Initial stages of growth of GaN over (0001) Al2O3 substrate using MBE: a crystallographic analysis of the defects

An AlN buffer layer grown on (0001) sapphire substrate by molecular beam epitaxy has been studied. It is found to be made of small grains having a common [0001] axis parallel to that of the substrate. Some grains are rotated around this axis and the angle rotation can reach 20° leading to a new epitaxial relationship (0001)_sap//(0001)_AlN and [11

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0]_sap//[21

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0]_AlN. A model for the atomic structure of one of these grain boundaries is proposed using high resolution electron microscopy and extensive image simulation.     

Comparison of luminescence and physical morphologies of GaN epilayers

In this paper we examine a series of four GaN epilayers grown by MOVPE on sapphire substrates with different AlN buffer layer thicknesses. We examine the effect of the buffer layer thickness on the physical and optical properties of the samples via optical microscopy, cathodoluminescence imaging, photoluminescence, and cathodoluminescence spectroscopy. While the morphological and optical properties of all the films (excepting that with the thinnest buffer layer of 30 nm) are good, i.e. the films are smooth and the luminescence is dominated by excitonic luminescence, a number of circular island like features are observed in all the films whose density decrease with increasing buffer layer thickness. A large circular island present on the sample with the thinnest buffer layer and surrounded by cracks in the 11

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0 directions, displays some interesting acceptor related luminescence.     

GaN thin films deposited by pulsed laser ablation in nitrogen and ammonia reactive atmospheres

Well-oriented, crystalline GaN films were grown on (11

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0) sapphire substrates in reactive atmospheres of N₂ and NH₃ by pulsed laser deposition. GaN targets were ablated at 2.8 J cm⁻² and the substrate temperature was varied from 500 to 700°C. The background gas pressure was varied from 0.04 to 0.3 mbar. All the films had a wurtzite structure. The crystal quality and preferential orientation depended on the substrate temperature, laser fluence and the presence of the nitriding atmosphere. For both N₂ and NH₃, the most resistive films were preferentially orientated in the [000l] direction. For 700°C the film resistivity was found to increase from 10⁻³ Ω cm when deposited in NH₃ to 10² Ω cm when deposited in N₂. The band-gap, obtained from optical transmission measurements shifted from 3.1 to 3.4 eV. Violet photoluminescence was found in all samples and was centered at 3.2 eV with a full width at half maximum of 0.2 eV. A broad peak in the yellow, centered at 2.1 eV, was detected for films grown in vacuum and ammonia.     

Classification of 2 × 2 non-strictly hyperbolic systems for plane waves in isotropic elastic solids

The governing equations for plane waves in generally nonlinear isotropic elastic solids are a system of 6 × 6 hyperbolic conversation laws. For the half-space Riemann problem in which the initial conditions at t = 0, x > 0 and the boundary conditions at x = 0, t > 0 are constant, the system is equivalent to 3 × 3 system in the full-space Riemann problem. It is further reduced to a 2 × 2 system due to the fact that one of the characteristic wave speeds is linearly degenerate. For hyperelastic materials for which there exists a potential W whose gradients provide the strains, the wave curves near an isolated umbilic point are represented by the potential of the form

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which contains two parameters k and m. The classification of the geometry of wave curves depends on the values of k and m and can be classified into five cases. The potential function considered here is equivalent to considered by Schaeffer and Shearer where a and b are parameters. The classification presented here seems to provide simpler algebraic expressions. It also renders more refined classification as shown in the paper.     

Near-tip fields of growing cracks and resistance curves

This paper gives the formulation and solution of near-tip fields of mode-I cracks growing quasi-statically in compressible elastic perfectly plastic materials. As Poisson's ratio v tends to , the solution approaches the solution of crack growth in incompressible elastic perfectly plastic materials. The rate of crack opening is determined as

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, where β = 5.454 for V = o.3. The evaluation of fracturing based on the criterion of the near-tip opening is discussed.     

Characterisation of dislocations, nanopipes and inversion domains in GaN by transmission electron microscopy

Transmission electron microscopy is used to analyse a range of defects observed in hexagonal GaN films grown on sapphire and GaN substrates by metalorganic chemical vapour deposition. Large angle convergent beam electron diffraction is used to analyse the Burgers vectors of dislocations and to show that hollow tubes, or nanopipes, are associated with screw dislocations having Burgers vectors±c. Weak-beam electron microscopy shows that dislocations are dissociated into partials in the (0001) basal plane, but that threading segments are generally undissociated. The presence of high densities of inversion domains in GaN/sapphire films is confirmed using convergent beam electron diffraction and the atomic structure of the {

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} inversion domain boundary is determined by an analysis of displacement fringes seen in inclined domains.     

