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Temperature-Dependent Structural Transition in Cu-Intercalated Trigonal CuYbSe 2

Rare-earth delafossites, ARCh 2 ; A = alkali metal, R = rare-earth, Ch = chalcogen which consist of intercalated rare-earth metal dichalcogenides, host frustrated triangular lattices that are fertile ground for exotic phenomena. In most cases, the triangular rare-earth sublattice arises from R-3m (No. 166) structures with three layers of rare-earth metal dichalcogenide octahedra or P6 3 /mmc (No. 194) structures with two such layers, analogous to those found in transition metal dichalcogenides. Substituting the alkali metal with Cu + yields a distinct trigonal crystal symmetry P-3m1 (No. 164) in these structures. This symmetry change alters the coordination environment from ASe 6 octahedra in R-3m AYbSe 2 to CuSe 4 tetrahedra in CuYbSe 2 , resulting in shortened rare-earth to rare-earth separations and significantly reduced interlayer distances. Using X-ray single-crystal diffraction, powder neutron diffraction, resistance, and specific heat measurements, a structural transition slightly below room temperature (258 K) is observed. The low-temperature structure is a lower-symmetry I2/m structure, accompanied by partial Cu-site vacancy ordering. The combination of Cu disorder and the triangular lattice geometry in CuYbSe 2 provides a promising platform for investigating frustrated magnetism and unconventional transport phenomena.

Chemical structure

Exploring the Links between Structural Distortions, Orbital Ordering, and Multipolar Magnetic Ordering in Double Perovskites Containing Re(VI) and Os(VII)

A combination of high-resolution powder diffraction techniques and solid-state NMR has been employed to explore the links between crystal structure, orbital ordering, and magnetism in three isostructural double perovskites containing transition metal ions with a 5d 1 configuration. In Ba 2 ZnReO 6 , both neutron and synchrotron X-ray powder diffraction data reveal a cubic-to-tetragonal transition at 23 K that breaks the degeneracy of the t 2g orbitals and leads to a pattern of orbital ordering that stabilizes magnetic ordering when the sample is cooled below 16 K. Similar behavior is observed in Ba 2 MgReO 6 , with an orbital ordering temperature of 33 K and a magnetic ordering temperature of 18 K. Prior theoretical works suggest that the pattern of orbital order seen in the P42/mnm space group is needed to stabilize the heavily canted antiferromagnetism of these compounds. Unfortunately, powder diffraction data is not sensitive enough to differentiate between the I4/mmm and P42/mnm structural models, as the distortions are too subtle to be unambiguously identified from either neutron or synchrotron X-ray powder diffraction methods. In contrast, both diffraction and 7 Li NMR data indicate that Ba 2 LiOsO 6 retains the cubic structure down to 1.7 K. The antiferromagnetic ground state and lack of any sign of orbital ordering in Ba 2 LiOsO 6 provide compelling evidence that the electronically driven tetragonal distortion seen in Ba2ZnReO6, and Ba2MgReO6 is intimately linked to the magnetic ordering seen in those compounds. The absence of magnetic reflections in high intensity neutron powder diffraction data collected on Ba 2 MgReO 6 strongly suggests ordering of multipolar moments on Re(VI), likely ferro-octupolar ordering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Analysis of Short and Long Range Atomic Order in Nanocrystalline Diamonds with Application of Powder Diffractometry

Fundamental limitations, with respect to nanocrystalline materials, of the traditional elaboration of powder diffraction data like the Rietveld method are discussed. A tentative method of the analysis of powder diffraction patterns of nanocrystals is introduced which is based on the examination of the variation of lattice parameters calculated from individual Bragg lines (named the "apparent lattice parameter", alp). We examine the application of our methodology using theoretical diffraction patterns computed for models of nanocrystals with a perfect crystal lattice and for grains with a two-phase, core-shell structure. We use the method for the analysis of X-ray and neutron experimental diffraction data of nanocrystalline diamond powders of 4, 6 and 12 nm in diameter. The effects of an internal pressure and strain at the grain surface is discussed. This is based on the dependence of the alp values oil the diffraction vector Q and on the PDF analysis. It is shown, that the experimental results support well the concept of the two-phase structure of nanocrystalline diamond.

Palosz, B.

