HAL Id: jpa-00227190
https://hal.archives-ouvertes.fr/jpa-00227190
Submitted on 1 Jan 1987
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
PREMARTENSITIC INTERNAL FRICTION IN INDIUM-THALLIUM ALLOY
I. Hwang, C. Lei, T. Suzuki, M. Wuttig
To cite this version:
I. Hwang, C. Lei, T. Suzuki, M. Wuttig. PREMARTENSITIC INTERNAL FRICTION IN INDIUM-THALLIUM ALLOY. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-547-C8-552.
�10.1051/jphyscol:1987886�. �jpa-00227190�
JOURNAL DE PHYSIQUE
Colloque C8, suppl6ment au n012, Tome 48, d6cembre 1987
PREMARTENSITIC INTERNAL FRICTION IN INDIUM-THALLIUM ALLOY
I.C. HWANG, C.Y. LEI, T. SUZUKI* and
M.
WUTTIG*.Metallurgy Department, University
ofMissouri-Rolla, Rolla, MO 65401, U.S.A.
' ~ n s t i t u t e of Applied Physics, University of Tsukuba, Sakura, Ibaraki, 305, Japan
" ~ n g i n e e r i n g Materials Group, Department
ofChemical and Nuclear Engineering, University of ~ a r y l a n d , College Park,
MD20742, U.S.A.
ABSTRACT-The internal friction in In-24at%T1 alloy prior to the martensitic transformation has been measured by use of the vibrating reed method in the frequency range up to 500 Hz. . - The internal friction is .found to be described
2 2
by the Debye relaxation process Q-~=&TU/ ( 1 + ~ W )
.
where the relaxation time is controlled by a thermally activated process with an activation energy of 0.78 ev and the relaxation strength A behaves according to the Curie-Weiss law 1/(T-Tc). A relaxed shift of the X-ray Bragg diffraction peak under the influence of uniaxial stress with the same activation energy has been found in the same alloy system. These experimental data indicates that the relaxation process responsible for the internal friction as well as the diffraction shift is to be associated with extended lattice defects-premartensitic solitons.I-INTRODUCTION
Although the martensitic transformation itself is undoubtedly extremely fast diffusion-less atomic process, special kind of lattice defects are prepared in the premartensitic stage before the transformation process itself is finally initiated.
The study of the premartensitic stage has been carried out by use of two entirely different experimental methods, diffraction and acoustic (1,2,3,4,5,6,7,8). While diffraction experiments can give a high resolution information about spacial extent of a lattice defect, they cannot give any informations on its low frequency dynamical behavior of lattice defects. While acoustic measurements cannot give any information about the extent of a lattice defect involved, they can give very precise data on its low frequency behavior. Hence, in order to construct a whole picture of lattice defects in the premartensitic stage, we need to combine the information obtained from diffraction and acoustic measurements.
In this paper, we wish to report our experimental data on the internal friction and the stress dependence of x-ray diffraction in the psemartensitic stage of the In-T1 alloy.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987886
JOURNAL DE PHYSIQUE
11-SAMPLE PREPARATION
Indium and Thallium of 99.99% purity was used for making the alloy. The In- 24at%T1 single crystal was grown in vacuum by the Bridgeman method. The as-grown crystals was etched with 50 % nitric acid to check the quality. The growing and checking procedure was repeated until satisffctory single crystals were obtained.
The crystals were homogenized in vacuum at 20 C below the melting point for seven days.
Laue back-ref lection ,method was then used for orienting the crystals.
Rectangular reeds with a (110) surface and (001) and (170) edges were spark cut from the crystals. An approximately cube shaped specimen with a (110) surface was prepared for the X-ray diffraction study. Wet chemical analysis indicated that the composition gradient was less than 0.5 % T1 over the long dimension of the reed.
111-EXPERIMENTAL PROCEDURES AND RESULTS
The experimental set-up, data acquisition system for the vibrating reed method is shown in Fig.1. An hp 3325A function generator was used to generate a sinusoidal signal whose frequency were controlled by the computer to sweep across the resonance frequencies of the clamped reeds. The sweeping speeds were also controlled by computer for complete on-line data-taking. The resonance curve data were stored by computer in serialized files.
