The residual stress instrument with optimized Si(2 2 0) monochromator and position-sensitive detector at HANARO

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Nuclear Instruments and Methods in Physics Research A 545 (2005) 480–489 www.elsevier.com/locate/nima

The residual stress instrument with optimized Si(2 2 0) monochromator and position-sensitive detector at HANARO Chang-Hee Leea, Myung-Kook Moona,, Vyacheslav T. Ema,1, Young-Hyun Choia, Jong-Kyu Cheona, Uk-Won Namb, Kyung-Nam Kongb a

Korea Atomic Energy Research Institute, Yusung, Daejon 305-600, Republic of Korea b Korea Astronomy Observatory, Yusung,Daejon 305-348, Republic of Korea

Received 26 August 2004; received in revised form 28 January 2005; accepted 31 January 2005 Available online 1 April 2005

Abstract An upgraded residual stress instrument at the HANARO reactor of the KAERI is described. A horizontally focusing bent perfect crystal Si(2 2 0) monochromator (instead of a mosaic vertical focusing Ge monochromator) is installed in a drum with a tunable (2yM ¼ 0–601) take-off angle/wavelength. A specially designed position-sensitive detector (60% efficiency for l ¼ 1:8 A) with 200 mm (instead of 100 mm) high-active area is used. There are no Soller type collimators in the instrument. The minimum possible monochromator to sample distance, LMS ¼ 2 m; and sample to detector distance, LSD ¼ 1:2 m; were found to be optimal. The new PSD and bent Si(2 2 0) monochromator combined with the possibility of selecting an appropriate wavelength resulted in about a ten-fold gain in data collection rate. The optimal reflections of austenitic and ferritic steels, aluminum and nickel for stress measurements with a Si(2 2 0) monochromator were chosen experimentally. The ability of the instrument to make strain measurements deep inside the austenitic and ferritic steels has been tested. For the chosen reflections and wavelengths, no shift of peak position (apparent strain) was observed up to 56 mm length of path. r 2005 Elsevier B.V. All rights reserved. PACS: 07.85.Jy; 61.12.Ld Keywords: Residual stress measurement; Neutron diffraction; Position-sensitive detector; Bent perfect silicon crystal; Monochromator; VAMAS

Corresponding author. Neutron Beam Application, Korea Atomic Energy Research Institute, 150 Duckjin-Dong, YusungKu, Daejon, Republic of Korea 305-600. Tel.:+82 42 868 8437; fax:+82 42 868 8448. E-mail address: [email protected] (M.-K. Moon). 1 Invited researcher from INP, Uzbekistan.

1. Introduction With the neutron diffraction method components of strain are obtained from the lattice spacing dhkl between the crystallographic planes

0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.337

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(hkl), which are determined using the Bragg equation, 2dhkl sin yhkl ¼ l; from measurements of the angular position of the diffracted peak, 2yhkl : For a monochromatic neutron beam with wavelength l; a small change Dd will result in a change Dy in the angular position y of the Bragg reflection so that the lattice strain  in the direction of the scattering vector is given by  ¼ ðd2d 0 Þ=d 0 ¼ ðy  y0 Þ cot y0 ; where d0 is the lattice spacing of a ‘‘stress free’’ sample of the same material composition and 2y0 is the corresponding diffraction angle (indices hkl are omitted for simplicity). Two slits in cadmium masks installed in the incident and diffracted beam define a sampling volume (gauge volume) in the center of the diffractometer. A large sample may be moved through the gauge volume to measure strain distribution. In general, to define the strain tensor at a point, measurements in six directions are required. However, when the principal directions are known, three directions will suffice. To measure the principal strains x ; y ; z in the coordinate directions x, y, z the sample must be rotated about the center of the gauge volume. For an isotropic material with a Young’s modulus E and Poisson’s ratio n, the principal stresses sx ; sy ; sz ; are obtained from: sx ¼ E½ð1  nÞx þ nðy þ z Þ=ð1 þ nÞð1  2nÞ sy ¼ E½ð1  nÞy þ nðx þ z Þ=ð1 þ nÞð1  2nÞ sz ¼ E½ð1  nÞz þ nðx þ y Þ=ð1 þ nÞð1  2nÞ. The main advantage of the neutron diffraction method for the residual strain/stress (RS) measurement is the possibility of measuring nondestructively the RS distribution within the bulk of materials. Available depth and spatial resolution are limited because, even at high flux neutron sources, the neutron flux is insufficient and measurement time is long. Optimization of RS measurements, including optimization of instrument components can shorten the measurement time and extend the achievable depth or increase spatial resolution. For RS measurements the diffraction/detector angle, 2yD ; in the vicinity of 901 is optimal for definition of the gauge volume, because such

