Concentration dependence of lipopolymer self-diffusion in supported bilayer membranes

Self-diffusion coefficients of poly(ethylene glycol)2k-derivatized lipids (DSPE-PEG2k-CF) in glass-supported DOPC phospholipid bilayers are ascertained from quantitative fluorescence recovery after photobleaching (FRAP). We developed a first-order reaction–diffusion model to ascertain the bleaching constant, mobile fraction and lipopolymer self-diffusion coefficient D_s at concentrations in the range c ≈ 0.5–5 mol%. In contrast to control experiments with 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(7-nitro-2-1,3-benzoxadiazol-4-yl) (ammonium salt) (DOPE-NBD) in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), the lipopolymer self-diffusion coefficient decreases monotonically with increasing concentration, without a distinguishing mushroom-to-brush transition. Our data yield a correlation D_s = D₀/(1 + αc), where D₀ ≈ 3.36 µm² s⁻¹ and α ≈ 0.56 (with c expressed as a mole percent). Interpreting the dilute limit with the Scalettar–Abney–Owicki statistical mechanical theory for transmembrane proteins yields an effective disc radius a_e ≈ 2.41 nm. On the other hand, the Bussell–Koch–Hammer theory, which includes hydrodynamic interactions, yields a_e ≈ 2.92 nm. As expected, both measures are smaller than the Flory radius of the 2 kDa poly(ethylene glycol) (PEG) chains, R_F ≈ 3.83 nm, and significantly larger than the nominal radius of the phospholipid heads, a_l ≈ 0.46 nm. The diffusion coefficient at infinite dilution D₀ was interpreted using the Evans–Sackmann theory, furnishing an inter-leaflet frictional drag coefficient b_s ≈ 1.33 × 10⁸ N s m⁻³. Our results suggest that lipopolymer interactions are dominated by the excluded volume of the PEG-chain segments, with frictional drag dominated by the two-dimensional bilayer hydrodynamics.     

The effect of nanoscale surface curvature on the oligomerization of surface-bound proteins

The influence of surface topography on protein conformation and association is used routinely in biological cells to orchestrate and coordinate biomolecular events. In the laboratory, controlling the surface curvature at the nanoscale offers new possibilities for manipulating protein–protein interactions and protein function at surfaces. We have studied the effect of surface curvature on the association of two proteins, α-lactalbumin (α-LA) and β-lactoglobulin (β-LG), which perform their function at the oil–water interface in milk emulsions. To control the surface curvature at the nanoscale, we have used a combination of polystyrene (PS) nanoparticles (NPs) and ultrathin PS films to fabricate chemically pure, hydrophobic surfaces that are highly curved and are stable in aqueous buffer. We have used single-molecule force spectroscopy to measure the contour lengths L_c for α-LA and β-LG adsorbed on highly curved PS surfaces (NP diameters of 27 and 50 nm, capped with a 10 nm thick PS film), and we have compared these values in situ with those measured for the same proteins adsorbed onto flat PS surfaces in the same samples. The L_c distributions for β-LG adsorbed onto a flat PS surface contain monomer and dimer peaks at 60 and 120 nm, respectively, while α-LA contains a large monomer peak near 50 nm and a dimer peak at 100 nm, with a tail extending out to 200 nm, corresponding to higher order oligomers, e.g. trimers and tetramers. When β-LG or α-LA is adsorbed onto the most highly curved surfaces, both monomer peaks are shifted to much smaller values of L_c. Furthermore, for β-LG, the dimer peak is strongly suppressed on the highly curved surface, whereas for α-LA the trimer and tetramer tail is suppressed with no significant change in the dimer peak. For both proteins, the number of higher order oligomers is significantly reduced as the curvature of the underlying surface is increased. These results suggest that the surface curvature provides a new method of manipulating protein–protein interactions and controlling the association of adsorbed proteins, with applications to the development of novel biosensors.     

