crystals Article
Neutron RTOF Stress Diffractometer FSD at the IBR-2 Pulsed Reactor Gizo Bokuchava
ID
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Joliot-Curie Str. 6, 141980 Dubna, Russia;
[email protected] Received: 18 July 2018; Accepted: 6 August 2018; Published: 9 August 2018
Abstract: The diffraction of thermal neutrons is a powerful tool for investigations of residual stresses in various structural materials and bulk industrial products due to the non-destructive character of the method and high penetration depth of neutrons. Therefore, for conducting experiments in this research field, the neutron Fourier stress diffractometer FSD has been constructed at the IBR-2 pulsed reactor in FLNP JINR (Dubna, Russia). Using a special correlation technique at the long-pulse neutron source, a high resolution level of the instrument has been achieved (∆d/d ≈ 2 ÷ 4 × 10−3 ) over a wide range of interplanar spacing dhkl at a relatively short flight distance between the chopper and sample position (L = 5.55 m). The FSD design satisfies the requirements of a high luminosity, high resolution, and specific sample environment. In this paper, the current status of the FSD diffractometer is reported and examples of performed experiments are given. Keywords: neutron diffraction; reverse time-of-flight (RTOF) method; residual stress; microstrain; crystallite size
1. Introduction To investigate internal stresses in materials, various non-destructive methods, including X-ray diffraction, ultrasonic scanning, and a variety of magnetic methods (based on the measurement of magnetic induction, penetrability, anisotropy, Barkhausen effect, and 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 due to their low penetration depth. Besides, the application of magnetic methods is restricted to ferromagnetic materials. In addition, magnetic and ultrasonic methods are greatly influenced by the texture in a sample. The method of mechanical stress investigations by neutron diffraction appeared about 35 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, and 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 the calibration of other non-destructive techniques. For these reasons, experiments for residual stress studies started to occupy a noticeable position in the research programs of leading neutron centers. To conduct such experiments, specialized neutron diffractometers were developed at both steady state reactors (e.g., ILL (Grenoble, France), Chalk River (Ontario, Canada), and HZB (Berlin, Germany)) and pulsed neutron sources (e.g., Los Alamos (Santa Fe, New Mexico, USA), ISIS (Didcot, UK), and J-PARC (Ibaraki, Japan)). 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 feature of the neutron experiment for internal stress study is the scanning of the Crystals 2018, 8, 318; doi:10.3390/cryst8080318
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investigated region in a bulk sample by means of a small scattering (gauge) volume, which requires a high luminosity of the diffractometer. The original idea of using the Fourier chopper for neutron beam intensity modulation in diffraction experiments was suggested in 1969 [1,2], which was later realized in neutron experiments with a single crystal [3,4]. These attempts were rather unsuccessful due to the insufficient accuracy and stability of the chopper rotation. In 1975, a new correlation method for detecting scattered neutrons, reverse time-of-flight (RTOF), was proposed [5] and successfully realized on the first RTOF Fourier diffractometer ASTACUS [6] at the FiR-1 250 kW TRIGA-reactor in the VTT Technical Research Centre (Espoo, Finland). This achievement stimulated the construction of two more Fourier diffractometers at steady state reactors: mini-SFINKS for structural investigations in PNPI (Gatchina, Russia) [7] and FSS for residual stress studies in GKSS (Geesthacht, Germany) [8,9]. In 1994, the RTOF method was successfully applied on a long-pulse neutron source, the IBR-2 pulsed reactor in FLNP JINR [10], where a high resolution Fourier diffractometer HRFD for structural studies of polycrystalline materials was designed and constructed [11,12]. Soon afterwards, the first stress experiments by the RTOF diffraction method were performed on an HRFD diffractometer [13–16]. It was shown that the RTOF technique is a unique method possessing a sufficient resolution and luminosity for the precise determination of residual strain from relative shifts of the diffraction peak, as well as for the reliable detection of peak broadening with subsequent microstrain calculation. This work experience made it possible to construct a specialized neutron stress diffractometer, the FSD (Fourier Stress Diffractometer), optimized for residual stress studies [17]. During the last years, a great number of experiments have been performed on the IBR-2 reactor in order to approve the method and to define the potential application domain. 2. Residual Stress Measurements by Neutron Diffraction The diffraction of thermal neutrons is one of the most informative methods when solving actual problems in the field of engineering and materials science, and it has a number of significant advantages 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 the high penetration power of the neutrons, the non-destructive character of the method, the good spatial resolution (up to 1 mm in any dimension), the determination of stress distributions for each component of the multiphase material separately (composites, ceramics, alloys, etc.), and the possibility to study materials’ microstructure and defects (microstrain, crystallite size, dislocation density, etc.). In combination with the TOF (time-of-flight) technique at pulsed neutron sources, this method allows researchers to record complete diffraction patterns in a wide range of interplanar spacing at a fixed scattering angle and to analyze polycrystalline materials with complex structures. In addition, with TOF neutron diffraction, it is possible to determine lattice strains along different [hkl] directions simultaneously, i.e., to investigate the 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 velocities of thermal neutrons are rather small and this gives the opportunity to analyze the energy of neutrons using their flight time during experiments at a pulsed neutron source. Depending on the neutron wavelength, the peak position on the TOF scale is defined by the condition t = L/v = L λ mn /h = 2mn L sin θ dhkl /h = C L sin θ dhkl ,
(1)
where C = 2mn /h, mn is the neutron mass, h is Planck’s constant, L is the total flight distance from a neutron source to the detector, v is the neutron velocity, λ is the neutron wavelength, dhkl is the interplanar spacing, and θ is the Bragg angle. Internal stresses existing in a material cause corresponding lattice strains, which, in turn, result in shifts of Bragg peaks in the diffraction spectrum. This yields direct information on changes in
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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 Bragg’s law: 2dhkl sin θ = λ,
(2)
On a two-axis constant wavelength diffractometer at a neutron source with continuous flux, the strain is determined by the change in the scattering angle: ε hkl = (dhkl − d0hkl )/d0hkl = −∆θ/ cot θ.
(3)
ε hkl = (dhkl − d0hkl )/d0hkl = ∆ t/t,
(4)
ν E · ε ii + · (ε X + ε Y + ε Z ) , σii = 1+ν 1 − 2ν
(5)
When using the TOF method at a pulsed source, the lattice strain is determined by the relative change in the neutron time-of-flight ∆t/t:
where dhkl is the measured interplanar spacing and 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 Hooke’s law:
where ii = X, Y, Z; σii and εii are components of the stress and strain tensors, respectively; E is Young’s modulus; and ν is Poisson’s ratio. The essence of the diffraction method for studying stresses is rather simple and, in a conventional layout of the experiment, consists of incident and scattered neutron beam shaping using diaphragms and/or radial collimators and the definition of a small gauge volume in the bulk of the specimen (Figure 1) [18]. The incident beam is usually formed using diaphragms with typical sizes from 1–2 mm to several cm, depending on the purpose of the experiment. To define a gauge volume of an 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 a 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. In this case, relative shifts of diffraction peaks from the positions defined by unit cell parameters of an unstrained material are measured. Based on known values of the Young’s modulus, the required interplanar spacing measurement accuracy can be estimated, so that the σ determination error does not exceed, e.g., 20 MPa, which is, as a rule, quite sufficient for engineering calculations. For aluminum, E ≈ 70 GPa, hence, it is sufficient to measure ∆a/a0 with an accuracy of 3·× 10–4 ; for steel, E ≈ 200 GPa, and the accuracy should be better than 1 ×·10–4 . These requirements appreciably exceed the capability of conventional neutron diffractometers with a typical resolution level of ~1–2%. Thus, for residual stresses studies, a diffractometer with an order of magnitude better resolution is needed. Existing practice has shown that a required accuracy can be achieved for diffractometers with monochromatic neutron beams, operating at stationary reactors, and for TOF diffractometers operating at pulsed neutron sources [19]. Without going into the details of experiments in these two cases, it should be noted that a main advantage of a constant wavelength instrument is a higher luminosity and, hence, the possibility of sample scanning with a good spatial resolution. In the case of a TOF instrument, 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 the analysis of strain anisotropy.
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Incident beam
-Fe (110)
Q1
Q2
Radial collimator
Detector 2
Detector 1
Radial collimator
0 MPa 20 MPa 100 MPa 200 MPa
Gauge volume
Sample
2.026
2.028
Beam stop
2.030
d, Å (b)
(a)
Figure 1. (a) Experimental layout for residual stress scanning in a bulk object. Incident and scattered Figure 1. (a) Experimental layout for residual stress scanning in a bulk object. Incident and scattered neutron beams are restricted by a diaphragm and radial collimators shaping a gauge volume within neutron beams are restricted by a diaphragm and radial collimators shaping a gauge volume within the specimen; (b) Visualization of diffraction peak (110) shift at stress values of 20, 100, and 200 MPa the specimen; (b) Visualization of diffraction peak (110) shift at stress values of 20, 100, and 200 MPa observed at the diffractometer with a resolution level of R = Δd/d ≈ 0.001 (ferritic steel, E ≈ 200 GPa). observed at the diffractometer with a resolution level of R = ∆d/d ≈ 0.001 (ferritic steel, E ≈ 200 GPa).
d 2, 10-4 Å2
An important possibility for microstructure investigation is an analysis of the width and shape An important possibility forprovide microstructure is microstrain an analysis of thecrystallite width andsize shape of of a diffraction peak, which can data oninvestigation crystal lattice and [20]. a diffraction peak, which can provide data on crystal lattice microstrain and crystallite size [20]. TOF TOF diffractometers at pulsed sources have a good potential for materials’ microstructure diffractometers pulsed have a good potential for materials’ microstructure characterization Crystals 2018, 8,at318 5 of 26 characterization due to sources the simplicity of the functional relationship between the instrument due to the simplicity of the functional relationship between the instrument resolution R(d) and the x FORinterplanar PEER REVIEW spacing dhkl, which is almost independent of dhkl within 5 of 26 a resolutionCrystals R(d) 2018, and7, the fairly interplanar dhkl , which is almost independent of dhklwide within a fairly wide range. In addition, wide range. spacing In addition, TOF instruments exhibit a rather range of interplanar spacing and, 12wide range of interplanar spacing and, consequently, possess a large TOF instruments exhibit a rather consequently, possess a large number of simultaneously observed diffraction peaks with the almost nano-Fe numbercontribution of simultaneously observed diffraction with theThis almost similar of the similar of the resolution function to peaks their enables onecontribution to estimate lattice 10 widths. = 140 Å resolution function to their widths. This enablesdomains one to estimate lattice microstrain and thewidths size of microstrain and the size of coherently scattering (crystallites) from diffraction peak 8 coherently scattering domains (crystallites) from diffraction peak widths in a rather simple way [21,22] in a rather simple way [21,22] (Figure 2): 1/2 3 (Figure 2): = 410 6 2 2 + C3 d22 + C4 d4,4 +2Cd22d+ (6) W2W = C=1 C+1 C C3 d + C4 d , (6) 4
where CC2 are the constants defining the diffractometer resolution function where W W is isthe thepeak peakwidth, width,CC11and and 2 are the constants defining the diffractometer resolution function 2 2 and known from measurements with a reference sample, CC3 == h〈εε22〉i == (a/a) and known from measurements with a reference sample, (∆a/a)2isisthe theunit unitcell cellparameter parameter Resolution 3 2 0 1/〈D〉 2is the constant related to the crystallite size. dispersion (microstrain), and C 4 ~ dispersion (microstrain), and C ~1/hDi is the constant related to the crystallite size. 4
0
1
2
3
4
d2, Å2
1.2x10-3
nano-Fe = 140 Å
d 2, Å2
1.0x10-3 8.0x10-4
1/2 = 4103
6.0x10-4 4.0x10-4 2.0x10-4
Resolution 0.0 0
1
2
3
4
d2, Å2 Figure 2. Typical dependences of d2(d2) demonstrating contributions to the diffraction peak width
2 (d 2 (d 2 )2 )demonstrating Figure 2. Typical dependences demonstrating contributions to to thethe diffraction peakpeak width Figure 2. Typical dependences of of ∆d∆d contributions diffraction width due to isotropic microstrain ε (straight line) and crystallite size 〈D〉 (parabolic dependence). to isotropic microstrain ε (straightline) line)and andcrystallite crystallite size i i(parabolic dependence). due todue isotropic microstrain ε (straight sizehD hD (parabolic dependence).
