Journal of Environmental Quality 31:494-499 (2002)
© 2002 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America
Article
SYMPOSIUM PAPERS
Stray Field Nuclear Magnetic Resonance of Soil Water
Development of a New, Large Probe and Preliminary Results
P. Kinchesha,
A. A. Samoilenkob,
A. R. Preston*,a and
E. W. Randalla
a University of London, Queen Mary and Westfield College, Chemistry Dep., London E1 4NS, UK
b Russian Academy of Science, Institute of Chemical Physics, Moscow, 117977, Russia
* Corresponding author (a.r.preston{at}qmul.ac.uk)
Received for publication June 2, 2000.
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ABSTRACT
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Development, characterization, and preliminary results of a recent technique capable of local measurements of pore-size distribution by a spatially resolved low resolution nuclear magnetic resonance (NMR) technique are described. Potential environmental uses include studying the change in pore-size distribution caused by surface compaction, which influences surface runoff, and obtaining information on the physical state of non-aqueous compounds in porous materials, which should aid the selection of appropriate soil remediation methods. Stray field (STRAFI) imaging is an NMR technique that allows distortion-free imaging of materials with short NMR relaxation times. The sample is placed in the strong axial fringe field gradient of a superconducting NMR magnet. We report on a new, unique, large 5-cm-diameter STRAFI probe, and its use for three preliminary test cases: water in ceramics of known pore size, paraffin wax and oil in sandstone rock, and water in soil at different matric potentials. The imaging is confined to one dimension with a spatial resolution of the order of 100 µm for protons. The optimum position for imaging occurs at 2.62 T and a gradient of 12.1 T/m. Water relaxation decay curves can be measured at any position in the 8-cm-long sample. These curves are decomposed into a series of terms each corresponding to a different pore size. Preliminary results show continuum fits to decay curves for a soil drained to three different matric potentials. Such information will be useful for interpreting water retention curves and will lead to understanding of the behavior of fluids in the vadose zone.
Abbreviations: MRI, magnetic resonance imaging • NMR, nuclear magnetic resonance • RF, radio frequency • STRAFI, stray field
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INTRODUCTION
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GASEOUS, LIQUID, and solid phases are present simultaneously in the vadose zone of a soil. The location of the fluid phases in the porous structure formed by the soil particles is very important both in soil physics and agriculture. In contaminated soil, non-aqueous liquids may also be present, and knowledge of their location, whether tightly bound to clay platelets or lying in droplets in interaggregate pores, would aid selection of appropriate remediation strategies. The study of such a multiphase system is a challenging problem. This paper describes the development of an NMR technique to measure both water content and the size distribution of occupied pores as a one-dimensional function of position in an undisturbed soil sample. Such depth-dependent behavior occurs, for example, in soils whose surface layers have been compacted by rain impact or the wheels of agricultural machinery. This compaction decreases the near-surface porosity and thus increases runoff.
Magnetic resonance imaging (MRI) is a well-established technique in which a sample is placed in the central region of a strong magnet where the magnetic flux density or field (B) is uniform and homogeneous. Spatial information is encoded in the output signal in conventional techniques by using coils that can produce a field gradient in any direction. Variation of the size and direction of the gradient allows the production of a spatial image in one, two, or three dimensions. The maximum gradient that can be produced by such coils is limited; moreover, the switching of the gradients takes time. The stray field (STRAFI) technique of Samoilenko et al. (1988) uses a static gradient, which is about two or three orders of magnitude greater: 10 to 100 T/m. This occurs away from the magnet center in the stray or fringe field. The place along the bore where the on-axis field is decaying rapidly with distance, z, that is, where 
Bz/z is large, occurs near the edge of the superconducting solenoid. The short radio frequency (RF) pulses that are used to excite the NMR signal are of finite bandwidth; this means that in general it is not possible to excite the entire sample simultaneously, instead information comes from a narrow "sensitive slice," which has a width on the order of 100 µm for protons. The STRAFI image in one dimension normally is produced by moving the sample through the sensitive plane between each pulse train. Higher dimensions can be reached by rotations of the sample. Many of the rapidly growing number of uses of the STRAFI technique for the study of problems in materials science are described in a recent review by McDonald and Newling (1998), which also treats the basic theory.