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geometry provides good spatial resolution and minimal variation of the gauge volume when a sample is reoriented to measure different strain components [1–4]. At 2yD ¼ 901 the diffraction cone becomes a plane and a position-sensitive detector (PSD), possibly with a high active area, increases the intensity without worsening the spatial and angular resolution [3]. However, a higher active area increases the uncertainty of the direction of the measured strain since the PSD subtends a larger vertical angle. A PSD with 100 mm high active window [5] designed for the previous RS instrument at the HANARO reactor increased the counting rate about 4 times in comparison with a 25 mm high PSD [6]. Bent perfect crystal (BPC) Si monochromators are advantageous for RS instruments as they provide gain both in intensity and resolution [7–10]. The crystal curvature in the horizontal plane can be adjusted for obtaining maximum intensity and resolution of the diffracted peak at 901. In previous studies [11–12], we showed that for a RS instrument with variable scattering angle monochromator, 2yM , the (2 2 0) reflecting planes in symmetrical diffraction (SD) geometry is one of the best choices for obtaining monochromatic neutrons in the range l ¼ 1:4–1.9 A˚, which is sufficient for RS measurements in most materials. The (2 2 0) planes of a Si crystal have an advantage over other possible planes with smaller d-spacing because for the same wavelength the reflectivity increases for smaller 2yM ; although the diffracted peak at 2yD 901 becomes slightly broader. Furthermore, the (2 2 0) planes have a larger structure factor and reflect the higher-order neutrons, which increases the reflected intensity. In an instrument with tunable monochromator angle the RS can be measured using different diffraction reflections hkl from materials by setting 2yM ; i.e. l; so that the 2yD of the chosen reflection is close to 901. However, for mosaic crystal monochromator, the angle 2yM should be set close to 901 to obtain high resolution at 2yD ¼ 901 (focusing condition) [13]. Therefore, only one or two reflections could have resolution acceptable for RS measurements. In case of a bent perfect crystal monochromator the number of such reflections is greater because by adjusting the

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crystal curvature high resolution can be obtained for 2yM ; considerably less (451) than 901 [12]. Resolution and intensity of a particular diffraction peak depends on many factors, including the neutron spectrum from the reactor, making it difficult to calculate them accurately. Therefore, optimal reflection(s) for RS measurements could be chosen experimentally. A new RS instrument with a tunable monochromator was installed recently on beam port ST1 of HANARO reactor. In order to decrease data collection times it was equipped with an upgraded 200 mm high PSD-2 and with a bent perfect crystal Si(2 2 0) monochromator instead of the 100 mm high PSD-1 used in our previous instrument [6], which shared a mosaic Ge(3 3 1) monochromator and the sample table with the high-resolution powder diffractometer (HRPD) on beam port ST-2. The aims of this work were: to test the performance of the new instrument by measuring the RS distribution in a standard aluminum VAMAS round robin sample; to experimentally choose the optimal diffraction reflections of austenitic and ferritic steels, aluminum- and nickel-based alloys for RS measurements using the Si(2 2 0) monochromator and to test the capability of the instrument for strain measurements deep inside ferritic and austenitic steels.

2. Description of the instrument A schematic diagram depicting the new RS instrument at beam port ST-1 is shown in Fig. 1. The monochromator unit consists of a bending device and a Si(2 2 0) crystal. It is installed in the monochromator drum with variable take-off angle in the range: 2yM ¼ 02601: The sample table and the PSD unit are installed on air cushions which are arranged such that 2yM ; LMS ; (monochromator to sample distance) and LSD, (sample to detector distance) are variable. The reactor core to monochromator distance is 6.2 m. An aperture 40(w) 70(h) mm2 at 150 mm from the drum center defines the beam impinging on the monochromator. The minimum possible monochromator to sample distance, LMS ¼ 2 m; was used as it