The resolution of the neutron TOF diffractometer in a first approximation is defined by three terms, The resolution of the neutron TOF diffractometer in a first approximation is defined by three terms, R = d/d = [(t0/t)2 + (/tan)2 + (L/L)2]1/2,
R = ∆d/d = [(∆t0 /t)2 + (∆θ/tanθ)2 + (∆L/L)2 ]1/2 ,
(7)
(7)
where t0 is the neutron pulse width, t = CLsinθdhkl is the total time-of-flight (μs), and L is the neutron where ∆t0 is the neutron pulse t =term CLsinθd is the totaluncertainty, time-of-flight and L isincludes the neutron source–detector distance (m).width, The first is thehkl time-of-flight the (µs), second term source–detector distance (m). The first term is the time-of-flight uncertainty, the second term all geometrical uncertainties associated with scattering at various angles, and the third term is includes the all geometrical uncertainties associated scattering at various angles, and the third term uncertainty in the flight path length. Thewith resolution will improve as the Bragg angle approaches 90°,is the ◦
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The resolution of the neutron TOF diffractometer in a first approximation is defined by three terms, R = ∆d/d = [(∆t0 /t)2 + (∆θ/tanθ)2 + (∆L/L)2 ]1/2 ,
(7)
where ∆t0 is the neutron pulse width, t = CLsinθdhkl is the total time-of-flight (µs), and L is the neutron source–detector distance (m). 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 neutron sources with a short pulse, 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 pulsed reactor, such a way to achieve a high resolution is a priori unacceptable; the only practical way is to use the RTOF method in combination with a Fourier chopper [10], which provides a higher luminosity of experiments in comparison with other correlation techniques. In the RTOF method [23], the spectrum acquisition is performed with continuous variation of the rotation frequency of the Fourier chopper from zero to a certain maximal value Ωmax . The modulation frequency of the neutron beam ω is defined by the rotational speed of the Fourier chopper Ω and by the number of slits transparent for thermal neutrons NS in the rotor disk: ω = ΩNS . 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 RC = ∆t/t0 =
ωZmax
g(ω ) cos(ωt)dω,
(8)
0
where ω max = Ωmax NS is the maximum frequency of neutron beam intensity modulation. With a reasonable choice of g(ω), the effective neutron pulse width is defined by the maximum modulation frequency: ∆t0 ≈ 1/ω max . For standard FSD parameters NS = 1024, Ωmax = 6000 rpm, and ω max = 102.4 kHz, the effective neutron pulse width is reduced to ∆t0 ≈ 10 µs. This means that even at a chopper–detector flight distance of ~6.6 m and scattering angle of 2θ = 90◦ , the contribution of the time component to the resolution function can be ∆t0 /t ≈ 2·× 10–3 at d = 2 Å [24]. When using thin detectors, the term ∆L/L in Equation (7) becomes negligible, and the geometrical contribution can be optimized based on 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 ≤1 cm, 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 strain/stress anisotropy. Furthermore, a sample place should be specially organized on the stress diffractometer, i.e., the possibility of installing large and heavy equipment (goniometers, loading machines, 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 comb-like water moderator-generating thermal neutron pulses of ~340 µs with a frequency of 5 Hz; the curved mirror neutron guide eliminating fast neutrons and γ-rays from the neutron beam; 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 heavy-load capacity goniometer, a diaphragm
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 comb-like water moderator-generating thermal neutron pulses of ~340 μs with a frequency of 5 Hz; the curved mirror neutron guide eliminating fast neutrons and γ-rays from the neutron beam; the Crystals 2018, 8, 318 6 of 25 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 ± 90°and and a backscattering detector; a heavy-load goniometer, a and setting primaryangles beam of divergence, radial collimators defining a gauge capacity volume in the sample; diaphragm setting primary beam divergence, and radial collimators defining a gauge volume in the data acquisition electronics including an RTOF analyzer (Figure 3) [25]. The FSD diffractometer sample; and data acquisition electronics including an RTOF analyzer (Figure 3) [25]. The FSD automation system [26] allows local or remote control of the experiment. diffractometer automation system [26] allows local or remote control of the experiment.
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(b) Figure 3. Layout (a) Layout FSDdiffractometer diffractometer (Fourier at the IBR-2 pulsed Figure 3. (a) of of thethe FSD (FourierStress StressDiffractometer) Diffractometer) at the IBR-2 pulsed reactor (FLNP JINR, Dubna); 3Dmodel model of of the the FSD The basic functional unitsunits of reactor (FLNP JINR, Dubna); (b)(b)3D FSD diffractometer. diffractometer. The basic functional of the FSD are the long mirror neutronguide guidewith with variable variable diaphragms, thethe fastfast Fourier chopper, the the the FSD are the long mirror neutron diaphragms, Fourier chopper, detector system consisting of ± 90°-detectors and a backscattering detector, the detector system consisting of ± 90◦ -detectors with withradial radialcollimators collimators and a backscattering detector, the HUBER goniometer at the sample position, and auxiliary equipment (furnaces, loading machines, HUBER goniometer at the sample position, and auxiliary equipment (furnaces, loading machines, etc.), etc.), adapted from [25], with permission from © 2010 Springer. adapted from [25], with permission from © 2010 Springer.
Mirror neutron guide. The neutron beam on the sample is formed by the mirror neutron guide made of neutron high-quality borated boron) K8 glass thatsample is 19 mm withby a Ni = 1). Theguide Mirror guide. The(14% neutron beam on the is thick formed thecoating mirror(m neutron neutron guide consists of two parts: one is 19 m long and bent with a curvature radius of R 2864.8 made of high-quality borated (14% boron) K8 glass that is 19 mm thick with a Ni coating =(m = 1). The m; the other is straight and 5.01 m long. The neutron guide is cone-shaped in the vertical plane neutron guide consists of two parts: one is 19 m long and bent with a curvature radius of R = with 2864.8 m; cross sections of 10 × 155 mm2 at the curved part input, 10 × 91.8 mm2 at the curved part output and the other is straight and 5.01 m long. The neutron guide is cone-shaped in the vertical plane with cross at the straight part input, and 10 × 75 mm2 at the straight part output. At the Fourier chopper removed sections of 10 × 155 mm2 at the curved part input, 10 × 91.8 mm2 at the curved part output and at from the beam, the total thermal neutron flux at the sample position is 1.8× 106 neutron/cm2sec; it 2 at the straight part output. At the Fourier chopper removed the straight part input, and 10 × 75 mm decreases to 3.7× 105 neutron/cm2sec due to a finite transmittance of the Fourier chopper. 2 ·sec; it from the beam, total thermal neutron flux at the sample position 1.8is·×540 106mm neutron/cm Fourierthe chopper. The Fourier chopper consists of a rotor disk is that in diameter, 5 2 decreases to 3.7 neutron/cm sec due to fixed a finite of 4a). the The Fourier installed on·× the10 motor axis, and a ·stator plate ontransmittance the stage (Figure disk chopper. and plate are made of high-strength aluminum alloy. At the disk periphery, on the radius of 229 mm, there are 1024 radial slits 60 mm long and 0.7026 mm wide, filled with a Gd 2O3 layer of a 0.8 mm thickness. Similar slits are made on the stator plate. The chopper is rotated by an M2AA 132SB-2 asynchronous bipolar motor (ABB Motors, Karlstad, Sweden) with a power of 7.5 kW. An incremental optical encoder TEKEL TK560 (Italsensor s.r.l., Pinerolo, Italy) with 1024 native pulses per revolution is fixed on the motor axis for measuring the disk velocity and for generating a pickup signal coming to the
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Fourier chopper. The Fourier chopper consists of a rotor disk that is 540 mm in diameter, installed on the motor axis, and a stator plate fixed on the stage (Figure 4a). The disk and plate are made of high-strength aluminum alloy. At the disk periphery, on the radius of 229 mm, there are 1024 radial slits 60 mm long and 0.7026 mm wide, filled with a Gd2 O3 layer of a 0.8 mm thickness. Similar slits are made on the stator plate. The chopper is rotated by an M2AA 132SB-2 asynchronous bipolar motor (ABB Motors, Karlstad, Sweden) with a power of 7.5 kW. An incremental optical encoder TEKEL TK560 (Italsensor s.r.l., Pinerolo, Italy) with 1024 native pulses per revolution is fixed on the motor axis for measuring the disk velocity and for generating a pickup signal coming to the RTOF analyzer (Figure 4b). The motor is supplied by a VECTOR VBE750 control drive (Control Techniques, Telford, UK) with a built-in microcomputer, which receives information about the disk velocity and acceleration. Crystals 2018, 7, x FOR PEER REVIEW 8 of 26
Rotor
Slit width 0.7 mm Stator
Transmission function
Binary signals
(a)
(b)
Figure 4. Design (a) Design the Fourierchopper, chopper, consisting rotor diskdisk and and a stationary stator.stator. Figure 4. (a) of of the Fourier consistingofofa rotating a rotating rotor a stationary Outer circumference therotor rotordisk disk is is aa system system of slits transparent and and opaque for for Outer circumference of of the ofinterleaving interleaving slits transparent opaque thermal neutrons. The diagram below shows a saw tooth function of transmission of such a chopper thermal neutrons. The diagram below shows a saw tooth function of transmission of such a chopper system and its approximating sequence of positive and negative binary (pickup) signals; (b) Photo of system and its approximating sequence of positive and negative binary (pickup) signals; (b) Photo of the Fourier chopper installed on FSD. the Fourier chopper installed on FSD.
