EVALUATION OF MICROPOROSITY BY MHz-ATTENUATION MEASUREMENTS

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EVALUATION OF MICROPOROSITY BY MHz-ATTENUATION MEASUREMENTS

H. Schmidt, D. Lenz, W. Uelhoff

To cite this version:

H. Schmidt, D. Lenz, W. Uelhoff. EVALUATION OF MICROPOROSITY BY MHz-

ATTENUATION MEASUREMENTS. Journal de Physique Colloques, 1983, 44 (C9), pp.C9-325-C9-

330. �10.1051/jphyscol:1983946�. �jpa-00223393�

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JOURNAL DE PHYSIQUE

Colloque C9, suppl6rnent au n012, Tome 44, decernbre 1983 page C9-325

EVALUATION OF MICROPOROSITY BY MHz-ATTENUATION MEASUREMENTS

H. S c h m i d t , D. Lenz and W. uelhoffr

Institut far AZZgemeine MetaZZkunde und MetaZZphysik, RWTH Aachen, F.R.G.

+IFF der KfA, JtlZich, F. R. G.

Abstract

-

Attenuation due to the scattering of ultrasound by micropores has been measured in Mn, S and Be doped copper single crystals grown by the Czochralski- and Bridgeman-techniques. After suppression of dislocation damping by y-irradiation the attenuation a due to pore scattering has been deter- mined quantitatively iK the frequency range 10 to 300 MHz. By

fitting the theoretical ap(f)-dependence for spherical holes to the measured a P (£)-data we obtain the porosity P and the mean pore-diameter d

P'

Pulsed ultrasonic techniques have found widespread use mainly as time- of-flight measurements e.g. for location of faults and as thickness gauges. There is current interest for measurements of back scattered sound for grain size measurements and for sound velocity effects to measure internal stresses / I / . The main problem for the evaluation of attenuation (and sound velocity) data is that a number of different physical phenomena simultaneously contribute to these sound transport properties /2/.

For the purpose of the present paper the measured total attenuation a is given by

where a ^apare scattering contributions due to the presence of internal G'surfaces" (grains aG, pores a ) ; is due to absorption caused by dislocations Bnd aB = PaBi ig th~D"back-ground" attenuation due to all other scattering-, absorption- and phase-effects /2/.

The present paper is concerned with ultrasonic measurements on single crystals (aG

-

0) containing micropores (porosity P, a p f 0) as well as mobile dislocations (dislocation density A , aD f O), i.e.

a = aP + aD + aB (2)

By y-irradiation the dislocation contribution can be suppressed (aD=O), i.e.

Furthermore the attenuation of a pore free (P = 0 , ap = 0) Cu-crystal of identical orientation and identical sample condition (surface flat- ness, roughness, planparallelity) after complete dislocation pinning

(aD = 0) is given by a

y ,P=O = a ~ , ~ = ~ ' Thus the pore scattering is given by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983946

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C9-326 JOURNAL DE PHYSIQUE

under the valid assumption a =

B ^a

,

i.e. that the background val- ues of porous and porefree specimg&=%e identical.

To our knowledge the present paper presents the first experimental scattering data over a broad freauency range for a well defined scattering process (spherical holes in single crystalline matrix). By comparison with scattering theory the pore diameter d the pore concentration n (number/cm3) and the porosity P ( = 4sr3g1/3) can be evaluat-

ed. P P

EXPERIMENTAL

Ultrasonic samples were spark-erosion-cut from Bridgeman single crystals grown of high purity (Elmore) Cu, Cu+5ppmS, Cu+440ppmBe and from a Czochralski crystal of (ASARCO) Cu+200ppmMn. After grinding off the highly disturbed surfaces (0.2 mm) the samples were lapped flat and planparallel (0.5pm/cm) to a final orientation accuracy of better than 0.5' from < I l l > . The attenuation was measured with standard MATEC- equipment between 10 and 300 MHz using 0.25"@ X-cut quarz transducers

(VALPEY) and NONAQ-bond. For dislocation pinning 3 MeV-y-Bremsstrah- lung was used /3/. After RT-irradiation the samples were annealed 1 h at 100°C for maximum ?inning /4/. A 3 MeV-y-dose of Q = 2.500 flAh results in about 1 - 2 - 1 0 Frenkel defects/cm3 /3/. Y

RESULTS

Fig. I shows the a (f) -data. The pure (Bridgeman) Cu-sample (curve 1 ,

a l = a D + ag) exhibits the highest attenuation due to strong dislocation resonance damping contributions (a ) . This is seen by comparison with curve 2 which is measured after strong y-irradiation of the above D sample (a2 = aB). Curve 3 is measured on the Cu200ppmMn (Czochralski) sample after very strong y-irradiation (a3 = a + a ) . The dose was chosen 4 times higher than for the pure sample becguse the initial P dislocation loop length in the doped crystal is smaller and a higher Frenkel defect concentration is needed in order to completely pin the dislocations. It is seen that after complete dislocation pinning a3>a2 at all frequencies. This excess attenuation is attributed to pore scattering. Curve 4 shows the frequency dependence of the pore scattering attenuation (ak = a 3

-

^a = a _P)

.

