Ni3InSb: Synthesis, Crystal Structure, Electronic Structure, and Magnetic Properties.

The ternary phase with the composition Ni3InSb has been synthesized by high-temperature synthesis and structurally characterized by a combination of X-ray analysis, neutron diffraction analysis, and theoretical calculations. The structure of Ni3InSb crystallizes in the orthorhombic space group Pnma with lattice constants a = 7.111(3) Å, b = 5.193(3) Å, and c = 8.2113(2) Å. The crystal structure contains ∼20 atoms in its unit cell, which are distributed over four crystallographically independent positions (two Ni, one In, and one Sb). The crystal structure can be considered as a ternary substitutional variant of Ni3Sn2 (Pnma, no. 62), where a trivalent In and a pentavalent Sb orderly occupy two tetravalent Sn sites of Ni3Sn2. This site decoration pattern of two neighboring elements, In and Sb, is unique and confirmed by first principles total energy calculations. The crystal structure can be described by two building units: Ni2Sb (building unit of Ni2In) and NiIn (NiAs-type). They alternate in the crystal structure and form infinite ac-slabs (puckered), and the slabs are stacked along [010]. A triangular lattice formed by Ni atoms indicates the existence of a geometrically frustrated structure. The calculated density of states and crystal orbital Hamilton population enlighten the stability and bonding characteristics of the structure. The temperature-dependent neutron diffraction study down to 5 K reveals that the crystal structure remains in the same orthorhombic symmetry with a weak anomaly in the lattice parameters at ∼100 K. Detailed temperature- and magnetic field-dependent magnetic properties of the title phase Ni3InSb show spin-glass- or spin-disorder-like behaviors below ∼300 K with an unusual magnetic behavior below 100 K, where an enhancement of magnetization with a decrease of the coercive field has been found.

Experimental Evidence of the Coexistence of Proper Magnetic and Structural Incommensurability on the [CH3NH3][Ni(COOH)3] Compound.

The present work is dedicated to characterization of the structural phase transition and incommensurate magnetic structure of the [CH3NH3][Ni(COOH)3] (1) perovskite-like metal-organic compound. The structural and magnetic characterization has been performed through variable-temperature single-crystal and powder neutron diffraction. Compound 1 crystallizes in the orthorhombic Pnma space group at room temperature. Below 84 K, a new phase has been observed. The occurrence of new reflections, which can be indexed with a wavevector along the c axis [q = 0.1426(2)c*], suggests the occurrence of an incommensurately modulated crystal structure. The structure was determined using the superspace group formalism on the Pnma(00γ)0s0 space group. This incommensurate phase remains unchanged with a decrease of the temperature up to the base temperature (ca. 2 K). Moreover, the magnetic susceptibility data, collected under zero-field-cooled and field-cooled conditions at different applied magnetic fields, show that compound 1 exhibits antiferromagnetic behavior below 34 K. In the current paper, we have confirmed that compound 1 presents the coexistence of nuclear and proper magnetic incommensurability below TN.

Observation of a spontaneous anomalous Hall response in the Mn5Si3 d-wave altermagnet candidate.

Phases with spontaneous time-reversal ( T ) symmetry breaking are sought after for their anomalous physical properties, low-dissipation electronic and spin responses, and information-technology applications. Recently predicted altermagnetic phase features an unconventional and attractive combination of a strong T -symmetry breaking in the electronic structure and a zero or only weak-relativistic magnetization. In this work, we experimentally observe the anomalous Hall effect, a prominent representative of the T -symmetry breaking responses, in the absence of an external magnetic field in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment. By symmetry analysis and first-principles calculations we demonstrate that the unconventional d-wave altermagnetic phase is consistent with the experimental structural and magnetic characterization of the Mn5Si3 epilayers, and that the theoretical anomalous Hall conductivity generated by the phase is sizable, in agreement with experiment. An analogy with unconventional d-wave superconductivity suggests that our identification of a candidate of unconventional d-wave altermagnetism points towards a new chapter of research and applications of magnetic phases.

Simulation of modulated protein crystal structure and diffraction data in a supercell and in superspace.