Detector system. In developing the detector system for the stress diffractometer, two mutually the detector system diffractometer, mutually Detectorrequirements system. In developing exclusive should be satisfied: the solid anglefor of the the stress detector system shouldtwo be large exclusive requirements should be satisfied: the solid angle the detector systemtime; should be large enough to acquire statistics from a small sample volume for aofreasonable exposition and the contribution of the detector system to the geometrical component of the resolution function should enough to acquire statistics from a small sample volume for a reasonable exposition time; and the not exceed component the high resolution of theofinstrument. There are two should well- not contribution of the thetime detector systemtotoretain the geometrical component the resolution function known versions of such ato type of detector on TOF of diffractometers: position-sensitive exceed the time component retain the highused resolution the instrument. There are twosystems well-known and detectors with geometrical TOF focusing during diffraction [27]. However, the need to use the versions of such a type of detector used on TOF diffractometers: position-sensitive systems and correlation principle of data recording in Fourier diffractometry almost excludes the possibility of detectors with geometrical TOF focusing during diffraction [27]. However, the need to use the using the position detector in this method. On the contrary, as for TOF focusing, it is successfully correlation principle of data recording in Fourier diffractometry almost excludes the possibility of used on all operating Fourier diffractometers. A disadvantage of this method is a significant usingdisproportion the positionofdetector in this method. On contrary, TOFgeometrical focusing, it is successfully the effective solid angle of thethe detector withas itsfor actual sizes. Progress in used on allthe operating Fourier diffractometers. A disadvantage of this method is a significant disproportion development of relatively low-cost correlation electronics based on digital signal processors made of theit effective solid angleaof theprinciple detectorof with actual geometrical sizes. Progress in the development possible to propose new the its development of the FSD detector system, namely, the multi-element detector with combined electronic geometrical [28]. made The schematic of relatively low-cost correlation electronics based and on digital signalfocusing processors it possible to representation of such of a detector, called the ASTRA, is shown in Figure 5. Each detector element is a propose a new principle the development of the FSD detector system, namely, the multi-element counter based on an ZnS(Ag) scintillation screen with a sensitive layer thickness of 0.42 mm and detector with combined electronic and geometrical focusing [28]. The schematic representation of such several hundred square centimeters in area. The scintillation screen consists of a powder mixture of a detector, called the ASTRA, is shown in Figure 5. Each detector element is a counter based on an 6LiF crystals (nuclear active additive) and ZnS(Ag) (scintillator) fixed in a Plexiglas optical matrix. ZnS(Ag) scintillation screen with a sensitive layer thickness of 0.42 mm and several hundred square The screen flexibility allows an approximation of the TOF focusing surface by conical surface centimeters in area. The scintillation screen consists of a powder mixture of 6 LiF crystals (nuclear segments with the required accuracy. Such an approximation method excludes dead areas on the sensitive layer and increases the quality of geometrical focusing. The detector efficiency is mostly defined by the 6Li concentration in the screen and is ~60%. In the final version (Figure 6a), the FSD detector system consists of one backscattering detector (BS) at the scattering angle 2θ = 140° and two ASTRA detectors at the scattering angle 2θ = ± 90°. The BS detector is assembled from 16 6Li-based elements, which are spatially arranged according to the
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active additive) and ZnS(Ag) (scintillator) fixed in a Plexiglas optical matrix. The screen flexibility allows an approximation of the TOF focusing surface by conical surface segments with the required accuracy. Such an approximation method excludes dead areas on the sensitive layer and increases the quality of geometrical focusing. The detector efficiency is mostly defined by the 6 Li concentration in the screen and is ~60%. In the final version (Figure 6a), the FSD detector system consists of one backscattering detector (BS) at the scattering angle 2θ = 140◦ and two ASTRA detectors at the scattering angle 2θ = ± 90◦ . The BS detector is assembled from 16 6 Li-based elements, which are spatially arranged according to the TOF focusing condition (Figure 6b). Each ASTRA detector includes seven independent TOF focused ZnS(Ag) elements, i.e., with independent outputs of electronic signals of elements [29]. The combined use ofCrystals electronic and TOF focusing of the scattered neutron beam allows researchers to increase the 2018, 7, x FOR PEER REVIEW 9 of 26 solid angle up to ~0.16 sr for each ASTRA detector. This sharply increases the instrument luminosity Crystals 2018, 7, x FOR PEER REVIEW 9 of 26 angle up ~0.16 resolution sr for each ASTRA This sharply increases instrument eight luminosity whilesolid retaining thetohigh level indetector. the interplanar spacing dhklthe . Currently, elements ◦ while retaining the high resolution level in the interplanar spacing d hkl . Currently, eight elements (among 14angle planned) of ASTRA 90 -detectors are installed on the FSD. The application of the RTOF solid up to ~0.16 sr for each ASTRA detector. This sharply increases the instrument luminosity (among 14 planned) of to ASTRA 90°-detectors are interplanar installed the ÷ FSD. The application of the RTOF method makes it possible obtain high-resolution (∆d/d on ≈spacing 0.2 0.4%) diffraction spectra with the while retaining the high resolution level in the dhkl . Currently, eight elements method makes it possible to obtain high-resolution (d/d 0.2 ÷ 0.4%) diffraction spectra with (among 14 planned) of ASTRA 90°-detectors are installed on the FSD. The application of the RTOF fairly short flight distance (~6.6 m) between the Fourier chopper and neutron detectors [30]. the fairly short flight m) between the Fourier chopper neutron detectors [30].with the method makes it distance possible (~6.6 to obtain high-resolution (d/d 0.2 ÷and 0.4%) diffraction spectra fairly short flight distance (~6.6 m) between the Fourier chopper and neutron detectors [30].
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(a) 90°-detector (b) (a) system of the FSD diffractometer, adapted from [25], (b) with permission from © Figure 6. (a) Detector 2010 Springer; (b) Time-focused backscattering detector BS (shielding removed). Figure 6. (a) Detector system of the FSD diffractometer, adapted fromis[25], with permission from ©
Figure 6. (a) Detector system of the FSD diffractometer, adapted from [25], with permission from © 2010 Springer; (b) Time-focused backscattering detector BS (shielding is removed). Gauge volume definitionbackscattering with radial collimator. To form the incident neutron beam, a 2010 Springer; (b) Time-focused detector BS (shielding is removed). diaphragm with precision step motors and variable aperture (0–30 mm for width neutron and 0–80beam, mm for Gauge volume definition with radial collimator. To form the incident a height) is installed on the neutron guide exit of FSD. The experimentally estimated horizontal diaphragm with precision step motors and variable aperture (0–30 mm for width and 0–80 mmand for vertical is divergences of the the neutron incident guide beam are andThe 0.002 radians, correspondingly. The scattered height) installed on exit0.001 of FSD. experimentally estimated horizontal and neutron beams are formed using two new multi-slit radial collimators with a wide acceptance angle vertical divergences of the incident beam are 0.001 and 0.002 radians, correspondingly. The scattered of ±20° (Figure allows a definition the gauge volume in the studied The performed neutron beams 7). areThis formed using two newof multi-slit radial collimators with asample. wide acceptance angle experiments showed that the radial collimators provide a spatial resolution of ~1.8 mm with an of ±20° (Figure 7). This allows a definition of the gauge volume in the studied sample. The performed
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Gauge volume definition with radial collimator. To form the incident neutron beam, a diaphragm with precision step motors and variable aperture (0–30 mm for width and 0–80 mm for height) is installed on the neutron guide exit of FSD. The experimentally estimated horizontal and vertical divergences of the incident beam are 0.001 and 0.002 radians, correspondingly. The scattered neutron beams are formed using two new multi-slit radial collimators with a wide acceptance angle of ±20◦ (Figure 7). This allows a definition of the gauge volume in the studied sample. The performed experiments showed that the radial collimators provide a spatial resolution of ~1.8 mm with an improved neutron transmission capacity and precisely form the required gauge volume within Crystals 2018, 7, x FOR PEER REVIEW 10 of 26 the studied sample. Performed test measurements with the VAMAS [31] shrink-fit ring and plug standard round robintosample with known stress profiles the high of the the FSD instrument strain gradients andresidual the high accuracy of confirmed the measured strainsensitivity values (Figure FSD instrument to strain gradients and the high accuracy of the measured strain values (Figure 8a). 8a).
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Figure 7. (a) Sample place at the FSD diffractometer. Huber goniometer, the diaphragm at the incident Figure 7. (a) Sample place at the FSD diffractometer. Huber goniometer, the diaphragm at the incident beam, and two radial collimators at the scattered beams are visible, adapted from [19], with beam, and two radial collimators at the scattered beams are visible, adapted from [19], with permission permission from © 2018 Springer; (b) Calculated transmission map for the new wide-aperture radial from © 2018 Springer; (b) Calculated transmission map for the new wide-aperture radial collimator. collimator.
Using neutron neutron scanning, scanning, the the gauge gauge volume volume position position can can be be easily easily determined determined with with respect respect to to the the Using sample surface; then, its position in the sample bulk can also be accurately positioned in further strain sample surface; then, its position in the sample bulk can also be accurately positioned in further strain measurements. The The neutron neutron scanning scanning method method involves involves measuring measuring the the dependence dependence of of the the diffraction diffraction measurements. peak intensity intensity on onthe thegauge gaugevolume volumecenter centerposition. position. The sample is sequentially displaced so that peak The sample is sequentially displaced so that the the gauge volume is gradually immersed into the sample (Figure 8b). The initial point in the plot gauge volume is gradually immersed into the sample (Figure 8b). The initial point in the plot corresponds to volume position outside the sample; in thisincase, diffraction peak intensity corresponds tothe thegauge gauge volume position outside the sample; thisthe case, the diffraction peak is zero (there is no diffraction from the sample material). Then, the gauge volume gradually enters the intensity is zero (there is no diffraction from the sample material). Then, the gauge volume gradually sample,the hence, the diffraction intensity, which is proportional to proportional the scatteringto material volume, enters sample, hence, thepeak diffraction peak intensity, which is the scattering begins to volume, increase. begins The point the maximum in theof plot approximately corresponds to the position material to ofincrease. The point the maximum in the plot approximately at which the gauge volume is completely immersed into the sample. During further to the corresponds to the position at which the gauge volume is completely immersed intomotion the sample. sample depth, the scattering material volume remains unchanged; however, the intensity begins to During further motion to the sample depth, the scattering material volume remains unchanged; decrease slowly due to neutron to thetoexponential law however, the intensity begins absorption to decreaseaccording slowly due neutron absorption according to the exponential law
I = I0 exp(−µD ), (9) I I0 exp( D) , (9) where µ is the material attenuation coefficient and D is the total neutron path in the sample. Thus, where μ scanning is the material coefficient andgauge D is the total neutron path in the asample. Thus, neutron allowsattenuation the determination of the volume in the sample with high enough neutron scanning allows the determination of the gauge volume in the sample with a high enough accuracy (~0.1 mm). accuracy (~0.1 mm).
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Figure 8. (a) Residual lattice strain measured in VAMAS shrink-fit ring and plug sample (set #1); (b) Figure 8. (a) Residual lattice strain measured in VAMAS shrink-fit ring and plug sample (set #1); Sample surface scanscan using a radial collimator: diffraction peakpeak intensity vs. gauge volume position in (b) Sample surface using a radial collimator: diffraction intensity vs. gauge volume position the material depth, adapted from [25],[25], with permission from © 2010 Springer. in the material depth, adapted from with permission from © 2010 Springer.
