Subsidiary Minima Research Articles

The solsticial pause on Mars: 1. A planetary wave reanalysis

Large-scale planetary waves are diagnosed from an analysis of profiles retrieved from the Thermal Emission Spectrometer aboard the Mars Global Surveyor spacecraft during its scientific mapping phase. The analysis is conducted by assimilating thermal profiles and total dust opacity retrievals into a Mars global circulation model. Transient waves are largest throughout the northern hemisphere autumn, winter and spring period and almost absent during the summer. The southern hemisphere exhibits generally weaker transient wave behaviour. A striking feature of the low-altitude transient waves in the analysis is that they show a broad subsidiary minimum in amplitude centred on the winter solstice, a period when the thermal contrast between the summer hemisphere and the winter pole is strongest and baroclinic wave activity might be expected to be strong. This behaviour, here called the ‘solsticial pause,’ is present in every year of the analysis. This strong pause is under-represented in many independent model experiments, which tend to produce relatively uniform baroclinic wave activity throughout the winter. This paper documents and diagnoses the transient wave solsticial pause found in the analysis; a companion paper investigates the origin of the phenomenon in a series of model experiments.

10.1007/s11451-008-1003-6

The conditions of the virial theorem imposed on the dependence of the total energy of a system consisting of two polarons on the distance between the centers of the polarization wells are analyzed for various trial two-electron functions in the limit of strong electron-phonon coupling. It is shown that the inclusion of the direct dependence of the wave function of the system on the interelectron distance (correlation effects) does not break the conditions of the virial theorem. This theorem holds for a single-center and a two-center configuration corresponding to a subsidiary minimum, which disappears when the electron correlations are included.

Corrections to the Kohn-Luttinger wave function for donors in silicon

Corrections to the Kohn-Luttinger ground state wave function from subsidiary minima are calculated using first order perturbation theory and a variational approach. The very precise Fermi contact constants ${a}_{hpf}({\mathbf{R}}_{nmm})$ of the Hale-Mieher data determine a set of linear equations based on donor-dependent ratios such as $\ensuremath{\mid}{\ensuremath{\psi}}_{d}(\underset{}{333})\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\psi}}_{d}(115)\ensuremath{\mid}={K}_{d}={[{a}_{hpf}(\underset{}{333})∕{a}_{hpf}(115)]}^{1∕2}$. The minima considered [${L}_{1}(\mathrm{cb}1)$, ${\ensuremath{\Gamma}}_{{2}^{\ensuremath{'}}}(\mathrm{cb}4)$, $\ensuremath{\Sigma}(\mathrm{cb}5)$, $\ensuremath{\Gamma}W(\mathrm{cb}2)$, ${\ensuremath{\Delta}}_{{2}^{\ensuremath{'}}}(\mathrm{cb}5)$, and $XU(\mathrm{cb}2)$] are each characterized by an $A(\mathbf{k}\ensuremath{-}{\mathbf{k}}_{j})$, a phase ${e}^{i\mathbf{k}j\ensuremath{\cdot}\mathbf{r}}$ and envelope functions ${F}_{\ensuremath{\alpha}j}$ $(\ensuremath{\alpha}=x,y,z)$. The ${\ensuremath{\psi}}_{d}$ employed contains four terms not included in the comprehensive Ivey-Mieher (IM) calculation with pseudopotential Bloch functions for eight bands. Two terms arise from the crucial tetrahedral potential ${U}_{t}\ensuremath{\propto}xyzf(r)$ ignored in most earlier work. The admixture coefficients are varied subject to the three constraint equations to minimize the mean-squared deviations of the calculated and experimental ${a}_{hpf}(nnm)$ of the 11 odd sites identified by IM. The results are not only vastly improved (compared to IM) for site (111) but also reverse the IM assignments for (331) and (551). Some of the inverted donor anomalies are explained. The average root-mean-squared deviation ⟨rmsd⟩ for the 11 sites is better than the IM results for these odd sites. The results suggest that additional changes in the zeroth order ${\ensuremath{\psi}}_{\mathrm{KL}}$ may be required to improve the overall agreement. The uniaxial stress parameters ${i}_{d}$ and $2f∕a(0)$ are also reconsidered with some of the new corrections and compared with experimental values.