Wurtzite-derived ternary I–III–O2 semiconductors

Ternary zincblende-derived I–III–VI₂ chalcogenide and II–IV–V₂ pnictide semiconductors have been widely studied and some have been put to practical use. In contrast to the extensive research on these semiconductors, previous studies into ternary I–III–O₂ oxide semiconductors with a wurtzite-derived β-NaFeO₂ structure are limited. Wurtzite-derived β-LiGaO₂ and β-AgGaO₂ form alloys with ZnO and the band gap of ZnO can be controlled to include the visible and ultraviolet regions. β-CuGaO₂, which has a direct band gap of 1.47 eV, has been proposed for use as a light absorber in thin film solar cells. These ternary oxides may thus allow new applications for oxide semiconductors. However, information about wurtzite-derived ternary I–III–O₂ semiconductors is still limited. In this paper we review previous studies on β-LiGaO₂, β-AgGaO₂ and β-CuGaO₂ to determine guiding principles for the development of wurtzite-derived I–III–O₂ semiconductors.     

New aspects of π–d interactions in magnetic molecular conductors

The 2 : 1 cation radical salts of bent donor molecules of ethylenedithio-tetrathiafulvalenoquinone-1,3-dithiolemethide (EDT-TTFVO), ethylenedithio-diselenadithiafulvalenoquinone-1,3-dithiolemethide (EDT-DSDTFVO), ethylenedithio-diselenadithiafulvalenothioquinone-1,3-diselenolemethide (EDT-DSDTFVSDS), ethylenedioxy-tetrathiafulvalenoquinone-1,3-dithiolemethide (EDO-TTFVO) and ethylenedioxy-tetrathiafulvalenoquinone-1,3-diselenolemethide (EDO-TTFVODS) with FeX₄⁻ (X = Cl, Br) ions are prepared by electrocrystallization. The crystal structures of these salts are composed of alternately stacked donor molecule and magnetic anion layers. The band structures of the donor molecule layers are calculated using the overlap integrals between neighboring donor molecules and are compared with the observed electronic transport properties. The magnetic ordering of the Fe(III) d spins of FeX₄⁻ ions is determined from magnetization and heat capacity measurements. The magnetic ordering temperatures are estimated by considering a combination of a direct d–d interaction between the d spins and an indirect π–d interaction between the conduction π electron and the d spins, whose magnitudes are separately calculated from the crystal structures with an extended Hückel molecular orbital method. The occurrence of a π–d interaction is proved by the negative magnetoresistance, and the magnitude of magnetoresistance reflects the strength of the π–d interaction. The effect of pressure on the magnetoresistance is studied, and the result indicates that the magnitude of magnetoresistance increases, namely, the π–d interaction is enhanced with increasing pressure. From these experimental results it is shown that (EDT-TTFVO)₂•FeBr₄ is a ferromagnetic semiconductor, (EDT-DSDTFVO)₂•FeX₄ (X = Cl, Br) and (EDT-DSDTFVSDS)₂•FeBr₄ are metals exhibiting antiferromagnetic ordering of the d spins, and (EDO-TTFVO)₂•FeCl₄ and (EDO-TTFVODS)₂•FeBr₄•(DCE)_0.5 (DCE =-dichloroethane) are genuine antiferromagnetic metals. Among them, the (EDT-TTFVO)₂•FeBr₄ salt is the first π–d molecular system where the d spins of FeBr₄⁻ ions are ferromagnetically ordered through antiferromagnetic interaction with the conduction π electrons. Corresponding to this ferromagnetic ordering, an anomalous dielectric slow-down phenomenon toward the ordering temperature is observed. The π–d interaction in (EDT-DSDTFVSDS)₂•FeBr₄ is very large and comparable to that in λ-(BETS)₂•FeCl₄, which has the highest reported value so far, while the d–d interaction is fairly small. Concerning the ratio between the magnitudes of π–d and d–d interactions (J_πd/J_dd), this salt is currently the best π–d molecular system.     

Free volume and mechanical properties of Palacos® R bone cement

The free volume and the mechanical properties of Palacos® R bone cement were determined from positron annihilation lifetime spectroscopy (PALS) and from dynamic mechanical thermal analysis (DMA) in the temperature ranges 24–220 °C and 30–120 °C, respectively. The heating of bone cement caused an appreciable reduction of the free volume, measured as a decrease in the ortho-positronium lifetime ₃ from 2.04 to 1.91 ns, as well as a clear increase in the storage modulus from 2.3 to 3.0 GPa. The changes in free volume and storage modulus after the heat treatment were interpreted as an effect of elimination of residual monomer from the bone cement. The free volume of the bulk-polymerized phase of bone cement was estimated from a simple difference method, suggesting that the residual monomer was eliminated from the bone cement between 60 and 90 °C, thus implying a glass transition temperature of only 60 °C for the bulk-polymerized phase. The spherical free volume cavity size estimated from the ortho-positronium lifetime V(₃), and the storage modulus E_storage from DMA measurements were found to correlate by a linear relationship throughout the studied temperature range, and the correlation appeared to be independent of the presence of residual monomer.     