List-mode DAQ system. Recently, a new unified MPD (Multi Point Detector) DAQ unit List-mode DAQ system. Recently, a new unified MPD (Multi Point Detector) DAQ unit intended intended for data registration from individual neutron detector elements was elaborated in FLNP for data registration from individual neutron detector elements was elaborated in FLNP JINR [32]. JINR [32]. The electronic part of the MPD unit is based on five ALTERA FPGAs and it is implemented The electronic part of the MPD unit is based on five ALTERA FPGAs and it is implemented on a on a modular principle. The elaborated MPD unit allows the connection of up to 240 detector modular principle. The elaborated MPD unit allows the connection of up to 240 detector elements. On elements. On the FSD diffractometer, the MPD-32 DAQ unit with 32 input detector signals is installed the FSD diffractometer, the MPD-32 DAQ unit with 32 input detector signals is installed for routine for routine operation. Due to the peculiarities of the RTOF method, four main types of events are operation. Due to the peculiarities of the RTOF method, four main types of events are registered registered by MPD-32 on FSD: detector events, reactor pulses, and rising and falling fronts of Fourier by MPD-32 on FSD: detector events, reactor pulses, and rising and falling fronts of Fourier chopper chopper pickup signals. The MPD-32 unit can operate simultaneously in two modes: histogrampickup signals. The MPD-32 unit can operate simultaneously in two modes: histogram-mode of mode of TOF-spectra accumulation and list-mode of raw data transfer [33]. In histogram-mode, the TOF-spectra accumulation and list-mode of raw data transfer [33]. In histogram-mode, the TOF TOF spectrum (low-resolution spectrum) is accumulated in internal memory (64 Mb) of the MPD unit spectrum (low-resolution spectrum) is accumulated in internal memory (64 Mb) of the MPD unit with a programmable fixed number of channels and channel widths, and can be visualized on screen with a programmable fixed number of channels and channel widths, and can be visualized on screen online. In list-mode, raw data events are recorded as a list of 32-bit words with a total maximum data online. In list-mode, raw data events are recorded as a list of 32-bit words with a total maximum data flow rate of 8·× 106 6events/sec. and maximum sampling frequency of 62.5 MHz, which corresponds flow rate of 8·× 10 events/sec. and maximum sampling frequency of 62.5 MHz, which corresponds to a discretization time of 16 ns. Thus, in this case, the absolute time of each event (timestamp) is to a discretization time of 16 ns. Thus, in this case, the absolute time of each event (timestamp) defined with a high precision and is written as raw data on a computer HDD. The elaborated LMis defined with a high precision and is written as raw data on a computer HDD. The elaborated algorithm provides a fast a posteriori reconstruction of high-resolution neutron diffraction spectra LM-algorithm provides a fast a posteriori reconstruction of high-resolution neutron diffraction spectra (RTOF spectra) from raw data in a wide dhkl range with flexibly configurable parameters of the TOF(RTOF spectra) from raw dataininthe a wide dhkl range with flexibly configurable parameters of the scale., i.e., number of channels spectrum, channel width, spectrum and strobe pulse delays, TOF-scale., i.e., number of channels in the spectrum, channel width, spectrum and strobe pulse delays, flight paths relation coefficient, etc. If necessary, this procedure can be performed repeatedly without flight pathsmeasurements. relation coefficient, etc. If necessary, this procedure cansome be performed without additional Moreover, the LM algorithm includes auxiliary repeatedly opportunities for additional measurements. Moreover, the LM algorithm includes some auxiliary opportunities for spectra correction (chopper phase shift correction, detector signal filtering, precise electronic focusing correction (chopper phase correction, detector filtering, precise electronic focusing ofspectra individual detector elements intoshift the single TOF scale, realsignal frequency window reconstruction, etc.). of individual elements the single TOF scale, frequencyprobability window reconstruction, The maindetector idea of the RTOFinto method is to examine thereal registration (high or low) etc.). for Theneutrons main idea ofThis the RTOF method examine the registration (high or low) for detected [5]. is realized by is thetoreverse analysis of “open”probability and “closed” states of the detectedsource neutrons Thischopper is realized thedetector reverse event. analysis of “open”neutrons and “closed” of the neutron and [5]. Fourier forby each Registering with states continuous neutron source and Fourier chopper for each detector event. Registering neutrons with continuous beam modulation according to the particular law (frequency window g(ω)), it is possible to obtain beam modulation according to thescattered particular law (frequency window g(ω)), is possible to to obtain the TOF distribution of elastically neutrons. In simplified form, the it unity is added the the TOFmemory distribution ofboth elastically scattered neutrons. simplified form, the unity is added to the analyzer cell if the neutron source and theIn chopper are in the “open” state. analyzer memoryintensity cell if both the neutron source and theatchopper in the “open” state. The neutron measured by RTOF method a pulsedare neutron source can be described The neutron intensity measured by RTOF method at a pulsed neutron source can be described as [10]: as [10]: Z Z II((tt))~ (t )RS S(t(t−τ) + cc RRSS((tt B (10) ∼ ± RR )σ((τ))ddτ −τ))σ((τ))d dτ + B((tt),) , (10) C C (t − τ ) R
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where RС is the resolution function of the Fourier chopper (see Equation (8)), RS is the function where RC is the resolution function of the Fourier chopper (see Equation (8)), RS is the function describing the neutron pulse from the source, is the coherent scattering cross section of the sample, describing the neutron pulse from the source, σ is the coherent scattering cross section of the sample, B B is the conventional background, and c ≈ 1 is a constant. is the conventional background, and c ≈ 1 is a constant. The width of the RS function is about WS ≈ 340 μs for the IBR-2 reactor, while the width of RС is The width of the RS function is about WS ≈ 340 µs for the IBR-2 reactor, while the width of RC is defined by the maximal modulation frequency ωmax of the Fourier chopper and it is about ∆t0 ≈ 10 μs defined by the maximal modulation frequency ω max of the Fourier chopper and it is about ∆t0 ≈ 10 µs for the FSD diffractometer. Thus, the first term in Equation (10) is a narrow peak with a width of 10 for the FSD diffractometer. Thus, the first term in Equation (10) is a narrow peak with a width of 10 µs, μs, and the second one is the broad peak-like distribution with a width of 340 μs, which is called the and the second one is the broad peak-like distribution with a width of 340 µs, which is called the correlation background. correlation background. The + or − sign before the first term in Equation (10) corresponds to correlation patterns I++(t) The + or − sign before the first term in Equation (10) corresponds to correlation patterns I (t) (“positive”) and I−(t) (“negative”) accumulated with non-inverted and inverted pickup signals of the (“positive”) and I − (t) (“negative”) accumulated with non-inverted and inverted pickup signals of the Fourier chopper, correspondingly (Figure 9). The non-inverted binary pickup signal is 1 for the high Fourier chopper, correspondingly (Figure 9). The non-inverted binary pickup signal is 1 for the high transmission (“open”) state of the Fourier chopper and 0 for the low-transmission (“closed”) state, transmission (“open”) state of the Fourier chopper and 0 for the low-transmission (“closed”) state, whereas the inverted pickup signal is 1 for the low-transmission state and 0 for the high-transmission whereas the inverted pickup signal is 1 for the low-transmission state and 0 for the high-transmission state. The high-resolution diffraction RTOF spectrum is calculated as a difference of “positive” and state. The high-resolution +diffraction RTOF spectrum is calculated as a difference of “positive” “negative” patterns: H(t) = I (t) – I–(t). The high-resolution spectrum H(t) contains narrow diffraction and “negative” patterns: H(t) = I+ (t) – I– (t). The high-resolution spectrum H(t) contains narrow Bragg peaks with widths corresponding to the diffractometer resolution function for a certain diffraction Bragg peaks with widths corresponding to the diffractometer resolution function for a interplanar spacing dhkl. The high-resolution peak position in the TOF-scale is defined as (cf. Equation certain interplanar spacing dhkl . The high-resolution peak position in the TOF-scale is defined as (1)): (cf. Equation (1)): thkl =thklC C · LRTOF sinθddhklhkl (11) LRTOF sin , , (1)
where is the the flight flight path path between between the the Fourier Fourier chopper chopper and and detector. detector. whereLLRTOF RTOF is
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Figure 9. (a) RTOF neutron diffraction spectra measured from a standard -Fe powder sample with Figure 9. (a) RTOF neutron diffraction spectra measured from a standard α-Fe powder sample with the maximal Fourier chopper speed Ωmax = 4000 rpm. At the bottom, “positive” I+(t) and “negative” I– the maximal Fourier chopper speed Ωmax = 4000 rpm. At the bottom, “positive” I+ (t) and “negative” (t) correlation spectra are shown. The upper pattern is the high-resolution diffraction RTOF spectrum I– (t) correlation spectra are shown. The upper pattern is the high-resolution diffraction RTOF spectrum calculated as a difference of “positive” and “negative” patterns: H(t) = I+(t) − I–(t); (b) Diffraction peak calculated as a difference of “positive” and “negative” patterns: H(t) = I+ (t) − I– (t); (b) Diffraction peak (211) region in the same RTOF spectra. (211) region in the same RTOF spectra.
Electronic focusing of detector elements. Usually, during stress scanning experiments, the Electronic focusing of in detector Usually, for during stress scanning radial collimators are used front ofelements. the 90°-detectors small gauge volumeexperiments, selection in the the radial depth ◦ -detectors for small gauge volume selection in the depth of the collimators are used in front of the 90 of the sample. Therefore, the intensity factor is a very important parameter and the whole detector sample. Therefore, the intensity is a veryFor important parameter and the whole solid solid angle should be used in suchfactor experiments. the summation of the spectra from detector the individual angle should be used in such experiments. For the summation of the spectra from the individual elements of ASTRA ± 90°-detectors, the electronic focusing method is used. This method implies the ◦ -detectors, the electronic focusing method is used. This method implies elements of ASTRA ± 90for use of scale coefficients each detector element and measuring RTOF spectra with individual channel widths τi,
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the use2018, of scale coefficients for each detector element and measuring RTOF spectra with individual Crystals 7, x FOR PEER REVIEW 13 of 26 channel widths τ i , k i = Li sin θi /L0 sin θ0 and τi = k i τ0 , (12) ki Li sini / L0 sin0 and i ki 0 , (2) where Li , L0 are the flight paths (i.e. distance between the Fourier chopper and neutron detector); Li, L0 are the flight paths (i.e. distance between the Fourier chopper and neutron detector); θi, θwhere i , θ 0 are the scattering angles; and τ i , τ 0 are the RTOF channel widths for the i-th and basic θ 0 are the scattering angles; and τi, τ0 are the RTOF channel widths for the i-th and basic detectors, detectors, respectively. respectively. Usually, τ i are real (noninteger) numbers and RTOF spectra with such channel width values Usually, τi are real (noninteger) numbers and RTOF spectra with such channel width values are are readily reconstructed from raw list-mode data with the required accuracy. Therefore, all spectra readily reconstructed from raw list-mode data withtothe accuracy. all Lspectra are are reduced to a unified TOF scale corresponding therequired basic detector withTherefore, parameters 0 , θ 0 , and reduced to a unified TOF scale corresponding to the basic detector with parameters L0, θ0, and τ0, and τ 0 , and can be summed channel by channel. The final diffraction spectrum is characterized by a can be summed channel by channel. The final diffraction spectrum is characterized by a multiple multiple increase in the intensity at the same resolution level as for the spectra from individual detector increase in the intensity at the same resolution level as for the spectra from individual detector elements (Figure 10). Thus, the luminosity of the experiment on FSD is increased by a factor of four elements (Figure 10). Thus, luminosity of the experiment on FSD increased by a factor of four using electronic focusing for the all elements of ASTRA ± 90◦ -detectors. A is similar approach was used for using electronic focusing for all elements of ASTRA ± 90°-detectors. A similar approach was used for additional fine tuning of individual elements of the BS detector with geometrical TOF focusing, which additional fine tuning of individual elements of the BS detector with geometrical TOF focusing, which allowed the detector resolution to improve by ~5%. allowed the detector resolution to improve by ~5%. 25
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FSD diffractometer diffractometerperformance. performance. To Tostudy study the the main main characteristics characteristics of of the the FSD FSD diffractometer, diffractometer, FSD a number of test experiments were performed to estimate the instrument resolution, sensitivity to the a number of test experiments were performed to estimate the instrument resolution, sensitivity to spatial distribution of of strains, and the materials under under the spatial distribution strains, and thepossibility possibilityofofstudying studying typical typical structural structural materials external loads. loads. The The spectral spectral distribution distribution of of the the incident incident neutron neutron beam beam intensity intensity on on the the FSD FSD allows allows external efficient operation at λ ≥ 1 Å. This makes it possible to measure diffraction spectra in the ranges dhkl = efficient operation at λ ≥ 1 Å. This makes it possible to measure diffraction spectra in the ranges ◦ dhkl = 0.51 ÷ 5.4 Å at 2θ = 140°, ◦which is an optimum range for most ÷ 6.7 Å at 2θ = 90° and d0.63 hkl = 0.63 ÷ 6.7 Å at 2θ = 90 and dhkl = 0.51 ÷ 5.4 Å at 2θ = 140 , which is an optimum range for most structural materials used in industry. The The typical typical high-resolution high-resolutiondiffraction diffractionspectra spectrameasured measuredon on the the structural materials used in industry. α-Fe reference powder sample at a maximum rotation speed of the Fourier chopper Ω max = 6000 rpm α-Fe reference powder sample at a maximum rotation speed of the Fourier chopper Ωmax = 6000 rpm are shown shownin in(Figure (Figure11). 11). are An analysis of the diffractometer resolution resolution function function showed showed that that FSD FSD detectors detectors indeed indeed have have aa An analysis of the diffractometer –3 –3 necessaryresolution resolutionlevel levelininthe theinterplanar interplanarspacing: spacing: Δd/d≈≈2.3 2.3×· ×10 detector necessary ∆d/d 10 for for the the backscattering backscattering detector −3 − 3 ◦ BS and Δd/d ≈ 4× 10 for both ASTRA ± 90°-detectors at d = 2 Å and at a maximum rotation speed of BS and ∆d/d ≈ 4·× 10 for both ASTRA ± 90 -detectors at d = 2 Å and at a maximum rotation speed the Fourier chopper Ω max = 6000 rpm (Figure 12a). Furthermore, the dependence of the shape of an of the Fourier chopper Ωmax = 6000 rpm (Figure 12a). Furthermore, the dependence of the shape of an individualdiffraction diffractionpeak peakon onthe themaximum maximum speed Fourier chopper resolution function individual speed of of thethe Fourier chopper andand resolution function for for all detectors were investigated (Figure 12b). According to expectations, the effective neutron pulse all detectors were investigated (Figure 12b). According to expectations, the effective neutron pulse width decreases as 1/ωmax, reaching a minimum of ~10 μs. Thus, the diffractometer parameters can be optimized, taking into account the required accuracy of peak position determination and scheduled beamtime. Main parameters of the FSD diffractometer are given in Table 1.