The toolbox for computational protein crystallography is full of easy-to-use applications for the routine solution and refinement of periodic diffraction data sets and protein structures. There is a gap in the available software when it comes to aperiodic crystallographic data. Current protein crystallography software cannot handle modulated data, and small-molecule software for aperiodic crystallography cannot work with protein structures. To adapt software for modulated protein data requires training data to test and debug the changed software. Thus, a comprehensive training data set consisting of atomic positions with associated modulation functions and the modulated structure factors packaged as both a three-dimensional supercell and as a modulated structure in (3+1)D superspace has been created. The (3+1)D data were imported into Jana2006; this is the first time that this has been performed for protein data.

A (3 + 3)-dimensional "hypercubic" oxide-ionic conductor: type II Bi2O3-Nb2O5.

The high-temperature cubic form of bismuth oxide, δ-Bi2O3, is the best intermediate-temperature oxide-ionic conductor known. The most elegant way of stabilizing δ-Bi2O3 to room temperature, while preserving a large part of its conductivity, is by doping with higher valent transition metals to create wide solid-solutions fields with exceedingly rare and complex (3 + 3)-dimensional incommensurately modulated "hypercubic" structures. These materials remain poorly understood because no such structure has ever been quantitatively solved and refined, due to both the complexity of the problem and a lack of adequate experimental data. We have addressed this by growing a large (centimeter scale) crystal using a novel refluxing floating-zone method, collecting high-quality single-crystal neutron diffraction data, and treating its structure together with X-ray diffraction data within the superspace symmetry formalism. The structure can be understood as an "inflated" pyrochlore, in which corner-connected NbO6 octahedral chains move smoothly apart to accommodate the solid solution. While some oxide vacancies are ordered into these chains, the rest are distributed throughout a continuous three-dimensional network of wide δ-Bi2O3-like channels, explaining the high oxide-ionic conductivity compared to commensurately modulated phases in the same pseudobinary system.

Multiple anion...π interactions in tris(1,10-phenanthroline-κ(2)N,N')iron(II) bis[1,1,3,3-tetracyano-2-(2-hydroxyethyl)propenide] monohydrate.

In the ionic structure of the title compound, [Fe(C12H8N2)3](C9H5N4O2)2·H2O, the octahedral tris-chelate [Fe(phen)3](2+) dications [Fe-N = 1.9647 (14)-1.9769 (14) Å; phen is 1,10-phenathroline] afford one-dimensional chains by a series of slipped π-π stacking interactions [centroid-to-centroid distances = 3.792 (3) and 3.939 (3) Å]. The 1,1,3,3-tetracyano-2-(2-hydroxyethyl)propenide anions, denoted tcnoetOH(-), reveal an appreciable delocalization of π-electron density, involving the central propenide [C-C = 1.383 (3)-1.401 (2) Å] fragment and four nitrile groups, and this is also supported by density functional theory (DFT) calculations at the B97D/6-311+G(2d,2p) level. Primary noncovalent inter-moiety interactions comprise conventional O-H...O(N) and weak C-H...O(N) hydrogen bonding [O...O(N) = 2.833 (2)-3.289 (5) Šand C...O(N) = 3.132 (2)-3.439 (2) Å]. The double anion...π interaction involving a nitrile group of tcnoetOH(-) and two cis-positioned pyridine rings (`π-pocket') of [Fe(phen)3](2+) [N...centroid = 3.212 (2) and 3.418 (2) Å] suggest the relevance of anion...π stackings for charge-diffuse polycyanoanions and common M-chelate species.

Dipole-Moment Modulation in New Incommensurate Ferrocene.

Despite 70 years of research on metallocenes and their applications, there are still unresolved regions in its phase diagram of the prototypic sandwich compound, ferrocene Fe2+[C5H5]-2 (FeCp2), and its molecular 5-fold symmetry cannot be reconciled with the dielectric response of this crystal. We found a new phase I″ of ferrocene, which reveals the relationships between the molecular conformation, intermolecular interactions, and electric permittivity of this compound. Between 172.8 and 163.5 K, the conformational disorder of ferrocene molecules transforms into the incommensurate modulation. The structure of phase I″ is described in the (3+2)-dimensional superspace, where the molecular conformations, rotations and inclinations of the Cp rings, molecular tilts, and displacements of the Fe2+ cations, as well as the CH···π bonds in the crystal environment, are modulated. These geometric changes combine into the FeCp2 bending distortion, breaking the 5-fold symmetry and generating waves of molecular dipole moments with their amplitudes approaching 4 × 10-30 C·m.

