Synthesis of (1R,cis,αS)-cypermethrine via lipase catalyzed kinetic resolution of racemic m-phenoxybenzaldehyde cyanohydrin acetate

A technical scale preparation of optically active (1R,cis,αS)-cypermethrine 4 from racemic m-phenoxybenzaldehyde cyanohydrin acetate (RS)-1 and (1R,cis)-3-(2,2-dichlorovinyl)-2,2-dimethylcyclopropanecarboxylic acid chloride (1R,cis)-3 is described. Key steps of the new procedure are a lipase catalyzed enantioselective transesterification of (RS)-1 with n-butanol and direct acylation of the mixture of (R)-1 and (S)-cyanohydrin (S)-2 with (1R,cis)-3 to give enantiomerically pure (1R,cis,αS)-4. The unchanged (R)-1 is removed from (1R,cis,αS)-4 by distillation, and is racemized with triethylamine to give (RS)-1 which is returned to the process. The total yield of (1R,cis,αS)-4 referred to (RS)-1 is 80%.     

Stereoselectivity control in Diels–Alder reactions of 4-thiosubstituted 5-alkoxyfuranones: synthesis and reactivity of enantiopure 4-sulfinyl and sulfonyl 5-(l-menthyloxy)furan-2(5H)-ones

The synthesis of enantiomerically pure (S)-4-phenylsulfinyl- and 4-phenylsulfonyl-(5S)-5-(l-menthyloxy)furan-2(5H)-ones 5a and 6 and (5R)-5-(l-menthyloxy)-4-phenylsulfonylfuran-2(5H)-one 8 and the study of their reactions with cyclopentadiene are described. The sulfur substituents at C-4 modify (sulfone 8, anti/syn=78/22) and invert (sulfoxide 5a and sulfone 6, anti/syn≈27/73) the trend imposed by C-5 on the π-facial selectivity and the syn-adducts become the favoured ones. The endo or exo approach mode is favoured for anti (endo/exo ratio ranging between 26 and 5) or syn (exo/endo ratio ranging between 4.5 and 2.3) attack, respectively.     

Divalent transition metal phosphonates with new structure containing hydrogen-bonded layers of phosphonate anions

A series of divalent transition metal phosphonates containing hydrogen-bonded layers of phosphonate anions, namely [M(phen)₃]·C₆H₅PO₃·11H₂O [M=Co(1), Ni(2), Cu(3)] and [Cd(phen)₃]·C₆H₅PO₃H·Cl·7H₂O (4) have been synthesized, structurally characterized by single-crystal X-ray diffraction method. These compounds all crystallize in the triclinic system, space group P-1. The lattice parameters are a=12.1646(5), b=12.4155(6), c=15.4117(10) Å, α=78.216(2), β=79.735(3), γ=77.8380(3)°, V=2205.1(2) Å³, Z=2 for 1; a=12.097(2), b=12.606(3), c=15.742(3) Å, α=76.66(3), β=80.04(3), γ=77.75(3)°, V=2263.4(8) Å³, Z=2 for 2; a=12.058(2), b=12.518(3), c=15.781(3) Å, α=77.77(3), β=80.02(3), γ=77.91(3)°, V=2255.5(8) Å³, Z=2 for 3 and a=12.47680(10), b=12.6693(2), c=16.1504(3) Å, α=82.600(1), β=71.122(1), γ=77.355(1)°, V=2352.37(6) Å³, Z=2 for 4. All structures are refined by full-matrix least-squares methods [for 1, R1=0.0602 using 6458 independent reflections with I>2σ(I); for 2, R1=0.0632 using 4657 independent reflections with I>2σ(I); for 3, R1=0.0634 using 6221 independent reflections with I>2σ(I); for 4, R1=0.0400 using 7930 independent reflections with I>2σ(I)]. In the crystal structures, the phenylphosphonate anions and water molecules are hydrogen-bonded to form layers, and there exist the cationic species [M(phen)₃]²⁺ between the adjacent layers of anions and water. Luminescence, thermal analysis as well as IR spectroscopic studies are also presented.     