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width decreases as 1/ω max , reaching a minimum of ~10 µs. Thus, the diffractometer parameters can be optimized, taking into account the required accuracy of peak position determination and scheduled beamtime. Main parameters of the FSD diffractometer are given in Table 1.
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Figure 11. Neutron diffraction patterns measured from the -Fe standard sample using BS (a) and Figure 11. Neutron diffraction patterns measured from the α-Fe standard sample using BS (a) and Figure 11. Neutron from the -FeΩstandard sample using BS (a) and 90°-detector ASTRA;diffraction (b) at the patterns maximal measured Fourier chopper speed max = 6000 rpm. The measured data 90◦ -detector ASTRA; (b) at the maximal Fourier chopper speed Ωmax = 6000 rpm. The measured data 90°-detector ASTRA; (b) at theby maximal Fourier chopper speed max = 6000 rpm. The measured data points, full profile calculated the Rietveld method, and the Ω difference curve are shown, adapted points, full profile calculated by the Rietveld method, and the difference curve are shown, adapted points, full profile calculated by the Rietveld method, and the difference curve are shown, adapted from [25], [25], with with permission permission from from © © 2010 2010 Springer. Springer. from from [25], with permission from © 2010 Springer.
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Figure 12. (a) FSD resolution function measured at maximal Fourier chopper speed Ωmax = 6000 rpm Figure 12. measured at ASTRA maximaldetectors Fourier chopper chopper speed Ω max = 6000 rpm for backscattering detector BSfunction (2θ = 140) and both (2θ = ± 90). (b)Ω Diffraction Figure 12. (a) (a) FSD FSD resolution resolution function measured at maximal Fourier speed rpm max = 6000 peak for backscattering detector BS (2θ = 140) and both ASTRA detectors (2θ = ± 90). (b) Diffraction ◦ ◦ shape dependencedetector vs. maximal speed Vmaxdetectors , adapted(2θ from [25], from for backscattering BS (2θFourier = 140 chopper ) and both ASTRA =± 90 with ). (b) permission Diffractionpeak peak shape Vmax, ,adapted from [25], with permission from © 2010dependence Springer. vs. shape dependence vs. maximal maximal Fourier Fourier chopper chopper speed speed V max adapted from [25], with permission from © 2010 Springer. © 2010 Springer. Table 1. Main parameters of the FSD diffractometer. Table 1. Main parameters of the FSD diffractometer.
Curved Neutron Guide: Curved Neutron length Guide: length curvature radius curvature radius Straight neutron guide: Straight neutron length guide: length Neutron beam size at the sample position Neutron beam size at the sample position (variable) (variable) Moderator–sample distance Moderator–sample distance Chopper–sample distance Chopper–sample distance Fourier chopper (Disk):
Mirror with Ni Coating Mirror with 19 Ni m Coating 19 m 2864.8 m 2864.8 mCoating Mirror with Ni Mirror with Ni 5.01 m Coating 5.01 m (0 ÷ 10) (0 ÷ 75) mm (0 ÷ 10) (0 ÷ 75) mm 28.14 m 28.14 m 5.55 m 5.55 m High-strength Al Alloy
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Table 1. Main parameters of the FSD diffractometer. Curved Neutron Guide:
Mirror with Ni Coating
length curvature radius Straight neutron guide: length Neutron beam size at the sample position (variable) Moderator–sample distance Chopper–sample distance
19 m 2864.8 m Mirror with Ni Coating 5.01 m (0 ÷ 10) × (0 ÷ 75) mm 28.14 m 5.55 m
Fourier chopper (Disk): outer diameter single slit width number of slits maximum speed of rotation maximum frequency of neutron beam modulation
High-strength Al Alloy 540 mm 0.7 mm 1024 6000 rpm 102.4 kHz
Thermal Neutron Pulse Width: in the low-resolution mode (TOF) in the high-resolution mode (RTOF) Neutron flux at the sample position: without Fourier chopper with Fourier chopper Wavelength range Detectors: 2θ = 140◦ (backscattering)
Water Moderator 340 µs 9.8 µs
2θ = ± 90◦
Detector resolution ∆d/d (at d = 2 Å): 2θ = 140◦ (backscattering) 2θ = ± 90◦ dhkl range: 2θ = 140◦ (backscattering) 2θ = ± 90◦
1.8·× 106 neutron/cm2 ·sec 3.7·× 105 neutron/cm2 ·sec 0.9 ÷ 8 Å 6 Li, with geometrical TOF focusing ZnS(Ag), with combined electronic and geometrical TOF focusing
2.3 × 10−3 4.0 × 10−3 0.51 ÷ 5.39 Å 0.63 ÷ 6.71 Å
Sample environment. Available supplementary equipment integrated into the experiment control system makes it possible to provide various conditions (load, temperature, etc.) at the sample. For precise sample positioning, a four-axis (X, Y, Z, Ω) HUBER goniometer with the maximal carrying capacity of 300 kg is used (Figure 13a). It can be equipped with an additional goniometer head with ± 15◦ -tilt (Figure 13b). To study the behavior of structural materials under an external load in situ in a neutron beam, an LM-29 uniaxial mechanical-type loading machine is used; it provides any required combination of external load and temperature, which considerably extends the range of possible experiments on the diffractometer. The device provides a tensile/compressive load at the sample of up to 29 kN. There is also the possibility to heat metallic samples by an electric current up to 800 ◦ C (with temperature control). The main advantage of this loading machine is the almost slack-free load transfer to the sample (Figure 13c). For neutron diffraction experiments at elevated temperatures (up to 1000 ◦ C) with small samples of typical dimensions of ~1 cm, the MF2000 water-cooled mirror furnace is used (Figure 13d). The furnace consists of two polished aluminum reflectors and two halogen lamps with temperature stabilization by the Lakeshore controller.
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(a)
(c)
(b)
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Figure 13. (a) Four-axis HUBER goniometer for precise sample positioning (max. load 300 kg); (b)
Figure 13. (a) Four-axis HUBER goniometer for precise sample positioning (max. load 300 kg); (b) Additional goniometer head with ± 15°-tilt; (c) Uniaxial mechanical loading machine LM-29 (Fmax = 29 Additional goniometer head with ± 15◦ -tilt; (c) Uniaxial mechanical loading machine LM-29 (Fmax = 29 kN, Tmax = 800 °C) installed on the HUBER goniometer during the experiment; (d) Water-cooled mirror ◦ kN, furnace Tmax = 800 installed on the HUBER goniometer during the experiment; (P = 1C)kW, Tmax = 1000 °C). A sample with a thermocouple heated during(d) theWater-cooled experiment ismirror ◦ furnace (P = 1 kW, Tmax = 1000 C). A sample with a thermocouple heated during the experiment shown. is shown. 4. Experimental Results
4. Experimental Results A significant place in applied researches on the FSD diffractometer belongs to experiments for residual stress place investigations structural on materials industrial products after various for A significant in appliedinresearches the FSDand diffractometer belongs to experiments technological operations. Another research area is the in situ study of the behavior of structural residual stress investigations in structural materials and industrial products after various technological materials (composites, steels, alloys, ceramics, etc.) under various conditions (external load, operations. Another research area is the in situ study of the behavior of structural materials (composites, temperature). Below, several examples of typical experiments performed on FSD are given.
steels, alloys, ceramics, etc.) under various conditions (external load, temperature). Below, several examples of typical experiments performed on FSD are given. 4.1. Welding Residual Stresses The neutron diffraction data are often used for a comparison with the results of calculations by 4.1. Welding Residual Stresses
the finite element method (FEM), for the consequent development of theoretical models for an The neutron diffraction data are often usedprocesses for a comparison with estimation the resultsofofthe calculations adequate description of various technological and the correct stress levelby the an entire product. For for example, in [34], thedevelopment residual stressof distribution a multi-pass finiteover element method (FEM), the consequent theoreticalinmodels for anbuttadequate welded joint of the low alloyed steelprocesses S355J2+N and was investigated. For the welding description of various technological the correct estimation of theexperiments, stress levelthe over an Gas Metal Arc Welding (GMAW) method was used for the first welding pass and the Submerged entire product. For example, in [34], the residual stress distribution in a multi-pass butt-welded joint
of the low alloyed steel S355J2+N was investigated. For the welding experiments, the Gas Metal Arc Welding (GMAW) method was used for the first welding pass and the Submerged Arc Welding (SAW) method was used for the second and third welding passes. The dimensions of the welded
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Arc Welding (SAW) method was used for the second and third welding passes. The dimensions of specimen were the following: 500 mm length, 300 mm width, and 20 mm thickness. The initial sample the welded specimen were the following: 500 mm length, 300 mm width, and 20 mm thickness. The temperature as well the interpass temperature were always equal to room temperature. initial sample temperature as well the interpass temperature were always equal to room temperature. For neutron diffraction experiments on FSD, a special specimen was cut from the entire multi-pass For neutron diffraction experiments on FSD, a special specimen was cut from the entire multiwelded joint (Figure 14a). The neutron measurements were performed at the middle of the sample’s pass welded joint (Figure 14a). The neutron measurements were performed at the middle of the thickness, with a gauge volume of the size of 5 × 2 × 20 mm3 for Y-3 and Z-components and of the sample’s thickness, with a gauge volume of the size of 5 × 2 × 20 mm for Y- and Z-components and size of 5 × 2 × 5 mm3 for the X-component. The measured diffraction spectra were processed using of the size of 5 × 2 × 5 mm3 for the X-component. The measured diffraction spectra were processed full profile analysis based on the Rietveld method [35]. The average residual strain was determined using full profile analysis based on the Rietveld method [35]. The average residual strain was as ε = (a − a0 )/a0 , where a is the lattice parameter for the studied specimen with residual stresses determined as ε = (a − a0)/a0, where a is the lattice parameter for the studied specimen with residual and a0 is the lattice parameter for stress-free reference material. The residual stress components were stresses and a0 is the lattice parameter for stress-free reference material. The residual stress determined from the obtained strain values according to Equation (5). In the investigated specimen, components were determined from the obtained strain values according to Equation (5). In the the distribution of the residual stress tensor components over scan coordinate X alternate in sign and investigated specimen, the distribution of the residual stress tensor components over scan coordinate vary within wide limits (Figure 14b). The maximum of the residual stress distribution agrees rather X alternate in sign and vary within wide limits (Figure 14b). The maximum of the residual stress well with the position of the weld seam. As would be expected, the residual stresses decrease sharply distribution agrees rather well with the position of the weld seam. As would be expected, the residual with distance from the weld seam region. stresses decrease sharply with distance from the weld seam region.
Stress, MPa
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Figure 14. (a) Multi-pass butt-welded (GMAW+SAW) specimen (300 × 100 × 20 mm3). (b) Longitudinal Figure 14. (a) Multi-pass butt-welded (GMAW+SAW) specimen (300 × 100 × 20 mm3 ). (b) σX and transverse σY stress distribution in a multi-pass butt-welded joint measured by neutron Longitudinal σX and transverse σY stress distribution in a multi-pass butt-welded joint measured by diffraction and calculated by FEM, adapted from [34], with permission from © 2017 Elsevier. neutron diffraction and calculated by FEM, adapted from [34], with permission from © 2017 Elsevier.