Dynamic fracture toughness at crack initiation, propagation and arrest for two pipe-line steels

The influences of temperature and loading rate on fracture toughness of two pipe-line steels at initiation, K_1d, and at arrest, K_1a, and on stretch zone height were measured using specific techniques. Particular attention was given to the mechanism of delamination, typical for the gas internal pressure pipe fracture.     

Spectroscopic studies of Nd-doped alkali fluoroborophosphate glasses

A new family of three optical glasses of the following chemical composition with 1 mol% of Nd³⁺ were prepared to examine the effects of alkali fluorides in unmixed form:

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, where RF=LiF, NaF and KF. On the basis of the measured values of densities and refractive indices, the dielectric constant, reflection losses, molar refraction, Nd³⁺ ion concentration in glasses and several other physical properties were determined. Absorption spectra of these glasses were recorded and Judd–Ofelt intensity parameters (Ω_λ) have been calculated. Radiative lifetimes (τ_R) and branching ratios (β_R) for the fluorescent levels have been determined. To understand the laser efficiency of these materials, the values of the spectroscopic quality factor (Ω₄/Ω₆) has been evaluated and it is found that glass C could be suggested as a suitable lasing material.     

Thermally induced logarithmic stress singularities in a composite wedge and other anomalies

Wedge paradoxes, which were first studied by Sternberg and Koiter (Sternberg E, Koiter WT. The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity. ASME Journal of Applied Mechanics 1958;4:575–81), occur due to multiple roots in the Williams (Williams ML. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. ASME Journal of Applied Mechanics 1952;19:526–28) eigenfunction expansion. The consequence of such a paradox is a change in behavior of the stresses from , to the ‘non-separable’ form,

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. The focus of this study is the problem of thermally induced logarithmic stress singularities in a composite wedge associated with ω=0. Both double and triple root examples are presented which lead to and behavior in the stresses, respectively. This behavior is primarily associated with incompressible materials for the clamped–clamped single material case, and for the full range of Poisson’s ratio for the clamped-free case. The study also includes non-separable eigenfunctions that occur when complex conjugate roots transition to double real roots. Perhaps the most interesting result is that for the clamped–clamped wedge with Poisson’s ratio equal to 1/2, the hydrostatic stress has a logarithmic singularity proportional to the thermal strain for all wedge angles. This result can be extended to conclude that for a confined, incompressible or nearly incompressible material with a relatively sharp corner, and subject to some expansion or contraction phenomena, high hydrostatic stresses can result.     

Fracture mechanical characterisation of mixed-mode toughness of thermoplast/glass interfaces

According to studies conducted by, e.g. Liechti and Chai [J. Appl. Mech. 58 (1991) 680], Yuuki et al. [Eng. Fract. Mech. 47 (3) (1994) 367] and Ikeda and Miyazaki [Eng. Fract. Mech. 59 (6) (1998) 725], a significant increase of interfacial toughness is observed, whenever the magnitude of the bond tangential shear load of the asymptotic elastic mixed-mode state is increased in either direction. Between these extremes the interfacial toughness curve exhibits a pronounced minimum, which, according to Hutchinson and Suo [Mater. Sci. Eng. A 107 (1989) 135] is believed to represent the so-called intrinsic adhesion, i.e. the failure toughness under pure local mode I loading. Within linear elasticity, the biaxial, singular near-tip solution for an open interface crack may be employed for characterising the local stress state as long as non-linearities such as, e.g. crack-wall contact and plastic flow are contained within a zone small enough compared to the extension of the singular opening-dominated fields. Then, the critical stress state is given in terms of bimaterial stress intensity factors K_1,c, K_2,c and the fracture toughness under mixed-mode loading may be expressed in terms of the critical energy release rate as a function of the mode-mixity ψ=tan⁻¹K_2,c/K_1,c. The stress intensities have to be extracted from a stress analysis of the specimen under the critical load, which in the present work is performed by means of an FE-model of the loaded sample.     