Spatial configuration of the bipolaron and the virial theorem

The conditions of the virial theorem imposed on the dependence of the total energy of a system consisting of two polarons on the distance between the centers of the polarization wells are analyzed for various trial two-electron functions in the limit of strong electron-phonon coupling. It is shown that the inclusion of the direct dependence of the wave function of the system on the interelectron distance (correlation effects) does not break the conditions of the virial theorem. This theorem holds for a single-center and a two-center configuration corresponding to a subsidiary minimum, which disappears when the electron correlations are included.

Stable bi-level and multi-level thresholding of images using a new global transformation

A new transformation for finding global valleys in 1D distributions, with particular application to the thresholding of grey-scale images is described. The applied criterion function estimates the global significance of all the valleys that are located, and thus can cope with multi-mode distributions. Examples make it clear that one of the main advantages of the resulting global valley method (GVM) is that it permits partially hidden minima to be reliably located without complicated analysis. Overall, the GVM is demonstrated to have very good stability properties and high sensitivity for the detection of subsidiary minima - including those arising near the ends of distributions that arise from practically important image detail (such as defects or contaminants in an automated inspection scenario). The global analysis around which the method is formulated is responsible for achieving these capabilities with modest computational demands.

Direct to Indirect Crossover in III-VI Layered Compounds and Alloys under Pressure

The pressure dependence of the optical absorption edge of In1± xGaxSe (0 < x < 0.2) and GaTe has been investigated in order to determine the direct to indirect crossover pressure and the energy difference between the absolute and subsidiary minima of the conduction band at ambient pressure. In the In1± xGaxSe alloy, the crossover pressure decreases with increasing Ga proportion. For InSe, from the extrapolation to x = 0 the band crossover is found to occur at 4.3 GPa and the subsidiary minimum of the conduction band is located, at ambient pressure, (0.32 0.02) eV above the absolute minimum. In addition, the energy difference between the conduction band minima is shown to decrease linearly with pressure, in agreement with previous transport results in InSe and optical results in GaSe. As regards GaTe, the behaviour of the absorption edge is similar to that of the other III±VI compounds, which suggests that, in spite of the different crystal structure, the electronic states close to the band-gap have the same character.

Investigation of conduction-band structure, electron-scattering mechanisms, and phase transitions in indium selenide by means of transport measurements under pressure

In this work we report on Hall effect, resistivity and thermopower measurements in n-type indium selenide at room temperature under either hydrostatic and quasi-hydrostatic pressure. Up to 40 kbar (= 4 GPa), the decrease of carrier concentration as the pressure increases is explained through the existence of a subsidiary minimum in the conduction band. This minimum shifts towards lower energies under pressure, with a pressure coefficient of about -105 meV/GPa, and its related impurity level traps electrons as it reaches the band gap and approaches the Fermi level. The pressure value at which the electron trapping starts is shown to depend on the electron concentration at ambient pressure and the dimensionality of the electron gas. At low pressures the electron mobility increases under pressure for both 3D and 2D electrons, the increase rate being higher for 2D electrons, which is shown to be coherent with previous scattering mechanisms models. The phase transition from the semiconductor layered phase to the metallic sodium cloride phase is observed as a drop in resistivity around 105 kbar, but above 40 kbar a sharp nonreversible increase of the carrier concentration is observed, which is attributed to the formation of donor defects as precursors of the phase transition.