In addition to the neutron diffraction experiments, numerical calculations were performed by addition to themodel neutron experiments, numerical calculations were by FEM.InThe developed of diffraction the multi-pass welding process makes it possible to performed calculate the FEM. The developed modeldepending of the multi-pass welding process makes it for possible to calculate the residual stress distributions on the welding process parameters the most widespread residual stress distributions depending on the welding process parameters for the most widespread structural materials. A comparison of the neutron data and the results of calculations carried out by structural materials. A comparison of thegood neutron data andwhich the results of calculations carried out by the finite element method showed their agreement, demonstrates that the developed the finite element method showed their good agreement, which demonstrates that developed theoretical model of the welding process is reliable. This information can be used as the a base for the theoretical model of the welding process is reliable. This information can be used as a base for the development of specific technological recommendations to obtain the desired level and profile of development of specific technological recommendations to obtain the desired level and profile of residual stresses. residual stresses. In similar research work [36], the residual stresses and microstrains in a thin C45 low-alloyed In similar research workbeam [36], the residual stresses The and sample microstrains a thin C45of low-alloyed steel plate welded by a laser were investigated. with in dimensions 100 × 100 ×steel 2.5 3 plate welded by a laser beam were investigated. The sample with dimensions of 100 × 100 × 2.5 mm 3 mm was mounted on three points and welded by a solid-state laser beam using a six-axis robotic was mounted on three and welded a solid-state laser(LBW) beam joint usingwas a six-axis robotic arm. The residual stresspoints distribution in this by laser beam welded investigated onarm. an The residual stress distribution in this laser beam welded (LBW) joint was investigated on an FSD 3 FSD diffractometer with a 2 × 2 × 10 mm gauge volume. The strain scanning was performed across 3 gauge volume. The strain scanning was performed across the diffractometer with a along 2×2× 10 mm the welding direction a path on the middle of the length (Y = 50 mm) and in the middle plane welding along a path The on the middle of the length (Y show = 50 mm) andagreement in the middle (Z = 1.25 direction mm) of the specimen. neutron diffraction results a good with plane FEM (Z = 1.25 mm) of the specimen. The neutron diffraction results show a good agreement with FEM calculations for longitudinal and normal stress components (Figure 15). calculations for longitudinal and normal stress components (Figure 15).
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-1 -50 -40 -30 -20 -10 0 10 20 30 40 50
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5 4 3 2 1 0 -50 -40 -30 -20 -10
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(c) Figure 15. Residual strain (a) and stress (b) measured by neutron diffraction and FEM calculations for
Figure 15. Residual strain (a) and stress (b) measured by neutron diffraction and FEM calculations thin steel plate sample with a laser beam welded (LBW) joint. (c) Dislocation density distribution for thin steel plate sample with laser beaminwelded (LBW) joint. (c) Dislocation density distribution estimated from diffraction peaka broadening the LBW sample, adapted from [36], with permission estimated diffraction peak broadening in the LBW sample, adapted from [36], with permission from © from 2017 SPIE. from © 2017 SPIE. The longitudinal residual stress exhibits two characteristic peaks at distances ± 3 mm from the weld center, which corresponds to the boundaries of the heat-affected zones (HAZ). In the HAZ area The longitudinal residual stress exhibits two characteristic peaks at distances ± 3 mm from (0 mm < X < 3 mm), a significant decrease of the longitudinal stress due to the martensite the weld center, which corresponds to the boundaries of the heat-affected zones (HAZ). In the microstructure formation is observed. For the transverse residual stress component, the results can HAZ area mm < X quite < 3 mm), a significant decrease the longitudinal stress due to the martensite also be (0 considered satisfactory. Nevertheless, theofexperimental data demonstrate a small but microstructure formationwhich is observed. For theby transverse residual stress component, theunder results can noticeable asymmetry, can be explained rapid non-equilibrium cooling after welding alsoconditions be considered quite satisfactory. Nevertheless, the experimental data demonstrate a small but of rigid fixation of the sample. noticeable which beregions, explained by rapid non-equilibrium cooling In asymmetry, the welded joint and can HAZ significant diffraction peak broadening is after often welding observed under due to the change in the material microstructure. Usually, these effects are caused by crystallite size conditions of rigid fixation of the sample. changes due to martensitic transformations and by the increase in the residual lattice microstrain, In the welded joint and HAZ regions, significant diffraction peak broadening is often observed
due to the change in the material microstructure. Usually, these effects are caused by crystallite size changes due to martensitic transformations and by the increase in the residual lattice microstrain, which directly characterizes the dislocation density in a material. From the broadening of diffraction
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which directly characterizes the dislocation density in a material. From the broadening of diffraction peak widths, the level of residual microstrain was evaluated for the studied sample. It was found that peak widths, the level of residual microstrain was evaluated for the studied sample. It was found that the microstrain distribution exhibits a sharp gradient at the weld seam position (X = 0 mm) with a the microstrain distribution exhibits a sharp gradient at −3 the weld seam position (X = 0 mm) with a maximal level of ~4.8·× 10−3− , 3which falls down to ~1·× 10 −for regions outside the HAZ area. The maximal level of ~4.8·× 10 , which falls down to ~1·× 10 3 for regions outside the HAZ area. The estimated dislocation density varies from ~2·× 101414m−2 −for the base material to the maximal value of estimated dislocation density varies from ~2·× 10 m 2 for the base material to the maximal value of −2 at the weld ~5.4·× 1015 m seam center (Figure 15c). ~5.4·× 1015 m−2 at the weld seam center (Figure 15c). Changes in the reactor pressure vessel (RPV) material properties due to neutron irradiation are Changes in the reactor pressure vessel (RPV) material properties due to neutron irradiation are monitored by means of surveillance specimen programs, which are used for the realistic evaluation monitored by means of surveillance specimen programs, which are used for the realistic evaluation of RPV lifetime. Due to the limited number of surveillance specimens, their proper reconstitution of RPV lifetime. Due to the limited number of surveillance specimens, their proper reconstitution procedure after Charpy impact tests is of great importance. In order to evaluate the feasibility of procedure after Charpy impact tests is of great importance. In order to evaluate the feasibility of various various reconstitution methods, the residual stress distribution and microstrain level in test Charpy reconstitution methods, the residual stress distribution and microstrain level in test Charpy specimens specimens welded by the most common techniques (electron beam welding—EBW, laser beam welded by the most common techniques (electron beam welding—EBW, laser beam welding—LBW, welding—LBW, arc stud welding—ASW) were analyzed on FSD [37,38]. Welding techniques are arc stud welding—ASW) were analyzed on FSD [37,38]. Welding techniques are based on the use of based on the use of highly localized energy sources to fuse or soften the material at the weld joint. highly localized energy sources to fuse or soften the material at the weld joint. Due to the concentrated Due to the concentrated heat input and temperature gradients, significant residual stresses and heat input and temperature gradients, significant residual stresses and distortions occur after the distortions occur after the welding process [39] The level of residual stress depends to a large extent welding process [39] The level of residual stress depends to a large extent on the parameters of the on the parameters of the welding procedure. The measured residual stress distribution exhibited welding procedure. The measured residual stress distribution exhibited alternating sign characters for alternating sign characters for all studied Charpy specimens (Figure 16a). Both EBW specimens all studied Charpy specimens (Figure 16a). Both EBW specimens demonstrated the lowest level of the demonstrated the lowest level of the residual stress varying from −85 MPa to 172 MPa for EBW1 and residual stresstovarying from 85 MPacorrespondingly. to 172 MPa for EBW1 −91 MPa to 308 MPa for EBW2, from −91 MPa 308 MPa for−EBW2, Two and otherfrom specimens exhibited significantly correspondingly. other exhibited higher from for −175 higher stress levels:Two from −175specimens MPa to 570 MPa forsignificantly LBW and from −204stress MPa levels: to 678 MPa theMPa ASWto 570 MPa for LBW and from − 204 MPa to 678 MPa for the ASW sample. sample. LBW2, 15 mm x
600
EBW2, (110) x = 17 mm x = 9 mm
y z
, MPa
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Figure 16. (a) Residual stress distribution in the test Charpy specimen (LBW2) reconstituted by the Figure 16. (a) Residual stress distribution in the test Charpy specimen (LBW2) reconstituted by the laser 3) with two weld seams laser beam welding technique. Inset: LBW2 Charpy specimen (10 × 10 × 55 mm beam welding technique. Inset: LBW2 Charpy specimen (10 × 10 × 55 mm3 ) with two weld seams at at X = 0 and X = 14 mm, adapted from [38], with permission from © 2016 Springer. (b) Diffraction X = 0 and X = 14 mm, adapted from [38], with permission from © 2016 Springer. (b) Diffraction peak peak profile a Voigt function the seam weld center seam center (X = 9and mm) andbase in the base (110)(110) profile fittedfitted with with a Voigt function at the at weld (X = 9 mm) in the material material (X = 17 mm). (X = 17 mm).
The pronounced peak broadening effect was observed at the centers of the welded joints due to The pronounced peak broadening effect was observed at the centers of the welded joints due to the change in the material microstructure during the welding process (Figure 16b). For further the change in the material microstructure during the welding process (Figure 16b). For further analysis, analysis, the individual diffraction peaks were fitted by the Voigt function using the least-squares the individual diffraction peaks were fitted by the Voigt function using the least-squares method. It is method. It is noteworthy that in the regions remote from the weld seam zone, the main contribution noteworthy that in the regions remote from the weld seam zone, the main contribution to the total to the total peak width gives the Gaussian component of the peak. On the contrary, in the weld centers peak width gives the Gaussian component of the peak. On the contrary, in the weld centers and HAZ and HAZ regions, the predominant contribution is defined by the Lorentzian component, which regions, the predominant contribution is defined by the Lorentzian component, which points to a points to a significant influence of the small sizes of crystallites on the peak broadening effect. significant influence of the small sizes of crystallites on the peak broadening effect. The volume-weighted crystallite size was estimated from (110) and (220) line profiles analysis The volume-weighted crystallite size was estimated from (110) and (220) line profiles analysis according to the Warren-Averbach method [40] (Figure 17a). The effect of a small crystallite size, according to the Warren-Averbach method [40] (Figure 17a). The effect of a small crystallite size, causing causing Lorentzian-type peak broadening, is clearly seen at the weld seam centers at X = 0 and X = 9
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Lorentzian-type peak broadening, is clearly seen at the weld seam centers at X = 0 and X = 9 mm (X 14=mm for LBW2 specimen). UsingUsing modified Williamson-Hall type dependencies ∆d2 (d2 )d [41,42], 2(d2) mm=(X 14 mm for LBW2 specimen). modified Williamson-Hall type dependencies the anisotropic peak broadening was analyzed and the microstrain level and dislocation density were [41,42], the anisotropic peak broadening was analyzed and the microstrain level and dislocation estimated for all studied samples. Similarly to microstrain, the distribution of the dislocation density density were estimated for all studied samples. Similarly to microstrain, the distribution of the 15 m−2 for exhibits quite highexhibits values quite at weld seams centers, a maximal levelaof 2.9 ×·10level dislocation density high values at weldreaching seams centers, reaching maximal of 2.9 15 − 2 15 − 2 15 − 2 EBW1, 2.1 ·× 10 m for EBW2, 1.2 ·× 10 m for LBW, and 1.7 ·× 10 m for ASW specimens, 15 −2 15 −2 15 −2 15 −2 ×·10 m for EBW1, 2.1·× 10 m for EBW2, 1.2·× 10 m for LBW, and 1.7·× 10 m for ASW 14 m−2 correspondingly. In regionsInaway from weld seams decreases sharplysharply down to ~2·× 14 specimens, correspondingly. regions away from welditseams it decreases down to 10 ~2·× 10 (Figure 17b). −2 m (Figure 17b).
