated that the synthesized TiO₂ and Pd/TiO₂ had a surface area of 53.4672 and 43.4 m²/g, respectively. The activity and selectivity of 1 mol % Pd /TiO₂ in the Heck reaction has been investigated towards the Mizoroki-Heck carbon-carbon cross coupling of bromobenzene and styrene. Temperature, time, solvent and base were optimized and catalyst recycled twice. ¹H NMR and ¹³C NMR indicated that stilbene, a known compound from literature was obtained in various Heck reactions at temperatures between 100 ºC and 140 ºC. but the recyclability was limited due to some palladium leaching and catalyst poisoning which probably arose from some residual carbon from the polymer. The catalyst was found to be highly active under air atmosphere with reaction temperatures up to 140 ºC. Optimized reaction condition resulted into 89.7 % conversions with a TON of 1993.4 and TOF value of 332.2 hr^-1

The microstructural characterization of spinel-ferrites has been long discussed in the literature [1]. Such interests are justified by the spinel-ferrites potential applications that involve spintronic and magnetic resonance imaging (MRI), gas sensors, magnetic recording, medical diagnostics, antibacterial agents and self-controlled magnetic hyperthermia [2]. In the present work, we have synthesized Co_xZn_1-xFe₂O₄ spinel ferrite nanoparticles (x= 0, 0.1, 0.2, 0.3 and 0.4) via the precipitation and hydrothermal-joint method. Structural parameters were cross-verified using X-ray diffraction (XRD) and electron microscopy based-techniques. The magnetic parameters were determined by means of vibrating sample magnetometry. The as-synthesized Co_xZn_1-xFe₂O₄ nanoparticles exhibit high phase purity with a single-phase cubic spinel-type structure of Zn-ferrite. The microstructural parameters of the samples were estimated by XRD line profile analysis using Williamson-Hall method. The calculated crystallite sizes from XRD analysis for the synthesized samples ranged from 8.3 to 11.4 nm. The electron microscopy analysis revealed that all powder samples are composed of regular spherical nanoparticles with highly homogeneous elemental composition. The Co_xZn_1-xFe₂O₄ spinel ferrite system exhibits paramagnetic, superparamagnetic and weak ferromagnetic behavior at room temperature depending on the Co²⁺ doping ratio, while ferromagnetic ordering with a clear hysteresis loop is observed at low temperature (5K). We concluded that the substitution of Zn with Co²⁺ ions impact both structural and magnetic properties of ZnFe₂O₄ nanoparticles.[3]

References:

[1] Frajera, G., Isnard, O., Chazal, H.& Delette, G. (2019). J. Magn. Magn. Mater. 473, 92

[2] Samavati, A.& Ismail, A. F. (2017). Particuology. 30, 158.

[3] Mohamed, W. S., Alzaid, M., Abdelbaky, M.S. M., Amghouz, Z., García-Granda, S.& Abu-Dief, A.M.(2019). Nanomaterials.9, 1602.

Keywords: spinel ferrite nanoparticles; hydrothermal method; magnetic parameters; electronmicroscopies; ferromagnetic ordering.

Acknowledgments

Spanish MINECO (MAT2016–78155-C2–1-R) and Gobierno del Principado de Asturias (GRUPIN-IDI/2018/0 0 0170) are acknowledged for the financial support

In the present investigation, silica gels have been synthesized via sol-gel method under microwave radiation. For that, precursor solutions were prepared using tetraethylorthosilicate (TEOS) as the silica precursor, varying the molar ratios of water and ethanol to it. HCl was added before heating to perform acid gelation, while NH₃ (2 M) was added after gelation to promote polycondensation and Ostwald ripening reactions during aging. The use of microwave radiation under these conditions resulted in a favourable effect on the final structure of the polymeric network [1]. This approach makes it possible to obtain mesoporous silica gels in a short time, but amorphous in all cases (Fig. 1). The XRD pattern displayed the presence of a broad peak at 2θ = 17–29° that corresponds to the formation of amorphous silica according to JCPDS-card 96-900-1582.

The magnesio-thermal reduction process has already been reported as a useful way to convert silica into silicon in the presence of magnesium as a reduction agent [2,3]. Thus, our amorphous silica gels were mixed with Mg in a weight ratio of 1:1 and treated at 750 °C for 12 h under an inert atmosphere (Ar, 300 mL/min). Many phases can be produced from the reduction process of SiO₂ and Mg, such as MgO and Mg₂Si. Thus, the reduced samples were subsequently washed with HCl (1 M) for 4 hours to eliminate the undesired secondary phases. The structural properties of the obtained silicon gels were analysed and measured by X-ray diffraction (XRD), X-ray fluorescence (XRF) and high-resolution transmission electron microscopy (HR-TEM). Fig. 1 shows the XRD data of the final reduced silicon gel, illustrating the complete removal of SiO₂, with only Si peaks remaining in the structure. The major diffraction peaks at 2θ = 28.4°, 47.4° and 56.2° are presented at (111), (202) and (131) planes, respectively, which can be attributed to high-purity silicon gel according to JCPDS-card 96-901-3109. Also, the absence of additional peaks indicates that no impurities are present in the structure.

