Please note, due to essential maintenance online transactions will not be possible between 02:30 and 04:00 BST, on Tuesday 17th September 2019 (22:30-00:00 EDT, 17 Sep, 2019). We apologise for any inconvenience.
To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Let G = 〈x, t | w〉 be a one-relator group, where w is a word in x, t. If w is a product of conjugates of x then, associated with w, there is a polynomial Aw(X) over the integers, which in the case when G is a knot group, is the Alexander polynomial of the knot. We prove, subject to certain restrictions on w, that if all roots of Aw(X) are real and positive then G is bi-orderable, and that if G is bi-orderable then at least one root is real and positive. This sheds light on the bi-orderability of certain knot groups and on a question of Clay and Rolfsen. One of the results relies on an extension of work of G. Baumslag on adjunction of roots to groups, and this may have independent interest.
This year we celebrate the centenaries of the births of B. H. Neumann and A. I. Mal'cev, two great pioneers in the study of ordered algebraic structures. This paper is a survey of our recent progress in this area, and amplifies the talks we gave in Bath at the Groups St. Andrews Conference there, and the first author gave at the Mal'cev Centenary Conference in Novosibirsk. A version of this paper in Russian will appear in honour of the Mal'cev Centenary and the 80th anniversary of A. I. Kokorin, another pioneer in the subject (Izvestia of Irkutsk Sate University, Series Matematika, Vol. 2 (2009), No. 2, 4–19). The heart of the paper for pure group theorists is Section 4.
Groups versus Lattice-ordered Groups
One way to obtain results in infinite group theory is through spelling and associated constructions, such as free groups, free products, free products with amalgamated subgroups, and HNN-extensions . The first two constructions are available in any variety of algebras, but for groups they are especially nice. This is for two reasons. The first is that every element of a free group has a unique easily obtained reduced spelling in terms of the generators and there is, similarly, a unique normal form for elements of a free product. Moreover, given any groups G1 and G2 with isomorphic subgroups H1 and H2, respectively (say φ : H1 ≅ H2), there is a group L and embeddings Τi : Gi → L (i = 1, 2) such that h1Τ1 = h1φΤ2 for all h1 ∈ H1.
Thin C films deposited from a CH4/Ar plasma on Si substrates kept at 20C are shown to be semiconducting. The semiconducting properties are associated with the poly-crystalline diamond grains present within the films. Diode type I-V characteristics observed from AVC/Si verticle structures are explained by the action of a C-Si heterojunction. A band gap of 2eV, a resistivity of 106Ω.cm and an electrical breakdown strength of 5.106 V/cm are estimated for the C.
Nuclear magnetic resonance spectroscopy has been used to study diamond thin films grown in a low-pressure hot-filament reactor from 13C-labeled acetone. Film quality is assessed, and the origin of deposited carbon determined. Carbon atoms from both bonding environments in the acetone molecule deposit to form only sp3-bonded material. The relative rate of incorporation of these carbon atoms is determined. Experimental results and equilibrium calculations demonstrate that CO acts as a precursor for diamond growth in the absence of heterogeneous kinetics.
The technology of low pressure chemical vapor deposition (CVD) of polycrystalline diamond films has advanced substantially in recent years [1–3]. However, fundamental understanding of the chemistry and physics occurring in this CVD process is still lagging. Although the key role that H atoms play in diamond CVD has long been recognized [4–6], the identity of the gaseous diamond precursors and the mechanism by which diamond is formed are still unclear. Only recently has interest in these critical issues grown. For example, theoretical predictions and quantum mechanical calculations of gas-solid reaction paths involving CH3 and CH3+  or C2H2  have been reported, and the thermodynamic analyses of diamond CVD processes have been examined [9,10]. In addition, experimental results and chemical models [11–16] have been presented in attempts to support specific species as the essential precursors of diamond growth. Nevertheless, no consensus has been reached concerning the growth species and mechanism in CVD diamond processes.
Experiments to study the temperature in the discharge produced using a dc spiral hollow cathode with CH4-H2 as the feed gas have been carried out during the rowth of diamond. Optical emission from the R branch of the 3d1 Σ v-O-2p Σ v-O rotational vibronic band are used to determine a rotational temperature. Limitations of this method are discussed.
We report on ohmic contacts on β-SiC. The contacts were formed using Ni, NiCr, W, Ti, Wsi2 and TiSi2. Contact resistance measurement and Auger Electron Spectroscopy (AES) were used to study annealing effects on contact materials. Auger analysis of Ni-SiC system indicates that during heat treatment, Ni reacts with Si to form silicide. Similar results are found for NiCr-SiC contacts.
Minimum contact resistance of tungsten and titanium on SiC is measured to be 6.l×10−3 ohm/cm2 and 7.6×10−3 ohm/cm2, respectively. High temperature annealing deteriorates both contacts although for titanium contacts the resistance increases less dramatically as compared to tungsten contacts. The silicides of tungsten and titanium yield lower contact resistance than metallic W and Ti contacts. The contact resistance for Wsi2 and TiSi2 after heat treatment decreases to 3.0×10−4 ohm/cm2 and 1.1×10−4 ohm/cm2, respectively.