800
·1015 m-2
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EBW1 EBW2 LBW1 LBW2 ASW
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Figure Crystallite sizes 〈D〉hDvs. scanscan coordinate X forX all Charpy specimens. (b) Figure17. 17.(a)(a) Crystallite sizes i vs. coordinate forstudied all studied Charpy specimens. Dislocation density distributions vs. scan coordinate X, adapted from [38], with permission from (b) Dislocation density distributions vs. scan coordinate X, adapted from [38], with permission from© © 2016 2016Springer. Springer.
4.2. Mechanical Properties of Structural Materials 4.2. Mechanical Properties of Structural Materials One more application of the TOF neutron diffraction is the in situ study of the behavior of One more application of the TOF neutron diffraction is the in situ study of the behavior of promising materials (composites, gradient materials, steels, alloys, ceramics, etc.) under various promising materials (composites, gradient materials, steels, alloys, ceramics, etc.) under various conditions (external load, temperature). Typically, the interaction of several phases in a material and conditions (external load, temperature). Typically, the interaction of several phases in a material and their joint effect on the elastic properties and residual stresses are studied. The results of their joint effect on the elastic properties and residual stresses are studied. The results of investigations investigations are important for designing new materials with the required physical, chemical, and are important for designing new materials with the required physical, chemical, and mechanical mechanical properties. As a rule, in such experiments, a sample of investigated material undergoes properties. As a rule, in such experiments, a sample of investigated material undergoes uniaxial uniaxial tension or compression in a special loading device directly in a neutron beam. Using tension or compression in a special loading device directly in a neutron beam. Using detectors at detectors at scattering angles of 2 = ±90, diffraction spectra at specified values of applied load are scattering angles of 2θ = ±90◦ , diffraction spectra at specified values of applied load are registered. registered. Thus, two independent strain components are measured at two different orientations of Thus, two independent strain components are measured at two different orientations of the sample: in the sample: in the direction of the external load, parallel and perpendicular to the neutron scattering the direction of the external load, parallel and perpendicular to the neutron scattering vector Q. Using vector Q. Using the TOF method, the strains of all observed reflections hkl are determined from the the TOF method, the strains of all observed reflections hkl are determined from the relative shifts of the relative shifts of the diffraction peaks. Usually, in the elastic strain regions, a linear dependence of diffraction peaks. Usually, in the elastic strain regions, a linear dependence of the lattice strain on the the lattice strain on the applied load is observed [19,20]. At the same time, the lattice strain exhibits applied load is observed [19,20]. At the same time, the lattice strain exhibits an anisotropic character: an anisotropic character: εhkl ~ Γhkl, where h, k, and l are the Miller 2indices, and Γhkl = (h2k2 + h2l2 + k2l2)/(h2 εhkl ~Γhkl , where h, k, and l are the Miller indices, and Γhkl = (h k2 + h2 l2 + k2 l2 )/(h2 + k2 + l2 )2 is the 2 2 2 + k + l ) is the orientation (anisotropy) factor (Figure 18a). In the elastic strain range, one can orientation (anisotropy) factor (Figure 18a). In the elastic strain range, one can determine from the determine from the linear dependences εhkl(σ) the inverse values of Young’s modulus for each linear dependences εhkl (σ) the inverse values of Young’s modulus for each crystallographic plane (hkl), crystallographic plane (hkl), which are also linear functions of the orientation factor Γhkl (Figure 18b). which are also linear functions of the orientation factor Γhkl (Figure 18b). The obtained dependences The obtained dependences can be used to estimate the elastic stiffness constants C11, C12, and C44 of can be used to estimate the elastic stiffness constants C11 , C12 , and C44 of the material in terms of the the material in terms of the chosen elasticity model (Reuss, Hill, Kröner) and calculate Young’s chosen elasticity model (Reuss, Hill, Kröner) and calculate Young’s modulus and the Poisson’s ratio modulus and the Poisson’s ratio for any crystallographic direction [hkl]. for any crystallographic direction [hkl].
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Figure 18. (a) Longitudinal and transverse lattice strain of ferrite steel vs. applied load for different Figure 18. (a) Longitudinal and transverse lattice strain of ferrite steel vs. applied load for different crystal planes. (b) Inverse values of longitudinal and transverse Young’s moduli vs. anisotropy crystal planes. (b) Inverse values of longitudinal and transverse Young’s moduli vs. anisotropy (orientation) factor Гhkl, adapted from [19], with permission from © 2018 Springer. (orientation) factor Гhkl , adapted from [19], with permission from © 2018 Springer.
An obvious advantage of neutron time-of-flight diffraction is the wide range of the interplanar An neutron time-of-flight diffraction is thesimultaneously. wide range of the interplanar spacing obvious with theadvantage possibilityofto observe a set of diffraction peaks This makes it spacing with the possibility to observe a set of diffraction peaks simultaneously. This makes it possible possible to study polycrystalline materials with a rather complex structure, including multiphase to study polycrystalline materials withvarious a ratherexternal complexconditions. structure, including materials, in a materials, in a fixed geometry under In earliermultiphase studies [43,44] of W/Cufixed geometry under variousitexternal conditions. earlier studies [43,44] ofpowder W/Cu-graded composite graded composite materials, was shown that theIn samples prepared by the sintering method materials, it was shown that the samples prepared by the powder sintering method demonstrate a demonstrate a relatively low level of residual stresses. However, they have a greater brittleness relatively low level of residual stresses. However, they have a greater brittleness compared with compared with samples prepared by the infiltration method, which limits the prospects of their samples prepared by the prepared infiltration whichmethod limits the prospects their The application. The samples bymethod, the infiltration have a higherof level of application. stresses between samples prepared by the infiltration method have a higher level of stresses between phases and better phases and better mechanical characteristics. The determining role in the residual stress distribution mechanical The determining role inwhile the residual stress profile distribution is played by cooling is played bycharacteristics. cooling conditions after fabrication, the gradient proves to be a secondary conditions after fabrication, while the gradient profile proves to be a secondary factor. In continuation factor. In continuation of these studies, the redistribution of the load at uniaxial compression between of studies, the redistribution of the load at uniaxial compression between “hard” and “soft” thethese “hard” and “soft” phases and the anisotropy of the crystal lattice strain in thethe homogeneous (with phases and the anisotropy of the crystal lattice strain in the homogeneous (with no gradient) composite no gradient) composite material W/Cu prepared by the infiltration method were investigated (Figure material prepared by the infiltration method wereshowed investigated (Figure [19]. Analysis of 19a) [19].W/Cu Analysis of the diffraction reflection intensities that the copper19a) phase demonstrates the diffraction reflection intensities showed that the copper phase demonstrates a moderate texture, a moderate texture, whereas in the tungsten phase, a texture is practically absent. From the results of whereas in the tungsten phase, a texture is practically absent. From the results of experiments, it was experiments, it was established that in the tungsten phase up to ~350 MPa, the strain is elastic, while established thatphase, in theplastic tungsten phase up tostarts ~350from MPa,~85 the MPa strainThus, is elastic, while in the copper in the copper deformation the redistribution of thephase, main plastic deformation starts from ~85 MPa Thus, the redistribution of the main load occurs into the load occurs into the plastically deformed copper phase upon the slight growth of strains in tungsten. plastically deformed copper phase upon the slight growth of strains in tungsten. Eхtended possibilities for studying the thermal and mechanical properties of materials arise for studyingare theperformed thermal and of materials arise when whenExtended neutron possibilities diffraction experiments inmechanical situ with a properties combination of external load and neutron diffraction experiments are performed in situ with a combination of external load and high high temperature [19]. Thus, for widespread D16 aluminum alloy, degradation of the elastic temperature for widespread D16 alloy, degradation of the elastic properties of[19]. the Thus, material was studied at aluminum various temperatures (Figure 19b). The properties precision of of the material was studied at various temperatures (Figure 19b). The precision of determining the lattice determining the lattice strain on the FSD diffractometer turned out to be high enough, which made strain on the diffractometer turned out tobetween be high enough, which made it possible to reliably it possible toFSD reliably observe the difference ε(σ) curves at different temperatures and observe the difference between ε(σ) curves at different temperatures and estimate the changes in the estimate the changes in the elastic properties of the material as a function of temperature. The results elastic properties of the material as atemperature function of temperature. results of experiments revealed of experiments revealed that in the range 13–150 The °C, the modulus of elasticity of the ◦ C, the modulus of elasticity of the material steadily decreases that in the temperature range 13–150 material steadily decreases from 76 to 62 GPa. A similar temperature dependence was also observed from 76ultimate to 62 GPa. A similar temperature for the strength of the material. dependence was also observed for the ultimate strength of the material.
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W phase: (110) (200) (211) Rietveld
200 Cu phase: (200) (220) Rietveld
100
3 0
2
1
150
70 65
0
T, °C 100
50
75 E, GPa
, MPa
300
Al (111) T = 13 °C T = 100 °C T = 150 °C
4
Lattice strain 10-3
400
Exp. Fit
0 -1.0
-0.5
0.0
0.5
Lattice strain 10
-3
(a)
0
50
100
150
200
250
300
350
400
, MPa
(b)
Figure 19. (a) Transverse lattice strain for different planes (hkl) of copper and tungsten phases in the Figure 19. (a) Transverse lattice strain for different planes (hkl) of copper and tungsten phases in the W/Cu composite vs. external load. (b) Lattice strain for the (111) plane in the aluminium alloy vs. W/Cu composite vs. external load. (b) Lattice strain for the (111) plane in the aluminium alloy vs. applied load measured at different temperatures: 13, 100, and 150◦ °С. Inset: temperature dependence applied load measured at different temperatures: 13, 100, and 150 C. Inset: temperature dependence of of the elasticity modulus for the aluminium alloy: symbols designate experimental values, with the the elasticity modulus for the aluminium alloy: symbols designate experimental values, with the solid solid line corresponding to the least square fit E = E0 − B∙T∙exp(−T0/T), adapted from [19], with line corresponding to the least square fit E = E0 − B·T·exp(−T0 /T), adapted from [19], with permission permission © 2018 Springer. from © 2018from Springer.
