‘ l_ y: . ‘ I '4 ; > . ' u. 1- ~ '. .... t- ; ‘ E 3‘ I“ I Y {th m :‘z‘i' 1'9! ‘ ' "5.'k-v-;1§‘:£I " ‘74? "4':o:§.§‘1““‘f".' .. ' “ . t , ‘ . w j '. 1‘ - ;' "‘ .1; II: ,-_\,:: .‘y’1s‘\&. .IW‘I‘ 1 Esif‘-‘[’:~;" .', 1' “L" , 7 , I "n ' "I. .. Hybrfiflnv 'mL‘z‘ : [- 3“: r: :. .- . ,- , r .. ' ; p! v 1.1- V ‘ v . ': q; u. L. ' ' "Jud . ~ . v ' . - - , 1" «2'8" "5:51;”? '. f \: .1 .~ n . : i . ‘ ‘ . ‘ I. - V"? l . . I, 4‘ .1 '. v . : 'X J." ‘z; iiié‘a§::g-J.5 s - é-n'fi?“ J: . *v-r‘ . ":U‘Fe‘i-i-‘z ~51- H‘“ ‘ «4:; $111; ,7 h "z::‘ ‘ ' 'lirzfiéf’h’lfi hi; i 1-111- 4 I ‘— ' , i=3} 1?; K V Jana -f ’fizfl“? All i-ffifl-"ai' " 3&3?" . 3:53.: z 2 ‘: Qingzfipfigijgg it ’fi’ o...__. b- n w—- , m ‘0 - . “3;“! .‘JLL’H .w “K .. a...“ m”... w...” < a... -.. ._ ..... . " A. . u .. ..x‘:.:~.r ~ o}-—-~ v A. -.-..—‘. lull\lllllllllllllllllllllllll l 9000 3 29 1834 59 LIBRARY Michigan State I Unlverslty This is to certify that the thesis entitled CRUSTAL GROWTH MECHAMSMS WA Gamma ARGMTE, GALesqu gives—mug SOUTH CEMTEAL Lu/scowsrtv‘ presented by ASTQ I D MA K0001 T2 has been accepted towards fulfillment of the requirements for M. . (I) Geology degree in Date (0/9/6261 0-7639 MS U is an Aflirmativc Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 1/98 cJCiRCJDmDmpGS-au CRYSTAL GROWTH MECHANISMS IN A QUARTZ ARENITE, GALESVILLE SANDSTONE, SOUTH CENTRAL, WISCONSIN By Astrid Makowitz A THESIS Submitted to Michigan State University In partial fulfillment of the requiremnts For the degree of MASTER OF SCIENCE Department of Geological Sciences 1 999 ABSTRACT CRYSTAL GROWTH MECHANISMS IN A QUARTZ ARENITE, GALESVILLE SANDSTONE, SOUTH CENTRAL, WISCONSIN By Astrid Makowitz Crystal growth is theoretically described as (1) dr/dt=k for polynuclear and spiral growth where dr/dt is the rate, r is the radius of a crystal, and k is some constant (2) dr/dt=kr2 for mononuclear growth and (3) dr/dt=k/r for diffusion limited growth. Empirical results in this study define another crystal grth mechanism, described by the rate law dr/dt=kr. Grain radii (r) and overgrth thickness (dr/dt) were measured in 16 thin-sections of quartz arenite fiom the Cambrian Galesville Sandstone and plotted on radius-rate plots. Correlation coefficients ranged fiom 0.145 to 0.855. Ten of 16 samples show statistically significant correlations between detrital grain radii and overgrth thickness representing dr/dt=kr. The remaining six measurement sets did not show a correlation representing dr/dt=kr. Detrital grain size standard deviation (sorting) correlates with the radius-rate correlation coefficient for each sample. Samples with large grain size standard deviation have higher correlation coefficients and samples with a smaller grain size standard deviation show lower correlation coefficients. Samples indicating no correlation may grow by dr/dt=kr, but for smaller grain size distributions the overgrowth thicknesses cannot be measured well enough to detect small variation. For Rainer iii ACKNOWLEDGMENTS My family deserves my first and foremost recognition for their ongoing support, enthusiasm and patience. I especially thank Rainer who has played a role model parent, scientist and thinker, my aunt Roswitha for having included me in her family as one of her own, and my grandparents Inge and Erich who are the reasons for why this all began: Mt. Vesuvius, 1989. They have also demonstrated over the years that the closeness of a family is not geographically dependent. Duncan Sibley has been a great teacher whom I will always look upon with great respect. Not only have I gained a valuable educational experience . through him but I have also gained a friend for life. Tom Vogel has given me valuable guidance through out my studies at MSU both as an undergraduate and a graduate student. Michael Velbel showed ongoing enthusiasms for my project and provided helpful suggestions along the way. Bill Carnbray played an important part in my research by providing his insights and suggestions in the initial stages of the project. I have depended on a number of people for their support, assistance and friendship: Kim Berry, Rebecca Richardson, Robin Sutka, Dave Szymansky and the “Riv Crew”. Thanks to Cheryl Webster for taking the time to proof read a preliminary copy of my work. Last but not least, my personal computer expert, Dave Boutt, has not only assisted with technical difficulties but also proven to be my greatest cheerleader. TABLE OF CONTENTS LIST OF TABLES ............................................................................. vi LIST OF FIGURES ........................................................................... vii INTRODUCTION ............................................................................. 1 Stereologic Effect Problem .......................................................... 5 Test 1: Grain Slicing Methods ....................................................... 6 Test 2: Grain Thinning ................................................................ 7 Radius-Rate Plots ..................................................................... 15 STUDY AREA .................................................................................. 19 METHODS .................................................................................... 24 RESULTS ...................................................................................... 27 Outcrop 1 ............................................................................... 27 Outcrop 2 and 3 ....................................................................... 30 Outcrop 4 .............................................................................. 30 Variation in R2 Values Assuming dr/dt=kt Growth Law ....................... 31 Dissolution and Growth Inhibiting Features ..................................... 31 DISCUSSION OF RESULTS .............................................................. 39 Effect of dr/dt=kr on Crystal Size Distribution ................................... 40 Justification of Data Removal ...................................................... 41 CONCLUSIONS ............................................................................. 54 APPENDIX A ................................................................................. 55 APPENDIX B ................................................................................. 72 APPENDIX C ................................................................................. 77 REFERENCES CITED ....................................................................... 80 LIST OF TABLES Table 1. Summation of sample characteristics: location, population of grains measured, correlation type and descriptive statistics ...................... 29 vi Figure 1. Figure 2. Figure 3. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. LIST OF FIGURES Grain Thinning Model 1: Linear regression for random slices of grain radii versus overgrowth thicknesses for one grain size ............... 8 Grain Thinning Model 2: Random slicing of various grain sizes. Grains follow dr/dt=kr ............................................................ 9 Grain Thinning Model 3: Random slicing of various grain sizes. Grains follow dr/dt=k ............................................................ 10 Sample 3a initial measurements of 28 grains before grain thinning. R2=73. 1% .......................................................................... 13 Maximum grain diameter versus overgrowth thickness for sample 3a from 4 data sets of5 um thinning. R2=58.2%, less than initial r2 value but not statistically different .............................................. 14 Frequency distribution of diameters for 120 random slices through a sphere ............................................................................... 16 Frequency distribution of overgrowth thickness for 120 random slices through a sphere. Notice largest frequency for small overgrth thicknesses ......................................................................... 17 Probability of random slices penetrating a sphere. Theoretically, 75% of slices do not show much change in diameter or overgrowth thickness and 25% of slice show a significant amount of change that would produce a stereologic efl‘ect. Probability data was generated by 120 random slices through a sphere ............................................. 18 vii Figure 9. Figure 10. Figure 11. Figure 12. Figure 13. Figure 14. Figure 15. Figure 16. Figure 17. Two radius-rate plots for dr/dt=k. Radii are variable and k’s are constant at 0.2 and 0.5 .......................................................... 20 Radius-rate plot for dr/dt=kr. Radii are generated at random with mean=2.0 and s.d.=0.5. K=0.5 ................................................. 