Cluster spin glass correlations and dynamics in Zn 0.5⁢ Mn 0.5⁢ Te

Here, we present a combined magnetometry, muon spin-relaxation (𝜇⁢SR), and neutron-scattering study of the insulating spin glass Zn 0.5 ⁢Mn 0.5 ⁢Te, for which magnetic Mn 2+ and nonmagnetic Zn 2+ ions are randomly distributed on a face-centered cubic lattice. The magnetometry and 𝜇⁢SR results confirm a spin freezing transition around 𝑇 𝑓 ≈ 23 K, with the spin-fluctuation rate decreasing gradually and somewhat inhomogeneously through the sample volume as the temperature decreases toward 𝑇 𝑓 . Characteristic spin-correlation times well above 𝑇 𝑓 are on the order of 10 −10 s, much slower than typically observed in canonical spin glasses but in line with expectations for a cluster spin glass. Using magnetic pair distribution function (mPDF) analysis and reverse Monte Carlo (RMC) modeling of the magnetic diffuse neutron-scattering data, we show that the spin-glass ground state consists of clusters of spins exhibiting short-range-ordered type-III antiferromagnetic correlations with a locally ordered moment of 3.1⁢(1)⁢𝜇 B between nearest-neighbor spins. The type-III correlations decay exponentially as a function of spin separation distance with a correlation length of approximately 5 Å. The diffuse magnetic scattering and corresponding mPDF show no significant changes across 𝑇 𝑓 , indicating that the dynamically fluctuating short-range spin correlations in the paramagnetic state retain the same basic type-III configuration that characterizes the spin-glass state; the only change apparent from the neutron-scattering data is a gradual reduction of the correlation length and locally ordered moment with increasing temperature. Taken together, these results paint a unique and detailed picture of the local magnetic structure and dynamics in Zn 0.5 ⁢Mn 0.5⁢ Te and provide strong evidence that this material is best described as a cluster spin glass. In addition, this work showcases a statistical method for extracting diffuse scattering signals from neutron powder diffraction data, which we developed to facilitate the mPDF and RMC analysis of the neutron data. This method has the potential to be broadly useful for neutron powder diffraction experiments on a variety of materials with short-range atomic or magnetic order.

magnetism

Structural Propensities in Cs2MBiX6 (M=Na, Ag; X=Cl, Br) Bismuth Halide Double Perovskites

A previously unreported low-temperature phase transition in the bismuth halide double perovskite Cs2AgBiCl6 is reported, thereby establishing trends in the structural ground state across Cs2NaBiCl6, Cs2AgBiCl6, and Cs2AgBiBr6. Using the combined toolkit of variable-temperature synchrotron X-ray and neutron powder diffraction, Raman spectroscopy, and density-functional theory–based electronic structure modeling, we demonstrate a cubic Fm¯3m → tetragonal I4/m transition upon cooling with distinct onset temperatures. Neutron powder diffraction refinements permit the unambiguously assignment of the low-temperature phase of Cs2NaBiCl6 to I4/m, correcting prior reports of an I4/mmm ground state. Cs2AgBiCl6 is also found to transforms to a structure crystallizing in the I4/m space group at low temperatures. Temperaturedependent Raman data and density-functional theory-based modeling capture the softening and freezing of out-of-phase octahedral-tilt modes and quantify relative instabilities. Solid-state nuclear magnetic resonance spectroscopy at room temperature completes the characterization and helps underpin the subtle differences in covalency across the compounds. Trends in the phase transition temperature Ts and tilt magnitudes emerge from coupled effects of halide identity, M(I)–site bonding character, and a mismatch between interatomic distances. These results establish the structure– dynamics–bonding framework for tuning tilt-driven instabilities in halide double perovskites.

