Wave Vector Q1 Research Articles

How can the effect of particle surface roughness on the contact area be predicted?

This paper describes a systematic study of the effect of fractal rough surfaces on the contact area with the aim of advancing contact constitutive laws used in the Discrete Element Method. An in-house Boundary Element code is adopted to investigate the mechanical behaviour of computer-generated surface roughness. Surfaces are generated to have methodically controlled root mean square height (Sq), root mean square gradient (Sdq), short wavevector (q0), large wavevector (q1), Hurst exponent (H) and fractal dimension (Df). The effect of each parameter on the contact area is investigated. Two recently proposed analytical solutions in tribology (i.e. Persson-Tosatti and Pastewka-Robbins) are applied to predict the real contact area. A parameter based on Sq, q0, and H is proposed and its sensitivity for real contact area prediction is demonstrated. Surfaces of natural sand are simulated and their mechanical response shows similar trend as the computer-generated surfaces, albeit more complex.

Ferroelectric transition and structural modulation in Sr2Na(Nb1−xTax)5O15 tungsten bronze ceramics

Effects of B-site Ta5+ substitution on the ferroelectric transition and crystal structure modulation were investigated for Sr2Na(Nb1−xTax)5O15 (x = 0–0.5) tungsten bronzes. The weakened ferroelectricity and enhanced relaxor behaviors were observed with increasing Ta, while the room temperature crystal structure changed from non-centrosymmetric to centrosymmetric. Raman spectra showed a decreasing intensity of the internal vibrations with increasing Ta, revealing different bonding mechanisms between Nb/Ta cations and O anions with reduced covalence by Ta-substitution, which resulted in weakened polarization. Two sets of superlattice reflections were detected in the selected area electron diffraction patterns: commensurate modulation for all compositions (type I), described by the wave vectors q1=14(a0∗+b0∗)+12c0∗ and q2=12(a0∗+b0∗); extra reflections of 1/2[0 0 l] at some local areas for Ta-containing compositions (type II), indicating the possible ordering of B-site cations. The distinct bonding state between the B-site cation and the O anion dominates the crossover from ferroelectric to relaxor behaviors in the present compounds.

LaTe1.82(1): modulated crystal structure and chemical bonding of a chalcogen-deficient rare earth metal polytelluride.

Crystals of the rare earth metal polytelluride LaTe1.82(1), namely, lanthanum telluride (1/1.8), have been grown by molten alkali halide flux reactions and vapour-assisted crystallization with iodine. The two-dimensionally incommensurately modulated crystal structure has been investigated by X-ray diffraction experiments. In contrast to the tetragonal average structure with unit-cell dimensions of a = 4.4996 (5) and c = 9.179 (1) Å at 296 (1) K, which was solved and refined in the space group P4/nmm (No. 129), the satellite reflections are not compatible with a tetragonal symmetry but enforce a symmetry reduction. Possible space groups have been derived by group-subgroup relationships and by consideration of previous reports on similar rare earth metal polychalcogenide structures. Two structural models in the orthorhombic superspace group, i.e. Pmmn(α,β,1/2)000(-α,β,1/2)000 (No. 59.2.51.39) and Pm21n(α,β,1/2)000(-α,β,1/2)000 (No. 31.2.51.35), with modulation wave vectors q1= αa* + βb* + 1/2c* and q2 = -αa* + βb* + 1/2c* [α = 0.272 (1) and β = 0.314 (1)], have been established and evaluated against each other. The modulation describes the distribution of defects in the planar [Te] layer, coupled to a displacive modulation due to the formation of different Te anions. The bonding situation in the planar [Te] layer and the different Te anion species have been investigated by density functional theory (DFT) methods and an electron localizability indicator (ELI-D)-based bonding analysis on three different approximants. The temperature-dependent electrical resistance revealed a semiconducting behaviour with an estimated band gap of 0.17 eV.

