Effect of mean-square amplitude of atomic vibrations on the creep behaviour of cubic crystals

Correlation between the activation energyQ of high-temperature creep and the Debye-Waller thermal parameterB, which is proportional to the mean-square amplitude of atomic vibrations, has been examined in the case of 17 faced-centred cubic, body-centred cubic and diamond-structure cubic elements. It is observed thatQ is a function ofB, irrespective of the crystal structure;Q decreases asB increases. The correlation is governed by the power-lawQ=Q ₀(B/B ₀) ^M0 , whereQ ₀=0.095eV andM ₀=−0.62 are numerical constants determined by least-squares fit method, and the constantB ₀=1 nm².     

Investigation of the activation-parameters of low-temperature slip in cubic metals

The macroscopic critical resolved shear stress (CRSS)τ of 9 body-centred cubic (BCC) and 5 face-centred cubic (FCC) metals has been found to vary with temperatureT in the range 0 to 300 K as given by: lnτ=A − BT, whereA andB are positive constants. Theτ−T data have been analysed within the framework of a kink-pair nucleation (KPN) model of plastic flow in crystals. The microscopic parameters of the unit activation process of yielding, e.g. the initial length of the glide dislocation segment, the critical height of the kink-pair nucleated in it, the activation volume associated with the CRSS, and the binding energy per interatomic spacing along the glide dislocation in the slip plane etc., have been evaluated. A consistent picture of the dislocation kinetics involved in the yielding of BCC and FCC metals emerges, which is adequately described by the KNP model of plastic flow in crystals.     

Simple calculation of the mean-square displacements of volume, (110) and (100) surface atoms of chromium

We use an analytic method based on the expansion of the dynamical matrix to determine the thermal dependence of the mean-square displacements 〈u²〉 of volume, and (100) and (110) surface atoms of Cr. For the volume and (110) surface the results are in satisfactory agreement with previous X-ray and low-energy electron diffraction data. In particular, the zero-point thermal motion of Cr-volume atoms is approximately reached at temperatures as high as 170°K in accordance with experiments.A discussion about the temperature at which the atomic vibrations are strongly frozen is carried out for b.c.c. crystals.     

Ablation yield and angular distribution of ablated particles from laser-irradiated metals: The most fundamental determining factor

Five metals (Zn, Cu, Ni, Ti, and Mo) were irradiated with 150 shots of a Q-switched Nd:YAG pulsed laser in a vacuum of 10⁻³ torr. The ions projected out of the laser-produced plasma (LPP) plume were detected by CR-39 detectors positioned at −15°, 0°, 30°, 60°, and 90° with respect to the target-surface normal at a distance of 5 cm from the target in each case. The angular distribution of LPP ions, which is characterized by the exponent n of cosⁿ θ distribution, is given by n = 2.5-11 for the five target metals. The value of the exponent n has no systematic correlation with the square-root of atomic mass of the target metals but exhibits systematic dependence on the room temperature Debye-Waller's thermal parameter B or the mean-square amplitude of atomic vibrations 〈u²〉. Likewise, the ablation yield (atoms/shot) of the twelve target metals investigated by Thestrup et al. (2002) [8] under identical irradiation conditions is a function of the room temperature B-factor or 〈u²〉.     

X-ray determination of the mean-square vibrational amplitudes of atoms in nearly perfect CdS crystals

The mean-square amplitudes of Cd and S atoms in CdS were determined for vibrations parallel as well as perpendicular to the c-axis. The results were obtained by measuring the temperature dependence of X-ray integrated intensities for reflections from both basal and prismatic planes in nearly perfect crystals. The analysis of the experimental data is given in detail. The following results were found for T = 295°K: 〈u²_Cd〉_∥ = 2.85±0.04×10^?18cm², 〈u²_s〉_∥ = 1.94 ± 0.08 × 10^?18cm², 〈u²_Cd〉_⊥= 2.39 ± 0.04 × 10^?18cm² and 〈u²_s〉⊥ = 1.63 ± 0.08 × 10^?18cm². The fact that Cd atoms have a larger vibrational amplitude than the S atoms is briefly discussed.     