Real time spectroellipsometry for optimization of diamond film growth by microwave plasma-enhanced chemical vapor deposition from CO/H2 mixtures

Real time spectroellipsometry has been applied to determine the deposition rate and thickness evolution of the nondiamond (sp2-bonded) carbon volume fraction in very thin (&amp;lt;1000 Å), but fully coalesced, nanocrystalline diamond films prepared on Si substrates by microwave plasma-enhanced chemical vapor deposition from gas mixtures of CO and H2. At a substrate temperature of ∼800 °C, high quality diamond films can be obtained over two orders of magnitude in the CO/H2 gas flow ratio, from 0.04, the lowest value explored, to ∼5. A well-defined minimum in the sp2 C volume fraction (0.03 in a 600 Å film) is observed for a CO/H2 ratio of 0.2, corresponding to the C–H–O diamond-growth phase-diagram coordinate XH/Σ=[H]/{[H]+[C]} of 0.9. Under these conditions, the deposition rate increases with increasing temperature over the range of ∼400–800 °C with an activation energy of 8 kcal/mol, behavior identical to that observed for diamond film growth from a CH4/H2 ratio of 0.01. This observation shows that the dominant film precursors in the diamond growth process from CO/H2=0.2 are hydrocarbons whose flux at the growing film surface is controlled through the reaction of excited CO with H or H2 in the plasma. A broad subsidiary minimum in the sp2 C content is observed, centered near a CO/H2 ratio of 2, corresponding to an XH/Σ value of ∼0.5. Under these gas flow conditions, the deposition rate is a complicated function of temperature, exhibiting a peak near 550 °C. This peak shifts to lower temperature with further increases in the CO/H2 ratio above 2, suggesting a nonhydrocarbon precursor and a different growth mechanism for diamond prepared at high CO/H2 ratio and low temperature.

Potential energy functions and the carbonyl sulphide dimer

The problem of the structure of the van der Waals dimer of carbonyl sulphide is considered. A number of empirical potentials are used. All suggest that the complex is planar with the molecules anti-parallel (the head to tail structure). A subsidiary minimum for the head to head structure is usually found. These results are in general agreement with available experimental evidence.

The molecular structure and conformational behaviour of 2-chloro-1,3-butadiene (chloroprene) studied by gas-phase electron diffraction and ab initio MO calculations

MO calculations establish a global minimum for chloroprene at the planar anti conformation (θ 1 = 180°). A subsidiary minimum appears at θ 2 = 40°, 8.3 kJ mol −1 above anti and 4.2 kJ mol −1 below planar syn with an rotational barrier of 20 kJ mol −1 at about 105°. Analyses of GED data for chloroprene at 655,565, and 298 K gave, in addition to a planar anti conformer (θ 1 = 180°), 25 (6), 18 (5), and 7(4)%, respectively, of a co-existing second form with θ 2=27(11)°. These quantities correspond to Δ E= E 2- E 1=6.4(12) kJ mol −1 and Δ S c = S 2– S 1 = − 6(3) J K −1 mol −1. The value of θ 2 was determined from the 655 -K data using a flexible backbone structure upon rotation as extracted from the MO results. Rigid rotation gave θ 2=41 (8)°, Δ E= 6.8(13) kJ mol −1, and Δ S c= -5(3) J K −1 mol −1. Some MO constraints were used in defining the positions of hydrogen atoms and for a difference r(C1C2) - r (C3C4) parameter. Important geometrical parameters ( r a,∠ α) of anti chloroprene as obtained in such refinements based on 298-K GED data and literature rotational constants are: r(C1C2)=134.4(2), r(C3C4)=134.4(2), r(CC)=146.9(3) and r(CCl)=174.2(2) pm; ∠CC2C = 123.5(1), ∠CC3C = 125.6 (2) and ∠CCCl = 117.2(1)°. Refinements based on the GED data alone gave the following changed parameters: r(CC)=146.0(3) pm; ∠CC2C = 123.9 (2), ∠CC3C = 126.2 (2)°.

An ab initio study of the isomerisation and fragmentation of CHO 2+ ions: An example of spin-controlled reactions?