Effect of External Factors on Magnetism of Fluctuating Low-Dimensional Electron and Spin Correlations in Frustrated Manganites La1 – ySmyMnO3 + δ (y = 0.85, 1.0)

The effect of external factors on the temperature dependences of the magnetization of frustrated manganites La1 – ySmyMnO3 + δ (δ ~ 0.1, y = 0.85, 1.0) is studied. Two sharp peaks M(T) of different intensities detected in both samples at close temperatures Т1 and Т2 slightly higher than the critical temperature Tc of the coherent superconducting transition corresponds to the Lindhard divergence χL(qnest) of the temperature dependence of the paramagnetic susceptibility of stripelike 1D electron/spin correlations modulated with wave vectors qnest1 = 2kF1 and qnest2 = 2kF2. The formation and evolution of magnetization features with increasing field are explained by the appearance of spatial modulation of electrical and magnetic properties in ab planes in the case of total nesting of electron–hole areas of the Fermi surface. This appears as two fragments of two fluctuating quasi-one-dimensional charge/spin density waves with wave vector q1 || a and q2 || b directions incommensurate with the lattice. It is assumed that the strong dependence of the magnetization of fluctuating 1D charge/spin density wave correlations on external influences is caused by the immediate vicinity of sample properties to the quantum critical point.

Влияние внешних воздействий на магнетизм флуктуирующих низкоразмерных электронных и спиновых корреляций в фрустрированных манганитах La-=SUB=-1-y-=/SUB=-Sm-=SUB=-y-=/SUB=-MnO-=SUB=-3+delta-=/SUB=- (y = 0.85, 1.0)

In this work, we studied the effect of external influences on the temperature dependences of the magnetization of frustrated manganites La1ySmyMnO3+ ( ~ 0.1, у = 0.85,1.0). The two sharp peaks M (T) of different intensities found in both samples at close temperatures Т1and Т2 just above the critical temperature Тс of the phase transition to the coherent superconducting state correspond to the Lindhard divergence χL(qnest) of the temperature dependence of the paramagnetic susceptibility of stripe-like 1D electron / spin correlations modulated with wave vectors qnest1 = 2kF1 and qnest2 = 2kF2. The appearance and evolution of the features of magnetization with increasing field are explained by the formation in ab planes with complete nesting of the electron-hole sections of the Fermi surface of spatial modulation of electronic and magnetic properties in the form of fragments of two fluctuating quasi-one-dimensional charge / spin density waves incommensurate with a crystal lattice with wave vectors q1 || a and q2 || b directions. It is assumed that the strong dependence of the magnetization of fluctuating 1D CDW / SCW correlations on external influences is caused by the close proximity of the properties of the samples to the quantum critical point.

The (3+3) commensurately modulated structure of the uranyl silicate mineral swamboite-(Nd), Nd0.333[(UO2)(SiO3OH)](H2O)2.41

Abstract The uranyl mineral swamboite has been redefined to swamboite-(Nd) and its structure has been solved and refined as a commensurate structure in six-dimensional superspace. The structure is monoclinic, superspace group P21 /m(a1,b1,g1)00(−a1,b1,g1)00 (a2,0,g2)0s, cell parameters a=6.6560(3), b=6.9881(5), c=8.8059(6), c=11.3361(16) Å, β=102.591(5)°, modulation wave-vectors q 1 =1/3 1/3 0; q 2 =−1/3 1/3 0; q 3 =1/2 0 1/2. The structure was refined from 8717 reflections to a final R=0.0610. The model includes modulation both of atomic positions and displacement parameters, as well as occupancy waves. The structure is based upon uranyl-silicate sheets of uranophane topology alternating with an interlayer of partly occupied Nd3+ sites and H2O molecules. The strong (3+3) dimensional modulation of the structure originates from the distribution of the Nd-dominated sites and further accommodation of the suitable geometry within the sheets and charge distribution within the structure. The separation distances between the corresponding occupied Nd sites are rationals of the super-cell vectors corresponding to the modulation vectors of the structure. The case of swamboite-(Nd) is the first example of a modulated structure within the oxysalts of U6+.