21 Radius-rate plot for dr/dt=kr. Radii are generated at random with mean=2.0 and s.d.=0.5. K=O.9 .................................................. 22 Radius-rate plot for dr/dt=kr. Radii are generated at random with mean=2.0 and s.d.=0.5. K is random with mean=0.5 and s.d.=0.1 to make plot appear more realistic ................................................. 23 Map of Wisconsin. Box is location of Baraboo Syncline and encompasses area of sample collection ........................................ 25 Sample locations for outcrop 1. Samples 2, 3 and 4 are sampled at 1/3 meter intervals within same cross-bed. Samples 8, 10 and 11 are also sampled within the same cross-bed. Samples within same units show different correlation ....................................................... 28 Regression plot of 30 randomly selected data from GrainThinning Model 2. R =90.0% ............................................................ 32 Regression plot of 30 randomly selected data fi'om Grain Thinning Model 2. R2=38.3% ............................................................. 33 Regression plot of 30 randomly selected data fiom Grain Thinning Model 2. R2=51.O% ............................................................. 34 viii Figure 18. Figure 19. Figure 20. Figure 21. Figure 22. Figure 23. Figure 24. Figure 25. Regression plot of 30 randomly selected data from Grain Thinning Model 2. R2=72.0% ............................................................. 35 Irregular grain surfaces and embayments as shown here are often associated with clays. Embayments may have been caused by calcite replacement and later the calcite dissolved ................................... 37 Regression plot showing correlation between grain standard deviation and correlation coefficients for each set of all samples ......... 38 Normal probability plot for the initial and final radii. The final radii are grown by the dr/dt=kr growth law (k=0.1). Differences in the initial and final radii distribution are apparent. The larger the radius the larger the deviation between the two ......................... 42 Normal probability plot for the initial and final radii. The final radii are grown by the dr/dt=k growth law (k=0.1). The distribution of initial and final radii are identical only that the final radii have larger values .............................................................................. 43 Normal probability plot for the initial and final radii. The final radii are grown by dr/dt=kr growth law (k=0.5). A larger k value results in a larger deviation between initial and final radii and therefore final radii are more lognormally distributed (when grown by dr/dt=kr) than in Figure 21 where k=0.1 ......................... 44 Regression plot for sample 5 prior to data removal. Data being removed due to stereologic effect is depicted as a circle .................. 46 Regression plot for sample 5 after data removal. R2 value changes from 31.7% prior to removal to 61.5% after removal. Both r2 ix Figure 26. Figure 27. Figure 28 Figure 29. Figure 30. Figure 31. values are significant ........................................................... 47 Regression plot for sample 13b prior to data removal. Circle represents eliminated point from final plot .................................. 48 Regression plot for sample 13b alter data point is removed. R2 value decreases from 43.4% to 26.8% ........................................ 49 Regression plot for sample 2 before data point removal. Data being eliminated is depicted as a circle in the upper left hand corner ............ 50 Regression plot for sample 2 after data removal. R-sq value decreased from 44.1% to 2.7% ................................................ 51 Sample 3b regression plot before data removal which is depicted as a star in upper right hand corner ............................................. 52 Sample 3b regression plot after data removal. R-sq decreases from 51.5% to 23.9% ............................................................ 53 INTRODUCTION The purpose of this study is to test the hypothesis that relationship exists between detrital quartz grain radii and their overgrowth thicknesses. The hypothesis is based on theoretical and empirical grounds. The theoretical grounds consists of equations that describe mechanisms of crystal growth which result in different growth rates versus crystal radii (Nielsen, 1964; Ohara and Reid, 1974). The empirical grounds are based on the width of growth zones in authigenic dolomite (Nordeng and Sibley, 1996) and the coarse-skewed to lognormal crystal size distribution in many natural (Eberl et al., 1998) and synthetic (Randolph and Larson, 1988; Mitrovic and Ristic, 1991) samples. White et a]. (1976) found very pronounced size dependent eflects for potassium sulfate crystallizing fi'om aqueous solution. Garside and Janie (1978) observed crystal growth rates appear size dependent over a wide range of sizes (3-2000um) in a potash alum/water system. These empirical results suggest a crystal growth mechanism that can be described by dr/dt=kr. In theory, the relationship between crystal radius and growth rate may be expressed as dr/dt=k, dr/dt=krz and dr/dt=k/r (Nielsen, 1964; Ohara and Reid, 1974) where dr/dt equals the change in radius over a time and k is a rate constant. The rate law dr/dt=k describes both spiral and polynuclear growth, dr/dt=kr2 represents mononuclear growth, and diffusion limited growth is described as dr/dt=k/r. Diffusion-limited growth is a flux-limited growth mechanism, which means that as a crystal grows, the volume of solute-depleted fluid around the crystal grows larger. Because the rate of flow of a diffusing substance is proportional to the concentration gradient, the larger the volume through which a substance must diffuse, the lower the concentration gradient. Therefore diffusion limited growth is described as dr/dt=k/r: the growth rate decreases with increasing crystal size. On the scale of a crystal, when the rate-limiting step is the attachment of ions to the surface, the process is referred to as surface-reaction limited growth. Mononuclear, polynuclear, and spiral growth are surface reaction limited growth mechanisms. Mononuclear growth occurs when surface nucleation rates are much less than lateral growth rates. When a cluster of ions attain a critical size on the surface of a crystal they form a critical nucleus. It is difficult for critical nuclei to form because clusters of ions are unstable until they have attained a critical size. Once a critical nucleus is formed, layer growth occurs rapidly because ions require less energy to attach to the edge of a supercritical nucleus. Another critical nucleus does not form until the previous layer has completely covered the crystal face. Surface nucleation rate is a function of the surface area of the crystal, thus mononuclear growth is described as dr/dt=kr2 (Nielsen, 1964; Ohara and Reid, 1973). In polynuclear and spiral growth, dr/dt=k, growth is independent of crystal size. In contrast to mononuclear growth, nuclei form anywhere on the surface and allow more than one nucleus to form at a time. In polynuclear growth, the rate of formation of nuclei greatly exceeds that of lateral growth. Individual layers form almost entirely by accretion of nuclei rather than lateral growth. The number of nuclei defines the differences between mononuclear growth and polynuclear growth (Nielsen, 1964; Ohara and Reid, 1973). Repeated surface nucleations are not required when screw dislocations produce spirals with persistent edges that serve as a constant source of attachment sites (Burton et al., 1951). Ions attaching at kinks on the spiral edge have less surface free energy than critical nuclei since ions at kinks attach to the crystal on three sides. This type of growth does not need constant formation of critical nuclei for crystal growth. Nordeng and Sibley (1996) found a linear correlation between width of cathodoluminescent (CL) zones and size of crystals in 4 dolomites: Seroe Domi Fm (Miocene, Netherland Antilles), Burlington-Keokuk Fm (Mississippian), Fort Payne Fm (Mississippian), and Saluda Fm (Ordovician). The correlation is expressed as dr/dt=kr where dr/dt is the zone width, r is the crystal radius, and k equals a constant. Each CL zone represents one period of grth under a constant fluid regime. In carbonate rocks, cathodoluminescence is caused by Mn incorporated into the mineral. F e2+ and Fe” have the opposite effect and result in dark zones. Each zone is assumed to be isochronous. Therefore the width of an individual CL zone describes the amount of crystal growth during one period in time. Eberl et a1. (1998) found log normal size distribution of natural dolomite, garnet, galena and illite. The lognormal distribution can be modeled