Typically, a STRAFI image is acquired from a sample less than 1 cm in diameter, but for soils (and rocks) a larger sample is desirable. One of the constraints is the size of the internal bore of the magnet, which is normally 89 mm. For this work we have used the 330-mm bore of a horizontal magnet (200/300 Mk II, Oxford Instruments, Oxford, UK) and a Unity Inova 200 console (Varian Associates, Palo Alto, CA).
Stray field imaging is advantageous for soil imaging because the strong gradient, Bz/z, typically 10 to 50 T/m, greatly reduces problems due to magnetic susceptibility variations arising from ferromagnetic particles in the soil and air in partially filled voids (Kinchesh et al., 1994). These susceptibility variations produce strong local internal gradients that are negligible in STRAFI imaging but are not negligible compared with the gradients used in conventional MRI and thus can lead to severe image distortions of conventional images.
The water in soil has much shorter relaxation times than bulk water. The value for any one pore depends on the size of the pore and whether the water is "solid-like," being bound to the pore surface. The T2 relaxation time of water is on the order of 1 s, but the value for ice is only about 5 µs (Nunes et al., 2000). Bound water such as water of crystallization also has very short relaxation times, on the order of microseconds (Randall et al., 1995). This is normally too short for conventional imaging, which can detect only down to milliseconds, so that an appreciable fraction of the water present, the bound water and the water in small pores, remains undetected (Hall et al., 1997). Stray field imaging, by contrast can detect virtually all the water present.
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PORE-SIZE DETERMINATION
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One of the most important areas of soil physics concerns the behavior of water within a soil (e.g., Childs, 1969). The water is present in pores of very different sizes connected by necks or throats that are also of variable diameter. One of the common methods used to determine the pore-size distribution in a soil uses the water retention curve. The water content of a series of samples of soil is determined gravimetrically after each has been equilibrated at a different matric potential. Differentiating this curve yields the amount of water lost during a given pressure increment. The soil is modeled as a bundle of capillary tubes, the pressure at which each drains depending on its diameter, and so the water retention curve can be converted into a pore-size distribution. This model is, however, oversimplified, since it ignores the narrow throats. The throat diameter rather than that of the pore will control the matric potential at which it drains. Large pores with particularly narrow throats will drain at the same potential as smaller ones with proportionately larger throats.
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RELAXATION TIMES
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Nuclear magnetic resonance spectroscopy is routinely used to measure pore-size distributions in porous materials. Spectroscopy, unlike conventional NMR imaging, can reach the very small relaxation times and hence detect water in small pores. However, there is no spatial information: the whole sample is used. In a porous medium, water molecules in a thin layer adjacent to the pore surface are able to relax much more rapidly than those in the bulk. In the fast diffusion limit the time taken for a molecule to cross a pore and enter the surface layer is much less than that needed to relax at the surface, thus all molecules in a given pore relax at a fixed rate given by a weighted average of the bulk and surface decay rates. Thus, the relaxation time for a given pore is the harmonic mean of the bulk and surface decay times. So, for a given pore shape the pore size d is related to the measured relaxation time Ti (i = 1 or 2 depending on experiment) by:
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where Tib is the relaxation time for the bulk liquid and 
i is the relaxivity factor, which includes the thickness of the surface layer, the efficiency of surface relaxation, and geometrical factors. The measured relaxation curve for a porous material will not in general be a simple exponential decay, and if the throats linking pores are narrow then the relaxation rate of each pore will be independent of that of its neighbors so that the overall decay contains contributions from each individual pore.
The T1 or T2 decay curves for the whole sample are obtained, and are then fitted as the sum of a series of discrete exponentials, or to a model distribution as in the stretched exponential approach (Kenyon et al., 1986), or to a continuous distribution of decay times, the coefficients of which are taken as a measure of the pore-size distribution. The relaxation method, in contrast to the water retention technique, is sensitive to the pore dimensions rather than those of the throats. Thus, in partially drained materials we expect to see a component with a long relaxation time corresponding to those large-diameter pores, which have been unable to drain because they are linked only to the rest of the material by narrow necks.
