8
3. V. Ya. Basevich, S. M. Kogarko, and V. S. Posvyanskiit Fiz. Goreniya Vzryva, 11,242 (1975). 4. V. Ya. Basevich, S. M. Kogarko, and M. G. Neigauz, Izv. Akad. Nauk SSSR, Ser. Khim., 42 (1976). 5. W.C. Gardiner, J. H. Owen, et al., in: The Fifteenth Symposium (International) on Combustion, Combus- tion Institute, New York (1976). 6. T.P.J. Jzod, J. Chem. Phys., 55, 4425 (1971). 7. V.V. Azatyan and L, B. Romanovich, Izv. Akad. Nauk SSSR, Ser. Khim., 941 (1971). 8. G. Pratt and J. Valtman, J. Chem. Soc., Faraday Trans., 70, 1841 (1974). 9. G.I. Kozlov and V. G. Knorre, Kinet. Katal., 4, 189 (1963). 10. N.R. Greiner, J. Chem. Phys., 53, 1284 (1970). 11. V.N. Kondrat'ev, Reaction Rates of Gas Phase Reactions [in Russian], Nauka, Moscow (1970). 12. J. O, Hirschfelder, et al., Molecular Theory of Gases and Liquids, Wiley-Interscience (1964). 13. R.C. Reid and T. K. Sherwood, Properties of Gases and Liquids, 2nd ed., McGraw-Hill (1966). 14. A. D'alessio, A. DiLorenzo, et al., in: The Fourteenth Symposium (International) on Combustion, Com- bustion Institute, New York (1974), 15. V.N. Antonov and A. S. Lapidus, Acetylene Production [in Russian], Khimiya, Moscow (1970). 16. V. Ya. Basevich, S. M. Kogarko, and V. S. Posvyanskii, Fiz. Goreniya Vzryva, 12, No. 2, 217 (1976). 17. V. Ya. Basevich, S. M. Kogarko, and V. S. Posvyanskii, Fiz. Goreniya Vzryva, 13, No. 2 (1977). THERMAL INSTABILITY OF A VIBRATIONALLY EXCITED MOLECULAR GAS A. D. Margolin and V. M. Shmelev In a system having a large reserve of nonequilibrium vibrational energy, which is relaxing at a rate depending strongly on the temperature, there is the possibility of a whole series of thermal instabilities. In [1] a criterion was obtained for thermal instability (the thermal explosion of a medium) in an electric-discharge laser, in the approximation of a theory with lumped parameters. In the present work, the methods of the theory of combustion are used to analyze instabilities of the following types : thermal explosion (in the approximation of a theory with distributed and lumped parameters), an adiabatic explosion; ignition, combustion, and detona- tion. Non-Steady.-State Theory of the Thermal Instability of a Relaxing Gas of the Type of an Adiabatic or Thermal Explosion Within the framework of the theory of a thermal explosion [2], we consider the heat balance and the vibrational energy of a relaxing system for values averaged over the volume. Let a molecular gas, vibrationally excited by a source of pumping (for example, by a flow of resonance quanta, by an electrical discharge) with a velocity q, have a reserve of nonequilibrium vibrational energy per unit mass ~, and let it relax toward an equilibrium state (energy ~) with a characteristic time, determined by a dependence of the Landau-Teiler type. r~ = Aexp(-- ~), (1) where A is a preexponential factor, depending weakly on the temperature; B is a coefficient, having a typical value in the range of 10-200~ -~. The relaxation process takes place in the volume V, bounded by the surface S. Then the heat-balance equation has the form V. dT/dt-~ Y. (e --e) /Crr -- aS ( T -- To)/pc, (2) where t is the time; c is the specific heat capacity of unit mass of the gas; w is the heat-transfer coefficient; T0 is the temperature of the Wall; p is the density o'f the gas. The corresponding relaxation equation for the vibrational energy of the gas is Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 14, No. 1, pp. 52-62, January-February, 1978. Original article submitted July 15, 1976. 40 0010-5082/78/1401-0040507.50 1978 Plenum Publishing Corporation

Composition and depth of oxidized layers on tungsten powders of various particle sizes

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apparent energy of activation. This may be linked with increased defectiveness of the c rys ta l s t ructure of iron (work-hardening).

C ONC L U S I O N S

A study was made of the disaggregation of metall ic iron powders at the boiling point of liquid nitrogen. Cryogenic comminution is shown to have advantages over mechanical comminution under ordinary conditions.

1 ,

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5. 6.