Figure 1. XRD data of a) silica gel before treatment and b) silicon gels after magnesio-thermal reduction.

[1] Flores-López, S.L., Villanueva, S.F., Montes-Morán, M.A., Cruz, G., Garrido, J.J. & Arenillas, A. (2020). Colloids Surf. Physicochem. Eng. Asp. 604, 125248.

[2] Xing, A., Zhang, J., Bao, Z., Mei, Y., Gordin, A.S. & Sandhage, K.H. (2013). Chem. Commun. 49, 6743.

[3] Jia, H., Gao, P., Yang, J., Wang, J., Nuli, Y. & Yang, Z. (2011). Adv. Energy Mater. 1, 1036.

The authors thank Prof. José R. García, University of Oviedo, Spain, for his appreciated contribution.

The structure identification of core-shell nanoparticles could be splitted into two parts. The first one was the structure of the core. In the literature two different structures of the core can be found: ℽ-Fe [1] and α-Fe[2]. The second one was the structure of the shell. Because iron is very reactive it is always covered by the oxide shell. Different structures of the oxide shell were reported: Fe₃O₄ [3], α-Fe₂O₃ [4], ℽ-Fe₂O₃[5] or the mixture of these oxides [2]. The long-time stability of Fe-Fe_xO_y core shell nanoparticles was studied in [2] where the increase of oxide shell thickness was observed. On the other hand, it was observed that the core shell nanoparticles were complete oxidized after 26 hours [6].

In this contribution, the structure identification of Fe-Fe_xO_y core shell nanoparticles were done by combination of X-ray diffraction and Mössbauer spectroscopy. The verification of structure indentification was done by computer simulation of powder X-ray diffraction pattern. The model of nanoparticle was created, and X-ray powder diffraction pattern was simulated using the Debye formula [7]. The long-time stability of the core shell nanoparticles was studied in period of 6 years. It has been found that the structure of the samples was not changed during this 6 years period. The powder X-ray diffraction data was fitted by program MStruct [8]. The program MStruct has special tool for refining bimodal distribution of particles. This tool was used for one sample, where the diffraction lines of oxide had exceptionally long tails (see Fig. 1). These long tails were originating from the core shell structure. After modelling the core shell particle and calculating the powder X-ray diffraction pattern by different methods, the best match was obtained by using the Debye formula and then the MStruct program.

[1] Fernardez-Garcia M.P., Gorria P., Bilanco J.A., Fuestes A.B., Sevilla M. Boada R., Chaboy J., Schmool D. & Greneche J.-M. (2010). Phys Rev. B. 81, 094418. [2] Linderoth S,. Morup S. & Bentzon D. (1995). J. Mat. Sci. Soc. 30, 3142. [3] Somaskandan K., Veres T., Niewczas M. & Simard B.(2008) ,New journal of chemistry, 32, 201

[4] Tong G.-X., Yuan J.-H., Ma J., Guan J.-G., Wu W.-H., Li L.-Ch. & Qiao R.(2011), Materials Chemistry and Physics, 129, 1189

[5] Rojas T.C., Sanchesez-Lopez J. C., Greneche J.M., Conde A. & Fernandez A. (2004) Journal of materials science, 39, 4877

[6] Bodker F., Morup S. & Linderoth S (1994), Physical review letters,72,282

[7] Warren B.E.(1990). X-ray diffraction, Dover publication.

[8] Matej Z., Kadlecova A., Janecek M., Matejova L.,Dopita M., & Kuzel R., (2014), Powder Diffraction, 29, S35

This work was supported by grant CZ.02.1.01/0.0/0.0/15_003/0000485

Scrap iron pieces were collected from Burka Gibe workshop and cut into 6X3 cm pieces. Metal pieces were washedwith dil.HCl and absolute alcohol and dried. These metal pieces were polished with grade 4800 Emery paper and washed and used as electrode in an electrolytic cell. 250 ml of distilled water mixed with 10mg NaCl was used as electrolyte. Electrolysis was carried out with a current of 2amp and voltage was maintained about 20 volts for 3 hours. Dark precipitate was obtained. These precipitates were collected, air dried for a day and subjected to X-ray diffraction studies for identification of phases present. Next about 20 gm of the dark precipitate was taken in a silica crucible and heated for 3 hours at 900⁰ C. A brilliant brick red material was obtained. It was subjected to x-ray diffractional studies and quantitative phase analysis, which shows that red substance is a mixture of α-ferric oxide (86.6%), Magnetite (12.3%) and maghemite (1,1%). Many of the XRD peaks due to α-ferric oxide were found to be in the nanometer range from size strain- analysis. Further studies are going on.