Resonance frequencies of the reeds were changed by changing the mass of magnets on the free end. Since the possible natural frequency range of loaded reeds is still limited by its
geometrical shape, two reeds were needed to cover the
frequency range up to five POWER
hundred Hz. CAPACITOR AMPLIFIER
The oscillation
displacement between the - - - I
pick up capacitor was kept I I
below 10 % of the width I 1
between reed and capacitor I
I I
surface in order to minimize
I I
induced higher harmonic
I I
signals.
The resonance frequency I I
of the reeds broke sharply I
-
Iat the published martensite I I
start temperature of -8 OC, I SAMPLE I
thus confirming a I I
satisfactory overall quality I
of the samples. Typical I
I HELMHOLTZ]
raw data of the vibrating I COIL I
reed resonance at .,. I
L - , - - - , ,
temperature between 19 O C
-T'""
and 70 " C are presented in
Fig. 2. It can be seen VACUUM CHAMBER
from Fig. 2 that a Fig. 1. Schematic diagram of the pronounced damping maximum vibratiing reed internal friction occurs at 39 O C at a apparatus.
frequency of 108.6 Hz.
The relaxation strtength A as a function of temperature, which is obtained from least square fits of raw data to the Debye relaxation relation
2 2
Q - l = ~ ~ W / ( l + ~ W ), is presented in Fig. 3. It can be seen from this figure that the relaxation strength
A
increases siibstantially following qualitatively the Curie-Weiss law, 1/(T-Tc), where T is the transformation temperature. Figure 4, the Arrhenius plot of the relaxation time T obtained from the condition for a damping maximum0
104 108 112 FREQUENCY (Hz)
Fig. 2. A typical set of resonance curves of In-T1 alloy at various temperatures. From right to left the temperatures of measurement were 70, 57, 43, 39, 31, 27 and 19 OC respectively.
Fig. 3. The relaxation strength A as a function of temperature.
C8-550 JOURNAL
DE
PHYSIQUE occuring at the frequency f max, 2 M m a x ~ 1 , yieldswhere &~=(0.78+0.07) ev and ~o=(3.12f0.05)10-15sec.
Measurements on the relaxation of the X-ray diffraction from the specimen under dynamically applied stress were carried out by use of the apparatus to be described in detail elsewhere. Weak intensity tail at the reciprocal space off approximately 1/4 degree from the (110) Bragg diffraction was measured as
Fig. 4. Arrhenius plot of the resonance frequency at the the temperature of maximum damping.
Fig. 5. Arrhenius plot of the relaxation time for the stress induced X
diffraction intensity shift.
a function of time after the stress is applied or released at several temperatures.
Figure 4 shows the ArrheniuS plot of the relaxation time Tx for the stress induced diffraction tail intesity shift. Comparison of Figs. 3 and 4 shows that, within the accuracy of the experimental data, the activation energy obtained from the X- ray diffraction is found to be equal to the one obtained from the internal friction data.
IV-DISCUSSIONS
Our internal friction data have been found to be described by the Debye relaxation process, with the activation energy of 0.78 ev, which is close to the activation energy for Indium diffusion, 0.81 ev ( 9 ) . The Debye relaxation process associated with isolated point defects has been well established (10). However, this does not imply that all the internal friction with Debye relaxation should be interpreted in terms of isolated point defects. The contribution from the isolated point defects to the diffraction is of higher order compared with the contribution to the total volume, as shown by the classical experiment on vacancies by Simmons and Balluffi (11). Lattice defects that give a first order contribution to the X-ray diffraction must have an extent of several hundred lattice spacings, at least, in one of the dimensions. The relaxed shift of the X- ray diffraction intensity under the applied stress with the same activation energy as observed in the internal friction indicates that extended defects, which respond to the applied stress with a thermally activated process, should also be responsible for the internal friction.