by the “Law of Proportionate Effect” (Xj+1= Xrl-Eij). X1 is some specified dimension of a crystal such as the radius, Ej is a small, randomly varied number similar to the k constant in Nordeng and Sibley (1996). The new crystal dimension after one grth cycle is represented as X341. In terms of crystal growth, the equation states that the rate of growth (per calculation cycle) depends on the crystal’s previous size multiplied by the system’s variability. The factors that may cause variability within the system include: thermal and chemical heterogeneities, the presence of favorable growth sites, the surface area and energy of crystals, and the porosity and permeability. The “Law of Proportionate Effect” states that on average, large crystals grow faster than small crystals and can also be expressed as dr/dt=kr. Kretz (1974) and Carlson (1989) investigated the growth of garnet crystals by examining compositional zones. Kretz (1974) considered growth rate as a function of radius, dR/dt=k; volume, dV/dr=k; and surface area, dA/dt=k. Carlson (1989) used a method for testing the predictions of a specified growth-rate law against observed zoning patterns discussed by Kretz (1973, 1974). In this method, the radial distance, c, between two close compositional contours in a garnet is proportional to the average rate of the radial growth over a short period of time. The radial distance, C, fiom the garnet center to the midpoint between the two contours represents the average radius of the garnet in the same interval of time. Carlson (1989) and Kretz (1974) both found actual measurements of garnet zones versus garnet radius did not fit any of the three models. Kretz found V= f (t3‘5'5'0), where the unit volume of a garnet crystal is a fitnction of time to the power of m, where m lies between 3.5 and 5. Kretz (1973, 1974) attributes difference from the models to changes in nucleation rate. Carlson (1989) found a non- linear trend, which did not fit any of the growth models and concluded that intergranular diffusion governed the crystallization of garnets. Carlson (1989) attributes the trend to changes in nucleation rate caused by an increase in temperature (thermally-accelerated nucleation). Mitrovic and Ristic (1991) documented that small synthetic MnC12-4H20 crystals followed a linear relationship between the growth rate versus the initial grain size in the direction normal to the (100) plane. The measured crystals followed both a symmetric and asymmetric distribution. At low temperature (20°C) and high supersaturation (o=5.9) the CSDs are symmetric. At a high temperature (30°C) and low supersaturation (o=0.9) the CSDs are asymmetric. Garside and Jancic (1978) also found a size dependent and linear relationship between growth rate and initial crystal size in a potash alum/water system for a wide range of supersaturations. White et a1. (1976) observed very pronounced size dependence for synthetic potassium sulfate crystallizing from aqueous solution. They found that for crystal sizes ranging from 2 to 1000um a two-thirds power law (dr/dt=krm) that fits all available data. This law does not pertain to very small and very large crystals for which the linear growth rate law does work: G/Go=1 +aL in which G/Go is the change in size, a is a constant and L is a size attribute of the crystal. This growth law is equal to the “Law of Proportionate Effect” and dr/dt=kr. In this study, the dr/dt=kr relationship found by Nordeng and Sibley (1996) in dolomites and Eberl et al. (1998) in dolomite, garnet, galena and other crystalline substances has been found in quartz cement. The physical basis for this dr/dt=kr growth equation has not been determined (Randolph and Larson, 1988; Nordeng and Sibley, 1996; Eberl et al., 1998). Randolph and Larson (1998) suggest that some crystals inherently have more defects than others and those crystals with more defects per unit area will grow faster. Nordeng and Sibley (1996) suggest that thin-section scale solution heterogeneity may cause some crystals to grow faster than others. Stereologic Effect Problem Determination of radius-rate relationship from thin-section measurements poses stereological problems. Grain diameters and overgrth thickness measured in thin section are apparent rather than true values. True values are the values one would measure across the center of a grain. Apparent values are measurements not from grain centers. It is impossible to distinguish the centers of quartz grains; therefore one needs to determine how the measuring of random grain slices effects the relationship between quartz overgrth thicknesses and detrital grain radii. Two tests were performed to determine the extent of this problem with quartz grains. Test 1:Grain Slicing Models Three models were created to determine the effect that random slicing of grains has on the grain diameter/overgrowth thickness ratio. One model is based on randomly slicing a sphere with an overgrowth This was done by drawing two superposed circles. The inner circle represented the detrital grain and the area between the inner and outer circle represented the overgrowth. Random slices were generated by random numbers between 0-359 to represent the intersection of the slice with the outer circle. Approximately 120 measurements from slices were used for Model 1. A Plot of grain diameter against overgrowth thickness produces a negative trend (Figure 1). When a sphere is sliced through the center, maximum diameter and minumum overgrowth thickness are intersected. When a sphere is sliced filrther toward the edge, the apparent diameter is smaller and the overgrth larger than the true measurements. This results in an exponential trend with a near -1 linear slope correlation if the grains in a thin section were all the same size (Figure 1). Model 1 represents random slicing of a single grain or grains of the same size. Model 2 was generated by randomly slicing different size spheres that obey dr/dt=kr. This was done using measurements taken from Model 1 and mutiplying overgrowth thickness and detrital grain measurements by 2, 3, 4, and 5, producing four sets of larger grains and overgrowth thicknesses. The same initial measurements were divided by 2, 3, 4, and 5, producing 4 sets of smaller grains and overgrowth thicknesses. This produces nine sets of measurements from which 60 random sets of measurements for each grain size were taken and compiled for Model 2. The diameter and overgrowth thickness were plotted (Figure 2) using data from nine different sized sphere. The regression plot shows a linear trend with r2=48.6%. Model 3 was generated by randomly slicing various size spheres, which obey dr/dt=k. This was done by using measurements from Model 1. Only detrital grain measurements were multiplied by 2, 3, 4, and 5 producing 4 sets of larger grains and divided by 2, 3, 4, and 5, producing 4 sets of smaller grains. This resulted in nine different grain size measurements. The overgrowth measurements were (not changed since overgrth remains constant according to dr/dt=k. Sixty measurements were randomly selected from each of the nine spheres and plotted. No relationship existed between overgrowth thickness and sphere diameter, thus no correlation between diameter and overgrowth thickness was found (Figure 3). One would expect this trend when plotting measurements from grains taken fiom thin section which obey dr/dt=k for different grain sizes. These models help in determining the stereologic effect of random grain thinning. The trend generated by Model 1 is not comparable to any of the plotted data therefore it is disregarded. Model 2 and 3 are useful since data trends are comparable to the generated trends of these models. Test 2:Grain Thinning To determine the effect of randomly slicing real grains, a thin section was serially sectioned at 5 pm intervals. The average grain diameter of the rocks based on thin section analysis is 408 pm. The thin section was thinned on a glass plate using #1000 grit silicon carbide. A micrometer was used for precise measurements of thin section thickness. Precision based on replicated analysis of the thickness of a thin section in the same location was +/- 0.45 pm. Overgrowth Thickness (mm) 0.01 0.008 0.006 0.004 0.002 0 0.05 0.1 0.15 0.2 0.25 Diameter (mm) Figure 1. Grain Thinning Model 1: Linear regression for random slices of grains radii versus overgrowth thicknesses for one grain size. Overgrowth Thickness (mm) 0.05 I j I l I T I T I I I l I I I I I I I 0.04 — ---------------- .~ ----- 3 ---------- -------- --------------- -— s a s 0.03 - ---------------- gr-wg ------------ gr-e- ------------- s- ----------------- g --------------- - ,3 . L - -------------- ‘s .,,, ...... 