Suppression of hidden order in URu2Si2 under pressure and restoration in magnetic field

We describe here recent inelastic neutron scattering experiments on the heavy fermion compound URu2Si2 realized in order to clarify the nature of the hidden order (HO) phase which occurs below T0 = 17.5 K at ambient pressure. The choice was to measure at a given pressure P where the system will go, by lowering the temperature, successively from paramagnetic (PM) to HO and then to antiferromagnetic phase (AF). Furthermore, in order to verify the selection of the pressure, a macroscopic detection of the phase transitions was also achieved in situ via its thermal expansion response detected by a strain gauge glued on the crystal. Just above Px = 0.5 GPa, where the ground state switches from HO to AF, the Q0 = (1,0,0) excitation disappears while the excitation at the incommensurate wavevector Q1 = (1.4, 0, 0) remains. Thus, the Q0 = (1, 0, 0) excitation is intrinsic only in the HO phase. This result is reinforced by studies where now pressure and magnetic field H can be used as tuning variable. Above Px, the AF phase at low temperature is destroyed by a magnetic field larger than HAF (collapse of the AF Q0 = (1, 0,0) Bragg reflection). The field reentrance of the HO phase is demonstrated by the reappearance of its characteristic Q0 = (1, 0, 0) excitation. The recovery of a PM phase will only be achieved far above HAF at HM ≈ 35 T. To determine the P-H-T phase diagram of URu2Si2, macroscopic measurements of the thermal expansion were realized with a strain gauge. The reentrant magnetic field increases strongly with pressure. Finally, to investigate the interplay between superconductivity (SC) and spin dynamics, new inelastic neutron scattering experiments are reported down to 0.4 K, far below the superconducting critical temperature TSC ≈ 1.3 K as measured on our crystal by diamagnetic shielding.

Competing multiple-q magneticstructures in HoGe3: II. Magneticstructures observed in HoGe3

The high temperature (HT) and the low temperature (LT)multiple-q vector magnetic structures of the antiferromagneticHoGe3 compound (TN = 11 K) are derived from refinements of high resolution neutron data in terms of Fourieranalysis. Various models are discussed. Over the HT range , T2 = 8.1 K (on heating), the magnetic phase is described with the wavevectors(q1,q2)where q1 = (q1x,0,0) and and , with T dependent length. It corresponds to an amplitude modulated magnetic phase with the moments at an angle of24° (2) with thec axis withinthe plane (b,c). Surprisingly this structure does not square up to a constant moment structure with and or alternatively (2a,b,3c).Instead of locking, the q2 vector jumps at T2 via a first-order transition to a long period structure with an almost 24-times larger cell≈(2a,4b,3c), or in terms of wavevectors to and , which dominates the (LT) range . The (LT) range subdivides into the lock-inLT1 range (T3 = 4.8 K on heating) where the components have a constant length and theLT2 range where q3y andq4y have a lengthvariable with T. In the intermediate temperature range, around the first-orderT2 transition (on heating or cooling), the two structures described with the wavevectors(q1,q2)and (q3, q4) coexist in varying proportions. The most probable LT magnetic structure corresponds toa complex monoclinic multiaxial canted structure with four independent Ho sites as aresult of geometric frustration related to the underlying trigonal prism arrangement of themagnetic atoms with antiferromagnetic interactions.

Magnetic transitions in lattice-matched, ordered FePt3 based antiferromagnetic/ferromagnetic films

Measurements of lattice-matched antiferromagnetic/ferromagnetic films which are ideal layered systems to study exchange bias are reported. Epitaxial films of FePt3 have two kinds of antiferromagnetic ordering. The spin ordering phase with wave vector Q1=(12120) has a Néel temperature TN=160K and that with wave vector Q2=(1200) has TN=100K. Neutron diffraction confirmed the presence of Q2=(1200) antiferromagnetic ordering in 200nm Fe25Pt75 grown on MgO(100). The loop shift and coercivity of a trilayer film of CoPt3∕FePt3∕CoPt3 decrease with increasing temperature, consistent with the observed Néel temperature of FePt3. The x-ray diffraction rocking curve widths of films grown on MgO(100) and Al2O3(112̱0) are compared and related to the loop shifts that are observed in the films with lattice-matched antiferromagnetic/ferromagnetic interfaces.