[CHO 2 +] ions exist in two isomeric forms, a quasi-linear carboxylic structure, OCOH + (I), and a formate structure, O(CH)O + (II). The latter is known to isomerise into the former with a low rate constant (about 10 5 s −1). Configuration interaction ab initio calculations reveal that the ion can exist in three low-lying electronic states of different multiplicity and symmetry species, a singlet ( X̃ 1 A′) and two triplets ( ã 3 A′ and b̃ 3 A′'). The potential energy surfaces cross so that the nature of the lowest state varies as a function of the nuclear geometry. The singlet surface ( X̃ 1 A′) has its deepest minimum for structure I and a subsidiary minimum for structure II. The situation is reversed for the ã 3 A′ state which has its deepest minimum for structure II and which exhibits a shallow minimum for structure I. Thus, at low energies, the carboxylic and formate ions are respectively in a singlet and in a triplet state. These ions lose an oxygen atom on a microsecond time scale by a composite mechanism which is subject to a large isotope effect. One of the components of the metastable peak corresponds to reaction ▪ giving rise to a small kinetic energy release. The second component is due to a spin-orbit controlled direct predissociation process, viz. ▪ The probability of surface hopping varies as a function of the internal energy between 0 and a maximum value of ca. 0.008. The corresponding kinetic energy release is expected to be larger for the deuterated than for the hydrogenated compound. Thus, the two components are resolved in the deuterated compound, but hardly distinguishable in the hydrogenated species.

Dependence of resonant tunneling current on Al mole fractions in AlxGa1−xAs-GaAs-AlxGa1−xAs double barrier structures

Electron transport in AlxGa1−xAs-GaAs-AlxGa1−xAs double barrier tunneling structures is studied as a function of Al content x in the barrier for the case where the thickness of the barrier is 11 atomic layers and that of the GaAs well layer is 7 nm. It is shown that the density JRT of resonant tunneling current varies systematically from 7.0×102 to 3.5×104 A cm−2 as x is varied from 1.0 to 0.43. These data are found to be quantitatively explained by the theoretical calculation, in which the band discontinuity at Γ valley is taken as the barrier height. This result indicates that the electron tunneling through the double barrier structure is dominated by the barrier height of Γ minimum even when the subsidiary minima have lower energies (0.45≤x≤1.0).

Propagation angle dependence of radar auroral E-region irregularities

The Sweden and Britain Radar aurora Experiment (SABRE) measures the phase velocity and backscatter amplitude of 1 m wavelength irregularities in the auroral zone E-region. These irregularities are produced by two types of plasma instabilities and theory predicts that the variation in backscatter amplitude with the angle between the electron drift velocity V d and the radar vector k, the so called propagation angle, is different for the two cases. An isotropic angular dependence is expected for gradient drift instabilities, but for the alternative two stream instability process a minimum is produced in the backscatter amplitude for directions orthogonal to the flow. The SABRE data have been averaged to remove small scale fluctuations and for drift velocities less than ~200 ms −1 the backscatter dependence on the propagation angle is isotropic, strongly suggesting that gradient drift processes are dominant. At higher drift velocities anisotropies develop in the angular dependence with deep minima at approximately 90° to the flow and a subsidiary minimum at 0° to this direction. Although these characteristics suggest a two stream instability mechanism, there are features in the experimental data that are not predicted by this simple theory. It is suggested that ion drifts may in part be responsible for these additional features.

Photoemission from activated gallium arsenide. II. Spin polarization versus kinetic energy analysis.

