Internal Friction Spectra Research Articles

Interplay of dislocation-related relaxation processes in iron-based materials

The internal friction spectra in various cold-worked iron-based alloys show that the intensity ratio of the peaks, corresponding to the relaxation processes at 0.52 eV ($\ensuremath{\beta}$ peak) and 0.96 eV ($\ensuremath{\gamma}$ peak), is proportional to the impurity concentration. Such correlated behavior of the two most dominant modes in the spectra is explained by a model which incorporates an increase in the $\ensuremath{\beta}$-relaxation process at the expense of the kink-antikink pair ($\ensuremath{\gamma}$-peak) nucleation process in pinned dislocation segments. Very good agreement between measured and calculated spectra is obtained by varying a single parameter: the ratio between the average size of the kink-antikink pairs and the average impurity-impurity distance.

Diffusion of hydrogen atoms and the internal friction spectrum of the PdH x system

The temperature dependences of dissipative loss spectra were studied by the internal friction method for the polycrystalline Pd system and interstitial solid solutions PdHx. Four relaxation processes related to the structural peculiarities of the crystal lattice were observed in Pd; two additional relaxation processes were observed in PdHx solid solutions. The latter were related to the mobility of hydrogen atoms in different phases of the face-centered cubic crystal structure.

Nitrogen Diffusion in the Nb-2.0wt%Ti Measured by Mechanical Spectroscopy

Metals that present bcc crystalline structure, when receiving addition of interstitial atoms as oxygen, nitrogen, hydrogen and carbon, undergo significant changes in their physical properties, being able to dissolve great amounts of those interstitial elements, thus forming solid solutions. Niobium and most of its alloys possess bcc crystalline structure and, as Brazil is the largest world exporter of this metal, it is fundamental to understand the interaction mechanisms between interstitial elements and niobium or its alloys. In this paper, mechanical spectroscopy (internal friction) measurements were performed in Nb-2.0wt%Ti alloys containing nitrogen in solid solution. The experimental results presented complex internal friction spectra and with the addition of substitutional solute, it was observed interactions between the two types of solutes (substitutional and interstitial), considering that the random distribution of the interstitial atoms was affected by the presence of substitutional atoms. Interstitial diffusion coefficients, pre-exponential factors and activation energies were calculated for nitrogen in the Nb-2.0wt%Ti alloys.

Internal friction spectra of cryptoheterogeneous polymer materials

Internal friction spectra of cryptoheterogeneous polymer materials

Tensile properties and internal friction study of dislocation movement in iron–copper system as a function of copper precipitation

Tensile properties and internal friction of thermally aged (at 773K) Fe–1wt% Cu alloys are measured as a function of copper precipitation in the temperature region between 100 and 600K. Two regimes have been clearly identified in terms of yield stress at low temperatures below 250K. It was found that in the over-aged samples the yield stress decreases much more abruptly with the temperature than in the specimens annealed at shorter time. The internal friction spectra show the existence of similar features in all samples, which indicates that no drastic change of the microstructure occurs during aging. These results suggest that the lack of softening at low temperatures originates principally from thermally-activated kink-pair formation and gliding processes, controlled by the size and/or density of Cu-precipitates.

Internal friction spectra of polymer materials in complex stressed states

A procedure for the quantitative characterization of complex stressed states and their effect on the relaxation properties of polymer materials has been proposed. Throughout the temperature interval where the thermal degradation of polymers can be ignored, three measurements runs for recording internal friction spectra Δ(T) are performed. As has been shown for cellulose diacetate and poly(vinylformals), a difference between attenuation decrements Δ1(T)–Δ2(T) for the initial samples and the same samples in the second measurement cycle reflects the presence of cryptoheterogeneity. This difference achieves its maximum values at temperatures close to the glass transition temperature T α but becomes noticeable even at temperatures several tens of degrees lower than T α.

Internal friction spectrum of the Pd/H x≤0.5 system

Internal friction spectrum of the Pd/H x≤0.5 system

Anelastic Properties of Mg+3vol.%Gr Prepared by Ball Milling

Internal friction in ultra-fine grained Mg with 3vol% of Graphite was measured by forced vibration method at low frequencies of 0.1, 0.5, 1.0, and 2.0 Hz over a temperature range from room temperature to 753 K with continuous heating. The specimens were prepared by milling procedure in an inert atmosphere and subsequent compacted and hot extruded. Two developed peaks in the internal friction spectrum were obtained at temperatures ≈ 350 K and ≈ 550 K. While the position of the first peak is frequency dependent, the second peak position is stable, independent of measuring frequency. The activation energy of the low temperature peak was estimated. In the light of internal friction measurements, the high temperature internal friction peak is attributed to the generation and motion of dislocations produced by the difference in the coefficient of thermal expansion between the Mg matrix and Gr phase at the matrix–particle interfaces.