Multi-phase coexistence in the organic conductor (TMTSF)2ReO4

We present here a complete description of the phase diagram of (TMTSF)2ReO4 when pressure is applied at room temperature using resistivity measurements along both a and c-axes. In a large range of pressure and temperature, the semiconducting order characterized by the wave-vector q1 = (1/2, 1/2, 1/2) coexists with the various phases (spin density wave and superconductivity) exhibited by the metallic ordered phase (q2 = (0, 1/2, 1/2)) down to the lowest temperatures.

Magnetic Ordering of DyCuSi and HoCuSi Studied by Neutron Diffraction.

AbstractFor Abstract see ChemInform Abstract in Full Text.

A combined temperature-dependent electron and single-crystal X-ray diffraction study of the fresnoite compound Rb2V4+V25+O8

High-purity Rb2V3O8 has been grown and temperature-dependent electron and single-crystal X-ray diffraction used to carefully investigate its fresnoite-type reciprocal lattice. In contrast to other recently investigated representatives of the fresnoite family of compounds, Rb2V3O8 is not incommensurately modulated with an incommensurate basal plane primary modulation wave vector given by q∼0.3 〈110〉*. A careful low-temperature electron diffraction study has, however, revealed the existence of weak incommensurate satellite reflections characterized by the primitive primary modulation wave vector q1∼0.16c*. The reciprocal space positioning of these incommensurate satellite reflections, the overall (3+1)-d superspace group symmetry, as well as the shapes of the refined displacement ellipsoids determined from single-crystal XRD refinement, are all consistent with their arising from a distinct type of condensed rigid unit modes (RUMs) of distortion of the Rb2V3O8 parent structure.

Magnetic ordering of DyCuSi and HoCuSi studied by neutron diffraction

The magnetic ordering of the hexagonal (P63/mmc) RCuSi (R=Dy, Ho) compounds has been studied by neutron powder diffraction. Magnetic ordering occurs below TN=11.9K for R=Dy and 9.5K for R=Ho and is associated with the wave vectors, q1=(0,0,q1z) and q2=(q2x,0,q2z) for both compounds. At 1.5K the length of the wave vector q1 is close to the commensurate value q1z≈1/6 for both compounds and that of q2≈(1/15,0,1/6) for DyCuSi and q2≈(1/13,0,1/7) for HoCuSi. The wave vector length displays more important changes with temperature for the R=Dy compound than for R=Ho. Various models are discussed. For amplitude modulated arrangements of the R moments the amplitude of the waves (Fourier coefficients) are for the q1 structures 3.1(1)μB/Dy and 3.9(1)μB/Ho and for the q2 structures 5.9(2)μB/Dy and 7.8(1)μB/Ho. The two structures coexist in form of domains. The present investigation is based on simultaneous refinements of high-resolution and high-flux data. Our results differ in several points from recently published data.

Structural studies on the Fresnoite type compound Ba2VSi2O8

Abstract Single crystals of Ba2VSi2O8 have successfully been grown from a high-temperature solution and single crystal X-ray diffraction used to refine its fresnoite type average crystal structure. In contrast to other recently investigated representatives of the fresnoite family of compounds, Ba2VSi2O8 did not at first appear to be incommensurately modulated. Neither single crystal X-ray diffraction nor powder neutron diffraction gave any indication for the existence of satellite reflections in addition to the strong average structure Bragg reflections. A careful electron diffraction study, however, has revealed the existence of weak incommensurate satellite reflections characterized by the primitive primary modulation wave-vectors q 1 = 0.297 [110]* ½c* and q 2 = 0.297 [11̅0]* + ½c*. The reciprocal space positioning of these incommensurate primary modulation wave-vectors, the overall (3 + 2)-d superspace group symmetry, as well as the shapes of the refined displacement ellipsoids determined from the single crystal XRD refinement are all consistent with their arising from condensed Rigid Unit Mode (RUM) modes of distortion of the Ba2VSi2O8 parent structure. The weakness of the satellite reflections in Ba2VSi2O8 relative to, for example, Ba2TiGe2O8 or Sr2TiSi2O8 arises from the significantly smaller amplitude of the condensed RUM mode as is clear from the magnitudes of the refined average structure anistropic displacement ellipsoids.