Comparisons of immersion and electrochemical properties of highly biocompatible Ti–15Zr–4Nb–4Ta alloy and other implantable metals for orthopedic implants

Metal release from implantable metals and the properties of oxide films formed on alloy surfaces were analyzed, focusing on the highly biocompatible Ti–15Zr–4Nb–4Ta alloy. The thickness and electrical resistance (R_p) of the oxide film on such an alloy were compared with those of other implantable metals. The quantity of metal released during a 1-week immersion test was considerably smaller for the Ti–15Zr–4Nb–4Ta than the Ti–6Al–4V alloy. The potential (E₁₀) indicating a current density of 10 μA cm⁻² estimated from the anodic polarization curve was significantly higher for the Ti–15Zr–4Nb–4Ta than the Ti–6Al–4V alloy and other metals. Moreover, the oxide film (4–7 nm thickness) formed on the Ti–15Zr–4Nb–4Ta surface is electrochemically robust. The oxide film mainly consisted of TiO₂ with small amounts of ZrO₂, Nb₂O₅ and Ta₂O₅ that made the film electrochemically stable. The R_p of Ti–15Zr–4Nb–4Ta was higher than that of Ti–6Al–4V, i.e. 0.9 Ω cm² in 0.9% NaCl and 1.3 Ω cm² in Eagle''s medium. This R_p was approximately five-fold higher than that of stainless steel, which has a history of more than 40 years of clinical use in the human body. Ti–15Zr–4Nb–4Ta is a potential implant material for long-term clinical use. Moreover, E₁₀ and R_p were found to be useful parameters for assessing biological safety.     

Three-dimensional reconstruction of anomalous eutectic in laser remelted Ni-30 wt.% Sn alloy

Laser remelting has been performed on Ni-30 wt.% Sn hypoeutectic alloy. An anomalous eutectic formed at the bottom of the molten pool when the sample was remelted thoroughly. 3D morphologies of the α-Ni and Ni₃Sn phases in the anomalous eutectic region were obtained and investigated using serial sectioning reconstruction technology. It is found that the Ni₃Sn phase has a continuous interconnected network structure and the α-Ni phase is distributed as separate particles in the anomalous eutectic, which is consistent with the electron backscatter diffraction pattern examinations. The α-Ni particles in the anomalous eutectic are supersaturated with Sn element as compared with the equilibrium phase diagram. Meanwhile, small wavy lamella eutectics coexist with anomalous eutectics. The Trivedi–Magnin–Kurz model was used to estimate undercooling with lamellar spacing. The results suggest that the critical undercooling found in undercooling solidification is not a sufficient condition for anomalous eutectic formation. Besides, α-Ni particles in the anomalous eutectic do not exhibit a completely random misorientation and some neighboring α-Ni particles have the same orientation. It is shown that both the coupled and decoupled growth of the eutectic two phases can generate the α-Ni + Ni₃Sn anomalous eutectic structure.     

High-pressure high-temperature synthesis and structure of α-tetragonal boron

Microcrystals of α-tetragonal (α-t) boron with unit cell parameters a=9.05077(6) and c=5.13409(6) Å and measured density 2.16–2.22 g cm⁻³ were obtained by pyrolysis of decaborane B₁₀H₁₄ at pressures of 8–9 GPa and temperatures of 1100–1600 ^○C. The crystal structure is in good agreement with the model proposed by Hoard et al (1958 J. Am. Chem. Soc. 80 4507). However, compared to the original model, we found small deformations of icosahedra and changes in the interatomic distances within the unit cell of the synthesized α-t boron.     

