Transport Phenomena Induced by the Energy Pulse in a Crystal
The phenomenon of rapid mass-transfer in solid state observed in metals after pulsed action is characterized by transfer of atoms within the short periods of action time to the depths significantly exceeding the diffusion depth under the conditions of stationary annealing. The features of other tran...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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irk-123456789-1069002016-10-09T03:02:37Z Transport Phenomena Induced by the Energy Pulse in a Crystal Pogorelov, A.E. Дефекты кристаллической решётки The phenomenon of rapid mass-transfer in solid state observed in metals after pulsed action is characterized by transfer of atoms within the short periods of action time to the depths significantly exceeding the diffusion depth under the conditions of stationary annealing. The features of other transport phenomena (mass-transfer, heat-transfer, etc.) arising in metal at pulsed energy action on a crystal are also discussed. The best instrument to study transformations in the matter under pulsed action is an easily controlled laser pulse. In a given work, the nature and correlations between transport phenomena in metals excited by the energy pulse are studied. Скоростная деформация металлов в твёрдой фазе приводит к генерации и переносу дефектов кристаллической решётки на значительные расстояния. В этих условиях атомы проникают на глубины, существенно превышающие глубину диффузии в условиях стационарного отжига за сопоставимые времена. Ускоренный перенос атомов может также сопровождаться и другими явлениями переноса (электро- и теплоперенос) в металле при воздействии энергетического импульса на кристалл. Наилучшим источником такого импульса является легкоуправляемое лазерное излучение. В данной работе установлены природа и взаимосвязь между транспортными явлениями в металлах, возбуждённых энергетическим импульсом. Швидкісна деформація металів у твердій фазі призводить до ґенерації і перенесення дефектів кристалічної ґратниці на значні віддалі. В таких умовах атоми проникають на глибини, які істотно перевищують глибину дифузії в умовах стаціонарного відпалу за такі ж самі терміни часу. Прискорене перенесення атомів може також супроводжуватися й іншими явищами перенесення (електро- і теплоперенесення) в металі за умов дії енергетичного імпульсу на кристал. Найкращим джерелом такого імпульсу є легкокероване лазерне опромінення. В даній роботі встановлено природу та взаємозв’язок між транспортними явищами в металах, збуджених енергетичним імпульсом. 2014 Article Transport Phenomena Induced by the Energy Pulse in a Crystal / A.E. Pogorelov // Металлофизика и новейшие технологии. — 2014. — Т. 36, № 3. — С. 383-389. — Бібліогр.: 13 назв. — англ. 1024-1809 PACS: 61.72.Bb, 61.72.Lk, 61.80.Ba, 62.20.fq, 62.50.Ef, 72.15.Eb, 81.40.Wx DOI: http://dx.doi.org/10.15407/mfint.36.03.0383 http://dspace.nbuv.gov.ua/handle/123456789/106900 en Металлофизика и новейшие технологии Інститут металофізики ім. Г.В. Курдюмова НАН України |
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Дефекты кристаллической решётки Дефекты кристаллической решётки |
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Дефекты кристаллической решётки Дефекты кристаллической решётки Pogorelov, A.E. Transport Phenomena Induced by the Energy Pulse in a Crystal Металлофизика и новейшие технологии |
| description |
The phenomenon of rapid mass-transfer in solid state observed in metals after pulsed action is characterized by transfer of atoms within the short periods of action time to the depths significantly exceeding the diffusion depth under the conditions of stationary annealing. The features of other transport phenomena (mass-transfer, heat-transfer, etc.) arising in metal at pulsed energy action on a crystal are also discussed. The best instrument to study transformations in the matter under pulsed action is an easily controlled laser pulse. In a given work, the nature and correlations between transport phenomena in metals excited by the energy pulse are studied. |
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Article |
| author |
Pogorelov, A.E. |
| author_facet |
Pogorelov, A.E. |
| author_sort |
Pogorelov, A.E. |
| title |
Transport Phenomena Induced by the Energy Pulse in a Crystal |