3...; ............. - 0.01 0 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 2. Grain Thinning Model 2: andom slicing of various grain sizes. grains follow dr/dt=kr. Overgrowth Thickness (mm) 0.01 0.008 0.006 0.004 0.002 “. .5. O : z E i - i g g g r2=8.1% I I I I ll11111lllLJllJllJllllLlllllllllll ITIIIIIIIIIIIIIIfIIIIIIIlIIIIIIIII I I I I 0 0.1 0.2 0.3 0.4 0.5 0.6 Diameter (mm) 0.7 Figure 3. Grain Thinning Model 3: Random slicing of various grain sizes. Grains follow dr/dt=k. 10 Locations of 28 grains were determined using a x-y mechanical stage on a petrographic microscope. Photographs were taken of all grains at each 5 pm interval. This was done to record original as well as changes in shape in response to each thinning interval. Measurement precision on replicated analysis of a grain diameter varies within +/- 0.01 mm. After three thinning intervals, four sets of grain diameter and overgrowth thickness measurements resulted: 30 um, 25, 20, 15 pm. For each data set, grain diameter/overgrowth thickness ratios were calculated. Theoretically, three types of grain diameter/overgrowth thickness changes may occur for each grain. These include: (1) The ratios may decrease, signifying that the initial grain diameter was closest to the center and each thinning interval thins the grain closer to the edge of the grain. (2) The ratio may increase, representing that each thinning interval is moving closer to the grain center. (3) The ratio may remain unchanged meaning that each interval is cutting through the central area of the grain where the diameter/overgrowth thickness ratio is least likely to change. Since the maximum grain diameter/overgrowth thickness ratio occurs at the grain center, only the maximum ratio for each grain was extracted from the four possible data sets. This produces one data set representing measurements closest to or at grain centers. The initial data are from 30 um section and the final extracted maximum diameter/minimum overgrowth data are the optimum from any of the four measurements of that grain. The initial data set regression plot was then compared to the final extracted grain diameter/overgrowth thickness data set. The initial data set has a r2 equal to 73.1% 11 (Figure 4) whereas the final data has a r2 equal to 58.2% (Figure 5). Performing a two sample t-test on the initial diameter and final diameter as well as the initial overgrowth thickness and final overgrowth thickness, the two sets of values are not statistically different. A spherical model was constructed of the average grain diameter and overgrowth thickness. The theoretical change in overgrowth thickness and grain diameter was calculated when thinned at 5 pm intervals. The change in overgrowth and diameter are minimal when thinning a grain originally sliced through the center. The theoretical calculated changes in diameter and overgrowth thickness are 9.0x10'5 mm and 4.5x 10'6 mm respectively. These changes are too small to be measured at 10x and 40x magnifications. The largest change in diameter and overgrowth thickness occurs at the edge of a grain. The theoretical model shows that the maximum change in diameter and overgrowth thickness is 3.0 x 10'2 mm and 1.7 x 10'2 mm. These changes are large enough to be measured. A slice furthest to the edge will have a very low diameter/overgrth ratio; in other words the overgrth is thicker than the grain diameter. None of the data collected include grain slices where the overgrth is thicker than the grain diameter. This is because there is a greater chance of slicing the grain in an area where the diameter and overgrowth thickness of a grain do not change much fi'om the central slice. Figures 6 demonstrates a larger fi'equency of grain intersections at maximum or near maximum diameter. The frequency exponentially decreases for slices further from the center. Overgrowth thickness follows an opposite trend. Figure 7 shows a higher frequency of small or close to the smallest overgrowth thickness. In this case, the fiequency exponentially increases for slices with increasing distance form the 12 0.035 I I I l T j I I I T I I j I j I I I I 0.03 o o N LII ! f i 0.02 _ ---------------- .23, --------------- i ----------------- i --------------- — 0.015 —-wo ----------------- E- --------------- - Overgrth Thickness (mm) °\ 0 1- cl L . . O . I I I I ._ I I I I q I I I I .I-------------J-----------------J-----------------* ............................... 0.01 — . . . 1- -* _ I I I I cl I I I I l- . ' -1 l- -l D I 0.005 - --------------- i ----------------- i ----------------- ----------------- ---------------- - 0 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 4. Sample 3a initial measurements of 28 grains before grain thinning. R2=73.1% l3 Overgrowth Thickness (mm) 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 5. Maximum grain diameter versus overgrowth thickness for sample 3a from 4 data sets of 5 um thinning. R2=58.2%, less than initial r2 value but not statistically different. 14 center. Figure 8 illustrates results fi'om measurements made by randomly slicing a gain having average diameter and overgrowth thickness dimensions. From 120 random slices 275% show small changes in overgrowth thickness and gain diameter fiom the central area of the gain. The probability of randomly slicing a sphere at or close to the center is most likely greater since the greatest amount of detrital gains size and overgrowth thickness change occurs at the edge of a gain. Larger changes occur for 525% of the measurements. The geatest amount of change occurs at the outer edge of a gain. Only one out of the 120 measurements had an overgrowth thickness equal to or geater to the diameter. Radius-Rate Plots Simple radius-rate models were created for comparison with real data sets. Radius-rate plots can be generated using a spreadsheet to model gowth of gains by different crystal growth mechanisms. The gain radii are plotted against the overgrowth thicknesses (growth rate). Variable radii and a constant rate can be expresses as dr/dt=k where larger k values yield larger rate values as seen in Figure 9. Growth is dependent on k only therefore this figure also shows that when given two sets of radii of the same size, a larger gowth rate applies when gown under the influence of k=0.5 versus k=0.2. Two model radius-rate plots were constructed using 100 random radii with a mean of 2.0 and a standard deviation of 0.5. In the models, two sets of crystals were gown at two different k values, 0.5 and 0.9. Each layer of gowth is multiplied by the designated R value for each model. The resulting plots of overgowth thickness (dr/dt) versus radius are linear with slopes equal to k (Figures 10 and 11). In both figures, dr/dt=kr. The larger k value corresponds to a faster overall gowth rate compared to the smaller R value. 15 Frequency 35 30 25 20 15 10 I I II I l I I I I l' I j I I I I I T I l I I I I I I T I I fl r I I - I I I | I d I I I I- I I I 1 I I I In I I I l I D I I I J I I I — ..................................................................... P ---------- q I I I p I I I d I I I I- I I I II I I I - I I I d I I I I I I p I I . d m ---------- t ------------ ‘ ------------ t ........... *noaonnnnnnnd. ................ _ I I I I I p I I I d u : : I I I ' . U I I I P nnnnnnnnnnn r ......................... I: nnnnnnnnnnnn J ............ J ---------------- _ I I b I . C I I l- . ' 4 h- . . q I I . : : .1 I I _ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn Q nnnnnnnnnnnn ‘ ------------ ‘ + nnnnnnnnnn - I I I- I I -l I I I " . T h I d I n l d L— ‘ J ................................................... _ I ' d I I f . 1 h I I .. ' J I —- .......... * ..... d cccccccccc fl ' 1 .- -1 P d h I l J l l l I l j I l l l I l l l L l l I L 0.15 0.2 Diameter (mm) 0.25 0.3 0.35 Figure 6. Fequency distribution of diameters for 120 random slices through a sphere. l6 Frequency 35 I I I I I I I I I I I I I I I I I P I I I I 1 n- I I I I 1 _ _. : - - - . . i i i n- I I I I ‘ I I I I 30 P. .................................................................... F .......... - I I I I r : I I I d I I I P ' I 0 I q I I I I n- 0 I I I d I I I I I. I I I I «I I I I I 25 b. C. p.-‘ OOOOOOOOOOOOOOOOOOOOOOOO k OOOOOOOOOOO * OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO - I I I I r i : : : ‘ r- : : : : -¢ I l- I I I I d 20 -----1 I..; CCCCCCCCCCC a. ------------- : ............ { uuuuuuuuuuuu J. oooooooooooo I CCCCCCCCCC - h I I I I q I I I I n- : : ' : q k —' l : d F : : d 15 b- --{ h-OCD-IC-.‘Q‘---.--------‘. ............ ' ------------ ; ............ t .......... d .— : : .. I I '- I I '1 I I r : : - . __ Lfi . . . I 10 b. .--------‘------------.-----.------.---.----.