ROMANIAN JOURNAL OF PHYSICS

RESIDUAL STRESS MEASUREMENTS BY NEUTRON DIFFRACTION AT THE IBR-2 PULSED REACTOR G.D. BOKUCHAVA, I.V. PAPUSHKIN, A.V. TAMONOV, A.A. KRUGLOV Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia E-mail: [email protected] Received September 22, 2015 Neutron diffraction is widely used for investigations of residual stresses in various constructional materials and bulk industrial components due to the non-destructive character of the method and high penetration depth of neutrons. Therefore, to study residual stresses, the Fourier stress diffractometer FSD has been constructed at the IBR-2 pulsed reactor (Dubna, Russia). Using a special correlation technique high resolution level of the instrument has been achieved: d/d ≈ 2÷4·10–3. The FSD design satisfies the requirements of high luminosity, high resolution and specific sample environment. In this paper, the design and current status of FSD diffractometer is reported. Key words: neutron diffraction, time-of-flight method, residual stress, microstrain. PACS: 61.05.F-, 07.10.Lw 1. INTRODUCTION

To investigate internal stresses in materials, various non-destructive methods, including X-ray diffraction, ultrasonic scanning, a variety of magnetic methods (based on the measurement of magnetic induction, penetrability, anisotropy, Barkhausen effect, magnetoacoustic effects) have been used for many years. All of them, however, are of limited application. For example, X-ray scattering and magnetic methods can be only used to investigate stresses near surfaces because of their low penetration depth. Besides, the application of magnetic methods is restricted to ferromagnetic materials. Also, magnetic and ultrasonic methods are greatly influenced by the texture in a sample. The neutron diffraction method of mechanical stress investigations appeared about 20 years ago. Since then it has been widely used because of a number of advantages. In contrast to traditional methods, neutrons can non-destructively penetrate into the material to a depth of up to 2–3 cm in steel and up to 5 cm in aluminum. For multiphase materials (composites, reinforced materials, ceramics, alloys) neutrons give separate information about each phase. Internal stresses in materials cause deformation of the crystalline lattice leading to Bragg peak shifts in the diffraction spectrum. Therefore neutron diffraction can be used for non-destructive stress evaluation as well as for calibration of other non-destructive techniques. The use of neutron diffraction in combination with the time-of-flight (TOF) method is important because of the possibility to measure mechanical stresses simultaneously for different (hkl) directions in the crystal. Rom. Journ. Phys., Vol. 61, Nos. 3–4, P. 491–505, Bucharest, 2016

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For these reasons experiments for residual stress studies start to occupy a noticeable position in the research programs of leading neutron centers. To conduct such experiments, specialized neutron diffractometers are being constructed. The strain caused by internal stresses is of the order 10-3–10-5 and requires a quite high resolution of the diffractometer, i.e. d/d  0.2–0.3%. A special feature of the neutron experiment to study internal stresses is the scanning of the investigated area in the bulk sample by means of a small scattering (gauge) volume separated using special diaphragms in the incident and scattered neutron beams, which requires a high luminosity of the diffractometer. During last year’s a great number of experiments were performed on IBR-2 reactor in order to approve the method and to define potential application domain. These investigations were conducted using the correlation Fourier technique at the high-flux IBR-2 reactor, which is a long-pulse type source with a pulse width of about 350 µs for thermal neutrons. It was shown that reverse time-of-flight (RTOF) technique is unique method possessing sufficient resolution and luminosity for precise determination of residual strain from relative shifts of diffraction peak as well as for reliable detection of peak broadening with subsequent microstrain calculation. First experiments for residual stress study with neutron diffraction in Dubna arouse vast interest on the side of science and industry. For this reason, the specialized neutron stress diffractometer FSD (Fourier Stress Diffractometer) – optimized for residual stress studies – has been constructed at the IBR-2 pulsed reactor in FLNP JINR.