Effect of Heat Treatments on the Damping Characteristics of TiNi-Based Shape Memory Alloys

Low frequency internal friction of Ti49Ni51 binary and Ti50Ni40Cu10 ternary shape memory alloys has been measured. The effect of solution and aging heat treatments on the damping property was examined. The temperature spectrum of internal friction for TiNi binary alloy consists, in general, of two peaks; one is a transition peak which is associated with the parent-martensite transformation and is rather unstable in a sense that it strongly depends on the frequency and decreases considerably when held at a constant temperature. The other one is a very high peak of the order of 10-2, which appears at around 200K. It appears both on cooling and on heating with no temperature hysteresis, and is very stable. The behavior of the peak is strongly influenced by the heat treatments. The trial of two-stage aging with a purpose of improving the damping capacity has been proved unsatisfactory. TiNiCu has a very high damping, the highest internal friction reaching 0.2, but by quenching from very high temperature, say 1373K, the damping is remarkably lowered. For the realization of high damping the quenching from a certain temperature range around 1173K seems the most preferable condition.

Internal friction in advanced Fe–Al intermetallics

We have measured the internal friction and the dynamic modulus of an Fe–38 at.% Al alloy using a forced torsion pendulum working between 10 −3 and 10 Hz. The measurements have been carried out as a function of temperature (from room temperature to 1200 K) and as a function of frequency. Two peaks have been observed in the internal friction spectra, at about 780 and 1100 K, which are largely superposed in the intermediate temperature range. Both peaks and the corresponding modulus defect shift in temperature with the oscillation frequency, and can be attributed to relaxation mechanisms. Previous results in the literature seem to indicate that the low temperature peak is the Zener relaxation of Al atoms. The activation energy of the high-temperature peak, referred to as P1 peak because it has not been studied previously, has been determined to be H act = 2.87 eV, from the results of measurements at different temperatures and frequencies. We discuss the possible mechanisms, which could be responsible of this P1 peak, and suggest that it could be attributed to the intrinsic movements of 〈1 0 0〉 perfect dislocations over the Peierls barrier by kink pair formation in the B2 ordered FeAl.

Diffusion processes in Cu–Al–Ni shape memory alloys studied by mechanical spectroscopy and in situ transmission electron microscopy at high temperatures

We have studied the mobility of defects in the frozen β phase of the Cu–Al–Ni shape memory alloys by mechanical spectroscopy as a function of temperature. In parallel, we have characterized the microstructure and their evolution with over-heating treatments. Thermal treatments have been performed in situ in a transmission electron microscope by using a heating stage. Internal friction and modulus defect measurements have been correlated with the microstructural observations by transmission electron microscopy. We discuss the behavior of the internal friction spectra, corresponding to over-heating in the β-phase, and propose microscopic mechanisms responsible for the evolution when the material is not in thermal equilibrium. In particular, the dislocations became mobile in the temperature range between 750 and 800 K where the L2 1 atomic order changes to the B2 order. A relaxation peak has been observed in the equilibrium β phase domain, which has been examined in detail by isothermal measurements as a function of frequency. The activation enthalpy of the peak has been determined to be 3.05 ± 0.1 eV, and possible microscopic mechanisms responsible for the peak are discussed.

Light-induced anelastic change in a-Si(H)

The thermal desorption spectra between 400 and 1100 K and the internal friction spectra between 80 and 423 K were studied for a-Si(H). The thermal desorption of hydrogen was observed around 650 K (TDH 650 K ) and around 900 K (TDH 900 K,L and TDH 900 K,H ). Both TDH 900 K,L and TDH 900 K,H with the activation energy of 1.6 eV were attributed to the desorption of bonded hydrogen. TDH 650 K was not a diffusion controlled process with the activation energy of 1.0 eV, where one part of TDH 650 K was attributed to the desorption of isolated hydrogen molecules. The hydrogen-induced internal friction, H- Q a-Si ( H ) − 1 , was observed between 80 and 423 K. Hydrogen responsible for H- Q a-Si ( H ) − 1 showed the thermal desorption around 650 K (TDH 650 K ), indicating that isolated hydrogen molecules in the amorphous structure may be responsible for H- Q a-Si ( H ) − 1 . Light soaking caused changes in H- Q a-Si ( H ) − 1 in the temperature ranges between 80 and 200 K and between 200 and 300 K, indicating that light soaking modified the local amorphous structures responsible for these changes in Q a-Si ( H ) − 1 .