7.

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L I T E R A T U R E C I T E D

B. Delmont, Kinetics of Heterogeneous Reactions [Russian translation], Mir, Moscow (1972). Yu. D. Tret 'yakov, N. N. Oleinikov, and V. A. Granik, Physicochemical Pr inciples of the Thermal P r o - cessing of Fe r r i t e s [in Russian], Moscow State Univ. (1972). B. E. Levin, Ya. D. Tre t 'yakov, and L. M. Letyuk, Physicochemical Pr inc ip les of Prepara t ion , P roper t i e s , and Applications of Fe r r i t e s [in Russian], Metallurgiya, Moscow (1979). W. D. Kingery et al., Introduction to Ceramics , Wiley (1975). G. S. Khodakov, The Physics of Comminution [in Russian], Metallurgiya, Moscow (1972). R. N. Pyagai , N. N. Oleinikov, and Yu. D. Tret 'yakov, ~Effect of cryogenic comminution on the acid d i s - solution of metallic zinc, ~ Poroshk. Metall., No. 3, 73-75 (1982). I. I. Gi lvarry, "The domain distribution function for f ragment size in comminution, n Zerkleinern, 57, 63-71 (1967). A. Ya. Rozovskii , Kinetics of Topochemical Reactions [in Russian], Khimiya, Moscow (1974).

C O M P O S I T I O N AND D E P TH OF O X I D I Z E D L A Y E R S

P O W D E R S O F V A R I O U S P A R T I C L E S I Z E S

O. A. K u l y a b i n a , I . N. S h a b a n o v a , V. A. T r a p e z n i k o v , Y u . S. M i t r o k h i n , S. F . L o m a e v a , a n d A. T . G a i v o r o n s k i i

ON T U N G S T E N

UDC 539.21

In the manufacture of parts f rom metal powders it is important to know the surface condition of their par t ic les . In this connection, it is of interest to study the composit ion and depth of oxidized layers and the reduction kinetics of oxides.

In the present work the surfaces of powders were analyzed by the e lec t ron-spec t roscopy method [1], which enables the surfaces of metals to be studied to a depth of the order of severa l atomic layers . Elec t ron spec t ra were obtained using an Institute of Metal Physics e lectron magnetic spec t rometer [2]. In the excitation of e l ec - t rons by A1 K s radiation (1486.6 eV) the inst rument had a resolution of 1 eV; the binding energy of e lect rons was measured with an accuracy of 0.3 eV. The residual gas p ressure in the spec t romete r chamber was ~10 -G hPa. The pulse count on the line maxima was on average 200, and on the background 40 per second. Spectra were cal ibrated against the energy of the C l s l lne (285 eV) f rom the hydrocarbon residue on the specimens.

o A study was made of the surfaces of a heterogeneous tungsten powder consist ing of par t ic les of 500-80,000-A radius (specimen 1) and of a powder of 50,000-~ part icle radius (specimen 2).

Elec t ron spect ra were obtained of the W4f~/2,5/2 and Ols levels of type 1 (Fig. la-d) and type 2 (Fig. 2a-d) specimens at 20, 200, 400, and 600~ and also, to enable these spec t ra to be identified, of a tungsten tablet (Figs. le and 2e). The W4_f~/2,5/2 e lectron spec t rum obtained f rom pure tungsten was a doublet of lines (maxima of 32.5 and 34.6 eV) corresponding to the spin-orbi ta l splitting of the 4f level. Swellings on the side of l a rger binding energies pointed to the presence of the W - O bond. Tungsten, of course , forms a number of oxides, W . 2, WO2.72, WO2.~5, WO2.9, WO2.9~, and WO3, in which it is present in three oxide states - W 4+, W 5+, and W 6+ [3]. The spectra , broken up into their components, revealed the doublet of the 4f lines of metallic

Udmurtsk State Universi ty. Translated f rom Poroshkovaya Metallurgiya, No. 5(233), pp. 12-17, May, 1982. Original ar t icle submitted, after revision, February 28, 1981.