Fig. 1. Schematic diagram of the RS instrument on beam port ST-1 of the HANARO reactor.

substantially increases the intensity of neutrons [12]. A convergent beam limiter, with a 60(w) 50(h) mm2 input and a 20(w) 50(h) mm2 exit window, is installed between the monochromator and the sample to decrease the background. The sample to detector distance LSD ¼ 1:2 m was chosen in order to provide sufficient distance for collimation before the PSD. X–Y–Z linear translators are mounted on the sample table for automated sample positioning. The control program allows setting of the measurement time for each point of a strain scan. Slits in cadmium masks (Fig. 1) define the beam impinging on the sample (Incident Slit) and beam diffracted from the sample and counted in the detector (Detector Slit), which together define the gauge volume. The PSD-2 which has a delay line type readout and increased height of active window (200(h) 100(w) mm2), like the PSD-1 [5], was designed specifically for the RS instrument. Its ( is increased at the efficiency (60% for l ¼ 1:8 A) expense of slightly worsened spatial resolution (2.5 mm) to increase the count rate. Sample to

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detector distance LSD ¼ 1:2 m was chosen because for 2.5 mm spatial resolution of the PSD and a typical horizontal slit width of 2 mm a high enough equivalent distance collimation before PSD (a3 ¼ 100 ) is achieved. We defined as acceptable a 751 uncertainty in the direction of the measured strain. Hence the 200 mm height of the PSD-2 is optimal as at LSD ¼ 1:2 m it accepts a 101 vertical angle. Thanks to the delay line type readout the number of PSD channels is variable. The channel number is determined by the time resolution of the TDC (Time to Digital Converter) and the total delay time of the detector. Since the total delay time of the detector is 144 ns and time resolution of the TDC is 0.25 ns, the number of channels of the detector is 576. This gives an angular acceptance for each channel of 0.008261 since the detector covers 4.76361. Therefore, the number of points in a peak diffracted from the gauge volume is quite sufficient for fitting to a Gaussian profile. Measuring a diffraction peak at 2yD 901 showed that for the PSD-2 the integrated intensity of the peak, I, is about 2 times (in proportion to the height) higher than for the PSD-1, while the full-width at halfmaximum, W, is practically the same. A four-point type bending device developed in NPI, Rez. [14], was used for cylindrical bending of a perfect Si crystal slabs up to the thickness of 5 mm. A slab is attached to a pair of two fixed rods (Fig. 2), the distance between which (120 mm) is less than length (l200 mm) of the slab. The bending is achieved by forcing at the ends of the slab by a moveable second pair of rods. Force of a remotely controlled stepping motor is transmitted to the moveable rods via a screw with differential threading and levers. The bending radius is calculated from the displacement, u, of the center of the slab, which is measured using a micrometer. After calibration u versus motor steps the curvature is tuned remotely to achieve optimal intensity and resolution for a particular diffraction peak. A 200(l) 40(h) 3.5(t) mm3 slab with (2 2 0) reflecting planes parallel to the slab surface (SD geometry) was used as a monochromator. The SD geometry is preferable for a RS instrument; though for this geometry the intensity and resolution of the diffracted peak strongly depends on

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crystal curvature, and adjustment of curvature should be made if 2yM or 2yS is changed [11–12]. Using the 3.5 mm thick slab the optimal curvatures (1=R ¼ 0:1220:16 m1 ) of crystal are safely available as they are well below the breaking limit (1=R0:2 m1 ) for a 3.5 mm thick Si crystal. Thanks to the small vertical size (40 mm) of the crystal the vertical divergence of the beam impinging on a gauge volume is comparatively small (70.51). Therefore, the size of penumbra is small and the vertical size of the gauge volume is well defined without additional vertical collimation [15]. The performance of the Si(2 2 0) monochromator was compared with the performance of the Ge(3 3 1) monochromator on the beam port ST-2 by measuring the same standard aluminum VAMAS sample with the same slit system. To exclude the effect of the PSD when comparing the monochromators, the measurements on beam port ST-2 were made with the same PSD-2. The 200 mm high Ge(3 3 1) monochromator is composed from 9 flat slabs for vertical focusing [6]. Each slab (ZE120 ) consists of plastically deformed Ge(3 3 1) wafers. Our earlier experiments showed that from the available take-off angles (2yM ¼ 451, 601, 901, 1201) and collimations (a1 ¼ 60 , 100 , 200 , 300 , open; a2 ¼ 300 , open), the take-off angle ( a ¼ 200 and a ¼ open 2yM ¼ 901ðl ¼ 1:834 AÞ; 1 2 (distant collimation 300 ) are optimal for RS measurements. For such a set-up a resolution curve of the HRPD (W versus 2yD ) has a minimum at 2yD 701. All experiments described bellow were carried out at a reactor power of 24 MW.

