Bordoni Peak Research Articles

A Model for the Signatures Observed in 5N Lead by the Two Wave Acoustic Coupling Method

The ultrasonic low-frequency coupling method was used to study the relaxation processes in cold worked and annealed lead, in particular the Bordoni relaxation. New high-temperature signatures were observed in 5N lead on each temperature side of the high-frequency Bordoni peak. The signatures, measured in a temperature range where a non-negligible internal friction background is observed at low frequency, present a kind of mirror symmetry around the temperature of the high-frequency Bordoni peak. These signatures can be interpreted by a model assuming (i) that the high frequency motion of the dislocations is controlled by a thermally activated KPF (Kink Pair Formation) mechanism and (ii) that the low-frequency motion of the dislocations is controlled by a dislocation-point defects interaction, involving a LDWRF (Limited Displacement Without Restoring Force) mechanism. In this model, the KPF mechanism is responsible for the ultrasonic attenuation and for the mirror symmetry of the signatures. The LDWRF mechanism is responsible for the low-frequency internal friction background and for the characteristic shape of the signatures. An excellent correspondence between the experimental signatures and signatures numerically simulated with this model strongly suggests (i) that the Bordoni peak is due to a KPF mechanism and (ii) that the internal friction background is due to a LDWRF mechanism.

Experimental Evidence of Kink Relaxation and Kink Resonance in Dislocations of FCC Metals

Many papers have been devoted to the motion of dislocation lines in crystals. The string model and the kink model presented the most relevant theoretical approach. However, each model independently can not describe all experimental data. In this paper is presented experimental data of logarithmic decrement associated to dislocation lines, measured in Hz and MHz ranges, on high purity copper single crystals plastically deformed by compression and torsion at room temperature. The experimental data obtained for the Bordoni Peak, analyzed on the basis of the kink model, shows the predicted temperature dependence of the effective enthalpy, a evidence of the kink diffusion mechanism. The data can be well fitted over all temperature range investigated, assuming the contribution of kink relaxation and kink resonance aging simultaneously. From the last mechanism a temperature dependent kink density is assumed. This procedure allows to explain the width and the asymmetry of the Bordoni peak.

Internal Friction Peaks at Low Temperatures : a Kink Model Analysis

Two internal friction peaks discovered in pure aluminum at increasingly low temperatures, respectively by Lax and Filson and by Kosugi and Kino, are interpreted as different occurrences of the very same mechanism responsible for the better-known Bordoni peak, namely the nucleation of thermal kink pairs.

Bordoni peaks in face-centered cubic metals at low temperatures

Two internal friction peaks discovered in pure aluminum at increasingly low temperatures, respectively by Lax and Filson and by Kosugi and Kino, are interpreted as different occurrences of the well-known Bordoni peak. The Lax–Filson peak is attributed to impurity assisted nucleation of thermal kink pairs; the Kosugi–Kino peak marks the onset of a new nucleation mechanism: the geometrical kinks (antikinks) rearrange themselves into superkink–antikink pairs in order to overcome the Schottky barriers. The experimental conditions for the direct observation of such peaks are discussed in some detail.

The Behavior of the Bordoni Peak in Ultra High Purity Cu and its Implication for Dislocation Mechanism

Recent results on ultra high purity Cu have shown that the Bordoni peak grow very large after annealing at 800 °C . The size of the peak suggests that the bow- out of clean network dislocations through the kink pair formation caused the peak. Based on these results, Takeuchi proposed the model in which the Bordoni peak and yield stress at low temperatures are associated respectively with kink pair formation in undissociated and dissociated dislocations. On the contrary, here, it is proposed that the above two phenomena are controlled by kink pair formation on dissociated dislocations without jogs and with jogs, respectively.

The Bordoni Relaxation in High Purity Copper Single Crystals at Low Frequencies

The aim of this work is to explore the low-frequency spectrum of 5N pure copper in a sub-resonant pendulum which allows in situ cycled torsion deformation and recovery. Samples were taken from the same single crystals used for ultrasonic attenuation studies in order to compare both results in an Arrhenius plot. In one sample prepared by electro-erosion, polished with nitric acid, recovered 4 hours at 650°C in preliminary vacuum and 1, 4 and 9% deformed at room temperature, the spectra show a main Bordoni peak whose height increases with deformation, and additional peaks in the 40-65K range, as important as the Bordoni peak, which are due to impurities generated during the preparation of the sample. In an uncontaminated sample cut by diamond disk, polished with a mixture of nitric, phosphoric and glacial acetic acids, and water, recovered in 5.10 -6 mmHg vacuum, deformed 3 and 5%, the internal friction spectra show the main Bordoni peak as the principal effect, accompanied by a defect modulus. The study of the influence of different parameters such as the amount of deformation, the amplitude and frequency of oscillation, the temperature rate and the recoveries may be an interesting contribution to the characterization of the Bordoni peak.