Pressure-Volume-Temperature Relations in Liquid and Solid Tritium

PVT relations in liquid and solid T₂ near the melting curve were measured over 20.5 K–22.1 K and 0 MPa–7 MPa (0 bar–70 bar) with a cell that used diaphragms for pressure and volume variation and measurement. Because of ortho-para self conversion, the melting pressure P_m and the liquid molar volume V_lm increased with time. The rates were consistent with a second order reaction similar to that for c the J = odd concentration: dc/dt = ?k₁c² + k₂c(1 ? c), where k₁ = 6−9×l0⁻²h⁻¹. By extrapolation, the ortho and para forms differed by ΔP_m~6 bar and ΔV_lm~0.5%. Measurements of the volume change on melting and the thermal expansion and compressibility for liquid T₂ were consistent with those for H₂ and D₂. Impurities such as H₂, HT, DT, and ³He were removed by a technique using an adsorption column of cold activated alumina. Corrections for ³He growth during an experiment were adequate except near the triple point.     

Measurement of the Neutron Lifetime Using a Gravitational Trap and a Low-Temperature Fomblin Coating

We present a new value for the neutron lifetime of 878.5 ± 0.7_stat. ± 0.3_syst. This result differs from the world average value by 6.5 standard deviations and by 5.6 standard deviations from the previous most precise result. However, this new value for the neutron lifetime together with a β-asymmetry in neutron decay, A₀, of −0.1189(7) is in a good agreement with the Standard Model.     

Experimental study and thermodynamic modeling of the Al–Co–Cr–Ni system

A thermodynamic database for the Al–Co–Cr–Ni system is built via the Calphad method by extrapolating re-assessed ternary subsystems. A minimum number of quaternary parameters are included, which are optimized using experimental phase equilibrium data obtained by electron probe micro-analysis and x-ray diffraction analysis of NiCoCrAlY alloys spanning a wide compositional range, after annealing at 900 °C, 1100 °C and 1200 °C, and water quenching. These temperatures are relevant to oxidation and corrosion resistant MCrAlY coatings, where M corresponds to some combination of nickel and cobalt. Comparisons of calculated and measured phase compositions show excellent agreement for the β–γ equilibrium, and good agreement for three-phase β–γ–σ and β–γ–α equilibria. An extensive comparison with existing Ni-base databases (TCNI6, TTNI8, NIST) is presented in terms of phase compositions.     

Cryoprotection–lyophilization and physical stabilization of rifampicin-loaded flower-like polymeric micelles

Rifampicin-loaded poly(ε-caprolactone)–b-poly(ethylene glycol)–poly(ε-caprolactone) flower-like polymeric micelles display low aqueous physical stability over time and undergo substantial secondary aggregation. To improve their physical stability, the lyoprotection–lyophilization process was thoroughly characterized. The preliminary cryoprotectant performance of mono- and disaccharides (e.g. maltose, glucose), hydroxypropyl-β-cyclodextrin (HPβCD) and poly(ethylene glycol) (PEG) of different molecular weights was assessed in freeze–thawing assays at −20°C, −80°C and −196°C. The size and size distribution of the micelles at the different stages were measured by dynamic light scattering (DLS). A cryoprotectant factor (f_c) was determined by taking the ratio between the size immediately after the addition of the cryoprotectant and the size after the preliminary freeze–thawing assay. The benefit of a synergistic cryoprotection by means of saccharide/PEG mixtures was also assessed. Glucose (1 : 20), maltose (1 : 20), HPβCD (1 : 5) and glucose or maltose mixtures with PEG3350 (1 : 20) (copolymer:cryoprotectant weight ratio) were the most effective systems to protect 1 per cent micellar systems. Conversely, only HPβCD (1 : 5) cryoprotected more concentrated drug-loaded micelles (4% and 6%). Then, those micelle/cryoprotectant systems that displayed f_c values smaller than 2 were freeze-dried. The morphology of freeze-dried powders was characterized by scanning electron microscopy and atomic force microscopy and the residual water content analysed by the Karl Fisher method. The HPβCD-added lyophilisates were brittle porous cakes (residual water was between 0.8% and 3%), easily redispersable in water to form transparent systems with a minimal increase in the micellar size, as determined by DLS.     

