COMPARISON OF QUANTITATIVE TEXTURE ANALYSIS RESULTS FROM TIME-OF-FLIGHT AND CONVENTIONAL NEUTRON DIFFRACTION

: The adaptability of time-of-flight neutron diffraction for quantitative texture analysis is demonstrated. Measurements with this technique on drawn steel wire show good agreement with the results from conventional neutron diffraction experiments. A short description of the neutron time-of-flight method is given. Its application for texture investigations especially on low-symmetry crystalline systems, multiphase materials and for in situ studies is discussed.


INTRODUCTION
The aim of the present work is to show that neutron timeof-flight (TOF) diffraction (equivalent to energy dispersive X-ray diffraction) is a suitable tool for quantitative texture analysis. For this purpose the fibre texture of iron wire has been measured, first by conventional angle-dispersive neutron scattering and then using the time-of-flight technique. By comparing the quantitative results obtained by both methods the mathematical procedure for texture analysis by TOF diffraction is verified and some aspects of this method are discussed.
Texture investigations by means of the conventional angle-dispersive method using X-ray I as well as neutron diffraction 2 have been known for a lon time. The series expansion technique proposed by Bunge made it possible to describe the texture of materials quantitatively by calculating the so-called orientation distribution function using three parameters, e.g. the three Euler angles. Recently the importance of energy-dispersive X-ray diffraction for texture investigations has increased, stimulated by efficient X-ray sources and synchrotron radiation. -6 A possibility of texture investigations using neutron time-of-flight technique was first shown by Szpunar et al. in 1968 in a qualitative way. Up to now no publication is known concerning quantitative texture analysis by TOF neutron diffraction. In the present paper a transition to quantitative texture analysis using TOF technique is performed. This experiment is a part of the work on texture investigations by neutron time-offlight diffraction planned for the new pulsed reactor IBR-2 of JINR Dubna.

EXPERIMENTAL METHODS
The conventional angle-dispersive neutron techniqu e has been well known for some years. The diffractometer at the RFR reactor of CINR Rossendorf is described by Kleinstck et al. 2 The TOF method uses the different velocities of neutrons with different energies and different wavelengths.   (2) where h is Planck's constant. The second flight path L2 should be small, because the intensity decreases proportionally to I/L. The neutron time-of-flight diffraction is described in more detail by Buras and Holas. 8 In the TOF method several Bragg reflections are recorded simultaneously. The information obtained at a fixed scattering angle and a fixed specimen orientation is sufficient for the determination of an inverse pole figure. Of course, the number of available Bragg reflections to construct inverse pole figure depends on spectrometer resolution. Alternatively, several normal pole figures can be measured with fixed scattering angle, varying the specimen orientation.
The neutron time-of-flight method is very suitable for studies on low-symmetry crystal systems, on multiphase materials and on axisymmetric samples. Furthermore, the TOF technique permits in sit investigations on specimens subjected to various controlled environments.

EXPERIMENTS
For all the investigations a steel wire of 3 mm diameter was used. Fastening several wires side by side in a special texture goniometer, a sample area of about 60 mm diameter was obtained. By suitable movement of the sample, the effective specimen volume in the beam was held constant. The intensities of one Bragg reflection were thus independent of absorption at various sample orientations.
The texture goniometer can be rotated independently about three perpendicular axes , , and . The smallest possible angular-step is 1 degree in each case. During the present investigation only the -rotation was used ( Figure 2). Q Figure 2. Schematic representation of the texture goniometer. Three independent axes for the transmission case are shown. (  At the pulsed reactor IBR-30 of JINR Dubna the TOF diffraction spectra were measured on the same specimen. The sample orientation was varied in the range from the fibre axis to transverse direction in steps of 6 degrees, i.e., normal pole figures were measured because only 8 reflections can be separated with the present spectrometer resolution.
In Figure 4

MATHEMATICAL TREATMENT
In the case of an axisymmetric specimen the inverse pole figure in the direction of the symmetry axis contains full information about the texture of investigated material. Unfortunately, the resolution of the spectrometer is too poor at present to determine inverse pole figure in a direct way. Therefore, the inverse pole figure of the symmetry axis has to be calculated from the normal pole figure data.
In the case of the conventional angle dispersive method the densities of unnormalized pole figures are measured directly. In TOF experiments the pole densities are proportional to the intensities of Bragg reflections. They have been determined by means of a fit program taking into account the background, energy spectrum of the reactor pulse and asymmetric form of Bragg peaks. This form has been approximated by the asymmetric Lorentzian shape. It has also been possible using a fit program to separate the diffraction peaks which are partly overlapped. For the determination of pole figures the intensities of a fixed Bragg reflection must be compared for all specimen orientations. With variation of the sample orientation at a fixed scattering angle the position of the peak (hk) does not change with respect to the wavelength (channel number of TOF spectrum). Therefore, all wavelength dependent quantities like Debye-Waller factor, absorption, extinction, etc., may not be taken into account. Ni ;Pi () sin d (6) Usually the texture coefficients C are calculated by the least squares method.  Figure   6. In Figure 7 inverse pole figures are represented, which have been calculated from the TOF data taking into account different sets of pole figures. In all cases the series expansions were truncated at 34 also. The original data have been interpolated Th angular step was A 1 after that. The deviation o F2 (h i) coefficients (see Table I) from zero was taken as a criterion for including or excluding the pole figures. This deviation may be used for characterizing the precision of pole figures. 3   In Table II, C-coefficients determined from the TOF data with and without interpolation are represented. The difference between the two sets is significant. The error is so large that the density maximum in the inverse pole figure is shifted from [II0].

CONCLUSION
The present work is the first quantitative texture analysis by the neutron time-of-flight diffraction known to the authors. This method is shown to be a suitable tool for texture investigations. Because of a lot of simultaneously measurable Bragg reflections it appears to be very useful for nonstandard research, e.g. on low-symmetry crystalline systems, multiphase systems, etc. The method (good resolution is assumed) can be used efficiently for direct measurement of inverse pole figures, i.e. for n 8tu studies on a specimen