We can extend this method to provide spatially resolved information using the STRAFI technique.
This paper has two parts. In the first half the design and characterization of the new STRAFI probe are described, and in the second part, application of the probe to three systems is reported. These case studies include:
(i) A comparison of images from blocks of sandstone into which oil and wax have infiltrated.
(ii) Spatially resolved measurements of the T1 relaxation time in a series of water-saturated ceramics, each with a different narrow pore-size distribution. Secondly, the spatial dependence of echo trains from a phantom having two known pore sizes is examined, to test the STRAFI method of measuring the relative numbers of the pore sizes as a function of position.
(iii) A sample of a natural loamy-sand soil is studied as a function of matric potential using a specially made holder that fits inside the STRAFI probe.
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DESIGN AND CHARACTERIZATION OF THE STRAY FIELD PROBE
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Most existing STRAFI probes (see, for example, McDonald and Newling, 1998) take samples with a maximum diameter of only about 10 mm. For soils, however, larger samples are preferred. Soils can be very heterogeneous and friable. We wish ultimately to study the pore-size distribution of undisturbed material, so it is important to minimize edge effects caused by compaction when a sample is extracted from the ground. We have, therefore, constructed a STRAFI probe that can take samples up to 50 mm in diameter and up to 80 mm long, which can be rapidly installed inside our 330-mm horizontal-bore imaging spectrometer.
The STRAFI probe consists of a silica tube on which the double turn RF saddle coil is wound, and into which the sample is placed. During preliminary testing of the coil, the field uniformity inside the coil had been empirically optimized by placing shaped copper shims adjacent to the longitudinal conducting strips.
The probe is contained in an RF shielding box through the walls of which the connections are made. This whole probe–assembly is mounted on a platform that can be moved in and out of the magnet on horizontal rails by a screw thread driven by a stepper motor. The controller for the stepper motor (PM341, Mclennan Servo Supplies Ltd., Camberley, UK) includes a position encoder to ensure repeatability of the slice locations during multiple repeat scans. Sample movement, RF pulsing, and image acquisition are all controlled from the spectrometer console. Profiles are obtained by a simple "step and pulse" method, rather than by continuous movement "on the fly." Currently adjacent slices are acquired consecutively rather than in an interleaved fashion.
The Selected Slice
In STRAFI imaging, when the RF pulse is applied the signal is produced only from a thin slice of the sample, Samoilenko's so-called "sensitive slice." At the position in the field at which Bz/z is a maximum the slice will be at its narrowest, but it will be nonplanar, thus although the volume of material contributing to the signal will be a minimum, the curvature of the slice will degrade the resolution in a projected one-dimensional profile. It is more important that the projected width of the slice, rather than its local thickness at the slice center, be a minimum. This occurs at a slightly different (optimum) position where the curvature 2Bz/r2 = 0 (cylindrical polar coordinates). This position was located from an examination of the manufacturer's field plots. The frequency, 
OPT, at this position, was then found to be 111.5 MHz. The gradient, G = Bz/z, at this position was measured to be 12.091 ± 0.016 (2
) T/m. This measurement was achieved by "field profiling": imaging a phantom consisting of a series of well-defined interfaces between silicone rubber and glass discs, and observing the displacement of these features at a set of frequencies over a frequency range of 11 MHz (Preston et al., 2000).
Resolution and Uniformity Test
It is important that the probe can be easily removed from the magnet and replaced without needing careful adjustment of the orientation of the translation mechanism relative to the magnet axis. The sensitive slice is at right angles to the magnet axis, z, and ideally the sample should move precisely along z, and should be mounted in the correct orientation in order to realize the best resolution in the one-dimensional projection.