356 0038-5735/82/2105-0:~56 $07.50 �9 1982 Plenmn Publishing Corporat ion

TABLE 1. Relative Intensities of Line Maxima

Specimen 1 (Fig. 1) Specimen 2 (Fig. 2) T, ~ iw iw4+ iwS+ Iwa+, % Iw :Iw4+ :Iw5+ :Iw o+, o]d

20 20:14:14:52 34:8:0:58 200 37:7:0:59 44:0:16:40 400 30:11:10:49 36:5:10:49 600 59:16:16:9 70:0:9:21

~~176

i 5 ~ ~ d 2

e

2~c ~Tungsten

J~ J s ~'o ' /es

0/r

a j \

b j \

C

/ \

5J0 5,U

Ebind, eV

d

e

2 0 ~ ~ en

0~

b

J\

/ \

, Ebind, 5'~f 5JO 5~I eV

Fig. 1 Fig. 2

Fig. 1. Elect ron spec t ra of W4f?/2,5/z and Ols levels of surface of powder of 500-80,000-/~ part icle radius .

Fig. 2. E lec t ron spec t ra of W4f?/2,5/2 and Ols levels of surface of powder of 50,000-3. part icle radius.

tungsten and, at distances of 1.8, 3.5, and 4.5 eV f rom it, doublets corresponding to W 4+, W 5+, and W e+, r e - spectively [4-6]. The IW:Iw4+:Iws+:Iw6+ maximum intensity rat ios are given in Table 1.

At room tempera ture (Figs. l a and 2a) the relative intensity of the lines corresponding to the oxide layers was higher for specimen 1 than for specimen 2. Heating to 200~ (Figs. lb and 2b) increased the intensity of the doublet f rom pure tungsten in the spec t ra of both specimens - reduction of oxides to metal took place. Carbon present inside the spec t romete r apparently promoted the reduction of oxides to metal during heating. The react ion may have taken place in stages, f i r s t f rom W 6+ to W 4+ and then to metal [3, 6]. Raising the t e m - pera ture to 400~ (Figs. lc and 2e) increased the contribution f rom oxide states to the spec t ra . Heating the specimens to 600~ (Figs. ld and 2d) once again increased the intensity of the doublet f rom pure tungsten, which was indicative of fur ther reduction of oxides to metal; reduction was more intense on the surface of specimen 1 than on specimen 2.

In the e lectron Ols spec t ra of specimens obtained at 20~ (Figs. l a and 2a) a maximum with an energy of 530.2 eV ref lected the W - O bond. Swellings on the side of l a rge r binding energies at a peak with an energy of 532 eV corresponded to oxygen adsorbed by a physical mechanism (COz, HaCO3, CO, and 02). These peaks d i s - appeared soon after the beginning of heating. The maximum with the energy of 532 eV corresponded to oxygen

357

TABLE 2. Depths and Compositions of Oxide Layers (R = 50,000 A)

r, oc x,~k [ W4-{-,% I W5-[-,% [ W6-}-,%

20 22 12 0 88 200 20 0 29 71 400 22 8 16 76 660 14 0 30 70

adsorbed chemically. The intensity of this maximum diminished on heating to 400~ when desorpt ion of the oxygen took place (this oxygen apparently part ial ly oxidized the specimen surface); it was this c i rcumstance that accounted for an increase in the intensity of the lines corresponding to oxide s tates in the W4f spec t rum at 400~ (Figs. lc and 2c).

The variat ion of the composition of the sur faces of Ni powders with particle size was studied by the e l ec - t ron spect roscopy method in [7]; it was found that heating to 250~ completely purified powders of small part icle size f rom nickel oxides; by contras t , in the spec t ra of c o a r s e r powders the line corresponding to the oxide de- c reased , but did not actually d isappear , This was apparently due to the fact that fine powder par t ic les are covered with thinner oxide layers [8]. Thus, the rapid reduction of surface oxides during the heating of spec i - men 1 compared with specimen 2 was a resul t of the presence of fine par t ic les . The reason why the lines c o r - responding to the oxide states in the spec t ra of specimen 1 were more intense was that this powder was finer, and consequently more par t ic les made their contributions to the spec t ra .

The e lectron spec t ra obtained were employed for determining the thickness of the oxide layers for spec i - men 2. During their passage through some layer of the mater ia l , e lectrons knocked out by x - r a y quanta lost par t of their kinetic energy, as a resu l t of which the intensity of the beam weakened,

d l = Im~Xe-X/~'dx, (1)

where x is the distance covered by electrons in the mater ia l and 7~ is the depth of emergence of electrons f rom the specimen. Consequently, the intensi t ies of the lines of the spec t rum corresponding to the oxidized and un- oxidized layers of a solid specimen may be expressed as

Io = I m~x (1 --- e-X/n~); I u == l~"~e-: ' /x ' , (2)

where x is the depth of the oxidized layer and X 1 is the depth of emergence of e lect rons f rom the oxide.