2. RESIDUAL STRESS MEASUREMENTS BY NEUTRON DIFFRACTION

Diffraction of thermal neutrons is one of the most informative methods when solving many applied engineering and materials science problems, and it has a number of significant advantages as compared to other techniques. The main advantages of the method are deep scanning of the material under study (up to 2 cm for steel) due to high penetration power of the neutrons, non-destructive character of the method, good spatial resolution (up to 1 mm in any dimension), determination of stress distributions for each component of the multiphase material separately (composites, ceramics, alloys, etc.), possibility to study materials microstructure and defects (microstrain, crystallite size, dislocation density, etc.). In combination with TOF technique at pulsed neutron sources, this method allows to record complete diffraction patterns in wide range of interplanar spacing at fixed scattering angle and to analyze polycrystalline materials with complex structures. In addition, with TOF neutron diffraction it is possible to determine crystal lattice

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strains along different [hkl] directions simultaneously, i.e. to investigate mechanical anisotropy of crystalline materials on a microscopic scale. The neutron diffraction method is very similar to the X-ray technique. However, in contrast to the characteristic X-ray radiation the energy spectrum of thermal neutrons has a continuous (Maxwellian distribution) character. The velocity of thermal neutrons is rather small and this gives the opportunity to analyze the neutron energy using it’s time of flight during the experiment at a pulsed neutron source. Depending on the neutron wavelength, the peak position on the time-of-flight scale is defined by the condition t = L/v = mL/h = 2mLdhkl sinθ/h,

(1)

where L is the total flight distance from a neutron source to detector, v is the neutron velocity,  is the neutron wavelength, m is the neutron mass, h is Planck’s constant, dhkl is the interplanar spacing, and θ is the Bragg angle. Internal stresses existing in a material cause corresponding lattice strains, which, in turn, results in shifts of Bragg peaks in the diffraction spectrum. This yields direct information on changes in interplanar spacing in a gauge volume, which can be easily transformed into data on internal stresses, using known elastic constants (Young’s modulus) of a material. The principle of the determination of the lattice strain is based on the Bragg’s law 2dhklsinθ = ,

(2)

where  is the neutron wavelength, dhkl is the interplanar spacing, and θ is the Bragg angle. The essence of the diffraction method for studying stresses is rather simple and, in conventional experimental design, consists of incident and scattered neutron beam shaping using diaphragms and/or radial collimators and definition of a small scattering volume (gauge volume) in the bulk of the specimen (Fig. 1, a) [1]. The incident beam is usually formed using cadmium or boron nitride diaphragms with characteristic sizes from 1–2 mm to several cm depending on the purpose of the experiment. To define a gauge volume of optimum shape in the studied specimen, at the scattered beam radial collimators with many (about several tens) vertical slits formed by Mylar films with gadolinium oxide coating are often used. A radial collimator is placed at a quite large fixed distance (usually 150÷450 mm) from the specimen and provides good spatial resolution of the level of 1–2 mm along the incident neutron beam direction. The lattice strain is measured in the direction parallel to the neutron scattering vector Q. The sample region under study is scanned using the gauge volume by moving the sample in the required directions.

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In this case, relative shifts of diffraction peaks from the positions defined by unit cell parameters of an unstrained material are measured. 0

n





Q1

Detector 2

Detector 1

Q2

Fig. 1 – Scheme of the experiment for residual stress investigation in a bulk object. Incident and scattered (at angles 2θ = ±90°) neutron beams are restricted by diaphragms shaping a gauge volume within the specimen. Measurement of neutron diffraction spectra by ±90° detectors allows simultaneous determination of strains in two mutually perpendicular directions.