The resolution seen in an image from a phantom consisting of a series of parallel-sided discs depends upon both specimen-dependent and instrumental factors. The former include the width of the excited slice and the intrinsic line width: small for 1H larger for other nuclei with I = 1/2 but significant for those with I > 1/2, that is, quadrupolar nuclei (Bodart et al., 1997). The instrumental factors are the gradient and the length of the RF pulse: large gradients and long pulses give narrow slices. The length of the pulse must, however, be short enough to allow detection of the small relaxation components. The instrumental considerations also include the curvature of the sensitive slice and the alignment of the phantom relative to the magnet axis (as described already), and if multiple scans are added to improve signal to noise, there should be no drift in origin of the translational scan.
During acquisition of a profile, the sample and the coil move along the axis of the magnet. At each slice the signal is generated from a different position in the coil, thus it is necessary to find the region of the coil over which the signal is uniform. A phantom was assembled from Perspex discs separated by successively thinner glass spacers, each of 5 cm diameter. The STRAFI probe was mounted on the translation mechanism and the latter bolted onto the front face of the magnet. The experiment was carried out to determine the resolution that would routinely be attainable relying simply on the precision of the machining.
The 1H profile (Fig. 1)
is the result of overnight averaging: 2143 complete scans were acquired. Figure 1 shows that with a 90-µm step size, the slice flatness and probe alignment are sufficiently good for a 40-µm-thick spacer to be detected. It also demonstrates that the Perspex signal is essentially uniform over the length of the phantom. The slight variation in the Perspex signal along the profile shows that the RF production of the coil is not entirely uniform. The large step size limits the spatial resolution, but this could be improved by using smaller steps. On other occasions with fewer averages, the 40-µm spacer was also readily detectable, demonstrating the reproducibility of the probe alignment. Overnight scanning is a test of the reliability of the stepper motor and position encoder.
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Fig. 1. One-dimensional 1H stray field (STRAFI) image of the resolution test phantom, made from alternating Perspex and glass discs each of 50 mm diameter. Thickness of each glass spacer is given above the appropriate minimum in the profile. The slice separation (step size) is 90 µm. The intensity profile is the sum of the first five echoes of the STRAFI echo train, with one point per echo.
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The resolution could be improved also by increasing the pulse duration. This would require a longer echo time and so would only be practical if the phantom were constructed from a material with a longer T2 relaxation time than 36 ± 3 µs (Kinchesh, unpublished data, 2000), which was found by STRAFI for Perspex.
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APPLICATIONS
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Sandstone
Two sandstone samples were prepared, each 15 mm thick by 30 mm square. They were placed with one face just immersed in mineral oil for one sample and in molten paraffin wax for the other. Capillary absorption of the liquids was followed visually by observing the side faces of the blocks. The latter were removed from contact with the liquids when the wetting front was about halfway up the faces. The paraffin was allowed to solidify.
One-dimensional STRAFI profiles were then acquired of each block using quadrature echo trains, 
x - (
- y - - echo)ne, where x and y are square RF pulses of duration 20 µs, and x and y denote the relative phases, which differ by 90 degrees. One complex point per echo was recorded for each of ne = 32 echoes. The time, , between the first two pulse centers was 35 µs, giving a time between successive echoes, te, of 70 µs. For the image (Fig. 2a)
, 140 slices were acquired. In Fig. 2b, markedly different behavior for the two samples is seen by comparing signal versus echo number. The signal for the solid paraffin steadily increases initially with echo number indicating that a tip angle considerably less than 90 degrees was used. The level after a few echoes shows very little decay, however, unlike the oil signal that decays rapidly. This rapid decay is caused by the much faster diffusion in the liquid as opposed to in the solid as well as by differences in the relaxation times. The diffusion effect is enhanced by the large size of the gradient in STRAFI experiments.
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Fig. 2. Stray field (STRAFI) profiles of two sandstone blocks into which molten paraffin wax and mineral oil have diffused from their right faces. Markers were placed in contact with the left faces. (a) Intensity distributions recorded from points at the peak of the first, second, and third echoes of the echo train. (b) Amplitude of the echoes along the echo train for paraffin and mineral oil. Points plotted are the averages over six adjacent slices at positions indicated in the profile by short bars.