Crystal growth nucleation and Fermi energy equalization of intrinsic spherical nuclei in glass-forming melts

The energy saving resulting from the equalization of Fermi energies of a crystal and its melt is added to the Gibbs free-energy change ΔG_2ls associated with a crystal formation in glass-forming melts. This negative contribution being a fraction ε _ls(T) of the fusion heat is created by the electrostatic potential energy −U₀ resulting from the electron transfer from the crystal to the melt and is maximum at the melting temperature T_m in agreement with a thermodynamics constraint. The homogeneous nucleation critical temperature T₂, the nucleation critical barrier ΔG_2ls∗/k_BT and the critical radius R∗_2ls are determined as functions of ε_ls(T). In bulk metallic glass forming melts, ε_ls(T) and T₂ only depend on the free-volume disappearance temperature T_0l, and ε_ls(T_m) is larger than 1 (T_0l>T_m/3); in conventional undercooled melts ε_ls(T_m) is smaller than 1 (T_0l>T_m/3). Unmelted intrinsic crystals act as growth nuclei reducing ΔG_2ls∗/k_BT and the nucleation time. The temperature-time transformation diagrams of Mg₆₅Y₁₀Cu₂₅, Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5, Pd₄₃Cu₂₇ Ni₁₀P₂₀, Fe₈₃B₁₇ and Ni melts are predicted using classic nucleation models including time lags in transient nucleation, by varying the intrinsic nucleus contribution to the reduction of ΔG_2ls∗/k_BT. The energy-saving coefficient ε _nm(T) of an unmelted crystal of radius R_nm is reduced when R_nm ≪R∗_2ls; ε_nm is quantified and corresponds to the first energy level of one s-electron moving in vacuum in the same spherical attractive potential −U₀ despite the fact that the charge screening is built by many-body effects.     

Neutron Lifetime Experiment Based on an Accordion-Like UCN Storage Volume Coated With “Low Temperature Fomblin”

A new type of per-fluorinated polymer, “Low Temperature Fomblin,” has been tested as a wall coating in an ultracold neutron (UCN) storage experiment using a gravitational storage system. The data show a UCN reflection loss coefficient η as low as ≈ 5 × 10⁻⁶ in the temperature range 105 K to 150 K. We plan to use this oil in a new type of neutron lifetime measurement, where a bellows system (“accordion”) enables to vary the trap size in a wide range while the total surface area and distribution of surface area over height remain constant. These unique characteristics, in combination with application of the scaling technique developed by W. Mampe et al. in 1989, ensure exact linearity for the extrapolation from inverse storage lifetimes to the inverse neutron lifetime. Linearity holds for any energy dependence of loss coefficient µ(E). Using the UCN source at the Institut Laue Langevin we expect to achieve a lifetime precision below ±1 s.     

Active vacuum brazing of CNT films to metal substrates for superior electron field emission performance

The joining of macroscopic films of vertically aligned multiwalled carbon nanotubes (CNTs) to titanium substrates is demonstrated by active vacuum brazing at 820 °C with a Ag–Cu–Ti alloy and at 880 °C with a Cu–Sn–Ti–Zr alloy. The brazing methodology was elaborated in order to enable the production of highly electrically and thermally conductive CNT/metal substrate contacts. The interfacial electrical resistances of the joints were measured to be as low as 0.35 Ω. The improved interfacial transport properties in the brazed films lead to superior electron field-emission properties when compared to the as-grown films. An emission current of 150 μA was drawn from the brazed nanotubes at an applied electric field of 0.6 V μm⁻¹. The improvement in electron field-emission is mainly attributed to the reduction of the contact resistance between the nanotubes and the substrate. The joints have high re-melting temperatures up to the solidus temperatures of the alloys; far greater than what is achievable with standard solders, thus expanding the application potential of CNT films to high-current and high-power applications where substantial frictional or resistive heating is expected.     

Investigation of ordering phenomenon in Me–Pt (Me=Fe,Ni) liquid alloys

The phase diagrams of Fe–Pt and Ni–Pt liquid alloy systems show the existence of FePt and NiPt intermetallic compounds, respectively, in their solid intermediate states, and the associative tendency between unlike atoms in these liquid alloys has been analysed using the self-association model. The concentration dependences of mixing properties such as the free energy of mixing, G_M; the concentration fluctuations, S_cc(0), in the long-wavelength limits; the chemical short-range order (CSRO) parameter, α₁; as well as the chemical diffusion, enthalpy and entropy of the mixing of Fe–Pt and Ni–Pt liquid alloys have been investigated to determine the nature of ordering in the liquid alloys. The results show that heterocoordination occurs in the alloys at all concentrations. The effect of CSRO on S_cc(0), chemical diffusion, D, and the order parameter, α₁, has been considered. The ordering phenomenon in the liquid alloys is also related to the effect of the atomic size mismatch volume on S_cc(0).     