The secondary molecular interactions are well known able to influence the organization behaviours and electrooptical responses of dispersed molecules. [1, 2] For dispersed phase domains of organic and inorganic components, including amorphous and crystalline phases, the mutual polarization is much less recognized. In general, the interactions among phases, specially crystallites, have not been envisaged yet as an approach of crystal engineering and capable factors to enhance the electrooptical features of phase domains.

Ferroelectric polymers are able to evolve unique polar crystalline phase below curie transition temperature via the lattice packing of all-trans conformers, which allocates most of substituted fluorine atoms on one side of molecular segments and hydrogen atoms on the other side. We found that the dielectric and piezoelectric responses of polymer ferroelectric lamellar crystals are significantly enhanced by the nearby ZnO nanorods crystals, and vice versa. The involved effects of mutual polarization cause both kinds of constituent crystals to adopt opposite polarization orientation. Besides, the extent of mutual interaction will decrease with the distance between nanorods region and PVDF-TrFE lamellae region increase, as shown on Figure 1. This is the first observation of mutual interaction among crystalline phases.

In our recent research success, we found that the stacking of ferroelectric lamellae has impact on piezoelectric and surface potential. With the growth of intact lamellae, the stacking of crystal will be better than the broken ones which is considered corresponding to the alignment of dipole moments. Therefore, the better stacking of lamellae will possess lower surface potential, however the piezoelectric response is lower, as shown on Figure 2. Besides, the mutual phases interactions have been identified between quantum dots and polymer ferroelectric crystals. With the average deposition of graphene and MoS₂ quantum dots, the piezoelectricity of dispersed ferroelectric polymer crystals has been dramatically enhanced, and graphene quantum dots are able to yield better contribution. This mutual phase interactions among ferroelectric polymer crystals and 2D material quantum dots have been explored as a helpful factor to improve the recombination issue of photocatalysts and therefore enhance the efficiency of water splitting. The involved phase evolution and growth mechanisms have been under investigation, which is expected to serve as a new direction to prepare hybrid crystalline materials able to overcome the current materials application bottlenecks.

[1] Ghosh, T., Panicker, J. S., & Nair, V. C. (2017). Self-assembled organic materials for photovoltaic application. Polymers, 9(3), 112.

[2] Liu, Y., Song, J., & Bo, Z. (2021). Designing high performance conjugated materials for photovoltaic cells with the aid of intramolecular noncovalent interactions. Chemical Communications, 57(3), 302-314.

Growth and stability of SmS-TaS₂ nanotubes studied by XAFS and DAFS methods.

It is known, that during the nanotube (NT) synthesis additional unwanted phases often occur (platelets, fullerenes, amorphic content, etc.)[1] and it is very hard or even impossible to disentangle the information about the NTs from the data achieved by macroscopic methods. The purpose of this study is to show the advantages of the DAFS (Diffraction Anomalous Fine Structure) spectroscopy technique in the analysis of NT powders containing a sufficient number of unwanted phases. This technique, based on the measurement of the diffraction peak intensity in the vicinity of the X-ray absorption edge, could bring additional spectroscopic information about the tubes in the powder mixture. Contrary to conventional XAFS (X-ray absorption Fine Structure) spectroscopy, DAFS allows to measure the XAFS-like signal from a certain phase or crystallographic site separately by choosing the proper diffraction peak [2].

NTs have several diffraction features, that distinguish them from the conventional 3D crystals and single 2D layers, that are based on the same structural units/layers (Carbon nanotubes vs Graphite, etc). Due to the lack of the out-of-plane symmetry diffraction patterns of the NTs usually doesn’t show the distinct reflections of the h0l and 0kl type, that distinguish them from the bulk particles; contrary to the single 2D layers the multilayered NTs show the reflections of 00l type due to diffraction from the basal planes of the NT [3]. These 00l and hk0 reflections can be used to get information about the NTs using the DAFS technique from NT raw powder.