On two-axis diffractometer at a neutron source with continuous flux, the strain is determined by the change in the scattering angle –Δθ∙cotθ. When using the TOF method at a pulsed source, the crystal lattice strain is determined by the relative change in the neutron time of flight Δt/t: 0 0 0 0  hkl  (d hkl  d hkl ) / d hkl ) / d hkl   / cot  ,  hkl  (d hkl  d hkl  t / t

(3)

0

where d hkl is the measured interplanar spacing and d hkl is the same interplanar spacing in a stress-free material, and t is the neutron time of flight. The components of the residual stress tensor can be determined from the measured residual strain according to the Hooke’s law:

 ii 

E   ( ii   ( X   Y   Z )) , 1  1  2

(4)

where ii = X, Y, Z, ii and ii are components of the stress and strain tensors, respectively, E is Young’s modulus and ν is Poisson’s ratio. Based on known values of the Young’s modulus, the required interplanar spacing measurement accuracy can be estimated, so that the σ determination error

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would not exceed, e.g., 20 MPa, which is, as a rule, quite sufficient for engineering calculations. For aluminum, Е ≈ 70 GPa, hence, it is sufficient to measure Δa/a0 with an accuracy of 3·10–4; for steel, Е ≈ 200 GPa, and the accuracy should be better than 1·10–4. These requirements appreciably exceed the capability of conventional neutron diffractometers whose resolution, as a rule, is ~1%, i.e., the diffractometer for measuring internal stresses should have high resolution. Existing practice showed that a required accuracy can also be achieved for diffractometers with monochromatic neutron beams, operating at stationary reactors, and for TOF diffractometers operating at pulsed neutron sources. Without going into details of experimental design in these two cases, we only note that a main advantage of the former version is a larger luminosity and, hence, the possibility of sample scanning with good spatial resolution. In the latter case, a fixed and most optimal 90° experimental geometry is easily implemented and, in contrast to the former case, several diffraction peaks are simultaneously measured, which allows analysis of stress anisotropy. An analysis of the shape (width in the simplest case) of diffraction peaks can yield information on lattice distortions in individual grains (microstrain) and their sizes. This is especially convenient to do that using a TOF diffractometer with the functional dependence of the peak width on the interplanar spacing, W2 = C1 + C2 d 2 + C3 d 2 + C4 d 4,

(5)

where W is the peak width, C1 and C2 are the constants defining the diffractometer resolution function and known from measurements with a reference sample, C3 = (a/a)2 is the unit cell parameter dispersion (microstrain), and C4 is the constant related to the crystallite size. The neutron diffractometer TOF resolution in a first approximation is defined by three terms, R = d/d = [(t0/t)2 + (/tg)2 + (L/L)2]1/2,

(6)

where t0 is the neutron pulse width, t = 252.778L is the total time of flight (μs), L is the source–detector flight distance (m), λ is the neutron wavelength (Å), and θ is the Bragg angle. The first term is the time of flight uncertainty, the second term includes all geometrical uncertainties associated with scattering at various angles, and the third term is the uncertainty in the flight path length. The resolution will improve as the Bragg angle approaches 90°, as the pulse width decreases, and as the flight distance increases. For pulsed neutron sources with short fast neutron pulses, the thermal neutron pulse width can be decreased to ~20 μs/Å; as the flight path length increases to 100 m, the resolution can be improved to 0.001 and, if required, to 0.0005. For neutron sources with long pulses, e.g., the IBR-2, such a way to achieve high resolution is a priori unacceptable; the only practical way is the use of the

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reverse time-of-flight (RTOF) method in combination with a Fourier chopper [2], which provides a higher luminosity of experiments in comparison with other correlation techniques. In the RTOF method, the spectrum acquisition is performed at continuous variation of the rotation frequency of the Fourier chopper from zero to a certain maximum frequency ωm. In this case, the time component of the resolution function is defined by the resolution function of the Fourier chopper RC, which depends on a particular frequency distribution g(ω) and can be written as 

t / t0 ~

  g ( ) cos(t )ddω,

(7)