Solid-state structure determination and solution-state NMR characterization of the (2R,4R)/(2S,4S)- and (2R,4S)/(2S,4R)-diastereomers of the agricultural fungicide propiconazole,the (2R,4S)/(2S,4R)-symmetrical triazole constitutional isomer,and a ditriazole analogue

Single-crystal X-ray diffraction analysis was used to determine the structure of a racemic diastereomer of the agricultural fungicide propiconazole [1-(2-(2,4-dichlorophenyl)-4-n-propyl-1,3-dioxolane-2-yl-methyl)-1-H-1,2,4-triazole] and of two by-products (a symmetrical 1,3,4-triazole racemic-constitutional isomer and a propiconazole ditriazole analogue). All three crystalline racemic-diastereomers had (2R,4S)/(2S,4R)-stereochemistry in which then-propyl group was observed in atrans-to-phenyl disposition. Propiconazole (2R,4S)/(2S,4R)-diastereomer gives crystals belonging to the monoclinic space group P2₁,/a, and, at 293 K,a=8.1192(3),b=18.9769(6),c=10.7137(4) å,Β=99.765(3)?,V=1626.8(1) å³, Z=4,R(F)=0.060, andR _w(F)=0.058. The constitutional isomer by-product (2R,4S)/(2S,4R)-1-(2-(2,4-dichlorophenyl)-4-n-pro-pyl-1,3-dioxolane-2-yl-methyl)-1-H-1,3,4-triazole gives crystals belonging to the monoclinic space group P2₁/n, and, at 293 K,a=11.1763(6),b=10.7716(4),c=14.5804(8) å,Β=107.445(4)?,V=1674.6(1) å³, Z=4,R(F)=0.043, andR _w(F)=0.043. The ditriazole byproduct (2R,4S)/(2S,4R)-1-(2-(2-chloro-4-(1,2,4-triazole-1-yl)phenyl)-4-n-propyl-1,3-dioxolane-2-yl-methyl)-1-H-1,2,4-triazole gives crystals belonging to the triclinic space groupP¯ 1, and, at 193 K,a=5.3329(8),b=8.3738(7),c=20.240(2) å, α=84.213(6)?,Β=87.20(1)?,γ=86.23(1)?,V=896.5(2) å³, Z=2,R(F)=0.046, andR _w(F)=0.051. The presence of both propiconazole (2R.4S)- and (2S,4R)-enantiomers enables the formation of a crystalline racemic modification, while the diastereomeric propiconazole (2R,4R)- and (2S,4S)-enantiomers are viscous oils. In the absence of its enantiomorphic partner, the propiconazole (2R,4S)- or (2S,4R)-enantiomers remain as viscous oils rather than form chiral crystals.     

Enantioselective synthesis of β-amino acids. Part 9: Preparation of enantiopure α,α-disubstituted β-amino acids from 1-benzoyl-2(S)-tert-butyl-3-methylperhydropyrimidin-4-one,

Double alkylation of enantiopure N,N-acetal pyrimidinone (S)-1, a masked chiral derivative of β-alanine prepared from (S)-asparagine, proceeds with high stereoselectivity to give C(5) disubstituted adducts (2S,5R)-6, (2S,5S)-6, (2S,5R)-7, and (2S,5S)-7. Acid hydrolysis of these derivatives affords enantiopure α,α-dialkylated β-amino acids (R)-8, (S)-8, (R)-9, and (S)-9 in very good yields.     