Bi1−xCrxO1.5+1.5x′, 0.05≤x≤0.15: A New High-Temperature Solid Solution with a Three-Dimensional Incommensurate Modulation

A new metastable solid solution Bi1−xCrxO1.5+1.5x with 0.05≤x≤0.15 was synthesized by quenching Bi–Cr–O melts and structurally investigated using electron microscopy and X-ray diffraction. The oxidation state of Cr was determined to be +VI by thermogravimetry, optical spectroscopy, and magnetic measurements. Infrared spectra indicate for x=0.05 isolated CrO2−4 tetrahedra and also smaller fractions of Cr2O−27 units. The phase exhibits an average structure of the Fm3m fluorite type and a 3D incommensurate modulation, with wave vectors q1=[α, 0, 0]*, q2=[0, α, 0]*, q3=[0, 0, α]*, a=5.6025(3) Å, and α=0.2866(2) for x=0.15, and with the 3+3D superspace group symmetry P:Fm3m:Fm3m. Atomic modulation functions and periodic nodal surfaces were deduced for observed satellite reflections and a commensurate structure model derived for x=0.05. The modulated structure was compared with that of Bi0.78Nb0.22O1.72, with symmetry P:Fm3m:Fd3m.

Two-dimensional incommensurately modulated structure of (Sr0.13Ca0.87)2CoSi2O7 crystals

The incommensurate structure of (Sr(0.13)Ca(0.87))(2)CoSi(2)O(7) at room temperature has been determined from single-crystal X-ray diffraction data. The compound has a non-centrosymmetric tetragonal basic cell of a = 7.8743 (4) and c = 5.0417 (2) A with the space group P4;2(1)m. The refinements of the basic structure converged to R = 0.038 for 757 main reflections. The two-dimensional incommensurate structure is characterized by the wavevectors q(1) = 0.286 (3)(a* + b*) and q(2) = 0.286 (3)(-a* + b*), where a*, b* are the reciprocal lattice vectors of the basic structure. With the (3 + 2)-dimensional superspace group P(p4mg)(P4;2(1)(m)), the refinements converged to R = 0.071 for 1697 observed reflections (757 main and 940 satellite reflections). The structure is described in terms of displacement of the atoms, rotation, distortion of CoO(4) and SiO(4) tetrahedra, and the partial ordering of the Sr and Ca atoms accompanied with the modulation. Correlated evolution of these features throughout the crystal gives rise to various oxygen coordination around Ca/Sr. Comparison of the derived modulated structure to that of Ca(2)CoSi(2)O(7) clarified that the partial substitution of Ca by large alkaline-earth atoms such as Sr should decrease the distortion of the polyhedra around the cations.

Molecular field calculations of the phase diagram in PrCo2Si2

PrCo2Si2 has a collinear antiferromagnetic structure with a wave vector Q1=(0,0,1) for T< T1=9K, a high-order commensurate one with Q2=(0,0,25/27) for T1⩽T<T2=17K and with Q3=(0,0,7/9) for T2⩽T<TN=30K. Molecular field calculations of the moment arrangements and magnetization processes of the compound were made with a molecular field model, and the field-temperature magnetic phase diagram was reproduced. The magnetic transitions are discussed in connection with the wave-dependent molecular field coefficients of the compound.