0

where Ω = Nωm is the maximum frequency of neutron beam intensity modulation and N is the number of Fourier chopper slits. At a reasonable choice of g(ω), the full width ∆t0/t at half maximum is -1; at N = 1024 and ωm = 100 kHz, it is ~10 μs. This means that even at a chopper–detector flight distance of ~6.5 m and scattering angle 2θ = 90°, the contribution of the time component to the resolution function can be ∆t0/t ≈ 2·10–3 at d= 2 Å. When using thin detectors, the third term in (6) becomes negligible, and the geometrical contribution can be optimized proceeding from the desirable relation between resolution and intensity. A typical solution is the choice of focusing geometry in the arrangement of detector elements with parameters providing a geometrical contribution equal to the time contribution to the complete resolution function. To increase the luminosity of the TOF diffractometer and decrease the background level, the primary neutron beam is formed using a curved mirror neutron guide. In this case, the neutron spectrum is cut off from the side of short wavelengths due to the neutron guide curvature radius chosen from the condition of the absence of line of sight of the neutron moderator. A calculation shows that, at a total flight path length from the source to the sample of ~20 m and a horizontal cross section of the neutron guide of ≤1cm, the curvature radius can be sufficiently large to pass neutrons up to λ ≈ 1 Å. In this case, the number of simultaneously observed diffraction peaks, even for materials with small unit cell sizes (steel, aluminum), is about ten, which is sufficient to analyze stress anisotropy. Furthermore, a sample place should be specially organized in the diffractometer for measuring internal stresses, i.e., the possibility of installing large and heavy equipment (goniometer, loading machine, etc.). 3. FSD DIFFRACTOMETER AT THE IBR-2 PULSED REACTOR

The basic functional units of the FSD diffractometer are the neutron source – IBR-2 reactor with grooved water moderator – generating thermal neutron pulses ~320 μs long with a frequency of 5 Hz; the long mirror neutron guide purifying the

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beam from fast neutrons and γ-rays; the fast Fourier chopper providing neutron beam intensity modulation; the straight mirror neutron guide shaping the thermal neutron beam on the sample; the detector system consisting of detectors at scattering angles of ±90° and a backscattering detector; a mechanical system, including a stage for placing goniometric and loading machines and a collimation devices setting primary beam divergence and separating the gauge volume in the sample; and data acquisition electronics including a RTOF analyzer (Fig. 2a) [3, 4, 5]. The FSD diffractometer automation system [6] allows local or remote control of experiment. IBR-2

Slit width 0.7 mm

FSD

Fourier Stress Diffractometer

Stator Rotor 0,184

FLNP 3,400

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5,500 VME control and operative visualization/analysis

"ISOMER" Instrument

VME

VME Station (OS/9) Data Acquisition

Transmission function

EtherNet Data Transfer

Moderator

Binary signals

Ni Guide Tube Detectors Fourier Chopper

a)

Full Circle Goniometer

b)

Fig. 2 – a) Layout of FSD diffractometer (Fourier Stress Diffractometer) at the IBR-2 pulsed reactor (FLNP JINR, Dubna). b) Design of the Fourier chopper, consisting of a rotating rotor and a stationary stator. Outer circumference of the rotor disk is a system of interleaving slits transparent and opaque for thermal neutrons. The diagram below shows a saw tooth function of transmission of such chopper system and its approximating sequence of positive and negative binary (pick-up) signals.

Mirror neutron guide. The neutron beam on the sample is formed by the mirror neutron guide made of high-quality borated (14% boron) K8 glass 19 mm thick with a Ni coating. The neutron guide consists of two parts: one 19 m long is bent with curvature radius R = 2864.8 m; the other is straight and 5.01 m long. The neutron guide is cone-shaped in the vertical plane with cross sections: of 10155 mm at the curved part input, 1091.8 mm at the curved part output and at the straight part input, and 1075 mm at the straight part output. At the Fourier chopper removed from the beam, the total thermal neutron flux at the sample position is 1.8106 neutron/cm2s–1; it decreases to 3.7105 neutron/cm2s–1 due to a finite transmittance of the Fourier chopper. Fourier chopper. The Fourier chopper consists of a rotor disk 540 mm in diameter, installed on the motor axis, and a stator plate fixed on the stage (Fig. 2b). The disk and plate are made of high-strength aluminum alloy. At disk periphery, on