| title_short |
Transport Phenomena Induced by the Energy Pulse in a Crystal |
| title_full |
Transport Phenomena Induced by the Energy Pulse in a Crystal |
| title_fullStr |
Transport Phenomena Induced by the Energy Pulse in a Crystal |
| title_full_unstemmed |
Transport Phenomena Induced by the Energy Pulse in a Crystal |
| title_sort |
transport phenomena induced by the energy pulse in a crystal |
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Інститут металофізики ім. Г.В. Курдюмова НАН України |
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2014 |
| topic_facet |
Дефекты кристаллической решётки |
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http://dspace.nbuv.gov.ua/handle/123456789/106900 |
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Transport Phenomena Induced by the Energy Pulse in a Crystal / A.E. Pogorelov // Металлофизика и новейшие технологии. — 2014. — Т. 36, № 3. — С. 383-389. — Бібліогр.: 13 назв. — англ. |
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Металлофизика и новейшие технологии |
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| fulltext |
383
PACS numbers:61.72.Bb, 61.72.Lk,61.80.Ba,62.20.fq,62.50.Ef,72.15.Eb, 81.40.Wx
Transport Phenomena in a Crystal Induced by the Energy Pulse
A. E. Pogorelov
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03680 Kyyiv-142, Ukraine
The phenomenon of rapid mass-transfer in solid state observed in metals af-
ter pulsed action is characterized by transfer of atoms within the short peri-
ods of action time to the depths significantly exceeding the diffusion depth
under the conditions of stationary annealing. The features of other transport
phenomena (mass-transfer, heat-transfer, etc.) arising in metal at pulsed en-
ergy action on a crystal are also discussed. The best instrument to study
transformations in the matter under pulsed action is an easily controlled la-
ser pulse. In a given work, the nature and correlations between transport
phenomena in metals excited by the energy pulse are studied.
Швидкісна деформація металів у твердій фазі призводить до ґенерації і
перенесення дефектів кристалічної ґратниці на значні віддалі. В таких
умовах атоми проникають на глибини, які істотно перевищують глибину
дифузії в умовах стаціонарного відпалу за такі ж самі терміни часу. При-
скорене перенесення атомів може також супроводжуватися й іншими
явищами перенесення (електро- і теплоперенесення) в металі за умов дії
енергетичного імпульсу на кристал. Найкращим джерелом такого імпу-
льсу є легкокероване лазерне опромінення. В даній роботі встановлено
природу та взаємозв’язок між транспортними явищами в металах, збу-
джених енергетичним імпульсом.
Скоростная деформация металлов в твёрдой фазе приводит к генерации и
переносу дефектов кристаллической решётки на значительные расстоя-
ния. В этих условиях атомы проникают на глубины, существенно превы-
шающие глубину диффузии в условиях стационарного отжига за сопоста-
вимые времена. Ускоренный перенос атомов может также сопровождать-
ся и другими явлениями переноса (электро- и теплоперенос) в металле
при воздействии энергетического импульса на кристалл. Наилучшим ис-
точником такого импульса является легкоуправляемое лазерное излуче-
ние. В данной работе установлены природа и взаимосвязь между транс-
портными явлениями в металлах, возбуждённых энергетическим им-
пульсом.
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2014, т. 36, № 3, сс. 383—389
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
2014 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
384 A. E. POGORELOV
Key words: mass transfer, heat transfer, laser pulse irradiation.
(Received 14 June, 2013)
1. INTRODUCTION
High-speed deformation of metals in a solid phase leads to generation
and transport of the crystal lattice defects to the significant distances.
As shown in [1], dislocations are the most probable mass carriers. Their
formation at the laser pulse action has been confirmed experimentally
in [2, 3]. Direct studies of the concentration changes with the applica-
tion of radioactive isotopes have shown that the region of increased
content of dislocations (30—40 m) is several times larger than the re-
gion of mass-transfer [4]. At the same time, the mass-transfer pro-
ceeds to the depths, which exceed the region of a laser pulse thermal
influence several times.