Dislocation-phonon interaction

The recent result that uniform screw dislocation motion can be sustained by an applied stress s < 10^?5 initiates a study of the influence of intrinsic, low energy atomic vibrations on the dislocation. This dislocationphonon interaction is examined for two types of interatomic potentials in a crystal with an anisotropic slip system. For realistic interatomic potentials, we find that, in the presence of an appropriate phonon, uniform motion can occur at velocities v?0.50 (in units of the speed of sound) with zero externally applied stress, or even against the direction of motion favored by such a stress.     

The magnetic circular dichroism spectrum of the hexaquocobalt (II) ion in the infra-red region

The magnetic circular dichroism (MCD) and absorption spectra in the range 5500–10 250 cm^-1 of a single cubic crystal of [Co(H₂O)₆](BrO₃)₂ have been measured at various temperatures between 5 and 300 K. An analysis of the temperature variation of the zeroth absorption and MCD moments shows that the intensity of the E′ (⁴αT _1g ) → ⁴ T _2g transition is provided mainly through the two cobalt-oxygen t _1u vibrations. The signs and magnitudes of the overall b and c term are in reasonable accord with previously published calculations. The low energy side of the MCD band exhibits some zerophonon lines and a complex vibronic structure which appears to involve low energy lattice vibrations as well as the cobalt-oxygen skeletal vibrations.     

Strain bursts during cyclic deformation and coarse slip

Summary Single crystals of 99·98% copper were cyclically deformed in push-pull at 50 cps by an electrodynamical vibrator designed to make the stress amplitude independent of changes in plastic compliance of the specimen. Over a period ofN cycles (280 < < N < 10⁶) the stress amplitude was increased linearly with time up to 3·2 kp/mm² giving a fatigue life of 10⁶. During this monotonic increase of stress amplitude withN > 5000 the plastic strain amplitude did not rise monotonically but showed about 20 regularly spaced, strong maxima. These slip bursts lasted typically about 50 cycles and originated from slip distributed throughout the specimen. The next burst occurred when the stress amplitude had increased by about 12%. Observations of the influence of the rate of stress amplitude increase, unidirectional prestrain, and orientation are reported. If one stops increasing the stress amplitude between two strain bursts at a stress amplitude of only about 1·5 kp/mm² and then pulls the specimen unidirectionally, a yield point with a lower yield stress is observed just at the stress where the next strain burst would have occurred had the increase of cycling stress been continued. During the subsequent yield elongation in a unidirectional test there form very strong (0·3 m) and widely spaced (5 m) slip lines. This coarse slip cannot be explained in terms of point defect clusters at the very beginning of a fatigue test of a pure metal. All of these observations can, however, be interpreted in terms of the formation and dissociation of dislocation dipoles formed by mutual trapping of dislocations of opposite sign on different slip planes. It seems reasonable that the main part of cyclic hardening is due to this mutual trapping even in tests performed so that no bursts occur. This is in agreement with the ample evidence supplied by electron microscopy that almost nothing but dipoles are observed after cyclic deformation.Published in Z. f. Metallkunde59 (1968), 927.     

Negative longitudinal expansion and the amplitude of longitudinal vibrations in poly(ethylene) crystals

The experimental temperature dependences of the thermal expansion coefficient and the mean-square amplitude of atomic vibrations in the longitudinal direction (along the axes of chain molecules) in poly(ethylene) crystals of different sizes are measured using x-ray diffraction in the temperature range 5–350 K. Theoretical calculations of the temperature dependences of the thermal expansion coefficient and the mean-square amplitude of atomic vibrations in poly(ethylene) crystals are carried out. It is shown that the results of calculations are in good agreement with experimental data. The temperature ranges in which the quantum character of lattice dynamics affects the thermal expansion coefficient and the mean-square amplitude of vibrations are determined. It is revealed that the shear longitudinal modes play an important role in the lattice dynamics of crystals with a chain structure.     