In recent experiments [45] on FSD, the main parameters of the microstructure of TRIP In recent experiments [45] matrix on FSD,and the amain of the microstructure of TRIP composites composites with an austenitic ZrOparameters 2 zirconium-dioxide reinforcing phase subjected to with an austenitic matrix and a ZrO2 zirconium-dioxide reinforcing phase subjected to plastic plastic deformation of different degrees were investigated. Two series of samples of the TRIP deformation of different degrees were investigated. Two phase series of of zirconium samples ofdioxide the TRIP composite composite with an austenitic matrix and a strengthening ZrO 2, partly with an austenitic matrix and a strengthening phase of zirconium dioxide ZrO2 , partly stabilized by stabilized by magnesium (Mg-PSZ, series 1) and by yttrium dioxide (Y-PSZ, series 2), were prepared magnesium (Mg-PSZ, series 1) and using by yttrium dioxide (Y-PSZ, prepared the2 ceramic powder by the powder metallurgy method hot pressing. In each series series,2), thewere content of theby ZrO metallurgy using In each series, thedesignated, content of respectively, the ZrO2 ceramic phase was 0,method 10, 20, 30, and hot 100 pressing. wt % and the samples were as S1,phase S2, S3,was S4, 0, 10, 20, 30, and 100 wt % and the samples were designated, respectively, as S1, S2, S3, S4, and S5. and S5. The samples of series 1 underwent plastic deformation in ex situ experiments by means of The samples of series 1 underwent plastic deformation in ex situ experiments by means of uniaxial uniaxial compression at different loads: σ = 0, 500, 650, 800, 950, 1100, 1250, 1400, and 1580 MPa. After compression at different loads: = 0, removed 500, 650, 800, 1100, 1250,spectra 1400, and 1580deformed MPa. After each each deformation cycle, the loadσ was and 950, the diffraction of the sample deformation cycle, the load was removed and the diffraction spectra of the deformed sample were were measured. The samples of series 2 were investigated in in situ experiments, during which they measured. The to samples oftension/compression series 2 were investigated in situ experiments, during which they were were subjected uniaxial up to in destruction in loading machine LM-29 directly subjected to uniaxial tension/compression up to destruction in loading machine LM-29 directly in the in the neutron beam. neutron beam. In the plasticity region at a load above 650 MPa, the formation of two martensitic phases was In the plasticity region at a load above 650 MPa, the formation of two martensitic phases was observed in the austenitic matrix of series 1 samples: the cubic α’-martensite (space group Im3m) and observed in the austenitic matrix of series 1 samples: the cubic α’-martensite (space group Im3m) and the hexagonal ε-martensite (space group P63/mmc) (Figure 20a). The phase distribution by Rietveld the hexagonal ε-martensite (space group P63 /mmc) (Figure 20a). The phase distribution by Rietveld analysis is shown in Figure 20b. In the ceramic sample S5 of pure zirconium dioxide (100% ZrO 2), analysis is shown in Figure 20b. In the ceramic sample S5 of pure zirconium dioxide (100% ZrO2 ), two two phases were observed: cubic (f ≈ 55%) and tetragonal (f ≈ 45%). The ratio between the phases was phases were observed: cubic (f ≈ 55%) and tetragonal (f ≈ 45%). The ratio between the phases was practically unchanged with an increasing degree of plastic deformation. In addition, in the plasticity practically unchanged with an increasing degree of plastic deformation. In addition, in the plasticity region, a considerable anisotropic broadening of the diffraction peak was observed. The anisotropy region, a considerable anisotropic broadening of the diffraction peak was observed. The anisotropy of peak broadening is due to the elastic fields of dislocations in the material and, correspondingly, a of peak broadening is due to the elastic fields of dislocations in the material and, correspondingly, a variation in the dislocation contrast factor at the neutron or X-ray scattering [42]. Thus, the estimated variation in the dislocation contrast factor at the neutron or X-ray scattering [42]. Thus, the estimated dislocation densities for the austenitic matrix demonstrate similar dependences for all samples. The dislocation densities for the austenitic matrix demonstrate similar dependences for all samples. The maximum values of dislocation density lie in the range (12 ÷ 20) × 101414 m−−22, depending on the maximum values of dislocation density lie in the range (12 ÷ 20) × 10 m , depending on the zirconium dioxide content in the composite. zirconium dioxide content in the composite. Strain-stress curves were measured during in situ neutron experiments with series 2 samples Strain-stress curves were measured during in situ neutron experiments with series 2 samples (Figure 21a). The Young’s modulus and the Poisson ratio determined from the linear dependences (Figure 21a). The Young’s modulus and the Poisson ratio determined from the linear dependences ε(σ) in the elastic region demonstrate a strong dependence on the zirconium dioxide content and a ε(σ) in the elastic region demonstrate a strong dependence on the zirconium dioxide content and a considerable difference in their values for compression and tension. The similar dependence on the zirconium dioxide content was also observed for the ultimate strength of the material (Figure 21b). Probably, the main factor explaining such behavior of the material is the formation of microcracks at
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considerable difference in their values for compression and tension. The similar dependence on the zirconium dioxide content was also observed for the ultimate strength of the material (Figure 21b). Probably, the main factor explaining such behavior of the material is the formation of microcracks at Crystals 23 of Crystals 2018, 2018, 7, 7, xx FOR FOR PEER PEER REVIEW REVIEW of 26 26 the interphase boundaries during the deformation process. Further, the small stress jumps,23observed on the strain-stressboundaries curves, are additional evidence in favorFurther, of this hypothesis. the the interphase interphase boundaries during during the the deformation deformation process. process. Further, the the small small stress stress jumps, jumps, observed observed The behavior of the austenitic matrix in the plastic deformation region is similar to that observed on the strain-stress curves, are additional evidence in favor of this hypothesis. on the strain-stress curves, are additional evidence in favor of this hypothesis. The of austenitic matrix the region is to that in the series with nearly same level ofin dislocation density in the material. The The1behavior behavior of the thethe austenitic matrix in the plastic plastic deformation deformation region is similar similar tomartensitic that observed observedphase in the series 1 with nearly the same level of dislocation density in the material. The martensitic phase formation in sample (pure started frominloads of 350The MPa and higher, in the series 1 withS1 nearly theaustenitic same level matrix) of dislocation density the material. martensitic phasewhile formation in sample S1 (pure austenitic matrix) started from loads of 350 MPa and higher, while formation in sample S1 (pure austenitic matrix) started fromS2–S4. loads of 350 MPa andthe higher, while no no martensitic phase formation was observed for samples Apparently, reason forno such a martensitic phase formation was observed for samples S2–S4. Apparently, the reason for such martensitic formationbetween was observed for samples S2–S4. the reason forformation such aa of behavior is load phase redistribution the austenitic phases andApparently, ZrO2 ceramics and the behavior load redistribution between austenitic phases and ZrO ceramics and formation behavioratis isthe load redistribution between the the andlevel ZrO22in ceramics and the the matrix formation microcracks interphase boundaries, dueaustenitic to whichphases the load the austenitic did not of microcracks at the interphase boundaries, due to which the load level in the austenitic matrix did of microcracks at the interphase boundaries, due to which the load level in the austenitic matrix did attainnot values sufficient for phase transformations. attain values sufficient for phase transformations. not attain values sufficient for phase transformations.
1.5 1.5
Phasecontent mass.% contentf,f,mass. % Phase
(111) (111) -M(002) (002) -M
(200) (200)
-M(101) (101) -M -M(110) (110) -M
(222) (222)
1.0 1.0
-M(100) (100) -M
(220) (220)
(311) (311)
0.0 0.0 0.5 0.5
-M(200) (200) -M
0.5 0.5
-M(211) (211) -M
1.5 1.5 1.0 1.0
100 100
Sample Sample 44 (30% (30% ZrO ZrO22)) =01580 MPa =01580 MPa
2.0 2.0
(420) (420) (331) (400) (331) (400) -M(310) (310) -M
Intensity10 1055, ,a.u. a.u. Intensity
2.5 2.5
Austenite: Austenite: S1, S1, S3, S3,
80 80 60 60
S2 S2 S4 S4
-Martensite -Martensite S1, S1, S3, S3,
40 40 -Martensite -Martensite 20 20 S1, S1, S3, S3,
S2 S2 S4 S4
S2 S2 S4 S4
00 00
2.0 2.0
200 200 400 400 600 600 800 800 1000 1000 1200 1200 1400 1400 1600 1600
, , MPa MPa
d, d, ÅÅ
(a) (a)
(b) (b)
Figure 20. (a) The evolution of the diffraction pattern of TRIP-composite as a function of plastic
Figure 20. The (a) The evolution thediffraction diffraction pattern pattern of as as a function of plastic Figure 20. (a) evolution ofofthe ofTRIP-composite TRIP-composite a function of plastic deformation deformation (sample (sample S4, S4, σσ == 00 ÷÷ 1580 1580 MPa). MPa). The The Miller Miller indices indices of of the the main main peaks peaks of of austenitic austenitic and and α’α’deformation (sample S4, σ = 0 ÷ 1580 MPa). The Miller indices of the main peaks of austenitic and α’and and ε-martensitic ε-martensitic phases phases are are indicated; indicated; (b) (b) Mass Mass content content of of the the observed observed phases phases vs. vs. plastic plastic and ε-martensitic phases are indicated; (b) Mass content of the observed phases vs. plastic deformation deformation deformation degree degree for for all all investigated investigated samples, samples, adapted adapted from from [45], [45], with with permission permission from from ©© 2018 2018 degree for all investigated samples, adapted from [45], with permission from © 2018 Springer. Springer. Springer.
22
00 -1 -1 -2 -2
1000 1000
S1 S1 S2 S2 S3 S3 S4 S4 S5, S5, a-axis a-axis S5, S5, c-axis c-axis
-3 -3 -4 -4 -5 -5
S1 S1 S2 S2 S3 S3 S4 S4 S5, S5, a-axis a-axis S5, S5, c-axis c-axis
-6 -6 -1000 -1000
-800 -800
100% 100% ZrO2: ZrO2: Tension Tension Compression Compression
800 800
-600 -600
-400 -400
, , MPa MPa
(a) (a)
-200 -200
00
MPa FF, ,MPa
Latticestrain 10-3-3 strain10 Lattice
11
600 600 TRIP TRIP composite: composite: Tension Tension Compression Compression
400 400 200 200 00
00
10 10
20 20
30 30
100 100
ZrO ZrO22 mass mass content, content, % %
(b) (b)
Figure Figure 21. 21. (a) (a) Longitudinal Longitudinal and and transverse transverse lattice lattice strain strain determined determined from from the the relative relative change change in in the the
Figure 21. (a) Longitudinal and transverseoflattice strain determined from the and relativethe change in the lattice lattice parameter parameter for for the the austenitic austenitic matrix matrix of the the TRIP-composite TRIP-composite for for samples samples S1-S4 S1-S4 and for for the ceramic ceramic latticesample parameter for the austenitic matrix of the TRIP-composite for samples S1-S4 and for the ceramic S5 (100% ZrO 2). (b) The ultimate stress of the TRIP composite vs. ZrO 2 content, adapted from sample S5 (100% ZrO2). (b) The ultimate stress of the TRIP composite vs. ZrO2 content, adapted from [45], with permission from © 2018 Springer. sample S5 (100% ZrO ). (b) The ultimate stress of the TRIP composite vs. ZrO content, adapted 2 from © 2018 Springer. 2 [45], with permission from [45], with permission from © 2018 Springer.
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5. Conclusions Accumulated work experience has shown that the correlation RTOF diffractometry at a long-pulse neutron source possesses many advantages and, therefore, can be considered as a suitable tool for residual stress investigations in bulk samples and for the precise characterization of the microstructure of modern structural materials. The achieved high resolution level at a relatively short flight path allows investigating important parameters of materials’ microstructure, such as lattice strain, microstrain, and size of crystallites. At present, the regular experiments for residual stress and microstrain studies in bulk industrial components and in new advanced materials are successfully performed on the FSD diffractometer. Further development of the FSD diffractometer will include an upgrade and expansion of the detector system: 14 new TOF focused ZnS(Ag) elements will be installed in the near future on both (right and left) banks of 90◦ -detectors, which will increase the scattering angle range by up to 40◦ for each detector. The spectral distribution of the incident neutron beam will be optimized by installing a new supermirror-coated neutron guide. Another important task is the replacement of the Fourier chopper. Currently, a new Fourier chopper is being developed that operates in a vacuum and has improved dynamic characteristics. This device is a rotor-stator system with real cut-away radial slits and 10 B absorbing layers. As the source of the pickup signal, it is supposed to use a laser beam passing through the chopper slits. Such design of the new chopper provides more precise PID control, no phase error (shift of pickup signal phase with respect to the neutron signal), no absorption and scattering from the chopper disc material, less vibration, and gamma background. Thus, all these developments can significantly enhance the quality of the diffraction spectrum, i.e., reduce the background, increase the intensity of the spectrum, and improve the profile and symmetry of the diffraction peak. Funding: At the initial stage of FSD construction, the work was financed within FLNP JINR Topical Research Plan. The development of FSD was partially supported within the JINR–BMBF (Germany), JINR-Romania, JINR-Poland cooperation projects as well as within projects of the Russian Foundation for Basic Research (grants No. 14-42-03585_r_center_a and 15-08-06418_a.) Acknowledgments: The author is grateful to A.M. Balagurov, V.V. Zhuravlev, P. Petrov and S.V. Guk for useful discussions. The author is in debt to I.V. Papushkin for experimental assistance. Conflicts of Interest: The author declares no conflict of interest.
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