A Possible Origin of the Discrepancy between the Peierls Stresses Estimated from the Bordoni Peak and Those from the Mechanical Test for fcc Metals

A Possible Origin of the Discrepancy between the Peierls Stresses Estimated from the Bordoni Peak and Those from the Mechanical Test for fcc Metals

The effect of gamma irradiation on the dislocation relaxation peak in gold

The effect of gamma irradiation on the dislocation relaxation peak, i.e. the Bordoni peak, of high purity polycrystalline gold has been studied at frequency of 10 MHz. It was found that the effect of gamma radiation is more significant in specimen irradiation at room temperature (1 A) than that irradiated at liquid nitrogen temperature. The variation of the peak height, and temperature of the dislocation relaxation peak as a function of gamma doses are explained in terms of the Kink-Pair formation model.

Internal friction by pinned dislocations: Theory of the Bordoni peak.

The two most prominent internal friction peaks in cold worked metals at low temperature are shown to be related manifestations of the same nucleation mechanism of kink-antikink pairs in pinned dislocation segments depending, respectively, on the absence (Bordoni peak) or the presence (Niblett-Wilks peak) of geometrical kinks (antikinks). Correspondingly, diffusion of the nucleated thermal pairs accounts for the observed background internal friction. Peak and background components are both computed analytically and compared with experimental data.

Behavior of the bordoni peak in zone-refined Cu during annealing at high temperatures

The Bordoni peak is thrown as a relaxation peak which appears at around 50K (for measuring frequency f {approximately} 1Hz) in various cold worked metals with the fcc structure. Seeger has proposed that this relaxation is associated with a kink pair formation (KPF) on dislocations. Since all the characteristics of the Bordoni peak so far observed experimentally are consistent with the KPF model, this model was widely accepted as the origin of the Bordoni peak. However, the flow stress at low temperatures expected from the temperature of the Bordoni peak is about two orders of magnitude larger than that observed in the macroscopic deformation experiments. If the Bordoni peak is attributed to the KPF model, the authors have to postulate the presence of preferential deformation sites on dislocations (deformation short-circuits) to explain the very low flow stresses in fcc metals. Possible candidates for such sites might be sites at bent corners of extended dislocations, and lubrication sites. They have, however, no definite model at present. In the present work, the behavior of the Bordoni peak in zone-refined Cu was studied during annealing after cold work. In contrast to the results on the ordinary pure Cu, the Bordoni peak was foundmore » to grow during annealing even after 800 C. The results will be shown to be in excellent agreement with the KPF model.« less

Low temperature internal friction spectrum of nanocrystalline Au

The resonant frequency and internal friction of nanocrystalline Au are measured in the temperature range from 5K to 275K. A well-defined relaxation peak is observed at around 130K(- 300Hz) for samples with grain size below 30nm. The annealing behavior of this peak is similar to that of the Bordoni peak (PB) reported for the coarse-grained Au so that this peak could be regarded as the BP of the nanocrystalline Au. However, the peak temperature of 130K is about 20K higher than that of the usual BP and it seems to be due to the variance of the dislocation structure between the nanocrystalline Au and coarse-grained Au.

Dislocation relaxation in silver single crystals at megahertz frequencies

The Bordoni peak in high-purity silver single crystals has been investigated by measuring the attenuation of longitudinal waves of 5, 10 and 30 MHz, using a conventional ultrasonic pulse technique with single quartz transducer. The crystals, of (100), (110) and (111) orientations, were deformed by compression, and the temperature-dependent ultrasonic attenuation was measured after applying resolved shear stresses ranging up to 60 N mm-2. The results lead to the following conclusions: (i) the temperature of the Bordoni peak in silver single crystals is essentially independent of the orientation; (ii) the temperature of the Bordoni peak in silver single crystals decreases as the prior deformation is increased up to resolved shear stress near 28 N mm-2, and then increases for higher prior stresses, (iii) the Bordoni peak height decreases as the frequency increases and (iv) the Bordoni peak height increases with increasing the amount of deformation.

Nucleation of kinks in 1+1 dimensions.

The nucleation rate of kink-antikink pairs in a sine-Gordon theory at finite temperature is calculated analytically and compared with the results of recent numerical simulations by other authors. The application to the theory of the Bordoni peak is discussed in some detail.

Dislocation damping and associated modulus defect in copper crystals

Ultrasonic attenuation and the modulus defect were investigated in (111)-deformed copper single crystals. Experimental results were interpreted as resulting from the contribution of two dislocation mechanisms: kink resonance and kink relaxation (stress-induced double-kink formation). Bordoni peak relaxation is described considering no distribution in activation energy or relaxation time. The kink density contributing to the resonance mechanism is shown to be dependent on temperature.