Study of solute atom-dislocation interactions in Al–Mg alloys by mechanical spectroscopy

Internal friction and elastic modulus have been measured as function of temperature, strain amplitude and frequency in Al–Mg solid solutions by means of free-decay and forced oscillation torsion pendula. Samples with 4 at.% of Mg were used. The internal friction spectrum measured in the 100–550 K temperature range was found to be mainly composed of a low temperature background between 100 and 400 K, which does not depend on temperature, but depends markedly on the strain amplitude in the range of 5 × 10 −6 to 10 −4 and of an internal friction peak (at about 440 K for 1 Hz), which evolves into a rapidly rising background at higher temperature. The mechanical spectroscopy results are discussed in terms of a solute-dislocation interaction model with variation of the average length of dislocation segments. Furthermore, the activation energies of the peak and high temperature background were found to be close to the activation energy of diffusion of Mg solute atoms in aluminium. As a consequence, both components could be interpreted by the high temperature dragging of Mg solute atoms by the dislocations.

Analysis of the internal friction spectrum of TiNiCu alloy

The internal friction spectra of TiNiCu shape memory alloy (SMA), which involves thermoelastic martensitic transformation, can be divided into three different terms: intrinsic, transitory and phase transition. In this paper, the damping behavior during the reverse martensitic transformation in Ti 50Ni 27Cu 23 SMA has been investigated using dynamic mechanical analyzer instrument. The internal friction spectra of Ti 50Ni 27Cu 23 SMA have been analyzed quantitatively and divided into intrinsic and transitory contributions using an iterative method. The internal friction spectra with different oscillation frequency have been predicted based on the quantitative analysis.

Stress induced ordering due interstitials in Nb–4.7 at.%Ta

The presence of interstitial elements in metals cause strong changes in their physical, chemical or mechanical properties. These interstitial impurities interact with the metallic matrix atoms by a relaxation process known as stress induced ordering. Relaxation processes give rise to a peak in the internal friction spectrum, known as Snoek effect. The presence of substitutional solutes has a strong influence on Snoek effect, particularly if the substitutional solute element is the one, which interacts with the interstitial element. Anelastic spectroscopy measurements provide information of the behavior of these impurities in the metallic matrix. In this paper, polycrystalline samples of Nb–4.7 at.%Ta alloy have been analyzed in the as-received condition. Measurements of anelastic spectroscopy were carried out using an inverted torsion pendulum, operating with frequency of 2.0–30.0 Hz and in a temperature range between 300 and 700 K. It was observed the presence of a relaxation structure that have been attributed to stress induced ordering due to interstitial atoms around atoms of the metallic matrix. The relaxation structure have been decomposed in its constituent peaks, what it allowed to identify the following relaxation processes: Ta–O, Nb–O and Nb–N.

Electronic and ionic relaxations in oxide glasses

A survey of relaxation processes in glasses exhibiting electronic and electronic–ionic conductivity mechanisms is presented. Electrical conductivity data on a range of transition metal oxide (TMO) glasses shows that a polaronic model of conductivity is generally applicable. It is shown that in TMO glasses both ac and dc conductivity processes are due to the same mechanism, which is hopping of small polarons between transition metal ions in different valence states. By applying scaling using the BNN relation it is possible to obtain universal conductivity curve and to find the relation between ac and dc activation energy. Complex plot of electric modulus gives a simple method of scaling analysis. An attempt of classification of mixed electronic–ionic behaviour in TMO containing alkali ions was performed on the basis of impedance spectroscopy. A deep minimum of conductivity at certain content of alkali ions is observed in glasses where TMO is a glass former. Two different behaviours can be distinguished in glasses where TMO is a glass network modifier. In glasses containing iron oxide electrical properties are only slightly influenced by alkali ions. A mixed electronic–ionic conduction is observed in glasses containing copper oxides. It is shown that the internal friction method is a powerful tool for the study of relaxation processes in glasses. In electronic and ionic conducting glasses internal friction spectra reveal a peak which activation energy is identical as for the dc conductivity. In mixed electronic–ionic conducting glasses the internal friction spectra reveal two peaks, which are attributed to the electronic hopping and the alkali ion migration. A comparison of internal friction and impedance spectroscopy investigations indicates that the internal friction is a more sensitive method for detecting local movement of ions or polarons in the glass network.