Structural, spectral and thermal studies of substituted N-(2-pyridyl)-N′-phenylthioureas

N-2-(3-picolyl)-N′-phenylthiourea, 3PicTuPh, monoclinic, P2₁/n, a=7.617(2) b=7.197(5), c=22.889(5) Å, β=94.63(4)°, V=1250.7(1) Å³ and Z=4; N-2-(4-picolyl)-N′-phenylthiourea, 4PicTuPh, triclinic, P-1, a=7.3960(5), b=7.9660(12), c=21.600(3) Å, α=86.401(4), β=84.899(8), γ=77.769(8)°, V=1237.5(3) Å³ and Z=4; N-2-(5-picolyl)-N′-phenylthiourea, 5PicTuPh, monoclinic, P2₁/c, a=14.201(1), b=4.905(3), c=17.689(3) Å, β=91.38(1)°, V=1231.8(7) Å³ and Z=4; N-2-(6-picolyl)-N′-phenylthiourea, 6PicTuPh, monoclinic, C2/c2, a=14.713(1), b=9.367(1), c=18.227(1) Å, β=92.88(1)°, V=2515.5(1) Å³ and Z=8 and N-2-(4,6-lutidyl)-N′-phenylthiourea, 4,6LutTuPh, monoclinic, C2/c, a=11.107(2), b=11.793(2), c=20.084(4) Å, β=96.10(3)°, V=2616(1) Å³ and Z=8. Intramolecular hydrogen bonding between N′H and the pyridyl nitrogen and intermolecular hydrogen bonding involving the thione sulfur are affected by substitution of the pyridine ring, as is the planarity of the molecule. ¹H NMR studies in CDCl₃ show the NH′ hydrogen resonance considerably downfield from other resonances in the spectrum for each thiourea.     

Molar excess volumes of ternary mixtures of nonelectrolytes

Molar excess volumes V^E_ijk of methylenebromide i + pyridine j + β-picoline (k, cyclohexane (i) + pyridine (j) + β-picoline(K), benzene(i)+toluene(j)+1,2-dichloroethane(k), benzene(i) + 0-xylene(j) + 1,2-dichloroethane(k) and benzene(i) + p-xylene(j) + 1,2-dichloroethane(k) mixtures have been determined dilatometrically at 298.15 K. The data have been examined in terms of Sanchez and Lacombe theory and the graph-theoretical approach, and it is found that they are described well by the latter. Self- and cross-volume interaction coefficients V_jk, V_jjk and V_jkk, etc., have also been evaluated and the values utilised to study molecular interactions between the jth and kth molecular species in the presence of the ith in these i + j + k mixtures.     

Practical and highly stereoselective method for the preparation of several chiral arylsulfinamides and arylsulfinates based on the spontaneous crystallization of diastereomerically pure N-benzyl-N-(1-phenylethyl)-arylsulfinamides

A novel and simple process for the preparation of enantiomerically pure (S_S)-benzenesulfinamide (S_S)-3a, (S_S)-p-toluenesulfinamide (S_S)-3b, (S_S)-p-chloro-benzenesulfinamide (S_S)-3c and (S_S)-p-fluorobenzenesulfinamide (S_S)-3d has been developed. The treatment of arylsulfinyl chlorides with (R)-N-benzyl-1-phenylethanamine in the presence of excess triethylamine gave diastereomeric mixtures of N-benzyl-N-(1-phenylethyl)-arylsulfinamides 1, which underwent spontaneous crystallization to furnish diastereomerically pure (R,S_S)-N-benzyl-N-(1-phenylethyl)-arylsulfinamides (R,S_S)-1a-1d in 28%, 29%, 27% and 31% yields, respectively. The diastereomerically pure compounds (R,S_S)-1 were then converted into four enantiopure (R_S)-methyl arylsulfinates (R_S)-2, and finally into four enantiopure (S_S)-arylsulfinamides (S_S)-3 in good yields.     