---I. ....................... — I I I I I I I - I I cl I I p I I d I I p I I I I I I 5 _.l p——-J - ..... ‘ ------------ h ........... *u-rouccuoodu .......... d I I I I _ i i i i 'l L E T] : d 0 r j I I I l I I I I J l; l I I I J I I I I L I II I II I .41 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Overgrowth Thickness (mm) Figure 7. Frequency distribution of overgrth thicknesses for 120 random slices through a sphere. Notice largest frequency for smaller overgrth thicknesses. l7 .Eonam a 3:85 80% 88:8 cm_ 3 wBfiofiw mm? 8% 9.5205 acute fiwo—oohxm m 8:on 2:03 35 $523 mo “5.2:: :58:in a 26% meow—m :0 $3 :5 8053:: £38305 8 56:86 5 $530 :02: 26% 8: o: meow—m mo 3? Szmozaoofiw 63:3 a gag—8:0: 80% 88:8 no b25305 .w onE / fawn famm 18 Measured data points will not have a perfectly linear relationship as in the models. Error in measurement, differences in grain shape and the stereologic effect cause measurements to deviate fi'om the perfect linear relationship even if crystal growth followed dr/dt=kr. Therefore, models for dr/dt=kr are rmde more realistic by randomly varying r and k. Figure 12 represents a radius-rate plot for which 100 random radii were generated with a mean of 2.0 and a standard deviation of 0.5. One hundred k values were generated randomly with a mean of 0.5 and a standard deviation of O. l. Mononuclear and diffusion limited growth trends are not expected in this study. Mononuclear growth has never been observed in nature therefore it is not expected to be seen here. Plotting a diffusion limited grth model results in a negative slope curvature, which does not fit data of this study or many previous crystal grth studies (cited in “previous work”). STUDY AREA Samples for this study were collected fiom the Upper Cambrian Galesville Sandstone located in the southeastern Wisconsin (Figure 13). The Galesville Sandstone is exposed in the same area as the Baraboo Syncline, but the Galesville unconformably overlies the Syncline and is not involved in the synclinal structure. The Galesville Sandstone was used in this study because it has a dominant quartz mineralogy of 2 99% (Wilson, 1977). All four sample locations extend about 160 square miles around the Baraboo region. Outcrop 1-3 are located in the western Baraboo Syncline area whereas outcrop 4 is located in the eastern Baraboo Syncline. The Galesville Sandstone is approximately 100 feet thick, lying unconformably over the Precambrian Baraboo Quartzite. It consists of white, friable, well-rounded, well-sorted, medium grained, pure quartz sand. The unit was deposited as a sheet in an 19 Rate 0.55 I I ‘ j ! I I I l ! I I I I E I I I I I I I I I C at 0,5 Ei-I-i-l-p-I-I-i-i-fi-i-I--I-i-§-i-I—-I-§-§ --------------- :- 0.45 __ """""""" " """"""""" " """"""""" 'i """"""""" ‘ """""""" 0.4 r """""""" """"""""" i """"""""" i """""" 0.35 L'"'"""""'" """"""""" .' """"""""" :' """""" i f f f . 0.3 r --------------- -;r ----------------- gr ----------------- gr ----------------- : --------------- r : : : i r s 0.25 __ """""""" ‘ """"""""" " """"""""" " """""""""""""""""" '2 0.2 L—o-+-+-o--+-o--o-+-e--:+-o--o-+-o--:o-o--e-our-:0 --------------- -‘ O 15 1 J l l I l l l l [A l l J l l l l l I J l I I d 0 L11 p—I O p—t kl! N O N M Radius Figure 9. Two radius-rate plots for dr/dt=k. Radii are variable and k's are constant at 0.2 and 0.5. 20 d 8 . Q q OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO — d fi .J d Radius Figure 10. Radius-rate plot for dr/dt=kr. Radii are generated at random with a mean of 2.0 and s.d.=0.5. K=O.5. 21 Rate Figure 11. Radius-rate plot for dr/dt=kr. Radii are generated at random with a mean=2.0 and s.d.=0.5. K=O.9. 22 Rate N I I Ii I I? I 5' I E h a- f: i.- 5- I ". I I I I I 1.5 — --------------- 1’?‘.l. ................. ............... _ :- /: ' : : -4 I I I .. / :? I. : i d p I I I J u- .. . E 2 -1 1 — OOOOOOO i-..-‘--------.--------*----------------*--------------.-; ............... - I I I I : i i ‘ p I I u I I I- . I cl I I r- ' I -I I I 0.5 :0 --------------- § ccccccccccccccccc J: ................. J ooooooooooooooooo J: oooooooooooooooo j I I r- : ° q .. g .4 r- ' d O I I I I I I I I I I I I I I I I I I I I I I I L Radius Figure 12. Radius-rate plot for dr/dt=kr. Radii are generated at random with a mean=0.2 and s.d.=O.5. K is random with mean=0.5 and s.d.=O.l to make plot appear more realistic. 23 aeolian-shallow marine environment (Runkel et al., 1998; Wilson, 1977). It contains small but variable amounts of quartz cement, 3.8% - 8.7%. The small amount of cement is an important criterion in chosing this sandstone for this study because the problem of crystal growth being limited by interference of overgrowths from different grains. METHODS In thin section dust rings can be used to distinguish the detrital grain from the overgrowth. Wilson (1977) observed prevalent dust rings in grains from the Galesville Sandstone. The original rounded grain outline is commonly revealed by the presence of small specks included in the grain as the overgrth grows. Therefore, the area surrounded by the dust ring is the detrital grain and the precipitated quartz around the dust ring is the overgrowth Only the detrital grains cut perpendicular to the c-axis were used to obtain consistent overgrth measurements. Quartz grows faster along the c-axis producing a thicker overgrth in this direction. Quartz grains cut parallel to the c-axis have thicker overgrowths on the c-axis than on the a or b-axis (Dana, 1985). Overgrowths on quartz grains cut perpendicular to the c-axis are more uniform since a and b-axes have the same growth rate. Grains cut perpendicular to the c-axis in thin section under cross-polars are extinct throughout 360 degrees of rotation thus are easy to recognize (Dana, 1985). Overgrowths may not completely surround a grain. Therefore only maximum grain diameter and maximum overgrth thickness were measured. Grains surrounded by abutting grains were not measured, only grains surrounded by free space on which the maximum overgrowth thickness could be measured. Point counts were performed to determine the amount of cement. Approximately 200 point counts were taken from six thin sections which appeared to have the most, two 24 the least and an intermediate cement content. The cement percentage for samples 2, 3b, 5, 11a, 13a and 13b are 7.7%, 7.9%, 3.8%, 8.7%, 7.8% and 4.7% respectively. The range of cement in this study ranges from a minimum of 3.8% in sample 5 to a maximum of 8.7% percent in sample 11a. Precision of overgrowth thickness measurements was tested by two separate measurements from three thin sections (sample 4, 8, 27). R2 values for two measurements sets for sample 4, 8, and 27 were 55.0% and 34.8%; 1.0% and 3.2%; 36.5% and 20.0%. No significant differences (two sample t-test, 95% confidence interval) were found between counts of the same sample. In some thin sections, pore space was very limited due to large amounts of cement and/or extensive pressure dissolution. Other thin sections showed pervasive iron oxide cement and/or chlorite rims. Due to these reasons, not all thin sections were used. From a total of 45 initial thin sections made, only 16 were used, coming from four different outcrop locations. Radius-rate plots were generated for each thin section using maximum overgrth thickness and maximum grain diameter measurements. Twenty to 30 grains were measured in per thinsection. Linear regression analysis was conducted on data from each thin section from which the best-fit line is retrieved. T-tests were performed to test for the significance of the correlation coefficient r. The equation for calculating t is: t= r((n-2)/(1-r2))”2 where r is the correlation coefficient and n represents the sample number (Mendenhall, 1993). 26 RESULTS A linear relationship between detrital grain radii and overgrth thickness was found. R2 values ranged from varied from 2.1% (the lowest value representing no correlation) to 73.1% (the highest value representing the stongest correlation). Ten out of 16 thin sections show a statistically significant correlation whereas six samples show no statistically significant correlation. Sample statistics are outlined in Table 1. Outcrop 1 In outcrop 1, samples 2, 3 and 4 were sampled at a 1/3 meter intervals within vertical succession of the same cross-bed set (Figure 14). Sample 2 shows no correlation between detrital grain radii and overgrth thicknesses whereas samples 3 and 4 show a correlation. Two thin sections were made and measured fiom sample 3 and have r2 values equal to 73.1% and 48.9%. Both r2 values are statistically significant (>0). Even though r-values are dissimilar, the two sample t-tests performed on overgrowth thicknesses and detrital grain radii show no statistical difference between the two thin sections. Similar results are found in another set of samples spaced at uneven meter intervals within the same crossbed. Samples 8 and 10, spaced at 2/3 meters, show a correlation and sample 11, spaced 1/3 meter fiom sample 10 shows no correlation. Two thin sections were made and measured from sample 11. Both measurements indicate no correlation between overgrth thickness and detrital grain radii with r2 values equal to 5.6% and 2.1%. Two sample t-test results for overgrowth thickness and detrital grain radii show no difference between the two thin sections. Sample 13 was collected one meter below sample 11. Two thin sections were made and measured. Both thin section measurements indicated a correlation between overgrowth thickness and detrital grain radii with r2 values equal to 23.5% and 26.8% and a t-test shows no 27 .m:o:a_otoo 88ob€ >38 38: 088 8:23 838% 63.380 088 05 82>» @0388 83 2a 2 can 2 .w 838$ .3: .380 088 .823 2.3858 :82: m: 3 3888 03 v :5 m .N 3888 A 988:6 :8 83:62 2:85 .3 oSmE 28 .8586 63.8.53: :8. 