The spin polarization of the electrons emitted by a GaAs photocathode under circularly polarized light excitation is investigated as a function of the electron kinetic energy. The photocathode is activated by cesium and oxygen coadsorption under ultrahigh-vacuum conditions to achieve a negative electron affinity. The spin polarization is measured by Mott scattering. The study is performed with a very-high-energy resolution (20 meV), at 300 and 120 K, under well-focused ${\mathrm{Kr}}^{+}$-laser light excitation (photon energy ranging from 1.55 to 2.60 eV). The polarization-versus-energy distribution curves show typical features related to those observed in the energy distribution curves, which are analyzed in detail in the preceding paper [H.-J. Drouhin, C. Hermann, and G. Lampel, Phys. Rev. B 31, 3859 (1985)]. A model is developed to account for the largest measured polarization, which arises from electrons excited from the heavy-hole band and emitted without suffering any collision: A (2/3) maximum value is expected, which is reduced by spin precession in the internal D'yakonov and Perel' (DP) field, due to the absence of space-inversion symmetry in GaAs. An estimation of the hot-electron mean free path (\ensuremath{\sim}0.1 \ensuremath{\mu}m for photon energy above 1.96 eV) is deduced. The photoemission polarizations of the electrons excited from each of the two other valence bands are also calculated using a nonparabolic Kane band model. The L and X subsidiary minima give rise to polarization plateaus originating from energy relaxation in the band-bending region. The main contribution to the photocurrent is due to electrons which were thermalized in the central minimum of the bulk crystal and have relaxed their energy in the band-bending region prior to emission into vacuum. Their polarization is studied in relation with the luminescence polarization, measured on the same samples, in the framework of a one-dimensional diffusion model. An additional depolarization, occurring during the escape process, is evidenced and attributed to the DP relaxation mechanism in the band-bending region. Finally, the performances of GaAs photocathodes as monochromatic and polarized electron sources are analyzed with use of the physical concepts developed in the present paper and in the preceding one.

Geometries and rotation barriers of 2-methyl-1,3-butadiene and of 2,3-dimethyl-1,3-butadiene by ab initio gradient calculation

The structures of 2-methyl-1,3-butadiene (isoprene) and 2,3-dimethyl-1,3-butadiene have been determined by ab initio gradient computation at the double-zeta Hartree-Fock level as a function of torsional angle around the central CC bond. Both compounds are most stable in the anti conformation and have subsidiary minima at a gauche conformation approximately 40° from syn. The dependence on torsional angle of the structural parameters and of the total energy is discussed together with similar results previously obtained for the parent molecule, butadiene. In terms of classical effects, the CC and CC bond lengths can be attributed mainly to hybridization of the carbon atoms. Resonance makes a minor contribution toward shortening the single bond and lengthening the double bonds in the planar forms and is mainly responsible for the rotational barrier around the central CC bond, since the absence of coplanarity at 90° hinders electron delocalization in the π system. Stability of the syn conformations is strongly decreased by CH 2⋯CH 2, CH 2⋯CH 3 and CH 3⋯CH 3 steric interactions, which are of comparable strength.

Transient electronic transport in staircase heterostructures

We present a Monte Carlo simulation of electronic transport in new forms of GaAs-GaAlAs heterostructures designed for achieving high drift velocities. Average electron speeds of ∼ 5.0 × 107cm/s through an entire structure length of 0.5 µm have been calculated. This represents a marked improvement in speed over a single barrier emitter structure. The basic physical principle is the following: the electrons are confined to the gamma valley by losing excess kinetic energy gained from an overlaid accelerating field. The mechanism for the energy loss is a series of ascending potential steps. In this way transfer to the subsidiary minima is avoided and very high velocities are possible. Paradoxically, this means that because the electrons lose kinetic energy their velocity remains high or actually increases.

The effect of paramagnetic impurities on proton spin relaxation in yttrium dihydride

Pulsed NMR measurements of the proton spin-lattice relaxation time, T1, in yttrium dihydride containing controlled amounts of gadolinium are reported over the temperature range 140-1250K. Addition of gadolinium produces a temperature-dependent relaxation contribution which is proportional to gadolinium concentration and gives rise to a subsidiary minimum on the low-temperature side of the main minimum due to proton-proton dipolar interactions. The results are interpreted in terms of a magnetic dipolar interaction between the Gd3+ paramagnetic ions and the protons. The possibility that some of the diffusion data deduced from previous NMR measurements has been affected by the unsuspected presence of paramagnetic impurities is discussed.