Fracture toughness of turbine-generator rotor forgings

A comprehensive program is being conducted relative to applying fracture mechanics technology to large turbine-generator rotors. One facet of this program involves the determination of plane-strain fracture toughness (K_Ic) over a range of temperatures for various types of rotor steels. Data have been obtained for ten large production forgings, representing three alloys, using various types of compact K_IC and spin burst test specimens. These results demonstrate that valid K_IC data can be obtained in these types of intermediate-strength, high-toughness steels in the temperature range of practical interest. Data indicate that the plane-strain fracture toughness of these steels increases rapidly with increasing temperature and is rather high (K_tc/σ_YS > 1 in^1/2), in the application range. As a result, the critical defect sizes for catastrophic failure upon a single cycle of loading are relatively large. The plane-strain fracture toughness measurements, as well as the application of these data, are presented and discussed.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Hardness, internal stress and fracture toughness of epitaxial AlxGa1−xAs films

Vickers microhardness indentations of 10 μm (001) oriented epilayers of Al_xGa_1−xAs on GaAs substrates have been utilized to evaluate the hardness H_v, the internal stress, and the fracture toughness K_Ic of the layers as a function of their composition parameter x. The hardness H_v varies linearly according to: (6.9-2.2x) GPa and K_Ic increases linearly with x according to: K_1c = (0.44+1.30x) MPa m^1/2. The influence of the substrate on these measurements was found to be negligible for the layer thickness (10 μm) and the indentation load (0.25 N) used, disregarding internal stresses.

Internal film stresses were evaluated by the bimorph buckling method, and were found to depend on the composition parameter according to σ = 0.13x GPa. These stresses did not notably affect the H_v measurements, but for K_Ic corrections as large as 25% had to be made.

The radial cracks observed were of the shallow Palmqvist type. In contradiction to previous reports on this type of cracking, it was found to initiate during unloading, not during loading, and a physical explanation for this deviation is given. No deep radial/median cracks were observed. It was found important to use expressions based on the correct crack geometry in the K_Ic evaluation. Also, a simple theory for the influence of internal stresses on the K_Ic results has been developed.     

Simple formulas for the energy loss of ultrarelativistic muons by direct pair production

Simple formulas for direct pair production are derived from the general equation for deeply inelastic lepton scattering. Applications to energy loss by ultrarelativistic muons are discussed. For muons above the critical energy, E_c^μ 200 GeV, where the radiative effects of direct pair production and bremsstrahlung are dominant, the expressions for energy losses are considerably simplified when quoted in terms of the fractional energy loss per radiation length. The differential probability for direct pair production in a thickness x of material of radiation length X₀ for an incident lepton of energy E, mass M, can be expressed as

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where ν is the energy of the produced pair, υ is the fractional energy loss, υ = ν/E, m_e is the electron mass and the variable z is defined by

For indicent muons, this simple expression agrees very well with the exact calculation to within 30% over the entire range of υ, for E 1 TeV. At higher energies complete screening occurs, and the agreement is further improved, to better than 15% (except for the range 0.005 ≤ υ ≤ 0.01 where it is 25%). The integral of this expression gives the energy loss due to direct pair production by muons (complete screening) which is accurate to 10%:

.     

Dynamic fracture toughness parameters for HY-80 and HY-130 steels and their weldments

Lower bound dynamic fracture toughness parameters for HY-80 and HY-130 steel and their weld metals are identified. Specific values of the parameters K_Id and K_Im obtained from direct measurements are reported together with estimates inferred from the large body of Charpy energy, nil ductility transition temperature and dynamic tear energy measurements. The emphasis is on reasonable lower bound values at 30°F, the lowest anticipated service temperature, for use in elastodynamic analyses of crack growth initiation, propagation, and arrest in ship structures. For these conditions, it has been found that the ratio K_Id/ σ_Y is approximately equal to 2 in^1/2 for HY-80 steel. For HY-130 steel and the HY-80 and HY-130 weld metals under these same conditions, K_Id/ σ_Y is approximately 1 in^1/2. Consequently, HY-80 plate appears to be substantially more resistant to fracture under dynamic loading than are the other three grades examined.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Mechanical and electronic properties of C60 under structure distortion studied with density functional theory