3. Experiment 3.1. Resolution function and stability The resolution function depends on monochromator angle (2yM ), bending radius (R), sample diameter (dS), monochromator to sample (LMS) and sample to detector (LSD) distance. Fig. 3 shows the resolution curves of the instrument for ( the monochromator angle 2yM ¼ 561ðl ¼ 1:8 AÞ; LMS ¼ 2; 000 m; LSD ¼ 1200 mm and d S ¼ 2 mm:

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Fixed rods

Silicon slab

Movable rods Fig. 2. Schematic of bending device, developed in NPI, Rez [14].

80

R 8.2m 7.5m 6.9m 6.4m 6.0m

FWHM [min. of arc]

70 60 50 40 30 20 10 50

60

70

80

90

100

110

120

o

2θ( ) Fig. 3. Resolution curves of the RS instrument with Si(2 2 0) ( monochromator (2yM ¼ 561; l ¼ 1:8 A).

Diffraction peaks from austenite and ferrite pins (2 mm), annealed to decrease residual stresses, were measured for different bending radii. A minimum width (W150 ) for the (2 2 0) reflection from austenite at 2yD ¼ 89:91 as obtained at R ¼ 6:9 m: For constant bending radius the peak width drastically changes with diffraction angle. Therefore, this geometry is not appropriate for powder diffraction, where a full diffraction pattern is measured, but it is appropriate for RS measurements where only one diffraction peak (preferably at 901) is measured. All parameters could be optimized to obtain maximal intensity and resolution for this particular peak [11,12]. It should be

noted that for a 200 mm high PSD the asymmetry effect due to the curvature of a diffraction cone deteriorates the resolution at diffraction angles different from 901. The position of the diffraction peak may change with time because of instability of wavelength and electronics. In order to estimate such instability, the same diffraction peak (2 2 0) of the austenite steel pin (2 mm) was measured for 50 h with 1 h time slices. Statistical error (from fitting) of the peak position for a 1 h exposure was 70.00041. The difference between two consecutive measured peaks positions was less than 70.00041. Smooth variation of peak position with time was observed. The maximum difference in peak position during 50 h measurement was much larger (70.0041) than statistical error. The shift of peak position was not regular with time. Therefore, the instability of peak position, which was also observed for the Ge monochromator, is not associated with an instability of the bending mechanism but with an instability of the electronics. Accuracy in peak shift, (y02y), rather than accuracy in absolute value of diffraction angles, y0 and y; defines accuracy of strain measurements. Therefore in case of long-time strain measurements the error, caused by instability of electronics can be easily eliminated or decreased by monitoring measurements of y0 : Usually, accuracy of peak position D2y ¼ 0:0061ð50mÞ is quite acceptable for strain/stress measurements and the error is mainly associated with statistical error.

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3.2. Aluminum VAMAS round robin sample The aluminum VAMAS (Versailles Project on Advanced Material and Standards) standard round robin sample (Fig. 4) is made from aluminum alloy A17075 and consists of a ring and a plug that had been joined in a way that mutual constraint occurred. The ring (50 mm outer diameter, 25 mm inner diameter and 50 mm height) had been expanded by heating, and plug (25 mm diameter, 50 mm height) had been contracted by cooling in liquid nitrogen. Then the ring was fitted on the plug and the assembly was brought to room temperature. At room temperature both the ring and the plug should have residual stress. From the same aluminum plate which had been used for the ring-and-plug sample another plug of diameter 25 mm and height 50 mm was prepared to measure the scattering angle 2y0 for the stress-free material. Measurement of strain was carried out at 11 points along the radius at the distances from the sample axis R ¼ 0; 2.5, 5, 7.5, 10, 11.25, 13.75, 15, 17.5, 20 and 22.5 mm at a height of 15 mm from the base. At every point the strain was measured in three principle directions: radial, hoop and axial (Fig. 4). An Incident Slit of 1.5(w) 20(h)mm2 at 70 mm from the diffractometer center and a detector Slit of 1.5(w) 30(h)mm2 at 35 mm from a