Diamond has an electric-field breakdown 20 times that of Si and GaAs, and a saturated velocity twice that of Si. This results in a predicted cut off frequency for high-power diamond transistors 40 times that of similar devices made of Si or GaAs. Boron is the only known impurity that can be used to lightly dope diamond. This p-type dopant has an activation energy of 0.3 to 0.4 eV, which results in high-resistivity material that is undesirable for devices. However, heavily boron doped diamond has a very small activation energy and a low resistivity and is of device quality. Transistors can be designed that use only undoped and heavily doped diamond. One of the steps in a device fabrication sequence is homoepitaxial diamond growth. Lightly and heavily doped homoepitaxial diamond films were characterized by scanning and transmission electron microscopy, x-ray diffraction, measurements of resistivity as a function of temperature, and secondary ion mass spectroscopy. It was found that under appropriate growth conditions these films are of device quality.
The behavior of tungsten filaments heated up to 2500°C in mixtures of CH4 or C2 H2 and H2 at P = 9 and 25 Torr is analyzed. It has been found that the filament resistance R, spectral emissivity ?, power consumption, and CH4 and C2H2 partial pressures depend critically onl the filament temperature as well as the reactant CH4/ H2 or C2H2/ H2 fraction. We interpret these results on the basis of a thermodynamic model which predicts that transitions between deposition and etching of solid carbon occur on the filament surface at high temperatures. The implications of these results for diamond CVD are discussed. Evidence for gas phase reactions is also presen ted.
We have used RBS/Channeling, perturbed angular correlation (PAC) and optical absorption to study the regrowth of disordered layers in diamond produced by implantation with carbon, or with carbon plus boron or indium ions. For C or C plus B implantation doses of 2 ×1015 cm−2 or less, complete recovery of channeling damage occurred after RTA at 1100°C or furnace annealing at 900°C. Optical measurements on samples implanted with high energy carbon ions show better recovery compared to the shallower implantations. PAC results showed that co-implantation with C and In caused a considerable fraction (∼15%) of the In-atoms to occupy well-defined lattice sites characterized by an electric field gradient having its major component along <111>, and a frequency of 116 MHz.
We report the synthesis, structural characterization, and preliminary optical studies of ultrathin Ge-Si superlattices with individual sublayers smaller than the Si unit cell, grown by MBE on (001) silicon substrates. Structures are fabricated one monolayer at a time in a configuration GeGeSiSiGeGe..., resulting in either ordered alloys or complex cell superlattices. Rutherford backscattering and channeling experiments on these highly strained heterostructures indicate excellent crystallinity with tetragonal distortion as high as 3.5%. Electron diffraction patterns exhibit characteristic superlattice reflections indicative of one-dimensional layering with periodicity of four monolayers. X-ray scans along the growth direction at the (002) position in reciprocal space reveal a strong peak not observed in random GeSi alloys. This scattering is attributed indirectly to the GeSi ordered phase. The optical transition energies measured by Schottky barrier electroreflectance correspond to those expected from homogeneous alloys of the same composition; however, the width of optical transitions is less than 30 meV at room temperature, allowing a clear resolution of the splitting of the valence band by strain. Modification of the unit cell of the diamond lattice in this way should permit the design of materials with novel opto-electronic characteristics. Preliminary Raman and photoconductivity measurements are also reported.
Thin films (2 Å - 1000 Å) of titanium, platinum, and hafnium were deposited via UHV electron beam evaporation at room temperature on n-type, (0001) alpha (6H)-SiC and compared in terms of interfacial chemistry, energy barriers to electrical conduction, and macroscopic electrical behavior. Current-voltage measurements have shown that these contacts are rectifying, all with ideality factors between 1.01 and 1.09. The lowest leakage currents (∼5 × 10−8 A/cm2 at -10 V) were determined for unannealed Pt contacts and for Hf contacts annealed at 700°C for 20 minutes. Current-voltage (I-V), capacitance-voltage (C-V), and x-ray photoelectron spectro-scopy (XPS) were among the techniques used to determine barrier heights, all of which were within a few tenths of an electron volt of 1.0 eV. The narrow range of calculated barrier heights along with the XPS valence spectrum of the chemically prepared SiC surface give evidence that the Fermi level is pinned at the semiconductor surface.
A new approach to achieving a large-area silicon-on-insulator technology without pre-patterning is described. (100) Si films are first grown epitaxially on (100) yttria-stabilized cubic zirconia (YSZ) substrates by the pyrolysis of SiH4. The Si side of the <Si>/<YSZ>interface is then oxidized in pyrogenic steam (at 925 °C) or dry oxygen (at 1100°C) to form the structure <Si>/amorphous SiO2/<YSZ>. The oxidation occurs by the rapid diffusion of oxidants through the 0.42 mm thick YSZ substrate; e.g., a 0.3 μm SiO2 layer is obtained in 6 h in steam. The samples are analyzed by Rutherford backscattering and channeling spectrometry, X-ray diffraction, infra-red reflectance, Auger electron spectroscopy and sheet resistance measurements. In addition to forming the preferred Si/SiO2 interface, the back-side oxidation eliminates the most defective part of the Si film.