Apparent molar volumes and apparent molar heat capacities of aqueous potassium hydrogen phthalate (KHP) and potassium sodium phthalate (KNaP) at temperatures fromT = 278.15 K toT = 393.15 K at the pressure 0.35 MPa

A vibrating-tube densimeter (DMA 512P, Anton Paar, Austria) was used to investigate the densities and volumetric properties of aqueous potassium hydrogen phthalate (KHP) and potassium sodium phthalate (KNaP). Measurements were made at molalities m from (0.006 to 0.66)mol · kg ^− 1, at temperatures from 278.15 K to 368.15 K and at the pressure 0.35 MPa. The densimeter was calibrated through measurements on pure water and on 1.0 mol · kg ^− 1NaCl(aq). We also used a twin fixed-cell, power-compensation, differential-output, temperature-scanning calorimeter (NanoDSC 6100, Calorimetry Sciences Corporation, Spanish Fork, UT, U.S.A.) to measure solution heat capacities. This was accomplished by scanning temperature and comparing the heat capacities of the unknown solutions to the heat capacity of water. Apparent molar volumes V_φand apparent molar heat capacities C_{p, φ}of the solutions were calculated and fit by regression to equations that describe the surfaces (V_φ, T, m) and (C_{p, φ}, T, m). Standard state partial molar volumesV₂^o and heat capacities C_p,2^owere estimated by extrapolation to the m =  0 plane of the fitted surfaces. Previously determinedC_{p, φ} for HCl(aq) and NaCl(aq) were used to obtain (Δ_rC_{p, m}, T, m) for the proton dissociation reaction of aqueous hydrogen phthalate. This (Δ_rC_p,m, T, m) surface was created by subtracting C_p,φfor KHP(aq) and for NaCl(aq) from the sum of C_p,φfor KNaP(aq) and for HCl(aq). Surfaces representing (Δ_rH_m, T, m) and (pQ_a, T, m), where pQ_adenotes the molality equilibrium quotient, were created by integration of our (Δ_rC_p,m, T, m) surface using values for (Δ_rH_m, m) and (pK_a, m) at T =  308.15 K from the literature as integration constants.     

Syntheses, structures, and vibrational spectroscopy of the two-dimensional iodates Ln(IO3)3 and Ln(IO3)3(H2O) (LnYb, Lu)

The reaction of Lu³⁺ or Yb³⁺ and H₅IO₆ in aqueous media at 180 °C leads to the formation of Yb(IO₃)₃(H₂O) or Lu(IO₃)₃(H₂O), respectively, while the reaction of Yb metal with H₅IO₆ under similar reaction conditions gives rise to the anhydrous iodate, Yb(IO₃)₃. Under supercritical conditions Lu³⁺ reacts with HIO₃ and KIO₄ to yield the isostructural Lu(IO₃)₃. The structures have been determined by single-crystal X-ray diffraction. Crystallographic data are (MoKα, λ=0.71073 Å): Yb(IO₃)₃, monoclinic, space group P2₁/n, a=8.6664(9) Å, b=5.9904(6) Å, c=14.8826(15) Å, β=96.931(2)°, V=766.99(13), Z=4, R(F)=4.23% for 114 parameters with 1880 reflections with I>2σ(I); Lu(IO₃)₃, monoclinic, space group P2₁/n, a=8.6410(9), b=5.9961(6), c=14.8782(16) Å, β=97.028(2)°, V=765.08(14), Z=4, R(F)=2.65% for 119 parameters with 1756 reflections with I>2σ(I); Yb(IO₃)₃(H₂O), monoclinic, space group C2/c, a=27.2476(15), b=5.6296(3), c=12.0157(7) Å, β=98.636(1)°, V=1822.2(2), Z=8, R(F)=1.51% for 128 parameters with 2250 reflections with I>2σ(I); Lu(IO₃)₃(H₂O), monoclinic, space group C2/c, a=27.258(4), b=5.6251(7), c=12.0006(16) Å, β=98.704(2)°, V=1818.8(4), Z=8, R(F)=1.98% for 128 parameters with 2242 reflections with I>2σ(I). The f elements in all of the compounds are found in seven-coordinate environments and bridged with monodentate, bidentate, or tridentate iodate anions. Both Lu(IO₃)₃(H₂O) and Yb(IO₃)₃(H₂O) display distinctively different vibrational profiles from their respective anhydrous analogs. Hence, the Raman profile can be used as a complementary diagnostic tool to discern the different structural motifs of the compounds.     