25

h

j 50


50 Fig. 4. Schematic of VAMAS sample and orientation of radial, hoop and axial strain components.

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the diffractometer center defined the gauge volume (Vg60 mm3). For measurement of the axial component the height of the Incident Slit was decreased to 3 mm (Vg8 mm3). For every strain component the measurement time was set so that the accuracy in peak position from fitting, Dð2yÞ; better than 70.0051 was achieved. The sample showed strong texture, therefore, the radial and hoop components were measured with the more intense (3 1 1) reflection and the axial component with the more intense (2 2 0) reflection as in our earlier experiments [6]. The measurement using the ( (3 1 1) reflection (2y ¼ 531; l ¼ 1:71 A; M

2yS ¼ 89:11) took 4 min for radial and 2 min for hoop components at each point (Fig. 5). In comparison with the Ge(3 3 1) monochromator ( 2y ¼ 97:51) the mea(2yM ¼ 901; l ¼ 1:834 A; D surement time was about 7 times shorter. In Fig. 6. the diffraction peaks (3 1 1) measured for the radial component at the center of the stress-free plug using the Si(2 2 0) and Ge(3 3 1) monochromators are shown for comparison. For the Si(2 2 0) monochromator the integral intensity is 4.5 times higher and the peak is 1.3 times narrower. The scattering angle of the Ge(3 3 1) monochromator was fixed (2yM ¼ 901) and the (3 1 1) peak of aluminum is situated (2yD ¼ 97:51) far from the angle, 2yD ¼ 701; where the HRPD has the minimum of the instrumental width. A 2 min exposure at each point was necessary to measure the hoop component with the (2 2 0) ( 2y ¼ 84:21). reflection (2yM ¼ 601; l ¼ 1:92 A; D This is about 4 times shorter than when using the Ge(3 3 1) monochromator. The gain is less than for radial and hoop components because the scattering angle of the (2 2 0) aluminum reflection with the Ge(3 3 1) monochromator, 2yD ¼ 79:61; is closer to the minimum of the resolution function of HRPD. Thus, using the tunable Si(2 2 0) monochromator all three components could be measured about 6 times faster. Taking into account a two-fold gain in counting rate for the new PSD-2, the measurement time in comparison with our previous instrument with the PSD-1 and Ge(3 3 1) monochromator is shortened about a factor of 12. With the new instrument the intensity of the (3 1 1) reflection was sufficient to measure the axial

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486 50

Xc = 89.151±0.004

Radial R = 0

o

200

o

w = 0.350±0.010 A = 1620±45 counts

Xc= 97.303±0.003

Ge (331) monochr. Al (311)

o

o

w = 0.432±0.006 A = 6523±73 counts

Counts / 3600 sec

Counts / 240 sec

40

30

20

150

100

50

10

0 88.0

88.4

88.8

89.2

89.6

0 96.0

90.0

50 Hoop R = 0

Xc= 89.240±0.004

96.4

96.8

(a)

2 θs

(a)

700

o

97.2

30

20

o

o

w = 0.332±0.003 A = 30691±237 counts

600

Counts / 3600 sec

Counts / 120 sec

40

98.0

Xc= 89.104±0.001

Si(220) monochr. Al (311)

o

w = 0.3140±0.009 A = 1292±37 counts

97.6

2θ s

500 400 300 200

10

0 88.0

(b)

100 0 88.0

88.4

88.8

89.2

89.6

90.0

2θ s

Fig. 5. Al(3 1 1) peak measured in the ring-and-plug sample at R ¼ 0 for (a) radial and (b) hoop components.

component (60 min) and intensity of the (2 2 0) reflection was sufficient to measure the radial (12 min) and hoop (40 min) components. The strain components measured with the (2 2 0) reflection were slightly smaller than those measured with the (3 1 1) reflection (Fig. 7). The difference may be caused by the difference of diffraction elastic constants for the (3 1 1) and

(b)

88.4

88.8

89.2

89.6

90.0

2θ s

Fig. 6. Al(3 1 1) peak measured in the plug at R ¼ 0 for the radial component using (a) the mosaic vertically focusing Ge(3 3 1) and (b) the bent perfect crystal Si(2 2 0) monochromator.