Tian, Haowen

Quenched disorder in the triangular lattice antiferromagnet YbZn 2⁢ GaO 5

We investigate the crystal electric field (CEF) excitations of Yb 3+ ions in powder samples of the triangular-lattice rare-earth-based antiferromagnet YbZn 2⁢ GaO 5 using inelastic neutron scattering (INS). Three CEF excitations from the ground-state Kramers doublet were observed, each exhibiting significant broadening beyond instrumental resolution. Combining temperature-dependent INS and neutron powder diffraction, we identify a significant static contribution to this broadening and attribute it to heterogeneous coordination of Yb 3+ ions due to Ga 3+ /Zn 2+ site mixing. Rietveld refinement of neutron powder diffraction indicates that 35% of Ga occupies the Zn site and 60% of Zn occupies the Ga site. We show with a point charge model for the CEF Hamiltonian that heterogeneous coordination of Yb3+ ions leads to broadened CEF peaks. First-principles calculations demonstrate that the random Ga 3+ /Zn 2+ distribution can produce the distortions of the YbO 6 octahedra observed from neutron diffraction. Because the documented heterogeneity will extend to exchange interactions, our results suggest that disorder is a significant factor in the unusual magnetism previously reported in YbZn 2 ⁢GaO 5 , including broad low-energy magnetic excitations and the absence of magnetic ordering down to 0.3 K.

Crystal field excitations

Competing magnetic phases in Cr 3+𝛿 ⁢Te 4 are spatially segregated

Cr 1+𝑥⁢ Te 2 is a self-intercalated van der Waals system that is of current interest for its room-temperature room-temperature ferromagnetic (FM) phases and tunable topological properties. In bulk samples, the strain from the interstitial Cr ions leads to distinct structural phases for different ranges of 𝑥. Early neutron powder diffraction (NPD) measurements on the monoclinic phase Cr 3 ⁢Te 4 (𝑥=0.5) presented evidence for competing FM and antiferromagnetic (AFM) phases. Here we apply neutron diffraction to a single crystal of Cr 3+𝛿 ⁢Te 4 with 𝛿=−0.10 and discover that it consists of two distinct monoclinic phases, one with FM order below 𝑇 C ≈321 K and another that develops AFM order below 𝑇 N ≈86 K. In contrast, we find that a crystal with 𝛿=−0.26 exhibits only FM order below 𝑇 C ≈285 K. The single-crystal analysis is complemented by results obtained with NPD, x-ray powder diffraction, and transmission electron microscopy (TEM) measurements on the 𝛿=−0.10 composition. From observations of spontaneous magnetostriction of opposite sign at 𝑇 C and 𝑇 N , along with the TEM evidence for both monoclinic phases in a single thin ( ≈100 nm) grain, we conclude that the two phases must have a fine-grained ( ≲100 nm) intergrowth character, as might occur from high-temperature spinodal decomposition during the growth process. Calculations of the relaxed lattice structures for the FM and AFM phases with density functional theory provide a rationalization of the observed spontaneous magnetostrictions. Correlations between the magnitude and orientation of the magnetic moments with lattice parameter variation demonstrate that the magnetic orders are sensitive to strain, thus explaining why magnetic ordering temperatures and anisotropies can be different between bulk and thin-film samples, when the latter are subject to epitaxial strain. Our results point to the need to investigate the supposed coexistence FM and AFM phases reported elsewhere in the Cr 1+𝑥 ⁢Te 2 system, such as in the Cr 5 ⁢Te 8 phase (𝑥=0.25).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Phase diagram and electrical behavior of silicon-rich iridium silicide compounds

The iridium-silicon phase diagram on the silicon-rich side was investigated by means of X-ray powder diffraction, density, differential thermal analysis, metalography, microprobe analysis, and electrical resistivity. Attempts were made to prepare eight previously reported silicon-rich iridium silicide compounds by arc melting and Bridgman-like growth. However, microprobe analysis identified only four distinct compositions: IrSi, Ir3Si4, Ir3Si5 and IrSi sub about 3. The existence of Ir4Si5 could not be confirmed in this study, even though the crystal structure has been previously reported. Differential thermal analysis (DTA) in conjunction with X-ray powder diffraction confirm polymorphism in IrSi sub about 3, determined to have orthorhombic and monoclinic unit cells in the high and low temperature forms. A eutectic composition alloy of 83 +/- 1 atomic percent silicon was observed between IrSi sub about 3 and silicon. Ir3Si4 exhibits distinct metallic behavior while Ir3Si5 is semiconducting. Both and IrSi and IrSi sub about 3 exhibit nearly temperature independent electrical resistivities on the order of 5-10 x 10 exp -6 ohms-m.

Allevato, C. E.