Preparation and Crystal Structures of 4-(4′-Pyridylthio)-1-methylpyridinium Salts: Assembly of a Donor-Acceptor-Type Molecule Containing a Sulfide Bridge

A series of ionic 4-(4′-pyridylthio)-1-methylpyridinium salts with different counteranions (1, I⁻; 2, BF⁻₄; 3, PF⁻₆; and 4, OTf⁻, where OTf=trifluoromethanesulfonate) have been prepared. Structural analysis reveals that the cation exhibits a variety of stacking structures dependent on the anion. Compound 1 crystallizes in space group P2_1/n (#14), with a=10.764(3) Å, b=9.601(5) Å, c=13.105(3) Å, β=108.35(2), V=1285.4(8) ų, and Z=4. In this compound, each cation moiety is stacked in a helical arrangement along the c-axis. Compound 2, which is isomorphous to 1, has space group P2_1/n (#14), with a=11.647(2) Å, b=9.203(3) Å, c=13.232(2) Å, β=108.42(2), V=1345.6(5) ų, and Z=4. Compound 3 crystallizes in space group P2_1/n (#14), with a=8.06(1) Å, b=17.43(1) Å, c=10.30(1) Å, β=103.0(1), V=1410(3) ų, and Z=4. In this salt, the cation molecules assume a head-to-tail stacking arrangement, forming a polar pseudo 1-D chain. Compound 4 crystallizes in space group Pb? (#2), with a=7.585(4) Å, b=15.443(7) Å, c=6.775(4) Å, α=99.33(4), β=108.35(2)^o, γ=98.37(4), V=756.6(7) ų, and Z=2. The structure of 4 consists of a columnar stacking of pyridine moieties, with the cation moieties surrounded by the counteranions. Calculations show that the 4-(4′-pyridylthio)-1-methylpyridinium cation may be a good building block for second harmonic generation (SHG) materials, even though salts 1-4 crystallized in centrosymmetric structures and were SHG inactive.     

Studies towards the synthesis of (1R,2S)- and (1S,2S)-1,2-epoxy-3-hydroxypropylphosphonates and (1S,2S)- and (1R,2S)-2,3-epoxy-1-hydroxypropylphosphonates

The trans-configured fosfomycin analogue, diethyl (1S,2S)-1,2-epoxy-3-hydroxypropylphosphonate, was synthesised by the intramolecular Williamson reaction of diethyl (1S,2R)-1,3-dihydroxy-2-mesyloxypropylphosphonate. The cis-analogue was obtained as O-ethyl or O,O-diethyl (1R,2S)-1,2-epoxy-3-hydroxypropylphosphonates, when (1R,2R)-1,3-dihydroxy-2-mesyloxypropylphosphonate or its 3-O-trityl derivative were used as starting materials, respectively. The intramolecular Williamson cyclisations of diethyl (1S,2R)- and (1R,2S)-1-benzyloxy-3-hydroxy-2-mesyloxypropylphosphonates led to diethyl (1S,2S)- and (1R,2S)-2,3-epoxy-1-benzyloxypropylphosphonates, respectively, with the concomitant formation of diethyl (E)-1-benzyloxy-3-hydroxyprop-1-en-1-phosphonate. From diethyl (1S,2S)- and (1R,2S)-2,3-epoxy-1-benzyloxypropylphosphonates, enantiomerically pure diethyl (1S,2S)- and (1R,2S)-1,2-dihydroxypropylphosphonates were obtained by catalytic hydrogenation, while diethyl (1S,2S)- and (1R,2S)-3-acetamido-1,2-dihydroxypropylphosphonates were produced after epoxide ring opening with dibenzylamine, acetylation and hydrogenolysis.     