DISCUSSION

- -

Sound scattering by pores: In the case of independent scattering cen-

-

ters the sound intensity dI scattered out of the sound wave of intensity I over the sound path length ax is given by

where in the present case n is the concentration of pores (number/cm3) and y= y (k-r) is the frequekcy- and sizedependent scattering cross section of a single pore (k = 2n/X = 2nf/v, v = sound velocity, r = pore radius). Since a = -0.5 d lnI/dx we obtain

a = n y / 2

P P ^{( 7}

Assuming a uniform pore size (delta function distribution) and using the normalized cross section y (k-r) = y/ar2 and the porosity P =

= n 4nr3/3 ( = total pore volume/cm3) N we obtain P

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In Fig.2 we have plotted the theoretical yN(k-r)-calculations by True11 et a1 /5/ on log/log scales as y (k.r)/k.r versus k-r. Such a plot is considered to be best suited forN comparison with experimental data.

In the range k-r<<l Rayleigh scattering,in the range k.r>>l stocha- stic scattering dominates.

Comparison with experiments: According to equ.(8) the theoretical mas-

-

tercurve given in Fig.2 is to be compared with a log/log plot of a /f versus f. Fig.3 shows such a plot of the alp /£-data for Cu2OOppmMn

(Cf. curve 4 in Fig.1). The fit by the master curve of Fig.2 is ex- tremely good indicating that in this sample the pores are of uniform size. This is not the case for the doped Cu-samples shown in Fig.4, which exhibit a less narrow a/f vs f dependence and where the delta function master curve (Fig.2) can only be used as an approximate de- scription of the data. The discussion of pore size distributions needed to fit the a -data for Cu5ppmS and Cu440ppmBe is postponed to an- other paper. ~ i g r o s c o ~ i c examinations of the electrolytically polished samples as function of depth below the (Ill)-surface indeed show very homogeneous pore diameters in the 10pm range for Cu200ppmMn but rath- er inhomogeneous pore sizes for the samples of Fig.4 (e.g. in CuSppmS relatively few very large (up to 100 pm) pores with most pores however in the 20 to 40 Dm diameter range).

Evaluation of pore diameter and porosity: The coordinates of the maximum in Fig.2 are given by

( ~ ~ / k - r ) ~ ~ ~ = 3.9 (9b) In the experimental data plot the maximum is observed at f m X , ( a p / f ~ X and we obtain from equ. (9a, b) and (8)

With these relations and the fits in Fig.3 and 4 resp. we derive the porosity data given in

Tab. 1

* ) effective pore radius

Sample

Cu200ppmMn Cu5ppmS Cu440ppmBe

Pore Radius r

[ ~ m l 6

17 * )

1 1 *

Porosity P [vol % I 6.

9 -

Pore Concentration n [pores/cm3

I

6.6.10' 4.9.10~

1 .6.104

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JOURNAL DE PHYSIQUE

Origin of Porosity: High purity Cu-crystals grown by the Czochralski technique are known to be highly perfect with respect to dislocation structure (low dislocation density 102-104cm-2, no small angle grain boundaries /6/). However, these crystals contain pores which have been attributed to vacancy condensation possibly assisted by simulta- neous precipitation of the residual gaseous impurities (oxygen and/or hydrogen / 7 / ) . In Mn-doped Czochralski crystals the pore concentration is increased and the pore size distribution is narrower. These effects are attributed to enhanced pore nucleation due to Mn/vacancy trapping.

In contrast pure Bridgeman crystals are known to have comparitively high dislocation densities ( 1 0 ~ - 1 0 ~ c m - ~ ) caused by contact with the hard crucible and additionaly small-angle grain boundaries /a/, however these crystals show negligible porosity. The latter is attributed to the increased vacancy sink density (dislocations) which favours an- nihilation of vacancies by dislocation climb. However, doped Bridgeman crystals also exhibit considerable microporosity which we attribute to impurity-vacancy trapping as in the doped Czochralski crystals.

Experimental limits for ultrasonic pore measurements: Fig.5 depicts

-

the limiting ranges for ultrasonic measurements of porosity and pore diameter. It is seen that PmX and P both are functions of d

.

^The

limits for d are derived from equ.