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the radius of 229 mm, there are 1024 radial slits 60 mm long and 0.7026 mm wide, filled with a Gd2O3 layer 0.8 mm thick. Similar slits are made on the stator plate. The chopper is rotated by an M2AA 132SB-2 asynchronous bipolar motor (ABB Motors, Sweden) with a power of 7.5 kW. An incremental magnetic encoder GEL208 (Lenord+Bauer and Co. GmbH, Germany) is fixed on the motor axis for measuring the disk velocity and acceleration and for generating a pick-up signal coming to the RTOF analyzer. The motor is supplied by a VECTOR VBE750 (Control Techniques, UK) control drive with a built-in microcomputer to which information on the disk velocity and acceleration comes (Fig. 3).

Fig. 3 – 3D model of the Fourier stress diffractometer FSD at the IBR-2 reactor (FLNP JINR, Dubna). The basic functional units of the FSD are the long mirror neutron guide with variable diaphragms, the fast Fourier chopper, the detector system consisting of ±90°-detectors with radial collimators and a backscattering detector, HUBER goniometer at the sample position, auxiliary equipment (furnaces, loading machines, etc.), specialised data acquisition electronics including RTOF analysers.

Detector system. In developing the detector system of the diffractometer for measuring internal stresses, two mutually exclusive requirements should be satisfied: the solid angle of the detector system should be large enough to acquire statistics from a small sample volume for a reasonable time; and the contribution of the detector system to the geometrical component of the resolution function should not exceed the time component to retain high resolution. There are two well-known versions of such a type of detectors used in TOF diffractometers: position-sensitive systems and detectors designed by the principle of geometrical time focusing during diffraction. However, the need to use the correlation principle of data recording in Fourier diffractometry almost excludes

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the possibility of using the position detector in this method. On the contrary, as for time focusing, it is successfully used in all operating Fourier diffractometers. A disadvantage of this method is a significant disproportion of the effective solid angle of the detector with its actual geometrical sizes. Progress in the development of relatively low-cost correlation electronics based on digital signal processors made it possible to propose a new principle of the development of the FSD detector system, namely, the multi-element detector with combined electronic and geometrical focusing [7]. The schematic representation of such a detector, called the ASTRA, is shown in (Fig. 4a). Each detector element is a counter based on an ND (Applied Scintillation Technologies Ltd., UK) scintillation screen with a sensitive layer thickness of 0.42 mm and several hundred square centimeters in area. The scintillation screen consists of a powder mixture of 6LiF crystals (nuclear active additive) and ZnS(Ag) (scintillator) fixed in a Plexiglas optical matrix. The screen flexibility allows approximation of the time focusing surface by conical surface portions with required accuracy. Such an approximation method excludes dead areas on the sensitive layer and increases the geometrical focusing quality. The detector efficiency is mostly defined by the 6Li concentration in the screen and is ~60%.

a)

b)

Fig. 4 – a) Multielement 90°-detector ASTRA assembled from seven ZnS(Ag) scintillation elements. In front of the detector, a radial collimator is placed for gauge volume selection in a bulk sample. b) Detector system of FSD diffractometer.