2:. 8:22.86 66.52.68 88w no 82.280: .858... ”8:83.688“. 2:83 .8 :o_.m88:m ._ 63.; 3...... .28.... 2. .3... 8...... om .. an 2.8.... 2.8.... 82 :2... 2mm... 8 v .n 22...... .32.... 2.. mg... 2.2.. R m R 32...... 83...... 2. .8... 3.... .N m mu 52...... 89.2.... 8. wow... .22. on . an. 82...... .22.... 22 RN... 2...... on . an. ....2...... .82.... 2. .8... mi... 8 . 8. 22...... $5.... 2. 22.... m8... 8 . a: 22...... $2.... 22 2.2. 2.2.. cm . ... 32...... 2.2.... 2. «2.... at... 20. . a 82...... 2.42.... 22 5... 8m... 8 . e .32.... 2.82.... 22 22.. 2:... E . m 82...... 282.... 2. 2.2. 2:... on . N 82...... 8.2.... 8.. 8mm... 2...... mm . 5. 22...... 82...... 82 5... m2... 8 . 2m 32...... J .32.... 22 a... 22... .N . .. ii agar—M905 .5.» 96am— EF—U EEG—2.50 Emu“ 02a>uh Siege-5&0: a: t % neg-Xv A: o—a—an 29 diflemme between the two thin sections. Samples 5 and 6 were taken from the same crossbed at a 3/2 meter distance. Both thin sections show a trend with r2 values of 61.5% and 15.7% respectively. T-test results show no difference between the data. The previous examples demonstrate that correlations between overgrowth thickness and detrital grain radii can vary within 1/3 of a meter. It has also been demonstrated that areas within one sample, approximately 3-6 cm apart show similar correlations. Outcrop 2 and 3 Outcrops 2 and 3 are located within the same vicinity and consist of sands with same physical characteristics: tan, fiiable, well-rounded and sorted. Radius-rate plots fi'om measurements of each outcrop show different correlations. Sample 25 from outcrop 2 has a r2 equal to 2.1%, representing no correlation whereas sample 27 from outcrop 3 has an r2 equal to of 36.5%. These results coincide with outcrop 1. Samples with similar physical characteristics within the same outcrop or outcrops with 0.25 mile separation show different radius-rate plot results. Outcmp 4 Outcrop 4 is located in the eastern side of the syncline opposed to outcrops l, 2 and 3, located on the western side of the syncline. Two samples were taken fiom outcrop 4 within the same bedding unit and 5 meter separation Sample 31 has an r- value of 28.1%, representing a correlation, whereas sample 32 has an r2 equal to 14.1%, representing no correlation. This is another example of localized correlation differences on an outcrop scale. 30 Variation in R2 Values Assuming drldt=kr Growth Law The radius-rate plot for grain thinning Model 2, representing random slicing of various grain sizes following drldt=kr growth law, produces a positive slope with an r2=48.6% (Figure 2), but the smallest and largest r2 values in this study are 2.1% and 73.1% respectively. Four sets of random radius-rate values were selected from Model 2 data set. Thirty values were taken for each set, approximately the same number of measurements collected from each sample. R2 values ranges from 38.3% to 90% (Figures 15-18). This shows that a change in 1'2 value is influenced by the stereologic effect when grains are grown by the dr/dt=kr growth law. Dissolution and Growth Inhibiting Features Petro graphic observations show embayments in detrital quartz grains and authigenic overgrowths. These are interpreted to have formed by the dissolution of pore filling and grain replacing carbonates, although no carbonate is present. However, carbonate cement is observed in Ordovician St. Peter and Cambrian Mount Simon Sandstones of the Illinois Basin south of the Baraboo Syncline (Hoholick et al., 1984). Carbonate cement may have been dissolved leaving evidence of dissolution features. Embayments have been observed by Burley and Kantorowicz (1986) although carbonate is present in their samples. However, embayments may also form from quartz that grew around calcite and calcite later dissolved. Highly birefi'ingent 2:1 clays are present in trace amounts but ubiquitous in samples. Muscovite is also observed. Green clays are presumed to be chlorite. Bjorkum (1996) has observed muscovite associated with dissolution of quartz. Petro graphic evidence supports the inference that clays may enhance dissolution because they are associated with quartz embayments and irregular grain surfaces (Figure 19). 31 0.025 0.02 ----------------- ---------- 7/ g --------------- - 0.015 ---------------- fr ----------------- i ------------- 74-;- ----------------- --------------- — Overgrowth Thickness (mm) . . 0.01 ------------ ;- -~;— ---------------- ~E ----------------- ~3- --------------- - 0.005 ------' ------ é ----------------- ----------------- ----------------- .f ---------------- - 0 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 15. Regression plot of 30 randomly selected data fi'om Grain Thinning Model 2. R2: 90.0%. 32 1 T T I I l U ' I I I I I I I I I t I I I I I I U I ' ' I I : 2_ o 5 5 : r —38.3/o ; g o 0.8 + ------------- .~ -------------- ------------ — 06 r- ------------- 1- -------------- :r -------------- 5’ ------------- i- -------- ;.d --‘- ------------ H 0.4 —/ ............... .5. ............. .i ............ .- Overgrowth Thickness (mm) o 0.2 —- ------- 7 -------------- é -------------- ------------- J by 1 Q: l l l 0 l1 1 I l l l l l J. 1 Lil l I 14 l l [—1 L14 1 l O 0.005 0.01 0.015 0.02 0.025 0.03 Diameter (mm) Figure 16. Regression plot of 30 randomly selected data from Grain Thinning Model 2. R2= 38.3%. 33 0.035 j I I l I 1' I I t I I l I I U l I I I 0.03 — ---------------- - 0.025 —- --------------- § ----------------- ----------------- ---------------- . a; ---------------- — 0.02 — ---------------- ----------------- yr ------------- i --------------- — 0.015 —- --------- 9- ------ «/ ----------------- --------------- - Overgrowth Thickness (mm) 0.01 _ ............... . ....... , ............... - 0.005 -------------- g ----------------- ----------------- ----------------- ---------------- - I /‘~ 5 : : : I L- 9 : 5 5 i - O 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 17. Regression plot of 30 randomly selected data from Grain Thinning Mode12. R2=51.0%. 34 0.03 0.025 P o N 0.015 0.01 Overgrowth Thickness (mm) 0.005 O 0.2 0.4 0.6 0.8 1 Diameter (mm) Figure 18. Regression plot of 30 randomly selected data fi'om Grain Thinning Model 2. R2=72.O%. 35 Irregular grain surfaces may also result in clays inhibiting grth where present (Bjorkum, 1986). Point counts of grains with irregular surfaces and embayments versus smooth grain surfaces, unaffected by embayments were performed. POint counts showed that there is a varying percentage of dissolution/grth inhibition in each sample. However quantifying dissolution/growth inhibiting features and relating these to corresponding r-values indicates no correlation. The correlation coefficients of samples were plotted against the standard deviations of the grains radii (a measure of sorting) to see if grain sorting has an effect on correlation between radii and overgrth thickness. If the standard deviation of grain radii is small, then only grains with similar sizes were measured. Figure 20 is a plot of grain radii standard deviation versus the correlation coefficient. The graph shows a trend in which more poorly sorted sands have a larger correlation coefficient better sorted sands. Therefore, radius-rate plots with low correlation coefficients are so because of the small distribution in grain size whereas radius-rate plots with a large correlation coefficient consist of measurements with a larger range on grain radii. In order to see the effect of the drldt=kr rate law, you must examine a broad range of grain sizes. DISCUSSION OF RESULTS Radius-rate plots for 10 out of 16 (62.5%) with examples fiom all four locations indicate linear trends between detrital grain radii and overgrth thickness, dr/dt= . However the linear crystal growth equation does not correspond to any of the published crystal growth mechanisms although it is commonly observed (White et al., 1976; Garside and Jancic, 1978; Mitrovic and Ristic, 1991; Nordeng and Sibley, 1996; Eberl et al., 1998). This is the first time a dr/dt=kr correlation has been observed in a quartz 36 Figure 19. Irregular grain surfaces and embayments as show here are ofien associated with clays. Embayments may have been caused by calcite replacement and later the calcite dissolved. 