(2 2 0) reflections. Because of strong texture and inter-granular stresses even for the same reflection the diffraction elastic constants become dependent on direction [4]. However, the difference between the stresses derived from the strain components measured with the strong but different reflections ((3 1 1) for radial and hoop component and (2 2 0)

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-100 -200

Strain [µε]

-300 -400 -500 -600 -700 -800

(a) Radial Strains (311) 4 min. (220) 12 min. 0

5

10

15

20

25

Distance from the sample axis [mm]

Fig. 7. Radial strain distribution in the VAMAS sample measured with the (3 1 1) and (2 2 0) Al peaks.

20 10 0

(a) Radial Stresses (311) (311) + (220)

Stress [MPa]

-10 -20 -30 -40 -50 -60 -70 0

5

10

15

20

25

Distance from the sample axis [mm]

Fig. 8. Radial stress distribution calculated using data for the (3 1 1) and the (3 1 1)+(2 2 0) Al peaks.

for axial component) and the stresses derived from the strain components measured with only one (3 1 1) reflection is noticeable but not large (Fig. 8). If one accepts this discrepancy, the measurement using the strong reflections (3 1 1) and (2 2 0) is preferable as it shortens the measurement time about seven times. 3.3. Choice of reflections To avoid the effect of texture the powder samples of 316L stainless steel, ferrite, aluminum and nickel were used to compare different reflec-

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tions for the RS measurements. For a chosen reflection the diffraction angle of the monochromator, and hence the wavelength, was chosen to set the diffraction peak at a 2yD close to 901. The curvature of the Si(2 2 0) monochromator was adjusted to obtain maximum intensity and resolution of the diffracted peak. For these measurements a powder sample in a vanadium can of 12 mm diameter and 50 mm height was positioned at the diffractometer center. 1.5 20 mm2 Incident and 1.5 30 mm2 detector Slits defined the gauge volume. For estimation of different reflections, similar to ref. [11–12], we used the figure of merit, F, defined as F ¼ I/W 2. Austenite and nickel, like aluminum, possess FCC type crystal structure with lattice parameters ( a ¼ 3:524 A; ( a ¼ 4:05 A ( and in aAust ¼ 3:608 A; Ni Al ( ( the the range of wavelength l ¼ 1:4 A21:9 A (2 2 0), (3 1 1), (2 2 2) and (4 0 0) reflections can be obtained at 2yD close to 901. Because of a smaller multiplicity factor, p, the intensity of the (2 2 2)(p ¼ 8) and (4 0 0)(p ¼ 6) reflections are significantly lower than those of the (2 2 0)(p ¼ 12) and (3 1 1)(p ¼ 24) reflections. Furthermore, because of smaller 2yM ; they are broader. Therefore only the (2 2 0) and (3 1 1) reflections are suitable for the RS measurements. From Table 1 one can see that for FCC materials the figure of merit F for the (3 1 1) reflection is higher than for the (2 2 0) reflection, though the difference is not large. The (3 1 1) reflection is preferable also because it has higher multiplicity and consequently the texture would result in minimal perturbations on the intensity of the diffraction peaks. Since in FCC materials the difference between the diffraction elastic constants for the (3 1 1) and (2 2 0) reflections is not large and they are close to the bulk constants [16], both reflections can be used for measurement in textured materials to shorten the measurement time. Ferrite possesses a BCC type crystal structure ( and the (2 0 0), with lattice parameter a ¼ 2:86 A (1 1 2) and (2 2 0) reflections can be obtained at 2yD close to 901. Because of sufficiently lower intensity of the (2 0 0) (p ¼ 6) reflection only the (1 1 2) (p ¼ 24) and (2 2 0) (p ¼ 12) reflections are suitable

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Table 1 Comparison of different diffraction reflections for RS measurements Material (powder)

Reflection

2yM(1)

l(A˚)

2yD(1)

Austenite

311 220

47 56

1.53 1.8

89.4 89.9

Nickel

311 220

46 55

1.5 1.77

Aluminum

311 220

53 60

Ferrite

112 220

51 44

Wmin(arc)