Incommensurate structures and radiation damage in Rb2V3O8 and K2V3O8 mixed-valence vanadate fresnoites.

The structures and phase transitions to incommensurate structures in Rb2V3O8 and K2V3O8 mixed-valence vanadate fresnoites are studied with synchrotron single-crystal diffraction at low temperatures and ambient pressure. Although mixed satellite reflections are absent, the modulated structure of K2V3O8 below 115 K is better described in (3 + 2)- than in (3 + 1)-dimensional space. The geometries of the VO4 and VO5 building units are rigid and it is mainly slight rotations of these polyhedra and small variation of the intermediate K-O distances that are modulated. Prolonged exposure to the high-brilliance synchrotron beam suppresses the incommensurate phase. The previously postulated phase transition to the incommensurate phase in Rb2V3O8 at 270 K was not observed. One of the reasons could be that the intense radiation also affects the modulation in this material. Strategies to collect and analyse single-crystal diffraction data measured with very intense synchrotron radiation using modern low-noise pixel area detectors are discussed.

Incommensurate magnetic structure of CrAs at low temperatures and high pressures.

The magnetic structure of chromium arsenide CrAs is studied with neutron powder diffraction at ambient pressure in the temperature range 1.5-300 K as well as with neutron single-crystal diffraction at 2 K and 0.12 GPa. The material undergoes an anti-isostructural phase transition at TN = 267 K and atmospheric conditions, in which both orthorhombic phases have the same space-group symmetry (Pnma, Z = 4) but different distortions of the parent hexagonal structure of the NiAs type (P63/mmc, Z = 2). The magnetic structure below TN is incommensurate with the propagation vector k = (0, 0, kc). At ambient pressure, the component kc decreases from kc = 0.3807 (7) at 260 K to kc = 0.3531 (6) at 50 K. Below this temperature, it is basically constant. With increasing pressure at 2 K, kc is also constant within standard uncertainties [kc = 0.353 (2)]. For the analysis of the magnetic structure, a group-theoretical approach based on the space group of the nuclear structure and its subgroups is used. To avoid falling into false minima in the refinements, a random search for magnetic moments in the models is implemented. In the literature, the magnetic structure has been determined on the basis of powder diffraction data as a double helix propagating along the c axis. Although this double-helical model leads to satisfactory agreement factors for our powder data, it does not reproduce the intensities of the magnetic satellite reflections measured on single-crystal data in a satisfactory way and can therefore be discarded. Instead, several other models are found that lead to better agreement. Each of them is spiral-like with directional components in all three directions and with no spin-density wave character that would cause a non-constant magnetic moment. In all these models, the ordering of the spins is neither a pure helix nor a pure cycloid. Instead, the unit vectors of the spin rotation planes make an angle α, 0° < α < 90°, with respect to the c* direction. The model in superspace group P21.1'(α0γ)0s yields the best agreement factors in the refinements of the neutron single-crystal and powder diffraction data. This model is unique as it is the only one in which all the magnetic moments rotate with the same chirality.

Unified (3 + 1)-dimensional superspace description of the 2212-type stair-like [Bi2Sr3Fe2O9]m[Bi4Sr6Fe2O16] family of compounds.

The (3 + 1)-dimensional superspace approach is applied to describe and refine a series of sheared compounds related to layered high T(c) superconducting oxides. Two commensurate members (m = 4, 5) of the 2212 stair-like [Bi(2)Sr(3)Fe(2)O(9)](m)[Bi(4)Sr(6)Fe(2)O(16)] family of compounds, previously studied using single-crystal diffraction data, are analyzed. A common average unit cell has been identified and a composition-dependent modulation wavevector is proposed. The model is built using only three independent atomic domains, one for the metal atoms and two for the O atoms. The three Sr, Bi and Fe species are described using close-connected crenel-like functions forming a continuous atomic domain along the internal space. The two oxygen domains are represented by crenel functions and the displacive modulation functions are built up by Legendre polynomials recently implemented in the program JANA2006. Surprisingly, the results of the refinements show a striking similarity of the displacive modulations for the two compounds analyzed, indicating that a unique model can be used to describe the correlations between the atomic displacements of the 2212 stair-like series. This final model is then applied to predict the structure of new members of the family.