Low-temperature fatigue behaviour and development of dislocation structure in aluminium single crystals with single-slip orientation

Al single crystals oriented for single slip were cyclically deformed under constant plastic strain amplitudes between 1?×?10^?3 and 5?×?10^?2 at 77?K. Al single crystals showed hardening to saturation at all applied shear stress amplitudes. The resultant cyclic stress–strain curve (CSSC) showed a stress plateau in a range of plastic strain amplitude from 2?×?10^?3 to 2?×?10^?2. Surface observation revealed that multiple slip systems were active even at the strain amplitude in the plateau region. At plastic strain amplitudes corresponding to the plateau of the CSSC, persistent slip bands (PSBs) were formed parallel to the primary slip plane. In the PSBs, well-developed dislocation walls parallel to the {100} planes were observed. The microstructure in the PSBs was explained by the fact of multiple activation of the primary and critical slip systems. The above results indicate that the high stacking fault energy of Al is an important factor affecting the fatigue behaviour even at 77?K.     

Dislocation retardation due to the destruction of short-range order in the L12 superstructure

The magnitude and temperature dependence of the dislocation retardation due to the destruction of short-range order are calculated in the quasichemical approximation. The atomic interaction in two coordination spheres and dislocation slip in cubic and octahedral planes are taken into account. The retardation stress for the first superdislocation is essentially the same in these planes for T < T _k (where T _k is the phase-transition temperature), while the retardation stress for subsequent superdislocations is much lower, so large planar accumulations of superdislocations may arise. The retardation stress is maximal at T = T _k , and for T > T _k the first dislocations should move in pairs. Comparison of the experimental cleavage stresses with calculated values shows that, by itself, superdislocation retardation due to correlation destruction cannot explain the behavior of the yield point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 78–85, April, 1971.     

Analysis of Similarity of Dislocation Interactions in Single Crystal Ni3Ge

Using the methods of diffraction electron microscopy and mechanical testing, the evolution of dislocation structure accompanied by deformation of single-crystal Ni₃Ge with different orientation of the axis of straining is studied at a range of temperatures. A linear relationship between shear stress and dislocation density ^0.5 is established. An analysis of the similarity of dislocation interactions is conducted in Ni₃Ge over a range of temperatures with developed octahedral and cubic slips, i.e. up to the anomaly peak temperature and higher, respectively. It is found out that under the octahedral slip, the dislocation interactions up to fracture deformations are similar at different temperatures in question. The similarity is also observed within the temperature range with developed cubic slip.     

Calculation of the Normal Vibrations of Benzene in the First Singlet Electron-Excited State 1 B 2u

Using the CIS/6-311+G^** method, the normal vibrations of the benzene molecule in the first singlet electron-excited state ¹ B _2u have been calculated. The algorithm of calculation of the force field in dependent coordinates by the method of generalized inversion is described. A method of autoscaling in dependent natural coordinates is suggested. For six groups of natural coordinates scaling factors have been obtained, the use of which has led to agreement between the calculated and experimental frequencies of the vibrations of benzene. The frequencies of the B _1u -symmetry-type vibrations, for which there is no experimental assignment, have been calculated. The problem of selection of the force field in dependent coordinates is discussed.     

On the existence of tetragonally deformed octahedrons in the cubic part of the system MnxFe3-xO4

The mean square amplitude of lattice vibrations has been measured in the cubic part of the Mn _x Fe_3-x O₄-system. The observed increase of the -value with increasing content of Mn ions in the system is interpreted as that, with gradual occupation of more and more octahedral sites by Mn³⁺ ions towards higher values ofx, the number of locally distorted Mn³⁺O ₆ ^2– octahedrons increases.     

Computer simulation of the vacancy defects interaction with shuffle dislocation in silicon

The interactions between the 60^° shuffle dislocation and two different types of vacancy defects in silicon are separately studied via the molecular dynamics simulation method. The Stillinger–Weber potential is used to describe the atomic interactions. The results show that the dislocation slip velocity will decrease due to the interaction with the vacancy cluster (V ₆). The simulation also reveals that the divacancy will be absorbed by the dislocation. Meanwhile, a climbing of the dislocation occurs during their interactions. However, the divacancy has little effect on the dislocation slip velocity. Based on the above results, the decrease in threading dislocation density in SiGe/Si heterostructures with the use of low-temperature Si buffer layer may be explained.     