37 0.1 T fir I I Ifi T I T I I I I I I T I I I 0.03 ----------------- --------------- — 2 0.06 ~ ---------------- ----------------- ----------------- 2+ ----------------- EL --------------- -— m i 1 2 . ' .. .2 ' : : O : /—/i/ .E : : . ///.( : .. as : : /// l : 5 0.04 r ----------------- »/ --* ------------------------- ~.- --------------- — . : // 0 .0 I. r : /// .3 . E u . ,7/ O . - - /// i . q 0.02 - --------------- ----------------- ‘5 ----------------- ----------------- ---------------- fl O 0.2 0.4 0.6 0.8 1 Correlation Coeficient Figure 16. Regression plot showing correlation between grain standard deviation and correlation coeflicients for each set of all samples. 38 cemented sandstone. Samples from outcrops separated between 0.25 and 16 miles follow the same growth rate law spread over a 160 mi2 area. The variation in the slope of k could result from solution variation, differences in porosity and permeability or non-uniform presence of calcite cement or other cements or clays. The phenomena that large crystals will grow faster than small crystals has been observed in various empirical examples from laboratory experiments using industrial cyrstallizers (White et al., 1976; Garside and Jancic, 1978; Mitrovic and Ristic, 1991; Nordeng and Sibley, 1996; Eberl et al., 1998). This is the first time a dr/dt=kr correlation has been observed in a quartz cemented sandstone. Samples fiom outcrops separated between 0.25 and 16 miles follow the same growth rate law spread over a 160 mi2 area. The variation in the slope of k could result from solution variation, differences in porosity and permeability or non-uniform presence of calcite cement or other cements or clays. The phenomena that large crystals will grow faster than small crystals has been observed in various empirical examples from industrial crystallizers (White et al., 1976; Garside and Jancic, 1978; Mitrovic and Ristic, 1991) and in examples from nature (Nordeng and Sibley, 1996; Eberl et al., 1998; Kessels, 1999). The reason for this effect is unclear, but some workers attribute it to a greater proportion of defects on surfaces of larger crystals leading to an increase in average grth rate (Garside and Janie, 1976; Eberl et al., 1998). Nordeng and Sibley (1996) state that it may be attributed to variations in the chemistry of pore fluids. Kessels (1999) collected zone width-crystal size data of different size crystals that share the same pore space or are in direct contact with each other. Large crystals were found to have thicker zones than smaller crystals 39 sharing the same pore; therefore solution variability was ruled out as a possible cause for larger crystals to grow faster than smaller crystals. A few samples do not show a linear trend in radius-rate plots. These trends may represent a different crystal growth regime expressed as dr/dt=k. Trends resulting in no correlation may have been affected by quartz replacement of calcite or the presence of clays and muscovite inducing dissolution or inhibiting growth. However, no correlation was found between percentages of dissolution/growth inhibiting features and corresponding correlation coefficients; therefore these processes do not affect dr/dt=kr. Effect of drldt=kr on Crystal Size Distribution Diagenetic processes must be identified in order to understand the variables that alter the parent rock during diagenesis and the effect it has on porosity and permeability. Two models were made to simulate the effect of dr/dt=k and drldt=kr on CSDs. A k was chosen that made it possible to generate gain radius/overgowth thickness ratios similar to real ratios of samples. The average gain radius/overgowth thickness ratio for measurements in samples is approximately 10, therefore k is equal to 0.10. One hundred random normally distributed initial gains were generated with a mean of 1.0 and s.d. of 0.6. The gains were gown by drldt=kr. The rate is added to the initial radius and results in the new radius. The initial and final radii were plotted on a normal probability plot (Figure 21). The distribution for the initial and final radii show changes in shape of the distribution of data. Larger gains deviate more than smaller gains indicating that the CSD becomes more lognormal as the gains gow. For dr/dt=k, gains gow at the same rate therefore 0.10 was added to the same set of initial radii resulting in a new radii- The initial and final radii were plotted on a normal probability plot (Figure 22). The plot shows that the distribution of gains 40 remains the same, the only difference being larger values for final radii. Initially normal distributed gains follow a normal CSD when gown by dr/dt=k However, the deviation on a normal probability plot for gains gown by drldt=kr also depends on k since k influences the rate of gowth. Another model was made exactly as the previous model for gains gowing by dr/dt=kr, using the same initial radii, only k was changed to 0.5. A normal probability plot was made of the initial and final radii for gains gown by drldt=kr (Figure 23). The normal probability plot shows a larger deviation between the initial and final radii than Figure 21 in which k=0.10. Therefore gains gown by a large k are more lognormal than gains gown by a small k. Grains gown by dr/dt=k and dr/dt=kr affect CSD differently. The varibility of k also influences CSD differently. Therefore these factors have varying effects on porosity and permeability of a medium. Justification of Data Removal Data points were removed from four data sets because they showed large deviation in the trend of the plots that dominate the regession. These data points either represent a stereologic effect, varying gain shape and/or an error in measurement. The removal of each data point is explained for each data set and regession plots were made before and after data removal and then compared. Prior to data removal, 11 of 16 (69%) samples had significant correlations. After data removal, 10 of 16 (62.5%) samples had significant correlations. The initial regession plot for sample 5 shows a deviating point with a large rate and a small radius. This may be an example of a measurement influenced by stereologic effect. As a sphere is sliced further and fiirther away from the edge of the center of a sphere, the overgowth thickness increases as the gain diameter decreases. As a result, 41 E , r .11.... ' ’ -Initial ~q$-----.-- ---- -- ---. a .4 O N .-------- ---- - mi Radius (mm) Figure 21. Normal probability plot for the initial and final radii. The final radii are gown by the dr/dt=kr gowth law (k=0.1). Differences in the initial and final radii distribution are apparent. The larger the radius the larger the deviation the two. 42 - Final - Initial Figure 22. Normal probability plot for the initial and final radii. The final radii are gown by the dr/dt=k growth law (k=0.1). The distribution of initial and final radii are identical only that the final radii have larger values. 43 0 0 0 0 J l I I I I I C C l i I]. I . I -'-F oooooooooooo f cccccccccccc ‘ ............ "-o s, ...... o. uuuuuuuuuuuuuuuuuuuuuuu I 0 0 0 'I ' a 0 0 0 '0 0 0 0 0 0 0 .' 0‘ 0 .s ......................... .0 ......... 7- -3. .......... .0... ........... 0. .......... 0 0 I; O 0 ,0 0 ........................................... ,5- --.--..----------....---------- 0 0 , 0 0 , 0 0 -L .............................. ,2 , ..... ' ............ ' ........................ O p t . O 0 0 0 0 0 ‘ , a ' , ' o 0 0 0 , o 0 . 0 a o o a , o 0 0 0 I 0 0 a j I ‘ ’ a a r I ' 0 O | o a! 0 o 0 . ' 0 0 -. ------------ ‘n-Q- - -O’.‘ OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 0 0 a 0 0 0 0 0 " o 0 0 0 ‘V ............ $.c. ....... ‘ ........................................ 0’ .......... 0 0 o 0 0 0 0 ’ ’0 ’ 0 0 0 0 o I 0 0 0 1..” ......... !-,- 4’40- ...................................... 0 ........................ I I I I D 0 ‘0'. 