It is assumed [5] that dislocations, moving under the influence of
stresses , spreading deep into the crystal away from the deformation
pulse Pi excited region, capture point defects and carry them away
deep into the crystal. The point defects, captured by a dislocation, are
carried into a crystal to the depth determined by the binding energy of
a defect with a dislocation and its velocity V. Based on this, the authors
of [6] were not only observing the mass-transfer, but were also regis-
tering the appearance of the electrical potential at the opposite sides of
the pulse-squeezed metal sample, and in [7]–the acceleration of the
heat transfer. In a given paper, we study the nature and correlation
between the transport phenomena in pulse-deformable metals.
2. EXPERIMENT
Transport processes taking place in a crystal have a threshold nature
and are determined by the criterion, which sets the boundary between
stationary and highly non-stationary states of matter [8]. This bound-
ary is determined by comparing the time ti of injection of the energy
portion into the substance and its relaxation time tr. In the case when
ti tr, the relaxation processes occur in a stationary or quasi-stationary
mode. If ti or tr, the mode turns from the quasi-stationary to a
highly non-stationary.
For generation of dislocations in a crystal, it is required that the
portion of injected energy is sufficient to induce stresses E
(Young’s module), and for the motion of dislocations (10
4—
10
2)E P (Peierls stresses). When selecting a mode, it is also im-
portant to remember that considerable portions of energy may result in
the crystal destruction. In this connection, it is necessary that the
temperature of the surface TS TL–temperature of thermal destruc-
TRANSPORT PHENOMENA IN A CRYSTAL INDUCED BY THE ENERGY PULSE 385
tion of the crystal.
When irradiating the region d with an axisymmetric laser beam, the
required criterion is determined in the first approximation as
2/(4 ),
c
t d k (1)
where k is the thermal diffusivity of material. As follows from (1), the
critical time tc of the energy injection strongly depends on the size of
the irradiated area d
2. When irradiating metals by laser pulses in the
free generation mode (i 10
3
s) or by continuous radiation, the relax-
ation is restricted only by thermal conductivity mechanism. The mag-
nitude of the arising temperature gradient does not cause the essential
strains, which would lead to the formation of excess number of struc-
tural defects such as dislocations and interstitial atoms.
When irradiating metals by giant laser pulses with i 10
8
s, the en-
ergy relaxation cannot be only provided by thermal conductivity
mechanism. This process causes very high temperature gradient ac-
companied by abrupt thermal expansion of irradiated area and appear-
ance of thermal stresses .
The relaxation of excess energy is additionally realized through the
appearance of a shock wave in a metal and generation of excess amount
of structural defects of all types, including point and linear ones. As a
result, taking into account the number n of laser actions, the density of
dislocations on depth z is determined from [5]:
1
1
2
( , ) (0, , ) ,
(1 ) |
n
i i
z t T z d
b |
(2)
where is the coefficient of metal thermal expansion, is the variable
of integration, T is the temperature gradient, is the time of laser
action, i is the number of laser action, b is the Burgers vector, and is
the Poisson coefficient.
3. RESULTS, ANALYSIS AND DISCUSSION
Distribution of the dislocation density after the pulsed laser action ob-
tained in [5] using Eq. (2) (continuous curve, i 10) and electron mi-
croscopy studies [2] (points), is presented in Fig. 1.
Figure 1, a shows that transfer of atoms occurs within the bounda-
ries of the area with the increased dislocation density. Dislocations,
being carried away from the laser-excited surface by the strain field ,
capture point defects and transfer them to the depth (Fig. 1, b). Flows
of mass or heat Q, described correspondingly by Fick and Fourier equa-
tions, in the case of presence of external driving force F can be written
as
386 A. E. POGORELOV
( / ) ,FQ K dM dz M v (3)
where K is the coefficient of proportionality characterizing certain
physical process, M is a physical quantity transferred in the direction
of z (with the average velocity <v> in the presence of driving force F):
in the case of mass transfer, this quantity is the concentration C, and
in the case of heat transfer, it is the temperature T. Thus, the ‘acceler-
ation’ of heat transfer should be expected during the pulse action along
with the accelerated mass transfer.