(vdz)

under the assumption taat the attenuation Reasurements cover the f-range from 2 to 300 MHz with the

( a /£)-maximum situated within the range 5 to 250 MHz; the latter raffge allows the proper observation of the maximum. According to Fig.5 the smallest observable pore diameter is about 6 fim whereas the maximum diameter is about 300 bm. The maximum porosity is determinated by the highest total attenuation a which can be measured by the standard pulse echo technique (a IM

glv

dB/fisec corresponds to just two pulse echoes i.e. 4 passage& of the pulse through a sample of about 1 cm length). Taking account of the £-dependent background attenuation aB (cf. curve 2 in Fig.1) the limiting pore scattering attenuation is glven by a = a IM

-

a

.

With this value the upper limit P (d ) in Fig.5 is dgriveh. On tae other side the lower limit P (dyXisPa con- ,,sequence of the fact that a can only be measured wit!!IYim!?ted accuracy. Thus we have to assume !?hat a must be at least 20% of the a -value in order to make reasonable seEaration and (a /f) plots (cf. Pf9.3) possible. As an example for the use of Fig.5 we Find that pores wlth 50 fim diameter can be ultrasonically measured in the porosity range 5.10-' to 1.5.10-~ Vol %. It can be shown that attenuation measurements are much more sensitive for porosity detection than sound velocity measurements which yield Av/v = 8.10- P; P[Vol % I / 9 / . We remind that Fig.5 only applies to the very special case of pores in a single- crystalline matrix. In polycrystals, however, sound scattering due to grain boundaries normally becomes very large (aG > aLIM) already at low frequencies (beyond 10 to 20 MHz) which makes the necessary broad- band measurements of a (f) impossible. However, we believe that ultrasonic techniques can bg used to evaluate porosity from measurements of backscattered sound instead of transmitted sound (pulse echo attenuation). These ultrasonic techniques would be of greatest interest for detection of voids and porosity e.g. in reactor materials.

ACKNOWLEDGEMENTS

Work supported by the Minister fur Wissenschaft u. Forschung, Nord- rhein Westfalen, W.-Germany.

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REFERENCES

-

/1/ E. S c h n e i d e r , K. Goebbels; VDI-Berichte

439

( 1 9 8 2 ) 91,

/ 2 / R . T r u e l 1 , Ch. Elbaum, B.B.Chick; " U l t r a s o n i c Methods i n S o l i d S t a t e P h y s i c s " Acad. P r e s s , New York ( 1 9 6 9 ) .

/ 3 / P. W i n t e r h a g e r , K-Lucke; J. Appl. Phys.

44

(1973) 4855.

/ 4 / H. I n a g a k i , F. H u l t g r e n , K . Lucke; A c t a Met.

2

(1970)713.

/ 5 / i n r e f . / 2 / pp. 391-405.

/ 6 / H. Fehmer, K. S c h u r , W. U e l h o f f ; B e i t r . e l e k t r o n e n m i k r o s k . D i r e k t a b b . O b e r f l .

2

(19701251.

/ 7 / H. Fehrner; T h e s i s Univ. Munster ( 1 9 7 1 ) .

H. Pehmer, W. U e l h o f f ; J. C r y s t . Growth 1 3 / 1 4 ( 1 9 7 2 ) 257.

/ 8 / T. I n o u e , J. Watanabg, M. Yamamoto; J. o f C r y s t a l Growth 24/25 (1974) 418,

/ 9 / C.M. S a y e r s , R.L. Smith; U l t r a s o n i c s

2

(1982) 201,

Frequency f [MHz1

F i g . 1 : Frequency dependence of a t t e n u a t i o n a f o r 3 d i f f e r e n t s a m p l e s t a t e s (c. f . i n s e r t e d t a b l e ) .

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C9-330 JOURNAL DE PHYSIQUE

Fig.2: Normalized sound scattering cross section for a spherical hole (radius r) in Cu versus k.r (k=21~f/v; f=

frequency, v= sound velocity).

Czochralski -X Cu 2 0 0 p p m Mn

Frequency f [MHz1

Fig.3: Measured ap/f-data for Cu200ppmMn (c. f. curve 4 in Fig.1) versus f fitted by the theoretical scattering dependence (dashed curve, c. f.

Fig.2).

Bridgeman XX _A _Cu Sppm S

o Cu040ppm Be

10 100

Frequency f lMHzl

Fig.4: a /£-data for Cu5ppmS and ~ u 4 4gppm?3e.

I . ^. ^. ^I ^. ^{. I} I

6 10' l o 2 3.10~

Pore Diameter d, [ p ml

Fig.5: Range of porosity P as function of por,e diameter dp

(shaded area) which is acces- sible by ultrasonic attenuation measurements in Cu in the f - range 2-300 MHz.