Conformational analysis of poly(MDI-butandiol) hard segment in polyurethane elastomers

As part of our study of the structure of the hard segments of polyurethane elastomers, we have used conformational analysis to predict the conformation of the polyurethane chain formed from diphenylmethane 4,4′-diisocyanate (MDI), with butandiol as the chain extender. X-ray diffraction indicates the chain conformation is highly extended in the solid state, with a monomer repeat of 18.95 Å. The chain conformation can be predicted from the interaction between the large contiguous groups. Semiempirical and CNDO/2 molecular orbital calculations have been used to investigate the phenyl-phenyl, phenyl-urethane, and urethane-butandiol interactions. Minimum energy for the diphenyl-methane section occurs for a CCH 2C bridge angle of θ = 110°. However, the more likely conformation in the polymer is probably that at the subsidiary minimum at θ = 118°, in which the phenyl rings are mutually perpendicular, which is comparable to the conformation seen for model compounds. For the phenyl-urethane interactions the energy minimum is at ч = ±90°, with the combination (ч 1, ч 2) = (−90°, +90°) leading to the necessary extended conformation. Calculations for the butandiol segment favour an all- trans conformation which is coplanar with the urethane groups. The predicted conformation of the polymer chain has a fibre repeat which matches the observed value, and this cannot be attained if the butandiol unit contains any gauche bonds. Model compounds show large variations for the phenyl-urethane conformation from the predicted minimum at ч = ±90°, indicating the importance of intermolecular stacking forces in determining the polymer conformation. However, provided the adjacent butandiol and urethane groups are coplanar, the fibre repeat is relatively insensitive to variations of ч.

Variations in air density from January 1972 to April 1975 at heights near 200 km

Variations in air density have been determined using the orbit of the satellite Cosmos 462, 1971-106A, which entered orbit on 3 December 1971 with an initial perigee near 230 km and inclination 65.75°, and decayed on 4 April 1975. Accurate orbits determined at 85 epochs give perigee height correct to about 200 m throughout the satellite's lifetime. Using these values of perigee height and orbital decay rates from NORAD elements, 604 values of air density at half a scale height above perigee have been evaluated. These densities have been compared with values from the COSPAR International Reference Atmosphere 1972, taking account of variations due to solar activity and geomagnetic disturbances, and day-to-night variations, to reveal the residual variations in density at a series of standard heights, 245, 240, 232 and 213 km. The main residual variation is semi-annual, with maxima usually in April and October, and minima usually in January and July; but it is irregular in phase and shape. The amplitude of the semi-annual variation is remarkably constant from year to year between 1972 and 1975, and considerably greater than that given by CIRA 1972: the April/July density ratio is 1.68, not 1.32 as in CIRA; the October–November maxima are all lower than the April maxima, whereas CIRA gives the opposite; the July minima are 18% lower than the January minima, as opposed to 10% in CIRA. A standardized semi-annual density variation for the early 1970s is presented, with January minimum of 0.94, April maximum of 1.28, July minimum of 0.77 and October–November maximum of 1.22. In addition, three other recurrent variations are recognizable: in each year the density has a subsidiary minimum in May and maximum in June; there are low values in mid November and high values in late December.

Limitations of the direct-indirect transition on In1−xGaxP1−zAsz heterojunctions

Because In1−xGaxP1−zAsz is the highest-energy direct-gap alloy employed in laser diodes, we attempt to establish where the direct-indirect transition (xc+0.516yc=1.235, 77 °K) hinders or possibly even limits the use of this sytem in large-barrier (ΔE∼250 meV) double-heterojunction (DH) structures. The behavior at 300 and 77 °K of the I-V characteristics of single-heterojunction and homojunction structures employing high Ga composition (x?0.72, z≲0.01) wide-gap In1−xGaxP1−zAsz layers, lattice matched on GaAs1−yPy substrates, show that the nature of the direct-indirect transition of the ternary boundary In1−xGaxP (x∼xc, y=1 or z=0) acts as a limiting factor on the DH diode and laser performance of the quaternary system. As in GaAs1−yPy, donor states associated with subsidiary minima (X) cause a premature onset of the direct-indirect transition, and limit the growth of lattice-matched large-barrier In1−xGaxP1−zAsz (ΔE∼250 meV) DH lasers, with all layers direct, to substrates of composition y≲0.40.