Collinear antiferromagnetic order in a quasi-two-dimensional triangular lattice compound DyNiAl 4 Ge 2

The two-dimensional magnetic triangular lattice, with rare-earth local moments coupled through long-range interactions and hosting strong spin-orbit coupling, serves as an ideal platform for exploring novel quantum phenomena. Here, we report the physical properties of DyNiAl 4 Ge 2 single crystals through comprehensive structural, magnetic, heat capacity, electrical transport, and neutron powder diffraction measurements. DyNiAl 4 Ge 2 crystallizes in a trigonal lattice with the space group $R\bar{3}m$, where Dy atoms form two-dimensional triangular lattice layers within the 𝑎𝑏 plane and stack along the 𝑐 axis. Magnetic susceptibility measurement reveals a magnetic phase transition at 𝑇 𝑁 = 9.0 K, further confirmed by the 𝜆-shaped peak in the heat capacity curve. The obtained temperature-magnetic field phase diagram is relatively simple compared to other isostructural compounds, suggesting the absence of magnetic frustration. This is further evidenced by neutron powder diffraction, which shows a collinear antiferromagnetic ground state with a propagation vector 𝒌 = (0, 0, 1.5), implying the absence of magnetic frustration in DyNiAl 4 Ge 2 . In this magnetic structure, Dy moments are aligned ferromagnetically within each triangular layer and arranged antiferromagnetically between adjacent layers along the 𝑐 axis. In conclusion, our results establish DyNiAl 4 Ge 2 as a model system for understanding the interplay between RKKY interaction and geometrical frustration in this family of compounds.

Wu, HengHeng [Chinese Academy of Sciences (CAS), S

Observation of Thermally Induced Piezomagnetic Switching in Cu 2 OSeO 3 Polymorph Synthesized under High-Pressure

A polymorph of Cu 2 OSeO 3 with the distorted kagome lattice is successfully obtained using the high-pressure synthesis technique (Cu 2 OSeO 3 -HP). The structural analysis using X-ray and neutron powder diffraction suggests that the tetrahedral Cu 2+ clusters [similar to those in Cu 2 OSeO 3 ambient-pressure phase (Cu 2 OSeO 3 -AP)] exist in Cu 2 OSeO 3 -HP but with three symmetry inequivalent sites. No structural change is observed between 1.5 K and the room temperature. The complex magnetic H-T phase diagram is established based on the temperature- and field-dependent magnetization data, indicating two distinct antiferromagnetic phases at low and intermediate temperatures, in addition to the higher-temperature spin-glass-like phase. The low temperature phase is identified by neutron powder diffraction refinements as a canted noncollinear antiferromagnetic order with a weak ferromagnetic component along the b-axis. Size of the refined ordered moment is ≈1.00(4) µ B in Cu 2 OSeO 3 -HP, indicating a large enhancement compared to that of Cu 2 OSeO 3 -AP (≈0.61 µ B ). By applying a uniaxial stress, finite enhancement of weak ferromagnetic component in the noncollinear antiferromagnetic phase in Cu 2 OSeO 3 -HP is observed, which is the clear evidence of the piezomagnetic effect. Interestingly, the sign of the induced magnetization changes on heating from the low-temperature to the intermediate-temperature phases, indicating a novel piezomagnetic switching effect in this compound.

36 MATERIALS SCIENCE

In situ characterization of metastable Pb3O5 and Pb2O3 phases during thermal decomposition of PbO2 to PbO

Nonstoichiometric lead oxides play a key role in the formation and cycling of the positive electrodes in a lead acid battery. These phases have been linked to the underutilization of the positive active material but also play a key role in the battery’s cycle life, providing inter-particle adhesion and the connection to the underlying lead grid. Similar phases have previously been identified by mass loss or color change during thermal annealing of PbO2 to PbO, suggesting that at least two intermediate PbOx phases exist. Using multiple in situ analysis techniques (powder diffraction, x-ray absorption, x-ray photoelectron spectroscopy) and ex situ nuclear magnetic resonance measurements, the structural conversion and changes in the lead oxidation states were identified during this process. Isolation of the PbOx phases enabled confirmation of Pb3O5 and Pb2O3 by diffraction and the first 207Pb NMR measurement of these intermediates.

Kinnibrugh, Tiffany L.