The (T,x) magnetic phase diagram of TbNi Ge2 (0.4&lt;x&lt;1) compounds. A neutron study

Abstract The magnetic structure of the TbNixGe2 (x=0.8, 0.6) compounds has been studied by neutron powder diffraction. The paramagnetic neutron data confirmed the CeNiSi2 type of structure reported earlier for this compound. The magnetic ordering is associated with the wave vector q1=0 over the entire magnetically ordered regime for both compounds. The Tb moments adopt a uniaxial antiferromagnetic arrangement (Gz mode) with c as the preferred axis, invariant under the magnetic space group C 2 m′ 2′ c 2 1 ′ m similar to the x=0.4 and 1.0 compounds. At 1.5 K the refined moment values are: μTb=8.7(1)μB for x=0.8 and 8.9(1)μB for x=0.6. The (T,x) magnetic phase diagram indicates that TN increases linearly with increasing Ni content (31–42 K) in the 0.6

Modulated Structures in Oxidized Cerium Niobates

Three previously reported oxidized cerium niobate phases CeNbO4+x(x=0.08, 0.25, and 0.33) have been synthesized and characterized by X-ray powder and electron diffraction. All three phases display structures which are modulated variants of a parent fergusonite-type CeIIINbO4structure (I2/a,a=5.5342 (2) Åb=11.4016(6) Å,c=5.1583 (3) Å,β=94.600(5)°). Thex=0.08 phase with parent unit cell (I2/a,a=5.3029(8) Å,b=11.483(2) Å,c=5.2515(8) Å,β=91.32(2)°) is a two-dimensional, incommensurately modulated phase characterized by incommensurate primary modulation wavevectors q1∼[0.345, 0, 0.138]*pand q2∼[−0.069, 0, 0.172]*p(p for parent). Thex=0.25 phase with parent unit cell (I2/a,a=5.3522(8) Å,b=11.374(3) Å,c=5.116(1) Å,β=93.34(2)°) is a commensurately modulated superstructure phase characterized by the reciprocal space unit cell a*r=112[402]*p, b*r=14[020]*p, and c*r=13[101]*p(r for resultant). Thex=0.33 phase with parent unit cell (I1,a=5.4374(8) Å,b=11.189(2) Å,c=5.1458(8) Å,α=90.56(1),β=94.37(1),γ=88.19(1)°) is again commensurately modulated with q=13[101]*p. The close structural relationship between the three oxidized phases and possible interstitial oxygen sites in the CeIIINbO4structure are discussed.

Characterization of the high-temperature modifications of incommensurate tridymite L3-To(MX-1) from 25 to 250 degrees C

Incommensurate tridymite L3-T O (MX-1) shows a cascade of five phase transitions at 65, 110, 150, 200, and 380 degrees C upon heating. The X-ray diffraction patterns were investigated with a Buerger precession camera revealing a sequence of four incommensurate phases in the range from room temperature to 200 degrees C. The phases formed between 65 and 110 degrees C and between 110 and 150 degrees C are new modifications of tridymite. At 65 degrees C the monoclinic tridymite L3-T O (MX-1) phase undergoes a first-order transformation to an orthorhombic phase. The incommensurate structural modulation of the room-temperature phase with the wavevector q1 = 0.663 a (super *) -0.498 c (super *) flips to q2 = 0.042 a (super *) -0.388 c (super *) . Simultaneously, a commensurate modulation with tripled b lattice parameter is formed. The wavelengths of both modulations do not depend appreciably on the temperature. The incommensurate modulation discontinuously disappears near 110 degrees C whereas the commensurate modulation along the b axis becomes non-integral with a temperature-dependent wavelength varying between 115 and 100 Aa. At 150 degrees C the symmetry is reduced to monoclinic again with gamma = 90.4 degrees . Between 150 and 200 degrees C the monoclinic angle gradually decreases to 90 degrees and the wavelength of the modulation from about 90 to 65 Aa. At higher temperatures, the satellite reflections fade into weak streaks and the normal orthorhombic high-temperature modification of tridymite is formed. The phase transitions are reversible upon cooling except for the first transformation that is partly irreversible for single crystals and reversible but incomplete for pulverized material at room temperature.