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Ceramics
An aim of the work is to use STRAFI to investigate pore-size distributions in soils. An initial feasibility test was to apply the technique to a series of highly porous ceramics, each with a narrow pore-size distribution. Discs of Coralith (Fairey Industrial Ceramics, Staffs, UK), made of alumina particles bonded by glass with mean pore sizes of 300, 30, 20, 3, and 1 µm, were used. (Further details on these materials together with water retention curves are given in Whalley et al., 2001.) Each disc was 8 mm thick and 31 mm in diameter. They were saturated with distilled water by placing them in a water-filled desiccator connected to a vacuum line for two hours. The saturated discs were separated from each other by acetate sheets, and stacked into a cylindrical phantom that was then wrapped in Parafilm sealing tissue (Gallenkamp, Loughborough, UK) to prevent evaporation during measurement. The STRAFI system was then used to address each disc in turn, and T1 values were determined for each disc using the progressive saturation method with 40 different recovery times spaced logarithmically.
A single exponential was fitted to the relaxation curve of each disc using the Varian VNMR software. Figure 3
shows the linear relationship obtained by plotting the reciprocal of T1 against that of pore diameter. This is as expected but the quality of the fit is a good illustration of the power of NMR to determine pore size. With the STRAFI method the spatial variation may be studied.
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Fig. 3. Dependence of the longitudinal relaxation time, T1, as determined by stray field (STRAFI) nuclear magnetic resonance (NMR) on the nominal pore diameter for a series of water-saturated ceramic discs in a single phantom, each with a narrow pore-size distribution and high porosity (ca. 35%). The T1 recovery curve was fitted with a single exponential. The line is a weighted least squares fit to the data.
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The relaxation of water in a pore is an average value because of the fast exchange of hydrogen between sites. The average is a weighted one; so that as the proportion of free to bound water varies, the average relaxation time will vary. Hence follows the relation between relaxation time and pore size. It is expected that in Fig. 3, the intercept should equal the relaxation rate of bulk water, and the slope should be the relaxivity. The values obtained are T1b = 1.027 ± 0.3 s (2) and relaxivity 1 = 1.96 ± 0.10 µm/s (2).
The following experiment was performed to check the feasibility of using STRAFI data for a phantom containing more than one pore size at any one position. A phantom was designed that contained only two pore sizes, the proportion of which varied in a controlled way with position. A composite ceramic cylinder, 31 mm in diameter and 24 mm long, was produced by cutting two Coralith cylinders of mean pore size 1 and 20 µm respectively at an angle of 45 degrees, and combining one piece from each. The two pieces were separated by an acetate sheet. After the composite bi-wedge cylinder was saturated with water as described above, it was wrapped in Parafilm, and two end pieces of matching pore size were added at the appropriate ends. The T2 values were then measured at eight positions along the phantom with a Carr–Purcell–Meiboom–Gill experiment having 912 repeats and 128 echoes.
The T2 data from the bi-wedge were analyzed by SPLMOD, a program by Provencher and Vogel (1983), in which a number of discrete exponentials are fitted to a decay curve. It was decided to find a single pair of exponentials to fit all eight positions across the composite cylinder while letting the program select the proportion of each needed for each slice. These proportions and their errors are plotted in Fig. 4
. The fit to the expected form arising from the known geometry is very good as indicated in the inset. The phantom is cylindrical, with the bisecting plane cutting the circular end faces so we do not expect the contribution of the minor component to vanish at the end slices, nor should the contribution of a given pore size vary strictly linearly with position, as would be expected if a cuboidal phantom had been used. Without the constraint that all slices had the same pair of exponentials, the fit was not as good. Part of the problem is the noise that occurs in the experimental results.
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Fig. 4. Spatial dependence of the amplitudes of two exponential decay terms needed to fit peak amplitudes in echo trains from a series of positions along a cylinder made up from two half cylinders in the form of a bi-wedge. The mean pore sizes are 1 and 20 µm and are shown above the graph.