Polymorphism and Phase Control in Dion–Jacobson 2D 3-(Aminomethyl)piperidinium-Based Metal Iodide Perovskites

Two-dimensional halide perovskites exhibit rich structural diversity and tunable optoelectronic properties, making them promising materials for energy, sensing, and photonic applications. In this work, we report the structural mapping of four distinct polymorphs, γ (P2 1 /c), β (P4/mbm), α (P4/mmm), and δ (Cmcm) in the two-dimensional iodoplumbate, iodostannate, and iodogermanate perovskite so-called Dion-Jacobson series (3AMP)MI4 (M = Sn, Pb, Ge), where 3AMP is 3-(aminomethyl)piperidinium. The phases exhibit systematic evolution in octahedral distortion, lattice symmetry, and metal–halide geometry, enabling structural control over optoelectronic properties. Notably, the α-phase of (3AMP)SnI 4 represents a rare, ambient-stable, high-symmetry structure for Sn-based perovskites, without a phase transition down to 100 K. Variable-temperature single-crystal diffraction, powder x-ray diffraction (PXRD), and calorimetry reveal metal- and temperature-dependent polymorph interconversions, including the emergence of long range supercell reflections in Pb-rich compositions at low temperature. Optical spectroscopy and photoelectron yield spectroscopy confirm band gap tunability and band alignment trends, highlighting symmetry-dependent shifts and anomalous band gap bowing in mixed-metal systems, verified by electronic structure calculations. Calculations additionally indicate that the higher symmetry phases have reduced electron and hole effective masses compared to the lower symmetry phases.

36 MATERIALS SCIENCE

Crystallization Kinetics of Barium and Strontium Aluminosilicate Glasses of Feldspar Composition

Crystallization kinetics of BaO.Al2O3.2SiO2 (BAS) and SrO.Al2O3.2SiO2 (SAS) glasses in bulk and powder forms have been studied by non-isothermal differential scanning calorimetry (DSC). The crystal growth activation energies were evaluated to be 473 and 451 kJ/mol for bulk samples and 560 and 534 kJ/mol for powder specimens in BAS and SAS glasses, respectively. Development of crystalline phases on thermal treatments of glasses at various temperatures has been followed by powder x-ray diffraction. Powder samples crystallized at lower temperatures than the bulk and the crystallization temperature was lower for SAS glass than BAS. Crystallization in both glasses appeared to be surface nucleated. The high temperature phase hexacelsian, MAl2Si2O8 (M = Ba or Sr), crystallized first by nucleating preferentially on the glass surface. Also, monoclinic celsian does not nucleate directly in the glass, but is formed at higher temperatures from the transformation of the metastable hexagonal phase. In SAS the transformation to monoclinic celsian occurred rapidly after 1 h at 1100 C. In contrast, in BAS this transformation is sluggish and difficult and did not go to completion even after 10 h heat treatment at 1400 C. The crystal growth morphologies in the glasses have been observed by optical microscopy. Some of the physical properties of the two glasses are also reported.

Hyatt, Mark J.

Higher Dimensionality in the Mg–Co–B System: Synthesis and Structure of Incommensurate Composite Mg 1+ε Co 4 B 4

Guided by high-temperature in situ X-ray diffraction, the discovery and synthesis of Mg 1+ε Co 4 B 4 (ε ≈ 0.272) using a MgH 2 hydride precursor is reported, along with a detailed crystal structure description and measurement of magnetic properties. The mismatch in lattice periodicities between Mg and Co–B substructures places Mg 1+ε Co 4 B 4 in the family of incommensurate composite crystals and prompted structural refinement in a (3 + 1)-dimensional model. The structure of Mg 1+ε Co 4 B 4 (P4 2 /ncm(00γ)s00s, a = 6.75847(7) Å, c = 3.94007(8) Å, q = (0, 0, 1.2721(3))) was refined from neutron powder diffraction and high-resolution powder X-ray diffraction data and confirmed by scanning transmission electron microscopy and electron diffraction. Mg 1+ε Co 4 B 4 is isostructural to Nd 1+ε Fe 4 B 4 and several related ternary borides with 0.07 ≤ ε ≤ 0.17, with Mg occupying the rare-earth site. Satellite reflections in the electron diffraction patterns hinted at positional modulation of the transition metal–boron substructure by Mg atoms, but this could not be refined from the neutron or X-ray diffraction data. Low-temperature magnetic measurements show no indications of long-range magnetic ordering or superconductivity down to 5 K. DFT calculations confirmed the absence of a magnetically ordered ground state and the stability of a 5:4 supercell (ε = 0.25) relative to the fully commensurate structure. Neutron diffraction and synthesis from elemental Mg demonstrated that Mg 1+ε Co 4 B 4 is not a hydrogen-stabilized phase. Mg 1+ε Co 4 B 4 represents the second compound reported in the Mg–Co–B system and the first superspace symmetry model of a Nd 1+ε Fe 4 B 4 -type incommensurate composite compound refined from powder diffraction data.