The presence of an extended defects, which can respond to the applied stress, is not entirely an invention of the present authors. The presence of such a premartensitic defect is proposed by Wilkins to understand the apparent inconsistency between the elastic stiffness reduced from the Debye-Waller factor and the one obtained from the acoustic experiment in the In-T1 alloy (1). A similar discrepancy has also been found between the phonon dispersion curve obtained from neutron inelastic scattering and the dispersion curve estimated from the sound velocity measurements in the In-T1 alloy (2). The presence of the strong central peak in the neutron scattering experiment has been confirmed even in the case where only a slight softening of the transverse acoustic lattice wave. is observed in the premartensitic state (12). Although there still exist some controversies about the origin of central peaks, the interpretation of the central peak in terms of solitons is gaining strength in view of recent theoretical studies (13). The characterisitcs of solitons as contrasted with phonons is the following; while both phonons and solitons have similar spatially extended character, the frequency of the phonon is of the order of lo1'
-
1012 Hz and the frequency associated with the soliton is of the order of loL~z, which is extremely low compared with the Debye frequency. Any of the diffraction experiments-- neutron scattering, X-ray scattering, and electron diffraction including high resolution electron microscopy--cannot have the frequency or energy resolution to determine the time constant involved with solitons.The presence of tweed in the high resolution electron microscopy of the premartensitic state has been established in many martensitic alloy systems (4,s).
The presence of tweed is to be interpreted as the indication of the quasi-static displacement pattern of a sizable extent. Because of the inherent limitation of the frequency or energy resolution, it is futile to argue'whether the tweed is due to static or dynamic displacement pattern solely from the results of the high resolution electron microscopy. The present authors support the viewpoint to identify the extended lattice defects responsible to the central peaks in the neutron scattering as the origin of the displacement pattern observed as the tweed in the high resolution electron microscopy.
Since the time constant involved with the soliton is extremely low compared with the Debye frequency, the acoustic method has to be mobilized to deterine experimentally its slow time constant. The combination of the diffraction and the internal friction, such as carried out in the present experimen in the In-T1
C8-55 2 JOURNAL
DE
PHYSIQUEalloy, is proposed to be the experiment to map out the complete picture of the premartensitic solitons in other martensitic alloys.
ACKNOWLEDGMENTS
The present research has been supported by National Science Foundation and by the Grant in Aid by the Ministry of Education. One of the authors(T.S.) wishes to acknowledge stimulating discussion with Professor S.W.Wilkins and Professor S.C.Moss.
REFERENCES
(1) S.W.Wilkins, M.S.Lehmann, T.R.Finlayson and T.F.Smith, Proc;Int.Conf.on Solid State Phase Transformation. 1982. Pennsylvania,U.S.A. A1ME.p 1235.
(2) T.R.Finlayson and H.G.Smith, to be published in Trans.AIME.
(3) S.M.Shapiro, Y.Noda, Y.Fujii and Y.Yamada, Phys. Rev. B30 (1984) 4314.
(4) L.E.Tanner, R-Gronsky and A.R.Pelton, to be published in Trans.AIME.
(5) G.Van Tendeloo, M.Chandrasekaran, F.C.Lovey, Proc.ICOMAT-86,Nara.JAPAN. p 868.
(6) J.E.Bidaux, R.Schaller and W.Benoit, Proc.ICIFUAS-85,Urbana,Ill.,U.S.A. p 601.
( 7 ) A.Steiner, R.G.Gotthardt and D.G,Maeder, Proc.ICOMAT-86,Nara,JAPAN. p 216.
( 8 ) N-Nakanishi, T.Shigematsu, M.Yasouka, H.Oshima and S.Miura, Proc.ICOMAT-
86,Nara,JAPAN. p 210.
(9) J.W.Cahn, Acta Met., 9(1961) 795.
(10) B.S.Berry and A.S.Nowick, Physical Acoustics 111-A edited by W.P.Mason, Academic Press, New York, 1965. p 1.
(11) R.O.Simmons and R.W.Balluffi, Phys. Rev. 117 (1960) 52.
(12) T.Makita, M-Iizumi, Y.Morii and A-Nagasawa, Proc.ICOMAT-86,Nara,JAPAN. p 154.
(13) W.C.Kerr and A.R.Bishop, Phys. Rev. B34 (1986) 6295.