This hypothesis is tested using the laser-flash method, described in
[9]. We perform a thermal sensing of the pair of similar flat disk-shape
samples of identical thickness (1 mm) made of preliminary annealed
pure Fe. The irradiation was carried out in two, according to (1), criti-
cal modes–quasi-stationary with 1 10
3
s and highly non-stationary
with 1 10
8
s, at which the effect of mass-transfer acceleration in a
solid phase was observed. After that, we compare the time of the tem-
perature rise to the half of its maximum Tm/2 on the side of the sample
opposite to laser irradiated one, using the differentially connected
thermocouple. Thermocouple signal was recorded using high-sensitivi-
ty and high-speed ADC and was also controlled with the storage oscillo-
scope. It was found that 1 2
/ /dT dt dT dt
when the matter is in a
highly non-stationary mode, t1/2 is approximately 10
6
s, i.e. smaller
than that in the case of irradiation in a quasi-stationary mode.
Considering the similarity of the approach in description of the
a b
Fig. 1. Generation of dislocations (a) and a scheme of mass-transfer (b) in
pulse-deformable metal induced by them. Inset in (a) shows the concentration
of
55Fe in Fe after 10 laser actions; F is a vector of external driving force de-
termined by a moving stress gradient.
TRANSPORT PHENOMENA IN A CRYSTAL INDUCED BY THE ENERGY PULSE 387
mass- and heat-transfer expressed by Eq. (3), and also the nature of the
heat-transfer in metals, the observed phenomena can be described as
follows. Thermal conductivity in metals is realized by both phonons
and, preferentially, conduction electrons, which in real metals are get-
ting scattered on structural defects, in particular, dislocations [10].
Thermal conductivity K is inversely proportional to the thermal re-
sistance Wd related to the scattering of phonons on dislocations and
following [10, 11] can be presented as
1 sin ,
d
K W l (4)
where l is the dislocation length, is the dislocation scattering cross
section, and is an angle between the axis of a dislocation and the di-
rection of thermal gradient propagation.
Thus, as follows from (4), there are several ways to reduce Wd.
Thermal resistance of the crystal is maximal when the dislocation line
is perpendicular to the thermal flow. Scattering of the phonons on dis-
locations will decrease both with the reduction of [11] and with the
reduction of time of the phonons’ interaction with the dislocation that
is proportional to .
It follows from the discussion above that when moving in one direc-
tion with the dislocations, phonons would either not be scattered on
synchronously moving dislocations, or will gain an additional impulse
in the direction of motion. Thus, in the case of collective and directed
motion of dislocations, playing role of scattering centres for phonons
and conduction electrons, the effective thermal resistance in this di-
rection will decrease. In our case, it is manifested by the registered in-
crease of the thermal diffusivity in the direction of a probing thermal
pulse.
Taking the mean free path of the particles scattered by dislocations
proportional to 1/2, we find out that time required for the thermal
pulse to pass through the crystal with 108
cm
2
and with
1010
cm
2
will differ by 10 times. These estimations are valid for the
thermal probing of samples with the constant value of i in each case
and may be useful for comparative assessment of the degree of sample
deformation. In our case, the thermal pulse was passing through the
sample simultaneously with the generation of the mobile dislocations.