In the final version (Fig. 4b), the FSD detector system will consist of two ASTRA detectors at scattering angles 2θ = ±90°; each detector includes seven independent ones, i.e., with independent outputs of electronic signals of elements [8]. The combined use of electronic and time focusing of the scattered neutron beam allows an increase in the solid angle to ~0.16 sr for each ASTRA detector. This sharply increases the instrument luminosity while retaining high resolution for

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the interplanar spacing of Δd/d ≈ 4·10–3. Currently, six elements (among 14 planned) of ASTRA detectors are installed and being tested on the FSD at scattering angles of +90°and –90°. Furthermore, the backscattering detector with time focusing, called the BS (backscattering), consisting of 16 scintillation 6Li elements at the scattering angle 2θ = 140°, is installed on the FSD. Electronic focusing method. An algorithm and software were developed for electronic focusing of multi-module ASTRA detectors. This method implies the use of scale coefficients for each measured TOF spectrum (Fig. 5a), ki = Lisin(i) / L0sin(0),

(8)

where L is the flight path length and θi and θ0 are the scattering angles for the i-th and basic detectors, respectively. Then the spectra reduced to a unified scale are summed. The diffraction spectrum summed in such a way is characterized by almost the same resolution as the spectra from individual modules of ASTRA detectors (Fig. 5b). Due to summation, a multiple increase in the intensity of the final diffraction spectrum is achieved. 5

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1x10

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a)

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500

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b)

Fig. 5 – a) Diffraction spectra from individual elements of the ASTRA detector. b) Diffraction spectra from individual elements of the ASTRA detector, reduced to a unified TOF scale and the final total spectrum.

Gauge volume definition with radial collimator. To form the incident neutron beam, a diaphragm (Huber GmbH, Germany) with a variable aperture (0÷10 mm for width and 0÷24 mm for height) was installed on the FSD neutron guide end. The motion of the diaphragm is provided by precision step motors. At present the scattered neutron beam is formed using a composite multislit radial collimator [5]. It allows definition of the gauge volume (gauge volume) in the sample under study. The radial collimator is assembled from four independent modules with apertures of 7° and 10°, arranged on a supporting alignment frame.

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Each module consists of Mylar films coated with gadolinium oxide with a total thickness of ~50 μm. The spatial arrangement of collimator modules corresponds to positions of individual elements of ASTRA detectors. The performed experiments showed that the radial collimator provides a spatial resolution of ~2 mm and precisely forms a required gauge volume within the sample under study. However, essential drawback of this system is difficulty of its adjustment and insufficient transmission. In order to improve gauge volume definition recently a new wide-aperture radial collimator with spatial resolution of 1.8 mm and acceptance angle of ±20 ° was designed and is being manufactured at the present time (Fig. 6a). This collimator is a single module with an improved neutron transmission capacity (Fig. 6b). It is expected that such a wide-aperture radial collimator will possess higher transmission function and ease of alignment.

Transmission Distribution

a)

b)

Fig. 6 – a) Design of new wide-aperture radial collimator with spatial resolution of 1.8 mm and acceptance angle of ±20 °. b) Calculated transmission map for the new wide-aperture radial collimator.

Using neutron scanning, the gauge volume position can be easily determined with respect to the sample surface; then its position in the sample bulk can be accurately positioned in further strain measurements as well. The neutron scanning method consists in the plotting of the dependence of the intensity of material diffraction peaks on the gauge volume position center. The sample is sequentially displaced so that the gauge volume is gradually immersed into the sample (Fig. 7a). The initial point in the plot corresponds to the gauge volume position outside the sample; in this case, the diffraction peak intensity is zero (there is no diffraction on the sample). Then the gauge volume gradually enters the sample, hence, the diffraction peak intensity, which is proportional to the scattering material volume,