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Soil
A loamy sand (Kingsmead, 80% sand, 11% silt, 9% clay) was selected because its water content could be varied significantly over the range of matric potentials obtainable with a vacuum pump. Air-dry soil, which had been passed through a 5-mm sieve, was packed into a glass cylinder in contact with a reservoir of distilled water via a saturated microporous glass sinter (Fig. 5) . After the soil had been saturated, the assembly was placed inside the STRAFI probe so that all three regions (soil, sinter, and water) lay within the uniform region of the coil.
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Fig. 5. Diagram of the apparatus developed to permit variation of the matric potential of a soil sample within the stray field (STRAFI) coil. The potential can be altered by raising or lowering the reservoir. It is important that the sintered plate is saturated with water.
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As a preliminary test, the matric potential was varied simply by lowering the water level in the reservoir relative to the midline of the probe by 20, 40, and 60 cm. Two-dimensional displays of echo-train amplitude versus position clearly revealed inhomogeneities in soil packing. A slice with strong intensity was selected and a decay curve obtained for each matric potential. The pulse sequence used was [x - ( - y - - echo)ne - D]nr with a (pulse center separation) of 55 µs, pulse lengths of 35 µs, a D of 1 s, ne = 768, and nr = 14000. The amplitude of the echo peaks, omitting the first four echoes, were fitted to continuous distribution of decay rates using the program CONTIN (Provencher, 1982).
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DISCUSSION
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These initial results are encouraging. As the matric potential is increased, the distribution peak moves to higher rates (see Fig. 6)
and becomes less skewed to the low rate (i.e., large pore end), and the overall area of the distribution curve decreases. The reduction in area occurs due to the reduction in total water content of the sample, while the preferential loss of low rate terms is evidence for the expected draining of large pores before smaller ones. However, there is not an abrupt cutoff at the large pore end, whose position moves steadily to higher rates on draining; instead, the distributions all start at the same minimum rate. This is consistent with the hypotheses that the sample does not behave as a bundle of capillary tubes, each draining at a fixed matric potential, but instead as interlinked pores and throats, and that not all pores of a given diameter are as easy to drain.
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Fig. 6. Distributions of exponential decay terms produced by CONTIN analysis of the peak amplitude of successive echoes from a long train of pulses applied to a loamy sand in the variable matric potential holder. Three distributions produced by successively draining the soil to 20 hPa (=20 cm), 40, and 60 hPa are shown. Fits were made to 54 logarithmically spaced decay terms.
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This preliminary work needs to be expanded. In particular, the signal from the soil at each potential must be normalized relative to that of the bulk water and that in the sinter (which will stay fully saturated at the matric potentials under investigation) because the RF properties of the coil vary significantly as the sample drains. The ideal pulse sequence is still being sought; a balance is needed between acquisition time, echo time, and the number of points in the decay curve. Additional work is needed on the theory of the form of the echo trains following the work of Bain and Randall (1996), which showed that there are contributions from both T1 and T2 to the relaxation characteristics of each of the echoes in the relaxation curves fitted to produce Fig. 6.
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CONCLUSIONS
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The advantages of the use of STRAFI-NMR techniques for the study of water in soils have been successfully demonstrated on a suitably large probe. Experiments have included the production of one-dimensional profiles free of distortions produced by magnetic susceptibility artifacts, and the measurement of the spatial variation of relaxation times, yielding information on the spatial variation of pore sizes. Other applications are easy to visualize: any liquid in any solid. Work on some of the potential applications mentioned in the introductory paragraph is in progress (Preston et al. [2001]).
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ACKNOWLEDGMENTS
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Thanks to Dr. Richard Whalley and Dr. Nigel Bird at the Soil Science Group of the Silsoe Research Institute for much useful advice and the supply of the ceramic and soil samples. Thanks also to John Cowley for construction of the holder for use in the experiments using variable matric potential. This work was supported by BBSRC Grants 68/E08576 and 68/E09853. The NMR instrumentation was provided by the University of London Intercollegiate Research Services scheme and is located at Queen Mary and Westfield College.
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REFERENCES
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TOP
ABSTRACT
INTRODUCTION