F

8571 3863

22.5 17.6

16.9 12.5

89.8 90.6

12913 6842

21.1 18.6

29 19.8

1.71 1.92

89.1 84.1

1893 946

16 13.8

7.4 4.9

1.65 1.44

90.1 90.6

12227 5393

14.7 18.6

56.6 15.6

0.016 o

89.44

90.1

0.014 o

o

89.9

0.012

89.40

0.010

89.38

0.008

SUS (311) SUS (220) Ferrite (112)

89.36 89.34

0.006 0.004

89.32

0.002 0.000

89.30

3.4. Depth measurements Two 35 mm thick discs of 90 mm diameter were cut from round bar stock of stainless steel SUS 304L and mild steel SS41 and used to estimate the available depth for the instrument. The (3 1 1) and (2 0 0) reflections of austenite and the (1 1 2) reflection of ferrite were used. We did not study texture in the samples. However, measurement of axial and radial strains at the center of the discs, where both components are measured with an equal neutron path length through the material, did not show a substantial difference in peak intensity, though it did in peak position. Therefore, we could assume that the texture in the center of the disc, if any exists, is weak. Depth scanning of axial strains with a 1 mm step along the axial axis at the center of the disc, with a 1 h measurement time at each point, was carried out for both discs. 1.5 20 mm2 Incident and 1.5 30 mm2 Detector slits defined the gauge volume (Vg60 mm2). The depth dependence of

∆ (2θ)

89.42

Peak position [ ]

for the RS measurements. Experiments showed that the (1 1 2) reflection is the best (Table 1). The (1 1 2) reflection is preferable also because it has a higher multiplicity factor and diffraction elastic constants close to the bulk values [17]. From data given in Table 1 one can compare different reflections of the same material but cannot compare different materials because powders could have different residual micro-stresses which broaden diffraction peaks.

I (counts)

10

12

14

16

18

20

Depth [mm]

Fig. 9. Depth dependence of peak position, 2yD ; and error in peak position, Dð2yD Þ; for austenitic and ferritic steel. Actual positions of (1 1 2) and (2 2 0) peaks, shown above the curves, are shifted.

peak position and accuracy is shown in Fig. 9. The accuracy of the peak position deteriorates with depth and is 70.0061(750me) at about 20 mm depth for both materials. It should be noted that in stainless steel for path lengths greater than 30 mm (10 mm depth) the accuracy of measurement with the (2 2 0) reflection is slightly better though experiments with the powder samples showed the advantage of the (3 1 1) reflection. No systematical displacement of the position of diffraction peaks with path length was observed up to 56 mm path length (20 mm depth). It shows the axial residual strains are uniform along the axial direction, which would be expected for the disc cut from a

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round bar stock. The results show also that the effect of wavelength-dependent attenuation on peak position (apparent strain) [18] for the wavelengths used in these experiments (1.53 A˚, 1.8 A˚ for austenite and 1.65 A˚ for ferrite) is negligible.

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optimization of the bent Si perfect crystal monochromators. This work was carried out under the Nuclear R&D Program by the Ministry of Science and Technology of the Republic of Korea.

References 4. Conclusion We have demonstrated a considerable advantage of a BPC Si(2 2 0) monochromator over a mosaic Ge(3 3 1) vertical focusing monochromator for residual stress measurements. It is especially important for an instrument to have a variable monochromator angle as by adjusting the crystal curvature a high intensity and resolution at 2yD 901 could be achieved in wide region of take-off angles, considerably less than 901. An optimized PSD and BPC Si(2 2 0) monochromator in combination with possibility to use an appropriate wavelength resulted in about a tenfold gain in data collection rate. For RS measurements in austenitic steel, aluminum and nickel the (1 1 3) and (2 2 0) reflections are most preferable. If these materials have strong texture then measurement with both reflections could greatly shorten the measurement time without large distortion of the derived stresses. For RS measurements in ferritic steel the (1 1 2) reflection is most appropriate. Strain distribution up to depth of 20 mm (56 mm path length) in austenitic or ferritic steel could be measured in a reasonable time. For the chosen wavelength the effect of wavelength-dependent attenuation on measured strain was found to be negligible.

Acknowledgements The authors thank T.M. Holden for the VAMAS sample and advice in residual stress measurements and P. Mikula for help with the

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