I max is determined by the number of atoms being photoionized, and hence

l'~ ax = kVoaDl~z; l ~ ~x = kVutzD2k2, (3)

where k is a coefficient depending on the pa ramete r s of the instrument; X 1 and X~, the depths of emergence of e lect rons f rom the oxide and metal , respect ively; ~, the photoionization c ros s section; V o and Vu, the volumes of the oxidized and unoxidized par ts of the mater ia l making their contributions to the spec t rum intensity, r e - spectively; D 1 and D2, the densit ies of a given atom in unit volume; and D = p �9 A /M, p being the density of the mater ia l (g/em3), A the mass of the given atom, and M the molecular mass of the mater ia l . Thus,

1 o VoDI~, 1 ( 1 - - e - x / ' ~ ' )

Q = ~ = V u O ~ - ~ / ~ , (4)

In [7] the ra t io Vo/V u was calculated for spherical par t ic les of the same radius R packed in dense l aye r s , without taking into account the effect of a second layer ,

Vo �9 h3 (12RZ ~ h2) - - 1, Vu ( t~ - - x ) 2 ( 1 2 R 2 h - - 2 h 2 x - - h 3 + 3 h x - - 12Rhx) (5)

where h is the depth of the layer being analyzed.

With Eq. (5) we can t r ans fo rm Eq. (4) as follows:

D1;~1 (1 - - e-~/~,) [ h 3 (12R ~ - h 2) Q = D2~2 e-:'/~, [ (h - - x) z (12R2h ~ 2h2x ~ h 3 + 3hx - - 12Rhx)

l]. (6)

358

In [5] de te rmina t ions on dense spec imens gave X W = 13 /~ and XWO 3 = 26 /~.

In the p re sen t work the depth of the oxidized l aye r was calculated by assigning var ious reasonable , f r o m an exper imen ta l point of view, values of h (h ~ Xl + X2), allowing fo r the loose s t ruc tu re of the oxidized su r face l ayer by varying X 1 in the range 30 A~_ X1 ~ 70 /~, and substi tuting exper imenta l ly obtained values of Q and R. After analyzing the r e su l t s obtained, the depth of the l aye r invest igated was taken to be equal to 45 A at X 1 =

o

60 A o The th icknesses of the oxidized l aye r s x and approximate composi t ions of the oxide l aye r s at d i f ferent ~ m p e r a t u r e s a re given in Table 2.

L I T E R A T U R E C I T E D

1o K. Siegbahn, K. Nordmeng, A. Falmann, et al. , E lec t ron Spect roscopy [Russian t rans la t ion] , Mir , Moscow (1971).

2. V . A . Trapeznikov, A. V. EvstafVev, V. P. Sapozhnikov, et al. , ~Elect ron magnet ic s p e c t r o m e t e r , n F iz . Met. Metalloved. , 36, 1293-1300 (1973).

3. M . P . Slavinskii , Phys icochemica l P r o p e r t i e s of the Elements [in Russian] , Meta l lu rg izda t , Moscow (1952). 4. B . A . de Angelis and M. G. Schiavello, ~X- ray photoelect ron spec t roscopy study of nons to ieh iometr ic

tungsten oxides, n Solid-State Chem., 2_~1, No. 1, 67-70 (1977). 5. T . A . Car l son and G. E. McGuire, "Study of t ungs t en - tungs t en oxide as function of th ickness of the sur face

oxide l ayer , " J . E lec t ron Spectry . , 1, No. 2, 161-166 (1973). 6o K. Hamrin , C. Nordling, and L. Kihlborg, n ESCA studies of oxidation s ta tes in W - V phases , " Ann. Acad.

Regieae Sci., Upsala, 14__, 1-7 (1970). 7~ V . A . Trapeznikov, I. N. Shabanova, A. E. E rmakov , et al. , " Inves t iga t ion of ae roso l powders of f e r r o -

magnet ic m a t e r i a l s by the e lec t ron spec t roscopy method and by sa tura t ion magnet iza t ion intensity m e a - su remen t , " in: X-Ray Photoe lec t ron Spec t roscopy [in Russian] , Naukova Dumka, Kiev (1977), pp. 63-67.

8. L . S . Pala tn ik , V. K. Kosevich, V. A. Antonova, and P . P . Arkhipov, "Phase composi t ion of cobalt con- densates in the i r initial s tage of fo rmat ion ," Fiz . Met. Metalloved., 22, No. 1, 58-61 (1966).

359