In order to understand the growth and stability of SmS-TaS₂ NT a set of NT powders were synthesized by chemical vapor transport method (CVT) [2] at different temperatures (800, 825, 850, 875, 900, 925, 975, 1050 C). It was found from XRD that a small amount of Ta_1.2S₂ and Ta_1.08S₂ present in all samples, intensity of Sm₂Ta₃S₂O₈ and SmTaO₄ phases starts to grow prominently at 875 C temperature. From XRD and electron microscopy studies it was also found that the NT abundancy falls down with temperature. XAFS-like spectra derived from NT 002 and 026 reflections DAFS also (Fig. 1) shows temperature dependence: the intensity of Ta L3 ‘white’ line decrease with temperature. Such dependence of ‘white’ line intensity on NT abundancy can be explained by the difference in the interaction of SmS and TaS₂ layers in bulk SmS-TaS₂ crystals and SmS-TaS₂ NT. In the bulk SmS-TaS₂ crystals (usually defined as (SmS)_1.19TaS₂) it was found that SmS layer act as a donor of electrons for the TaS₂ part [4]. In the NT due to the curvature of the layer, the number of the SmS units is smaller than in the bulk crystals, thus SmS part donates fewer electrons. Therefore, in NT there should be more Ta 5d band vacancies in comparison to bulk, thus providing a more intense Ta L3 ‘white’ line in XANES spectra.

Figure 1. XAFS-like spectra derived from 002 reflection (left) DAFS, ‘white’ intensity derived from 002 (right-top), and 026 (right-bottom) reflections DAFS.

[1] Serra, M. et al. (2020). Appl. Mater. Today. 19, 100581.

[2] Kawaguchi, T., Fukuda, K. & Matsubara, E. (2017). J. Phys. Condens. Matter. 29, 113002.

[3] Khadiev, A. & Khalitov, Z. (2018). Acta Crystallogr. Sect. A Found. Adv. 74, 233.

[4] Wiegers, G. A., Meetsma, A., Haange, R. J. & de Boer, J. L. (1991). J. Less Common Met. 168, 347.

The Debye scattering equation, as an orientation average of summation of electromagnetic waves scattered by scattering objects, was derived by Peter Debye in 1915 [1]. The intensity scattered by isotropic ensemble of scattering objects can be expressed as

I(q) = ∑_i∑_j f_i(q)f_j(q) sin(qr_ij)/qr_ij (1)

where q = 4π sinθ / λ is the magnitude of scattering vector, 2θ is the scattering angle, λ is the wavelength of used radiation, r_ij is the distance between scatterer centres (atoms) i and j and f_i, f_j are the atomic scattering factors of atoms i and j.

Since its derivation, because of its generality, the equation was successfully used for calculation of scattered intensity from various ensembles of isotropic atomic clusters and structures. The biggest drawback, significantly restricting its use, is its computational demandingness. The evaluation of double sum is computationally time consuming since it scales as N(N-1)/2, N being the number of atoms in the cluster. Various approaches and tricks were adopted in past, as binning of inter-atomic distances, etc. to overcome this drawback and speed up the calculation.

Another approach, driven by a fast development of personal computers and graphics processing units (GPU), in past years, is the use of parallel computation for the Debye equation evaluation. This concept is described and discussed in details in [2, 3] who used the NVIDIA graphics processing units with CUDA (Compute Unified Device Architecture) for calculation of Debye equation on GPU in C or C++ languages. The parallel computing approach using GPU significantly speeds up the calculation.

Using the GPU one can calculate the Debye equation for nanomaterials, nanoclusters, nano-scaled objects, clusters violating the crystallographic symmetry or disordered materials directly without any additional structural assumptions or atomic distances histogram binning. In that case the Debye equation evaluation using modern GPU is relatively fast, however significant time consuming part of the whole process is the real space atomic cluster generation and mainly passing of the atomic cluster parameters (atomic types, coordinates, occupancies and temperature factors) into GPU.

In our work we used parts of the C++/CUDA cuDebye code [3] combined with Matlab GPU computing support for Debye equation calculation. This procedure strongly benefits from simple and flexible atomic cluster generation performed in Matlab and mainly from fast memory access and data transfer of atomic cluster parameters (even for a big clusters) to GPU for Debye equation calculation. Fast atomic cluster generation and modification in Matlab together with fast data transfer to GPU memory allows not only the intensity simulation for individual atomic clusters, but as well nanoparticle real structure fitting using the Debye equation. This procedure was successfully tested on non crystallographic nanoparticle clusters and relaxation effects modelling, and fitting of stacking faults, defects and the real structure parameters in Si, Ag, Au, Cu, Pt and Ir nanoparticles, and Fe@FeO, NaYF₄ and Ag@Ti core@shell nanoparticles.

[1] Debye, P. (1915). Ann. Phys., 46, 809. [2] Gelisio L, Azanza Ricardo CL, Leoni M, Scardi P. (2010) J Appl Cryst, 43, 647. [3] Rudolph, M., Motylenko, M., Rafaja, D., (2019). IUCrJ, Vol. 6, pp. 116-127.