A nanodiamond thin film is deposited on a single crystal silicon substrate by dip-coating technique. Surface characterization of the unannealed nanodiamond sample, and the samples annealed at various temperatures in nitrogen ambient, is conducted by XPS and Raman spectroscopy. The fitting data of the C1s core level XPS peak reveal that the sp 2 /sp 3 ratio in the unannealed sample and the sample annealed at 900• C and 1500• C are 0.44, 0.55 and 6.08 respectively. All spectra including the C1s core level XPS spectrum, the plasmon energy-loss spectrum associated with C1s peak, C KVV Auger spectrum of the sample annealed at 900• C are similar to those of the unannealed sample. However, the spectra of the sample annealed at 1500• C are very different. Annealing at 900• C fails to produce appreciable graphitization, and an onion-like carbon structure with a small diamond core is formed when the nanodiamond is heated to 1500• C. Copyright c 2010 John Wiley & Sons, Ltd.Keywords: X-ray photoelectron spectroscopy (XPS); Raman spectroscopy; nanodiamond; sp 2 -hybridised; sp 3 -hybridised IntroductionNanodiamond is a potential cold cathode material in the electron field emission process [1,2] and has potential application in vacuum micro-and nanoelectronic devices. [3] The unique properties of nanodiamond are directly related to the microscopic structure, elemental and carbon bonding structure. [4] It is well known that the structure property of carbon material is determined by the sp 2 /sp 3 bonding ratio. Thermoannealing is an effective method to alter the structure of carbon material.[5] High-temperature annealing not only varies the chemical bonding structure of carbon material but also affects its field emission property. [6,7] The formation of a large fraction of sp 2 bonding carbon in the DLC film plays an important role in the enhancement of field emission property. [6] So far, in order to characterize carbon materials, a correct estimate of the abundance of sp 2 -hybridised atoms is of extraordinary importance. Raman spectroscopy can be used to identify sp 2 and sp 3 hybrids in C-based material owing its high sensitivity to light scattering. However, Raman technique has a poor capability in quantitative analysis. XPS can be used to estimate the fraction of sp 2 -hybridised atoms in carbonaceous materials. [8,9] XPS is a surface analytical technique which provides both chemical and binding information for a variety of materials. For carbon materials, the C 1s core energy level at around 280-290 eV, [10] the plasmon-loss energy at around 0-60 eV relative to C1s main peak [11] and the X-ray-excited Auger peaks at higher binding energy [11] all give phase information on the carbon present. Fitting the C1s core level peak is a common method used to quantify the sp 2 hybrids in C-based material. The C1s photoelectrons whose loss features reflects the different bond organization, and the Auger region whose width is correlated to the amount of sp 2 hybridised C-atoms. [12] In this paper, the unannealed nanodiamond sample a...

The hyperbolic perturbation method is applied to determining the homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators of the formẍ + c 1 x + c 3 x 3 = εf (μ, x,ẋ), in which the hyperbolic functions are employed instead of the periodic functions in the usual perturbation method. The generalized Liénard oscillator with f (μ, x,ẋ) = (μ − μ 1 x 2 − μ 2ẋ 2 )ẋ is studied in detail. Comparisons with the numerical simulations obtained by using R-K method are made to show the efficacy and accuracy of the present method.

Bifurcations and route to chaos of the Mathieu-Duffing oscillator are investigated by the incremental harmonic balance (IHB) procedure. A new scheme for selecting the initial value conditions is presented for predicting the higher order periodic solutions. A series of period-doubling bifurcation points and the threshold value of the control parameter at the onset of chaos can be calculated by the present procedure. A sequence of period-doubling bifurcation points of the oscillator are identified and found to obey the universal scale law approximately. The bifurcation diagram and phase portraits obtained by the IHB method are presented to confirm the period-doubling route-to-chaos qualitatively. It can also be noted that the phase portraits and bifurcation points agree well with those obtained by numerical time-integration.

a b s t r a c tThis paper presents a new precise Hsu's method for investigating the stability regions of the periodic motions of an undamped two-degrees-of-freedom system with cubic nonlinearity. Firstly, the incremental harmonic balance (IHB) method is used to obtain the solution of nonlinear vibration differential equations. Hsu's method is then adopted for computing the transition matrix at the end of one period, and the precise time integration algorithm is adjusted to improve the computational precision. The stability regions of the system obtained from the precise Hsu's, Hsu's and improved numerical integration methods are compared and discussed.

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