Glide of dislocations in <1 1 1>{3 2 1} slip system: an atomistic study

Atomistic calculations are performed to investigate plastic slip in the <1?1?1>{3?2?1} system in body-centred cubic iron. Several modern interatomic potentials, developed over the last decade, are applied to compute the stacking fault γ-line energy in the {3?2?1} plane and the results are compared with the ab initio prediction. The applied potentials have shown strong deviations, but several potentials acquired good qualitative agreement with the ab initio data. Depending on the applied potential, the lowest value of the Peierls stress for the edge dislocation (ED) is 50 MPa (Ackland and Bacon from 1997) and the highest is 550 MPa (Dudarev and Derlet from 2005), while for the screw dislocation it is much higher, in the range 1–2 GPa. At finite temperature, however, the flow stress of the ED is found to decrease exponentially reaching a negligible value at about 200 K, irrespective of the applied potential. On the basis of the data obtained using Ackland–Mendelev potential from 2004, we conclude that the slip resistance of the <1?1?1>{3?2?1} system is in between the resistance of the <1?1?1>{1?1?0} and <1?1?1>{1?1?2} slip systems.     

Thermodynamical properties and defect energetics of an n-body potential adapted to Cu3Au

By using molecular statics, molecular dynamics, and Monte Carlo techniques we validate a previously developed empirical n-body potential adapted to Cu₃Au. At T=0 K, predicted cohesive energies, lattice parameters, and elastic constants in CuAu and CuAu₃ as well as the formation energy of vacancies in Cu₃Au are in good agreement with experimental data. A satisfactory behavior is also obtained at T 0 K in Cu₃Au, for atomic mean-square displacements and elastic moduli. However, this model underestimates the vacancy migration energy and the order-disorder critical temperature when the latter is evaluated by Monte Carlo including both exchanges between atoms of different species and atomic moves simulating vibrations.     

Effect of atomic displacement on the parameters of the grain boundary ensemble in nickel-based alloys with <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript> superstructure

The effect complex stacking fault energy and mean-square atomic displacement have on the parameters of the grain boundary ensemble in nickel-based alloys with L1₂ superstructure is established experimentally. The higher the complex stacking fault energy, the lower the average number of special grain boundaries per parent grain. The lower the mean-square atomic displacement, the smaller the proportion of the Σ3 twins in the special grain boundary spectrum.     

Elastic,micro- and macroplastic properties of polycrystalline beryllium

The Young’s modulus and the internal friction of beryllium polycrystals (size grain from 6 to 60 μm) prepared by the powder metallurgy method have been studied as functions of the amplitude and temperature in the range from 100 to 873 K. The measurements have been performed using the composite piezoelectric vibrator method for longitudinal vibrations at frequencies about 100 kHz. Based on the acoustic measurements, the data have been obtained on the elastic and inelastic (microplastic) properties as functions of vibration stress amplitudes within the limits from 0.2 to 30–60 MPa. The microplastic deformation diagram is shown to become nonlinear at the amplitudes higher than 5 MPa. The beryllium mechanical characteristics (the yield strength σ _0.2, the ultimate strength σ _u , and the conventional microscopic yield strength σ _y ) obtained with various grain sizes are compared. At room temperature, all the parameters satisfactorily obey the Hall-Petch relationship, although there is no complete similarity. The temperature dependences are quite different, namely: σ _0.2(T) and σ _u (T) decrease monotonically during heating from room temperature to higher temperatures; however, σ _y (T) behaves unusually, and it has a minimum near 400 K. The different levels of stresses and the absence of similarity indicate that the scattering of the ultrasound energy and the formation of a level of the macroscopic flow stresses in beryllium occur on dislocation motion obstacles of different origins.     

Zeitliche Entwicklung des Reflexionskoeffizienten einer Plasmaschicht bei starker elektromagnetischer Einstrahlung

We have calculated numerically the temporal evolution of the nonlinear reflection coefficient R of an overdense plasma layer by solving the system of partial differential equations consisting of the wave equation for the slowly varying amplitude of the electric field and the hydrodynamic equations for the ion motion, including a ponderomotive force term. In dependence of the (normalized) amplitude of the incident wave u_A two regimes exist: Below a critical amplitude u_A^* ? 1 the reflection coefficient is approximately independent on the amplitude u_A and temporally constant. In the opposite case u_A>u_A^*, on the other hand, ‖R‖² decreases slowly with time down to a minimum value and after that it increases rapidly to the initial value. We think, that our results are important to interpret the anomalous reflectivity observed in some experiments when strong electromagnetic waves are incident on an overdense plasma.