Engineering of Yeast Old Yellow Enzyme OYE3 Enables Its Capability Discriminating of (E)-Citral and (Z)-Citral

The importance of yeast old yellow enzymes is increasingly recognized for direct asymmetric reduction of (E/Z)-citral to (R)-citronellal. As one of the most performing old yellow enzymes, the enzyme OYE3 from Saccharomyces cerevisiae S288C exhibited complementary enantioselectivity for the reduction of (E)-citral and (Z)-citral, resulting in lower e.e. value of (R)-citronellal in the reduction of (E/Z)-citral. To develop a novel approach for the direct synthesis of enantio-pure (R)-citronellal from the reduction of (E/Z)-citral, the enzyme OYE3 was firstly modified by semi-rational design to improve its (R)-enantioselectivity. The OYE3 variants W116A and S296F showed strict (R)-enantioselectivity in the reduction of (E)-citral, and significantly reversed the (S)-enantioselectivity in the reduction of (Z)-citral. Next, the double substitution of OYE3 led to the unique variant S296F/W116G, which exhibited strict (R)-enantioselectivity in the reduction of (E)-citral and (E/Z)-citral, but was not active on (Z)-citral. Relying on its capability discriminating (E)-citral and (Z)-citral, a new cascade reaction catalyzed by the OYE3 variant S296F/W116G and glucose dehydrogenase was developed, providing the enantio-pure (R)-citronellal and the retained (Z)-citral after complete reduction of (E)-citral.     

Fine structure and hyperfine structure in the excited configuration 5p 26s of the antimony I spectrum

By optical interference and VUV spectroscopy the doublet system of SbI 5p ²6s was investigated, so that now the hyperfinestructure of all 8 levels of 5p ²6s (A- andB-splitting constants) are known. From the analysis we receive a spin-orbit parameter ζ_5p =3,538(57) cm^?1 and from the hyperfine-analysis single electron splitting constantsa _5p ⁰¹ =52.4(4.6),a _5p ¹⁰ =?1.6(7.3),a _5p ¹² =72.3(2.3),a _6s ¹⁰ =91.7(4.1),b _5p ⁰² =?49.6(1.1) andb _5p ¹¹ =30.4(3.2) (all values in mK). For all calculations in the fs- and hfs-analysis the 5p ²6s ² D _3/2 has to be excluded (see discussion). With the figures given above the quadrupole moment¹²¹ Q(5p ²6s)=?0.44(3) barn was obtained. It is in good agreement with the¹²¹ Q(5p ³). For the core-polarization by the 5p electron in the innerfieldns-shells (n=1, 2, 3, 4, 5) and the unpaired 6s electron a field of +500(300) kG was obtained.     

Semiclassical variational study of size effects in neutral and charged jellium droplets

An analytic expression for the total energy of metallic clusters composed ofN identical atoms of valencev and with net chargeQ is obtained by means of a variational solution of the Thomas-Fermi-Weizsäcker energy density functional within the spherical jellium model. The minimum energy is given as an expansion in decreasing powers of the cluster radiusR=r _s Z ^1/3, withZ=vN andr _s the radius per electron of the bulk metal. The coefficients are obtained as functions ofr _s . Terms of volume (R ³), surface (R ²), curvature (R), constant (R ⁰), (1/R) and (1/R ²) are clearly separated in the formula, as well as the different contributions (kinetic, coulombic and exchange-correlation) to each of them. The asymptotic values (R→∞) for the work functions,W(r _s ), and surface energies σ(r _s ), are compared to analogous semiclassical and Kohn-Sham calculations of jellium-like surfaces and to the experimental values. The size dependent behaviour of chemical potentials, μ(R), electron affinities,AF(R), and ionization potentials,IP(R), are easily obtained for any kind of metallic clusters. In particular we discuss the Coulomb and quantum corrections to the coefficients β, δ in the asymptotic formulae:IP?W+β/R andAF?W+δ/R.     