Metal-free enantiomorphic perovskite [dabcoH2]2+[H3O]+Br- 3 and its one-dimensional polar polymorph.

The structure and stoichiometry of a new metal-free and ammonium-free compound [dabcoH2]2+H3O+Br- 3 (where [dabcoH2]2+ = 1,4-di-aza-bicyclo-[2.2.2]octane dication) correspond to the general formula ABX 3 characteristic of perovskites. In enantiomorphic trigonal polymorph α of [dabcoH2]2+H3O+Br- 3, the corner-sharing [H3O]Br6 octahedra combine into a 3D framework embedding [dabcoH2]2+ dications in pseudo-cubic cages. In the more dense polymorph ß, the face-sharing [H3O]Br6 octahedra form 1D polyanionic columns separated by [dabcoH2]2+ dications. These different topologies correlate with different crystal fields around the cations and their different disorder types: orientational disorders of [dabcoH2]2+ dications and H3O+ cations in polymorph α and positional disorder of [H3O]+ cations in polymorph ß. The orientational disorder increases the lengths of OH⋯Br hydrogen bonds in polymorph α, but NH⋯Br distances of ordered dabcoH2 dications are longer in polymorph ß. The presence of polar [H3O]+ cations in [dabcoH2]2+H3O+Br- 3 polymorphs offers additional polarizability of the centres compared with analogous metal-free [dabcoH2]2+[NH4]+Br- 3 perovskite.

Phase Transitions and Physical Properties of the Mixed Valence Iron Phosphate Fe3(PO3OH)4(H2O)4.

Iron phosphate materials have attracted a lot of attention due to their potential as cathode materials for lithium-ion rechargeable batteries. It has been shown that lithium insertion or extraction depends on the Fe mixed valence and reduction or oxidation of the Fe ions' valences. In this paper, we report a new synthesis method for the Fe3(PO3OH)4(H2O)4 mixed valence iron phosphate. In addition, we perform temperature-dependent measurements of structural and physical properties in order to obtain an understanding of electronic-structural interplay in this compound. Scanning electron microscope images show needle-like single crystals of 50 µm to 200 µm length which are stable up to approximately 200 °C, as revealed by thermogravimetric analysis. The crystal structure of Fe3(PO3OH)4(H2O)4 single crystals has been determined in the temperature range of 90 K to 470 K. A monoclinic isostructural phase transition was found at ~213 K, with unit cell volume doubling in the low temperature phase. While the local environment of the Fe2+ ions does not change significantly across the structural phase transition, small antiphase rotations occur for the Fe3+ octahedra, implying some kind of electronic order. These results are corroborated by first principle calculations within density functional theory, which also point to ordering of the electronic degrees of freedom across the transition. The structural phase transition is confirmed by specific heat measurements. Moreover, hints of 3D antiferromagnetic ordering appear below ~11 K in the magnetic susceptibility measurements. Room temperature visible light absorption is consistent with the Fe2+/Fe3+ mixed valence.

Real-space measurement of orbital electron populations for Li1-xCoO2.

The operation of lithium-ion batteries involves electron removal from and filling into the redox orbitals of cathode materials, experimentally probing the orbital electron population thus is highly desirable to resolve the redox processes and charge compensation mechanism. Here, we combine quantitative convergent-beam electron diffraction with high-energy synchrotron powder X-ray diffraction to quantify the orbital populations of Co and O in the archetypal cathode material LiCoO2. The results indicate that removing Li ions from LiCoO2 decreases Co t2g orbital population, and the intensified covalency of Co-O bond upon delithiation enables charge transfer from O 2p orbital to Co eg orbital, leading to increased Co eg orbital population and oxygen oxidation. Theoretical calculations verify these experimental findings, which not only provide an intuitive picture of the redox reaction process in real space, but also offer a guidance for designing high-capacity electrodes by mediating the covalency of the TM-O interactions.