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begins to increase. The point of the maximum in the plot approximately corresponds to the position at which the gauge volume is completely immersed into the sample. During further motion to the sample depth, the scattering material volume remains unchanged; however, neutron absorption in a material begin to appear, and the intensity begins to slowly decrease according to the exponential dependence (9) I  I 0 exp( D) , where μ is the material attenuation cofficient and D is the total neutron path in the sample. Thus, neutron scanning allows the determination of the gauge volume in the sample with high enough accuracy (~0.1 mm). Sample environment. Available supplementary equipment integrated into the experiment control system makes it possible to provide various conditions (load, temperature, etc.) at the sample. It includes a four axis (X, Y, Z, Ω) HUBER goniometer (Fig. 7b) for positioning the sample with an accuracy better than ~0.1 mm and with the maximal carrying capacity of 300 kg; an LM-20 loading machine (Fig. 8a) with a maximal load of 20 kN and maximal temperature of 800 °C for uniaxial tension/compression of samples in the neutron beam (the main advantage of this machine is almost slack-free load transfer to the sample; samples 30– 100 mm long with a screwed cylindrical head can be studied; and the sample elongation is measured by a mechanical strain gage); and an MF2000 water-cooled mirror furnace (Fig. 8b) based of halogen lamps with a maximal temperature of 1000°С and with temperature control by an Euroterm controller.

7500

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Region 1

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Fig. 7 – a) Sample surface scan using the radial collimator: diffraction peak intensity vs. gauge volume position in the material depth. b) Sample place at FSD: end part of the neutron guide with incident beam diaphragm, 4-axis HUBER goniometer (max. capacity 300 kg) and multi-sectional radial collimator are visible.

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Fig. 8 – a) Uniaxial mechanical loading machine LM-20 (Fmax = 20 kN, Tmax = 800°C). b) Water-cooled mirror furnace (P = 1 kW, Tmax = 1000°C).

4. INSTRUMENT PERFORMANCE

To study main characteristics of the FSD diffractometer, a number of test experiments were performed to estimate the instrument resolution, sensitivity to the spatial distribution of strains, and the possibility of studying typical structural materials under external loads. The spectral distribution of the incident neutron beam intensity on the FSD allows efficient operation at λ ≥ 1 Å. This makes it possible to measure diffraction spectra in the ranges dhkl = 0.63÷6.71 Å at 2θ = 90° and dhkl = 0.51÷5.39 Å at 2θ = 140°, which is an optimum range for most structural materials used in industry. The typical high resolution diffraction spectra measured on the α-Fe reference sample at a maximum rotation speed of the Fourier chopper Vmax = 6000 rpm is shown in (Fig. 9). An analysis of the diffractometer resolution function showed that FSD detectors indeed have a necessary resolution level in the interplanar spacing: Δd/d ≈ 2.310–3 for the backscattering detector BS and Δd/d ≈ 410–3 for both ASTRA detectors at a maximum rotation rate of the Fourier chopper Vmax = 6000 rpm (Fig. 10). Furthermore, the dependence of the shape of an individual diffraction peak on the maximum speed of the Fourier chopper and resolution function for all detectors were investigated (Fig. 10). According to expectations, the effective neutron pulse width decreases as 1/Vmax, reaching a minimum of ~10 μs. Thus, the diffractometer parameters can be optimized proceeding from a required accuracy of the determination of the diffraction peak position and from a scheduled beam time.

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Fig. 9 – Neutron diffraction patterns measured from -Fe standard sample using BS (left) and 90°– detector ASTRA (right) at the maximal Fourier chopper speed Vmax = 6000 rpm. Shown are the measured data points, full profile calculated by Rietveld method [9] and the difference curve.

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Fig. 10 – a) Diffraction peak shape dependence vs. maximal Fourier chopper speed Vmax. b) FSD resolution function measured on -Fe powder at maximal Fourier chopper speed Vmax = 6000 rpm for backscattering detector (2θ = 140) and both ASTRA detectors (2θ = ±90).

5. CONCLUSIONS

The experiments demonstrated that the FSD performance parameters correspond to the expected ones. Achieved resolution level of the instrument is suitable for residual stress investigations in most constructional materials with required accuracy of 20–30 MPa. Available auxiliary equipment (loading machine, mirror furnace, Huber goniometer, etc.) make it possible to vary experimental conditions in a wide range. At present the regular experiments for residual stress and microstrain studies in bulk industrial components [10, 11] and in new

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advanced materials [12] are successfully performed on FSD diffractometer. The future plans of the FSD development include further improvement of the detector system, electronics, and software. Acknowledgements. This work was partially supported by the Romania-JINR Programme 2014-2015, by the Russian Foundation for Basic Research (RFBR) within the project No. 15-0806418_a and jointly by RFBR and the Moscow Region Government within the project No. 14-4203585_r_center_a.