B3PW91/6-31G density functional method was employed to investigate the elastic, strength and electronic properties of C₆₀(I_h) in its ground electronic state (X ¹A_g). Most of the properties were examined for larger structure distortions. The over-all elastic constant were derived from the near-equilibrium potential energy curves (PECs) in five independent directions [according to symmetries by 1. D_5d, 2. D_3d, 3. D_2h, 4. C_2h(1), 5. C_2h(2)]. By extension of the distortions as large as the structure of C₆₀ was destroyed, the necessary energies were obtained, which quantitatively illuminated the stability of C₆₀ theoretically. Analytical polynomial fit of the full PECs reproduced the energy data accurately. Time-dependent B3PW91/6-31G analysis showed significant electronic spectra changes associated with the structure distortions. Elongation in the direction of D_5d and compression in that of D_2h encountered potential energy surface cross-linkages, which might be considered as a single electron pump for further application in designs of single electron devices.     

The mechanics and mechanisms of fracture in stress corrosion cracking of aluminium alloys

A fracture mechanics approach to stress corrosion cracking is highlighted. The mechanisms of stress corrosion cracking is presented. Experiments on 2024 and 7075 aluminium alloys are carried out to determine their mechanical properties, microstructure and plane strain fracture toughness (K_IC). Stress corrosion cracking tests, namely, cantilever beam tests as well as wedge opening loading tests using sea water as a corrosive medium, are conducted to establish the critical stress intensity factor for stress corrosion cracking (K_ISCC) for each aluminium alloy. It is found that the K_ISCC is in the range of (1/5) to (1/6) of the plane strain fracture toughness, K_IC, depending on the alloy. The scanning electron microscopy of fracture surfaces reveals a great dependence of the cracking and/or pit severity on the applied stress intensity factor. A brief discussion on the dislocation's role in stress corrosion cracking is given.     

Plane strain fracture toughness of MP35N in aged and unaged conditions measured using modified CT specimens

The multiphase alloy MP35N (35% Ni, 35% Co, 10% Mo, 20% Cr) is a high strength, high toughness alloy of choice for several safety-critical applications in aerospace, oil drilling, and biomedical industries. Several previous attempts in literature to measure the plane strain fracture toughness of commercially drawn MP35N did not produce reliable values since they violated one or more of the criteria stipulated by ASTM standards for a valid measurement of K_Ic. In most cases, the requirements for plane strain and small scale yielding conditions were not met, since the commercially drawn material was available only with limited cross-sectional dimensions. In this investigation specially designed specimens (modified compact tension (CT) specimens) have been used to measure the plane strain fracture toughness of MP35N in both the unaged and the aged conditions. The K_Ic of the commercially drawn (53% reduction level) MP35N was measured to be 126 MPa√m, while that of the commercially drawn and aged MP35N was measured to be 98 MPa√m. Both these measurements satisfied all the required criteria stipulated by ASTM standards for valid measurements of K_Ic. The new procedure used in this study has been verified by the measuring of fracture toughness of Al alloy, using both the modified specimen, as designed here, and the standard one. The results for plane strain fracture toughness of MP35N alloy have been verified by the standard measurement of J_Ic values for both the aged and the unaged alloys. Finally, on a suitably normalized plot, introduced in this paper, the toughness-strength envelop for MP35 is higher than most of structural alloys, but significantly lower than that of the TRIP steels.     

An analysis of the crack tip fields in a ductile three-point bend specimen subjected to impact loading

Analyses of an impact fracture test of a precracked, three-point beam of HY100 steel were performed to determine the dynamic fracture toughness. During impact, the crack tip opening displacement (CTOD) 100 μm behind the crack tip was measured using an optical measuring device called the interferometric strain/displacement gage. Since fracture initiates when stress wave effects dominate, a numerical simulation of the fracture event was conducted to obtain relevant near crack tip field parameters. The specimen was modeled by a plane stress finite element simulation using a rate sensitive elastoplastic material law. Since the simulated CTOD was to be compared with the measured CTOD in a region of residual strains due to crack closure, this effect was included in the model. The simulation produces a CTOD versus time response within 10% of the observed response, indicating that the other field quantities (such as the J-integral) should also be reliable. The loading rate /.K₁ was approximately 8 × 10⁶MPa√m/sec. If the fracture initiation time is assumed to coincide with the time at which the simulated and observed CTOD curves diverge, then the impact fracture toughness is 56% higher than the static fracture toughness.