The bordoni peak in silver single crystals at megahertz frequencies

The dislocation relaxation maximum has been investigated at frequencies of 5, 10 and 30 MHz. The three (very high-purity) silver crystals of crystallographic orientation 〈111〉, 〈110〉 and 〈100〉 which are given a resolved shear stress of 20 MPa were found to produce dislocation relaxation maximum at 107 K in all the three samples. The maximum shifts to 117 K when measurement is carried out at 10 MHz and to 127 K at 30 MHz. The results reveal that the maximum is orientation independent. The activation energy and the attempt frequency were calculated and found to be equal to 0.105 eV and 2·109 Hz, respectively. Meanwhile the larger magnitude of the maximum was found on the 〈111〉 crystal and the least was on the 〈100〉 crystal. Finally, it was clearly shown that the dislocation relaxation strength decreases as the frequency increases.

Ultrasonic Attenuation and Modulus Defect Associated with the Bordoni Peak in Copper Single Crystals

Ultrasonic Attenuation and Modulus Defect Associated with the Bordoni Peak in Copper Single Crystals

Effects of neutron and gamma irradiation on the dislocation relaxation peak in very pure copper single crystal of 〈110〉 concentration

The effects of neutron and gamma irradiation on the height and temperature of the dislocation relaxation peak (Bordoni peak) have been studied in four very high purity copper single crystals having the orientation 〈110〉. Two crystals have width to length ratio 1:10 and the other two 1.3:1. Samples with different width to length ratio were used so that different dislocation loop lengths could be achieved by initial prestrains. In all samples the peak height and the peak temperature were reduced by irradiation. The samples with width to length ratio 1:10 exhibited a larger peak, due to the longer loops created in them. Gamma irradiation was found to have more effect on the characteristics of the peak than neutron irradiation. The results were in full agreement with the kink pair generation model.

Effect of isothermal annealing on the Bordoni relaxation in cold worked copper

The Bordoni relaxation in ultra-purity cold worked copper subsequent to isothermal annealing in the temperature range 298–423 K at 700 Hz frequency is investigated using a set up based on the electrostatic system. The Bordoni peak is observed at 79±2 K. The annealing characteristics of the Bordoni peak are found to be of complex nature. The decay and subsequent regrowth of the peak following annealing above room temperature are interpreted in terms of defects diffusing to dislocations and their removal from dislocations, respectively. The calculated activation energy values for the first decrease (0.55 eV), first increase (0.24 eV) and first minimum (0.27 eV) are in good agreement with the activation energies for interstitial and divacancy diffusion estimated by different workers. The activation energy for divacancy diffusion is computed to be 0.49 eV.

THE EFFECT OF GAMMA IRRADIATION ON THE DISLOCATION RELAXATION PEAK OF COPPER

The effect of gamma irradiation on the dislocation relaxation maximum, i.e. the Bordoni peak, of two high purity copper single crystals of orientation <110> has been studied at a frequency of 10 MHz. It was found that as the irradiation dose increases the Bordoni peak height [Formula: see text] and its temperature Tm decreases in both specimens. A specimen of width to length ratio 1:10, i.e. easy glide, seems to be more sensitive to gamma irradiation than one of aspect ratio 1.3:1. The peak height and its temperature in the former specimen was found to be always higher than in the latter when both were irradiated with a similar dosage. The relation between [Formula: see text] and the gamma irradiation dose is of the form [Formula: see text] where y equals 1.4 or 1.5 depending on the mechanical treatment. Moreover, the study suggests that Q−1 is proportional to the dislocation loop length L in the form [Formula: see text] where n has values of 1.4 and 1.5 which agrees with the pair-kink generation model first proposed by Seeger.

Relaxation Spectrum Analysis of the Bordoni Peak in Cu by Nonlinear Least-Squares Fitting

Relaxation spectrum analysis using the computer program SALS (Statistical Analysis with Least-Squares fitting) is applied to the Bordoni peak in Cu. After the validity of the method of analysis was tested on simple model peaks, the analysis was performed on the experimental data of internal friction and Young's modulus obtained at ≈ 1 kHz. The results of analysis suggested that the Bordoni peak in Cu is composed of at least more than ten subpeaks of single relaxation. Die Analyse des Relaxations-Spektrums mit Hilfe des Rechner-Programms SALS wird auf den Bordoni-Peak in Cu angewandt. Nachdem die Gultigkeit des Verfahrens an einfachen Modell-Peaks getestet worden ist, werden die experimentellen Ergebnisse zur inneren Reibung und zum Young-Modul ausgewertet. Die Ergebnisse lassen darauf schliesen, das der Bordoni-Peak in Cu aus mindestens mehr als zehn Einfach-Relaxations-Peaks zusammengesetzt ist.