Zener relaxation peak in a Cu–Al–Mn shape memory alloy

We have studied the temperature spectra of internal friction and relative dynamic modulus of a Cu–11.9Al–2.5Mn (wt.%) alloy. It is found that a peak appears at around 350 °C during the first heating process of the quenched specimen. The peak occurs not only during heating but also during cooling. Its activation energy has been calculated to be 1.85±0.17 eV in terms of the Arrhenius relation. In addition, the peak disappears in specimens during the second or more heating process, because an overlap occurs between the peak and the reverse martensitic phase transition peak. During cooling, however, the peak can be seen all the time. It is suggested that the peak originates from Zener relaxation.

Study of atom diffusivity and related relaxation phenomena in Fe 3Al–(Ti,Nb)–C alloys

Mechanical spectroscopy, positron annihilation spectroscopy (PAS), and the radiotracer diffusion technique ( 59Fe self-diffusion measurements) were applied to interpret anelastic relaxation effects caused by C atoms and vacancies in Fe 3Al-based alloys with and without strong carbide forming elements (Ti and Nb). The decrease of the Snoek-type relaxation peak (denoted as S-peak) in the internal friction (IF) spectra of Fe–26Al–(2&4)Ti and Fe–26Al–0.3Nb alloys with respect to the S-peak in binary Fe–26Al alloy (all compositions in at.%) is related to a decrease in the amount of interstitially dissolved C atoms. Kinetic aspects of the removal of C atoms from the solid solution are discussed with respect to the annealing temperature. The so-called X peak, which is observed in the IF spectra of Fe–26Al alloy, also almost disappears after alloying with Ti. The results indicate that the change in the content of interstitially dissolved C is the main reason for the observed changes of the S and X peak intensities. The effect of heat treatments on thermal vacancy concentration is evaluated by PAS. A minor influence of the addition of Ti and Nb on the total concentration of vacancies is deduced from the positron annihilation and radiotracer diffusion studies.

Low-temperature damping behavior of cast iron with aluminum addition

Recently, many investigations found that the damping capacity of cast iron is due to dislocation processes in the graphite inclusions. The experimental results of Adams and Fox [1, 2] indicated that at room temperature, the high-damping capacity for flake-graphite cast iron occurs principally within the graphite rather than the matrix or the matrix-graphite interface. Millet [3–5] further confirmed that this conjecture by comparing the internal friction spectra of cast iron and graphite, which were both characterized by a drastic increase in damping capacity from a relatively low level for T 250 K. However, cast iron can exist in a great number of different forms depending on the chemical composition, the degree of nucleation of melt and casting conditions. If the carbon equivalent was suitable or if there were appreciable quantities of graphite stabilizing elements, then the carbon solidified mainly as the free graphite. It was known that aluminum was a graphite stabilizing elements, which favored the graphite formation. Correspondingly, the cast iron with aluminum addition had a high damping capacity at room temperature [6–8]. But the damping capacity at room temperature was connected with the evolution of the low-temperature internal friction spectrum. Therefore, it is necessary to study the low-temperature damping capacity of cast iron with aluminum addition. In the present work, the damping behavior of cast iron with aluminum addition at low temperatures was investigated in detail. Meanwhile, the effect of aluminum on the damping capacity of cast iron was analyzed. The compositions of the cast iron specimens used in the experiments were listed in Table I. High purity iron, carbon, silicon and aluminum (purity better than 99.9%) were used to prepare samples. The melting process was carried out in an induction-melting furnace and then the melts were cast into the sand mold. In order to remove the residual stress of cast iron, some samples were annealed at 873 K for 2 hr and continuously cooled to room temperature in a sealed quartz tube. Model 2980 DMA was used to measure the damping capacity of samples by the methods of dual cantilever with the mode of temperature and frequency sweeping under a fixed strain amplitude. Meanwhile, the Young’s modulus of the materials was tested. The surface strain amplitude of the specimen was sustained at about 2.0 × 10−5 when heating the samples from ∗Author to whom all correspondence should be addressed. 123 K to 373 K with a heating rate 5 K/min. Before the damping measurement, all the samples were cut into beam shapes, 1×10×60 mm3, and then were symmetrically bonded to the clamp. The damping capacity was evaluated by the tangent of phase lag, φ, between the stress and strain. It was expressed as:

Grain-Boundary Internal Friction in Alloys with Dispersed Inclusions

The role of dispersed particles in the grain-boundary slip in alloys with such second phase inclusions is considered. An equation for the grain-boundary slip velocity, formulated with allowance for an external variable load and the internal reverse stress produced by the dispersed particles, is solved and the contribution of the latter factor to the internal friction is determined. The frequency spectrum of internal friction in this system has the shape of a broad peak.