Chiral synthesis of (2s,3s,7s)-3,7-dimethylpentadecan-2-yl acetate and propionate,potential sex pheromone components of the pine saw-fly neodiprion sertifer (geoff.)

A synthesis of (2S,3S,7S)-3,7-dimethylpentadecan-2-yl acetate ($\text{2}$) and propionate ($\text{3}$) is described. (2S)-2-Methyldecan-1-yl lithium ($\text{5}$) was reacted with (3S,4S)-3,4-dimethyl-γ-butyrolactone ($\text{6}$) to yield the ketoalcohol $\text{19}$ which upon Huang-Minlon reduction furnished (2S,3S,7S)-3,7-dimethylpentadecan-2-ol ($\text{1}$). Acylations gave the esters $\text{2}$ and $\text{3}$. The (2S)-2-methyldecan-1-yl lithium was obtained via asymmetric synthesis. The chiral lactone $\text{6}$ was obtained from (2S,3S)-trans-2,3-epoxybutane and dimethyl malonate.     

New quaternary carbon and nitrogen stabilized polyborides: REB15.5CN (RE: Sc, Y, Ho, Er, Tm, Lu), crystal structure and compound formation

A new family of quaternary carbon and nitrogen containing Rare Earth (RE: Sc, Y, Ho, Er, Tm and Lu) borides: REB_15.5CN, has been synthesized and structurally characterized by powder X-ray diffraction data. They are all isotypic with Sc_1−xB_15.5CN whose structure was solved based on single-crystal X-ray data and HRTEM investigations. The structure refinement converged at a R(F²) value of 0.044 for 364 reflections. The new structure type of Sc_1−xB_15.5CN is composed of a three-dimensional network based on interconnected slabs of boron (B₁₂)^ico icosahedra and (B₆)^oct octahedra. A linear [CBC] chain and nitrogen tightly bridges icosahedra. Sc partially occupies voids in the sheets of boron octahedra. It crystallizes with the trigonal space group P³m1, with Z=2. Lattice parameters (nm) are as follows: for RE: Sc, a,b=0.5568(4), c=1.0756(2); Y, a,b=0.55919(6), c=1.0873(2); Ho, a,b=0.55883(7), c=1.0878(6); Er, a,b=0.55889(5), c=1.0880(6); Tm, a,b=0.5580(1), c=1.0850(6); Lu, a,b=0.55771(9), c=1.0839(4). Magnetic characterization of ErB₁₇C_1.3N_0.6 has been performed.     

Crystal structures of three intermetallic phases in the Mo-Pt-Si system

The crystal structures of three ternary Mo-Pt-Si intermetallic compounds have been determined ab initio from powder X-ray diffraction data. All three structures are representative of new structure types. Both the X (MoPt₂Si₃, Pmc2₁, oP12, a=3.48438(6), b=9.1511(2), c=5.48253(8) Å) and Y (MoPt₃Si₄, Pnma, oP32, a=5.51210(9), b=3.49474(7), c=24.3090(4) Å) phases derive from PtSi (FeAs type) structure while the Z phase (ideal composition Mo₃₂Pt₂₀Si₁₆, refined composition Mo_29.9(2)Pt_21.0(3)Si_17.1(1), Cc, mC68, a=13.8868(3), b=8.0769(2), c=9.6110(2) Å, β=100.898(1)°) present similarities with the group of Frank-Kasper phases.     

A model for transitional plane Couette flow

A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U₀(x,z,t)+[1+U₁(x,z,t)]sin(πy/2), v=V₁(x,z,t)cos(πy/2), w=W₀(x,z,t)+W₁(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).