It can be concluded that at highly non-stationary conditions, caused
by pulsed action, the decrease of scattering of the particles responsible
for thermal-transfer should result in a noticeable increase of the elec-
tric conductivity of the metal. It is related to the possibility that un-
der such conditions there will be an effect of entrainment of conduc-
tion electrons by phonons [12, 13]. This phenomenon is supported by
the appearance of the electric potential at pulsed mechanical action on
the metal [6]. It does not contradict with the Wiedemann—Franz law
388 A. E. POGORELOV
that establishes the relation between thermal conductivity K of metal
and its electric conductivity . Thus, the transport phenomena induced
in the crystal by the energy pulse may be represented by the flow chart
shown in Fig. 2.
4. CONCLUSIONS
We discuss the peculiarities of some transport phenomena (mass-
transfer, heat-transfer, etc.) arising in metal at pulsed energy action
on a crystal. As shown, the connection between these phenomena is
based on interaction of electrons and phonons with dislocations gener-
ated in a crystal. Dislocations with entrapped point defects are moving
in the stress fields caused by the pulsed action and are directed away
from an excited surface deep into crystal. The correlation between the
transport processes is supported by experimental results showing the
accelerated transport of both marked atoms and thermal pulse, and by
the appearance of the electric potential. Studies of thermal character-
istics were performed using laser-flash method in two modes deter-
Fig. 2. Flow chart showing the links between the transport phenomena in-
duced in a crystal by the energy pulse.
TRANSPORT PHENOMENA IN A CRYSTAL INDUCED BY THE ENERGY PULSE 389
mined by the criterion for the appearance of the non-stationary condi-
tions at the pulse action. The established correlation between the time
of heat-transfer and dislocation density in a crystal may be used for the
comparison of the degree of sample deformation. Taking into account
the electronic character of thermal conductivity in metals, we propose
a general character of heat- and electro-transport to pulse-deformable
crystals. The generality of the nature of observed transport phenome-
na is in a good agreement with known physical laws.
REFERENCES
1. A. Pogorelov and A. Zhuravlev, Defect and Diffusion Forum, 194—199: 1247
(2001).
2. P. Yu. Volosevich and A. E. Pogorelov, Poverhnost’ (Fizika, Khimiya,
Mekhanika), 9: 126 (1986) (in Russian).
3. L. N. Larikov, E. A. Maksimenko, and A. E. Pogorelov, Metallofiz. Noveishie
Tekhnol., 7, No. 2: 116 (1985) (in Russian).
4. A. E. Pogorelov, Napravlennyj Massoperenos v Fe i Al pri Impul’snom
Lazernom Obluchenii (Thesis of Disser. for PhD) (Kiev: Institute for Metal
Physics, Ukr.A.S.: 1985) (in Russian).
5. A. E. Pogorelov, K. P. Ryaboshapka, and A. F. Zhuravlev, J. Appl. Phys., 92:
5766 (2002).
6. V. P. Bevz, V. F. Mazanko, A. V. Filatov, and S. P. Vorona, Metallofiz.
Noveishie Tekhnol., 28: 271 (2006) (in Russian).
7. A. E. Pogorelov, Proc. of the 1-st International Conference on Nanomaterials:
Applications and Properties NAP-2011 (September 27—30, 2011), vol. 2, p. 414.
8. A. Pogorelov, Proc. of International Conference NANO-2010 (October 19—22,
2010) (Kyiv: 2010), p. 162.
9. M. E. Gurevich and A. E. Pogorelov, Fizicheskie Metody Issledovania Metallov
(Physical Methods of Metals Investigation) (Kiev: Naukova Dumka: 1981)
(in Russian).
10. V. S. Oskotskii and I. A. Smirnov, Defekty v Kristallakh i Teploprovodnost’
(Defects in Crystals and Heat Transfer) (Leningrad: Nauka: 1972) (in
Russian).
11. N. V. Lugueva, S. M. Luguev, and A. A. Dunaev, Phys. Solid State, 45: 449
(2003).
12. L. Gurevich, J. Phys., 9: 477 (1945); ibid., 10: 67 (1946).
13. J. Bardeen and D. Pines, Phys. Rev., 99: 1140 (1955).
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|