An incommensurately modulated structure of η'-phase of Cu(3+x)Si determined by quantitative electron diffraction tomography.

The diffraction data of η'-Cu(3+x)(Si,Ge) were collected by 3D quantitative electron diffraction tomography on a submicrometer-sized sample, and the structure was solved by the charge-flipping algorithm in superspace. It is shown that the structure is trigonal, and it is incommensurately modulated with two modulation vectors q(1) = (α, α, 1/3) and q(2) = (-2α, α, 1/3), superspace group P31m(α, α, 1/3)000(-2α, α, 1/3)000. The modulation functions of some atoms are very complicated and reach amplitudes comparable with the unit cell dimensions. The modulated structure can be described as sheets of Cu clusters separated by honeycomb layers of mixed Si/Ge positions. The shape of the Cu clusters in the sheets strongly varies with the modulation phase, and the predominant form is an icosahedron. The striving of the Cu layers to form icosahedral clusters is deemed to be the main driving force of the modulation. The combination of methods used in this work can be applied to other structures that are difficult to crystallize in large crystals and opens new perspectives, especially for investigations of aperiodic or otherwise complex metallic alloys.

Modulated structure of nepheline.

The incommensurately modulated structure of a natural nepheline of composition K(0.54)Na(3.24)Ca(0.03)Al(3.84)Si(4.16)O(16) has been determined in superspace. The compound crystallizes in the trigonal centered superspace group X3(00γ)0 with γ = 0.2048 (10), X = (0, 0, 0, 0), (1/3, 2/3, 0, 2/3), (2/3, 1/3, 0, 1/3), a = 17.2889 (8) and c = 8.3622 (10) Å. The structure is characterized by a framework of corner-connected (Al,Si)O(4) tetrahedra. The additional cations are incorporated in two different types of channels of the framework. All atoms in the structure are displacively modulated with amplitudes below 0.1 Å. The modulation can be well described taking into account harmonics of first order only. Atomic positions in the smaller channels of the framework are fully occupied by Na(+). Cationic positions in the larger channel are occupationally modulated, yet the variation of electron density as a function of the internal coordinate t is very small and indicates that the incorporation of different types of cations (K(+), Na(+), Ca(2+)) and vacancies is realised in a highly disordered way. Average T-O distances indicate a nearly complete Al/Si ordering in the tetrahedral framework. A large part of the O atoms are approximated by split-atom positions, which are additionally affected by occupational modulation resulting in a high degree of disorder in the modulated structure. Occupational probabilities for the split-atom positions are complementary. Occupational modulations of the cations in the larger channels and the O atoms of the tetrahedral framework are coupled and correlations between occupational and displacive modulations exist.

Crystal structure of the uranyl arsenate mineral hügelite, Pb2(UO2)3O2(AsO4)2(H2O)5, revisited: a correct unit cell, twinning and hydrogen bonding.

Revisiting the structure of uranyl arsenate mineral hügelite provided some corrections to the available structural data. The previous twinning model (by reticular merohedry) in hügelite has been corrected. Twinning of the monoclinic unit cell [a = 7.0189 (7) Å, b = 17.1374 (10) Å, c = 8.1310 (10) Šand ß = 108.904 (10)°], which can be expressed as a mirror in [100], leads to a pseudo-orthorhombic unit cell (a = 7.019 Å, b = 17.137 Å, c = 61.539 Šand ß = 90.02°), which is eight times larger, with respect to the unit-cell volume, than a real cell. Moreover, the unit cell of chosen here and the unit cell given by the previous structure description both lead to the same supercell. A new structure refinement undertaken on an untwinned crystal of hügelite resulted in R = 4.82% for 12 864 reflections with Iobs > 3σ(I) and GOF = 1.12. The hydrogen-bonding scheme has been proposed for hügelite for the first time.