chemical structure

Laser, vacuum and gas reaction chamber for operando measurements at NSLS-II's 28-ID-2

We present a laser reaction chamber that we have developed for in situ/operando X-ray diffraction measurements at the NSLS-II 28-ID-2 X-ray powder diffraction beamline. This chamber allows for rapid and dynamic sample heating under specialized gas environments, spanning ambient conditions down to vacuum pressures. We demonstrate the capabilities of this setup through two applications: laser-driven heating in polycrystalline iron oxide and in single-crystal WTe 2 . Our measurements reveal the ability to resolve chemical reaction kinetics over minutes with 1 s time resolution. This setup advances opportunities for in situ/operando X-ray diffraction studies of both bulk and single-crystal materials.

36 MATERIALS SCIENCE

Multidimensional Rietveld refinement of high-pressure neutron diffraction data of PbNCN

High-pressure neutron powder diffraction data from PbNCN were collected on the high-pressure diffraction beamline SNAP located at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (Tennessee, USA). The diffraction data were analyzed using the novel method of multidimensional (two dimensions for now, potentially more in the future) Rietveld refinement and, for comparison, employing the conventional Rietveld method. To achieve two-dimensional analysis, a detailed description of the SNAP instrument characteristics was created, serving as an instrument parameter file, and then yielding both cell and spatial parameters as refined under pressure for the first time for solid-state cyanamides/carbodiimides. The bulk modulus B 0 = 25.1 (15) GPa and its derivative B ′ 0 = 11.1 (8) were extracted for PbNCN following the Vinet equation of state. Surprisingly, an internal transition was observed beyond 2.0 (2) GPa, resulting from switching the bond multiplicities (and bending direction) of the NCN 2− complex anion. The results were corroborated using electronic structure calculation from first principles, highlighting both local structural and chemical bonding details.

Meinerzhagen, Yannick

Shifting and tilting towards enhanced piezoelectricity in high-temperature ceramics: an average structure study of (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 through X-ray and neutron diffraction

A comprehensive report is provided of the average structure of a high Curie temperature ferroelectric ceramic, (1 − x)BiFe 2/8 Ti 3/8 Mg 3/8 O 3 –xPbTiO 3 (BFTM–xPT) when x = 0.25–0.375 at room temperature. Both neutron and synchrotron X-ray powder diffraction data were collected and combined Rietveld refinements were completed. These data revealed that, of the compositions studied, BFTM–xPT crystallizes as mixed phase material. At x = 0.25–0.275, the average structure of each phase is best described by space groups R3c and Cc. At 0.30 ≥ x ≥ 0.35, a morphotropic phase boundary is present and is best modelled by space groups P4mm and Cc, where space group Cc is the dominant phase. As the concentration of PbTiO 3 increases, the amount of octahedral tilting decreases and x = 0.375 exhibits a loss of octahedral tilting and crystallizes in space groups P4mm and Cm. In conclusion, an updated phase diagram at room temperature of this novel system is given and structural intricacies responsible for its piezoelectric properties are revealed.

high Curie temperature

High Pressure X-Ray Diffraction Studies on Nanocrystalline Materials

Application of in situ high pressure powder diffraction technique for examination of specific structural properties of nanocrystals based on the experimental data of SiC nanocrystalline powders of 2 to 30 nrn diameter in diameter is presented. Limitations and capabilities of the experimental techniques themselves and methods of diffraction data elaboration applied to nanocrystals with very small dimensions (< 30 nm) are discussed. It is shown that due to the complex structure, constituting a two-phase, core/surface shell system, no unique lattice parameter value and, consequently, no unique compressibility coefficient can satisfactorily describe the behavior of nanocrystalline powders under pressure. We offer a tentative interpretation of the distribution of macro- and micro-strains in nanoparticles of different grain size.

Palosz, B.