The radioactive decay heat from nuclear waste packages may, depending on the thermal load, create coupled thermal-mechanical-hydrological-chemical (TMHC) processes in the near-field environment of a repository. A group of tests on a large block (LBT) are planned to provide a timely opportunity to test and calibrate some of the TMHC model concepts. The LBT is advantageous for testing and verifying model concepts because the boundary conditions are controlled, and the block can be characterized before and after the experiment. A block of Topopah Spring tuff of about 3 × 3 × 4.5 m was sawed and isolated at Fran Ridge, Nevada Test Site. Small blocks of the rock adjacent to the large block were collected for laboratory testing of some individual thermal-mechanical, hydrological, and chemical processes. A constant load of about 4 MPa will be applied to the top and sides of the large block. The sides will be sealed with moisture and thermal barriers. The large block will be heated by heaters within and guard heaters on the sides so that a dry-out zone and a condensate zone will exist simultaneously. Temperature, moisture content, pore pressure, chemical composition, stress, and displacement will be measured throughout the block during the heating and cool-down phases. The results from the experiments on small blocks and the tests on the large block will provide a better understanding of some concepts of the coupled TMHC processes. The progress of the project is presented in this paper.
Individual screw dislocations along the  axis in 6H-SiC single crystals have been characterized by means of Synchrotron White Beam X-ray Topography (SWBXT). The magnitude of the Burgers vector was determined from: (1) the diameter of circular diffraction-contrast images of dislocations in back-reflection topographs, (2) the width of bi-modal images associated with screw dislocations in transmission topographs, (3) the magnitude of the tilt of the lattice planes on both sides of dislocation core in projection topographs, and (4) also the magnitude of the tilt of the lattice planes in section topographs. All of the four methods showed reasonable consistency. The sense of the Burgers vector can also be deduced from the abovementioned tilt of the lattice planes. Results revealed that in 6H-SiC a variety of screw dislocations can be found with Burgers vector magnitude ranging from 1c to 7c (c is the lattice constant along  axis). This work demonstrates that SWBXT can be used as a quantitative technique for detailed analyses of line defect configurations.
Cadmium zinc telluride crystals were grown by vertical Bridgman processes using in situ compounding from high purity elements into pyrolytic boron nitride crucibles within sealed fused quartz ampoules containing cadmium vapor at a pressure of roughly one atmosphere. These conditions produce material having the low etch pit density, low precipitate density, high infrared transmission and high purity required for use as substrates for infrared focal plane detector arrays fabricated in epitaxial mercury cadmium telluride. Similar processes should be satisfactory for producing cadmium zinc telluride for gamma ray detectors.
The γ ray (57Co) and α particle (241Am) detector response of Cdl-xZnxTe crystals grown by vertical Bridgman technique was studied under both positive and negative bias conditions. Postgrowth processing was utilized to produce a high-resistivity material with improved chargecollection properties. Samples of various Zn concentrations were investigated by I-V measurements and thermally stimulated spectroscopies to determine the ionization energies of deep levels in the band gap. When the post-processing conditions were optimized the lowenergy tailing of the γ-ray photopeaks was significantly reduced and an energy resolution of under 5% was achieved for the 122 keV γ-photon line in crystals with x=0.2 Zn content at room temperature. A peak to background ratio of 14:1 for the 122 keV photopeak from 57Co was observed on the best sample, using a standard planar detection geometry. The low-energy 14.4 keV X-ray line could also be observed and distinguished from the noise.
Cadmium zinc telluride crystals were grown by vertical Bridgman processes using in situ compdunding from high purity elements into pyrolytic boron nitride crucibles within sealed fused quartz ampoules containing cadmium vapor at a pressure of roughly one atmosphere. These conditions produce material having the low etch pit density, low precipitate density, high infrared transmission and high purity required for use as substrates for infrared focal plane detector arrays fabricated in epitaxial mercury cadmium telluride. Similar processes should be satisfactory for producing cadmium zinc telluride for gamma ray detectors.
The CZT boule was grown by a modified vertical Bridgman process using in-situ compounding, Cd over-pressure and a pyrolytic boron nitride crucible within a fused ampoule. During growth, the Cd vapor pressure was near 1 atmosphere. These growth conditions tend to give high purity, good stoichiometry, few precipitates, and dislocation densities in the low to mid-104 cm−2 range. The crystals, after polishing, were annealed in a nearly saturated Cd, Zn atmosphere to fill residual Cd-site vacancies and achieve high resistivity in the 1010 γ-cm range. Low temperature photoluminescence study shows very good crystalline quality and a very low concentration of deep level recombinations. Single crystal samples were diced into 1 cm squares for evaluation as gamma ray detectors. The best detector results (4.5% resolution at 60 keV) were achieved for a 2 hour anneal at 850°C.