Measurement of the Neutron Lifetime by Counting Trapped Protons

We measured the neutron decay lifetime by counting in-beam neutron decay recoil protons trapped in a quasi-Penning trap. The absolute neutron beam fluence was measured by capture in a thin ⁶LiF foil detector with known efficiency. The combination of these measurements gives the neutron lifetime: τ_n = (886.8 ± 1.2 ± 3.2) s, where the first (second) uncertainty is statistical (systematic) in nature. This is the most precise neutron lifetime determination to date using an in-beam method.     

Yield stress of duplex stainless steel specimens estimated using a compound Hall–Petch equation

In this study, the 0.2% yield stress of duplex stainless steel was evaluated using a compound Hall–Petch equation. The compound Hall–Petch equation was derived from four types of duplex stainless steel, which contained 0.2–64.4 wt% δ-ferrite phase, had different chemical compositions and were annealed at different temperatures. Intragranular yield stress was measured with an ultra-microhardness tester and evaluated with the yield stress model proposed by Dao et al. Grain size, volume fraction and texture were monitored by electron backscattering diffraction measurement. The k_γ constant in the compound equation for duplex stainless steel agrees well with that for γ-phase SUS316L steel in the temperature range of 1323–1473 K. The derived compound Hall–Petch equation predicts that the yield stress will be in good agreement with the experimental results for the Cr, Mn, Si, Ni and N solid-solution states. We find that the intragranular yield stress of the δ-phase of duplex stainless steel is rather sensitive to the chemical composition and annealing conditions, which is attributed to the size misfit parameter.     

Electronic conduction in La-based perovskite-type oxides

A systematic study of La-based perovskite-type oxides from the viewpoint of their electronic conduction properties was performed. LaCo_0.5Ni_0.5O_3±δ was found to be a promising candidate as a replacement for standard metals used in oxide electrodes and wiring that are operated at temperatures up to 1173 K in air because of its high electrical conductivity and stability at high temperatures. LaCo_0.5Ni_0.5O_3±δ exhibits a high conductivity of 1.9 × 10³ S cm⁻¹ at room temperature (R.T.) because of a high carrier concentration n of 2.2 × 10²² cm⁻³ and a small effective mass m∗ of 0.10 m_e. Notably, LaCo_0.5Ni_0.5O_3±δ exhibits this high electrical conductivity from R.T. to 1173 K, and little change in the oxygen content occurs under these conditions. LaCo_0.5Ni_0.5O_3±δ is the most suitable for the fabrication of oxide electrodes and wiring, though La_1−xSr_xCoO_3±δ and La_1−xSr_xMnO_3±δ also exhibit high electronic conductivity at R.T., with maximum electrical conductivities of 4.4 × 10³ S cm⁻¹ for La_0.5Sr_0.5CoO_3±δ and 1.5 × 10³ S cm⁻¹ for La_0.6Sr_0.4MnO_3±δ because oxygen release occurs in La_1−xSr_xCoO_3±δ as elevating temperature and the electrical conductivity of La_0.6Sr_0.4MnO_3±δ slightly decreases at temperatures above 400 K.     

Interlaboratory Comparison of Magnetic Thin Film Measurements

A potential low magnetic moment standard reference material (SRM) was studied in an interlaboratory comparison. The mean and the standard deviation of the saturation moment m_s, the remanent moment m_r, and the intrinsic coercivity H_c of nine samples were extracted from hysteresis-loop measurements. Samples were measured by thirteen laboratories using inductive-field loopers, vibrating-sample magnetometers, alternating-gradient force magnetometers, and superconducting quantum-interference-device magnetometers. NiFe films on Si substrates had saturation moment measurements reproduced within 5 % variation among the laboratories. The results show that a good candidate for an SRM must have a highly square hysteresis loop (m_r/m_s > 90 %), H_c ≈ 400 A·m⁻¹ (5 Oe), and m_s ≈ 2 × 10⁻⁷ A·m² (2 × 10⁻⁴ emu).