Hidden and apparent twins in uranyl-oxide minerals agrinierite and rameauite: a demonstration of metric and reticular merohedry.

In this work, the structures of chemically related uranyl-oxide minerals agrinierite and rameauite have been revisited and some corrections to the available structure data are provided. Both structures were found to be twinned. The two minerals are chemically similar, and though their structures differ considerably, their unit-cell metrics are similar. Agrinierite was found to be twinned by metric merohedry (diffraction type I), whereas the structure of rameauite is twinned by reticular merohedry (diffraction type II). The twinning of the monoclinic unit cells (true cells) leads to pseudo-orthorhombic or pseudo-tetragonal supercells in the single-crystal diffraction patterns of both minerals. According to the new data and refinement, agrinierite is monoclinic (space group Cm), with a = 14.069 (3), b = 14.220 (3), c = 13.967 (3) Å, ß = 120.24 (12)° and V = 2414.2 (12) Å3 (Z = 2). The twinning can be expressed as a mirror in (101) (apart from the inversion twin), which leads to a supercell with a = 14.121, b = 14.276, c = 24.221 Šand V = 2 × 2441 Å3, which is F centered. The new structure refinement converged to R = 3.54% for 6545 unique observed reflections with I > 3σ(I) and GOF = 1.07. Rameauite is also monoclinic (space group Cc), with a = 13.947 (3), b = 14.300 (3), c = 13.888 (3) Å, ß = 118.50 (3)° and V = 2434.3 (11) Å3 (Z = 2). The twinning can be expressed as a mirror in (101) (apart from the inversion twin), which leads to a supercell with a = 14.223, b = 14.300, c = 23.921 Šand V = 2 × 2434 Å3, which is C centered. The new structure refinement of rameauite converged to R = 4.23% for 2344 unique observed reflections with I > 3σ(I) and GOF = 1.48. The current investigation documented how peculiar twinning can be, not only for this group of minerals, and how care must be taken in handling the data biased by twinning.

Realization of the kagome spin ice state in a frustrated intermetallic compound.

Spin ices are exotic phases of matter characterized by frustrated spins obeying local "ice rules," in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole and can lead to different types of orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering, and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e., nonartificial) system that realizes the kagome spin ice state. The system features a variety of partially and fully ordered states and a sequence of field-induced phases at low temperatures, all consistent with the kagome ice rule.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study.

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

Structure determination of two modulated gamma-brass structures in the Zn-Pd System through a (3 + 1)-dimensional space description.

The structure determination of two composite compounds in the Zn-Pd system with close relationships to the cubic gamma-brass structure Zn(11-delta)Pd(2+delta) is reported. Their structures have been solved from single crystal X-ray diffraction data within a (3 + 1)-dimensional [(3 + 1)D] formalism. Zn(75.7(7))Pd(24.3) and Zn(78.8(7))Pd(21.2) crystallize with orthorhombic symmetry, superspace group Xmmm(00gamma)0s0 (X = [(1/2,1/2,0,0); (0,1/2,1/2,1/2); (1/2,0,1/2,1/2)]), with the following lattice parameters, respectively: a(s) = 12.929(3) A, b(s) = 9.112(4) A, c(s) = 2.5631(7) A, q = 8/13 c* and V(s) = 302.1(3) A(3) and a(s) = 12.909(3) A, b(s) = 9.115(3) A, c(s) = 2.6052(6) A, q = 11/18 c* and V(s) = 306.4(2) A(3). Their structures may be considered as commensurate because they can be refined in the conventional 3D space groups (Cmce and Cmcm, respectively) using supercells, but they also refined within the (3 + 1)D formalism to residual factors R = 3.14% for 139 parameters and 1184 independent reflections for Zn(75.7(7))Pd(24.3) and R = 3.16% for 175 parameters and 1804 independent reflections for Zn(78.8(7))Pd(21.2). The use of the (3 + 1)D formalism improves the results of the refinement and leads to a better understanding of the complexity of the atomic arrangement through the various modulations (occupation waves and displacive waves). Our refinements emphasize a unique Pd/Zn occupancy modulation at the center of distorted icosahedra, a modulation which correlates with the distortion of these polyhedra.