REFERENCES 1. A.J. Allen, M.T. Hutchings, C.G. Windsor, Adv. in Physics, 34(4), 445-473 (1985). 2. P. Hiismäki, H. Pöyry, A. Tiitta, J. Appl. Cryst., 21, 349-354 (1988). 3. G.D. Bokuchava, V.L. Aksenov, A.M. Balagurov, V.V. Zhuravlev, E.S. Kuzmin, A.P. Bulkin, V.A. Kudryashev, V.A. Trounov, Appl. Phys. A: Mater. Sci. & Proc., 74[Suppl1], s86-s88 (2002). 4. A.M. Balagurov, G.D. Bokuchava, E.S. Kuzmin, A.V. Tamonov, V.V. Zhuk, Zeitschrift für Kristallographie, Suppl. Issue 23, 217-222 (2006). 5. G.D. Bokuchava, A.M. Balagurov, V.V. Sumin, I.V. Papushkin, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 4(6), 879-890 (2010). 6. A.A. Bogdzel, G.D. Bokuchava, V.A. Butenko, V.A. Drozdov, V.V. Zhuravlev, E.S. Kuzmin, F.V. Levchanovskii, A.V. Pole, V.I. Prikhodko, A.P. Sirotin, JINR preprint P10-2004-21 (2004). 7. V.A. Kudryashev, V.A. Trounov, V.G. Mouratov, Physica B, 234-236, 1138-1140 (1997). 8. E.S. Kuzmin, A.M. Balagurov, G.D. Bokuchava, V.V. Zhuk, V.A. Kudryashev, J. of Neutron Research, 10(1), 31-41 (2002). 9. H.M. Rietveld, J. Appl. Cryst., 2, 65-71 (1969). 10. G. Bokuchava, I. Papushkin, P. Petrov, Comptes rendus de l'Académie bulgare des Sciences (ISSN 1310-1331), 67(6), 763-768, (2014). 11. G.D. Bokuchava, R.N. Vasin, I.V. Papushkin, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 9(3), 425–435 (2015). 12. G.D. Bokuchava, I.V. Papushkin, V.I. Bobrovskii, N.V. Kataeva, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 9(1), 44-52 (2015).

[1] [2] [3]

[4] [5] [6]

[7]

A.J. Allen, M.T. Hutchings, C.G. Windsor, Adv. in Physics, 34(4), 445-473 (1985). P. Hiismäki, H. Pöyry, A. Tiitta, J. Appl. Cryst., 21, 349-354 (1988). G.D. Bokuchava, V.L. Aksenov, A.M. Balagurov, V.V. Zhuravlev, E.S. Kuzmin, A.P. Bulkin, V.A. Kudryashev, V.A. Trounov, Appl. Phys. A: Mater. Sci. & Proc., 74[Suppl1], s86-s88 (2002). A.M. Balagurov, G.D. Bokuchava, E.S. Kuzmin, A.V. Tamonov, V.V. Zhuk, Zeitschrift für Kristallographie, Suppl. Issue 23, 217-222 (2006). G.D. Bokuchava, A.M. Balagurov, V.V. Sumin, I.V. Papushkin, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 4(6), 879-890 (2010). A.A. Bogdzel, G.D. Bokuchava, V.A. Butenko, V.A. Drozdov, V.V. Zhuravlev, E.S. Kuzmin, F.V. Levchanovskii, A.V. Pole, V.I. Prikhodko, A.P. Sirotin, JINR preprint P10-2004-21 (2004). V.A. Kudryashev, V.A. Trounov, V.G. Mouratov, Physica B, 234-236, 1138-1140 (1997).