0 0 0 0 0 "0 0 I 0 o I, 0 0 u 0 0 ,1 0 0 0 0 0 O I I I I O 0 0 u 0 u I D I I I A A A A A I I T I I I Figure 23. Normal probability plot for the initial and final radii. The final radii are gown by drldt=kr gowth law (k=0.5). A larger k value results in a larger deviation between initial and final radii and therefore final radii are more log- normally distributed (when gown by dr/dt=kr) than in figure 21 where k=0.1. the radius measurement is smaller and the overgrowth thickness is larger than would be expected of a grain sliced closer to the center. The outlying point represents this trend and therefore the rate is much larger than would be expected for a comparable grain size which follows the trend of the data. Prior to removal the r2 for sample 5 is 31.7% (Figure 24) compared to 61.5% post removal (Figure 25). Both regressions are significant. The data sets for samples 13b, 3b, and 2 show a similar effect in which one data point shows a large deviation fiom the rest of the data, having a rate and radius much larger than the other data points. While most grains are well-rounded very few are perfectly spherical in three dimensions. Some grains are very elliptical and elongate. Since the maximum diameter was measured, grains with one axis much longer than the other are subject to deviate fiom the data since most grains are spherical. This deviating measurement is effected by differences in grain shape. The data also exhibit large rates, which may be influenced by a stereologic effect. The r2 for 13b before and after data removal are 43.4% (Figure 26) and 26.8% (Figure 27) respectively. Both 1'2 are significant. The r2 before removal of the sample 2 is 44.1% (Figure 28) whereas post removal the value is 2.7% (Figure 29). Initial r2 is significant and after data removal is no longer significant. The r2 for sample 3b prior to data removal is 52.4% (Figure 30) compared to 23.9% afier removal (Figure 31). Both r2 are significant. CONCLUSIONS A linear correlation exists between detrital grain radii and overgrth thickness in the Galesville Sandstone suggesting dr/dt=kr. Samples showing no correlation between overgrowth thickness and detrital grain radii may represent drldt=k. A non- correlation can also be attributed to these samples having a low range of grain sizes therefore a trend is less likely to be discernable. Calcite and clay may also induce 45 0.035 0.03 0.025 0.02 Rate 0.015 0.01 0.005 O 0.05 0.1 0.15 0.2 0.25 Radius (mm) Figure 24. Regression plot for sample 5 prior to data removal. Data being removed due to stereologic effect is depicted as a circle. 46 Rate 0,035 r I I I I I I I I I I 1 j # I I I I I I I I I I , r2=61.5% i ; 0.03 ~— ---------------- 1 0.025 - --------------- é ----------------- é ----------------- é ------- +-+---§c~9r-/- ------ ‘1 0,02 — ---------------- i ----------------- i ---------------- '+ no ---------- i -------- +---- i E 24““ . i 5 O : 0.015 —- --------------- 01/ ----------------- ;. --------------- P d h - _ O .. I I I I I- I I I I II I I I I O O] _ nnnnnnnnnnnnnnn Juno-unnounuInc-ood.coo-Qununcucnonud-n-0..--..---.---* ............... _ . I I I I b I I I I I I I I I p I I I d h I I I I J _ I I l I q I I I I 0.005 —. nnnnnnnnnnnnnnn i ooooooooooooooooo J. ooooooooooooooooo J. ................. J. OOOOOOOOOOOOOOOO - '- i i i i ‘ I- ' : ' ' I: . g . h . II 0 I I I I l I I l I l I I I I I I I L I I I I I I O 0.05 0.1 0.15 0.2 0.25 Radius (mm) Figure 25. Regression plot for sample 5 after data removal. R2 value changes from 31.7% prior to removal to 61.5% after removal. Both r2 values are significant. 47 003 J--J..J-..I--{--J--.I.-J..J-.{.-J--J--J--J-..{--J..T-J--J..4--J--J--J--J.-+.7.-J.-J--Jfl 0.025 - ------------ -------------- i ---------- ..-.§---. ........ .§ .......... / .......... _ 0.02 - ------------- §~ -------------- --------- .---f. ------- «I ------------ - Rate 0.015 — ------------- I~ -------------- two-+4.- -------- +---§- -------------- :- ------------ — 0.01 _ ------------- g- ------------ 4 L .. I- II . s a a s a . 0.005 - -------------- ~: -------------- ~: -------------- ~: ------------- - b : : : : : a r- ' ' -1 r- 1 )- . I I I I I 0 lllllIIIJIIIIIJIJJJIIIJJIIILI 0 0.05 0.1 0.15 0.2 0.25 0.3 Radius (mm) Figure 26. Regression plot for sample 13b prior to data removal. Circle represents eliminated point fiom final plot. 48 0.03 I I I T I I I I I I I I l I T j I I I l I I r I l I I I I : I I I I 0.025 —- ------------ é -------------- 5 ---------- o--:---o -------- a -------------- i ------------- - E . 9 E 0.02 _ ------------- ;. -------------- ;. --------- ...--, ------ .2. -------------- g ------------ - 0.015 — ------------ .f. -------------- ;r---+ o +.. -------- +---fr -------------- j+ ------------ — Rate 0 : o - 3. 0.01 +- ------------ ~E -------------- -------------- -§ -------------- «f --------------- i ------------- -4 0.005 —- ------------ é -------------- é -------------- «E -------------- i -------------- i ------------- — !- d .- cl 7- '1 I I I I I d O I I 1 J I J I I 1 J l J I I I l I l I J I I I l I I I I 1 0 0.05 0.1 0.15 0.2 0.25 0.3 Radius (mm) Figure 27. Regression plot for sample 13b after data point is removed. R2 value decreases fiom 43.4% to 26.8%. 49 Rate 0.06 0.05 0.04 0.03 0.02 0.01 _ F I I I ! I I T I ! I I I I ! I I I I I I I I I ! I I I I I I I I I I I I I r - -------- ~: ----------- :« ---------- . ---------- é ---------- -§ ----------- :r ---------- inc-"- - a a 2 s a a = ‘ ' : :r =44.1% : : : E ‘ ~ --------- a ---------- -s ----------- é- ---------- ---------- ----------- : ----------- ;~ 7..--.- P I I I I I I I 'l - a a a s = x” z a — --------- : ---------- s-; ------- ~54 ------- // ------ 4 ---------- ,. -------- - . 5 o o / o; 5 I r --------- r ---------- r30,- -4 ------ on; ----------- y ---------- s ---------- , --------- - '- ‘E’/ . . 3 E d , a « oz 0 a a 2 P'- -------- fi ----------- é- ---------- I ---------- 'i ----------- E ----------- " ---------- ‘ --------- - I. I I I I LJ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I_L I I I + 0 0.05 0.1 0.15 0.2 Radius (mm) 0.25 0.3 0.35 0.4 Figure 28. Regression plot for sample 2 before data point removal. Data being eliminated is depicted as a circle in the upper lefi hand comer. 50 Rate 0.06 0.05 0.04 0.03 0.02 0.01 I : : . : : : 1 ' : : : : : - a s s a s 4 —- ------------------- -.- ---------- 5 ---------- 5 ---------- -: ----------- l- ---------- o --------- .4 - r =2.7%5 5 5 5 : j " I I I I I I n : : : : ‘ P- --------- 1 ---------- 'I ----------- r ---------- r ---------- 4 ---------------------- ‘- -------- -—i I I I I I I I IIIIIIIIJII_II_LIIIILiIIJJJIIIIIIIIIIIIII O 0.05 0.1 0.15 0.2 Radius (mm) 0.25 0.3 0.35 0.4 Figure 29. Regression plot for sample 2 after data removal. R2 value decreased from 44.1% to 2.7%. 51 Rate 0.06 I I I I I I I I I l I I I I I I I I I l I I I I I I I T I I I I I I I I I : I I . d . 4 i i 3 J I b I I I I I I " I I I p D 0.05 ~---------~f ------------ 5 ------------ é ------------ fr ------------ ------------ i ---------- — ' r2=51.5% : : : E ‘ l- I I I I I- . I I I ' q I h D 0.04 0.03 0.02 0.01 l I I I OLILIIJIIIIIIIIIIIIIIIIIIIIIIIIIIII 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Radius (mm) Figure 30. Sample 3b regression plot before data point removal which is depicted as a circle in the far upper right hand comer. S2 0.06 I I I I ! I I I I ' I I I I l I I I I I I I I I l I I I I [I1 I I p I I I I I 1 ~ 4 5 4 - : : : : E E 4 0.05 —' """"" r"""2 """ I' """""" 1' """""" ‘1' """""" “E """""" 1 """""" ‘ : r=51.5% = = : = 1 0.04 I —l : + : J 3 003 i 1 cu . , d a: 5 . 0.02 I + J - : = ’i E E 5 5 j 0.01 '" """"" i """""" i """""" 2' """""" r """""" ’: """""" '1 - : : : : : : i . ' J 0 I I I III I I I J I I I I I I I I I I I I_I I I I I I I 14 J L O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Radius (mm) Figure 31. Sample 3b regression plot after data removal. R2 decreased from 51.5% to 23.9%. 53 dissolution or inhibit growth of quartz, but preliminary studies show that these processes to not affect grains grown by dr/dt=kr. The rate law dr/dt=kr is a new type of mineral water interaction that has been observed in ancient dolomites as well as metamorphic garnets, galena and other various minerals grown in industrial crystallizers and now in a quartz cemented sandstone. It is a relationship widely observed yet it does not correspond to a theoretical crystal growth mechanism. This indicates that crystal grth theory may not include some significant grth mechanisms. 54 APPENDIX A Radius-Rate Plots for All Samples 55 Outcrop 1, sample 2. ddidfi‘ududq uun—uuuu—dfidd fidd-u—Id-d T u n u u u u I m m u m m m . . u u m u u u u u 4 n n u m .. ........ to»... 1 m u I u m n I“ T n u u u u n .. u u I O u u u I u u , . . u n I u u , u o . u I - a n u n n J l. ........ m ......... a-» ..... .m: -Iiiw ......... m ......... a” ........ I r m m m u m m . r m m a m m m . I u u o u u u . m m . . . m 1 u o u o + u u . u ........ . ......... .n .................. m ......... . ......... .m ........ 1 m u u o u m u u o m m n u m . MW. m m m w m . . = u " ... . u .2 . . . I n r u u u u n I l ........ .u ......... .m. ......... ”r ......... m ......... .m ......... .m. ....... l . m m m m m m . . m m m m m m L n b h h _ h h b blFP P b h m b P? b — n D rh — n p p P _ h b b P 5 3 5 2 5 l 5 0. 0 0. 0 0. 0 0. 0 0 0 0 0.5 0.4 0.3 0.2 0.1 Radius (mm) 56 Rate 0.035 0.03 0.025 0.02 0.015 0.01 0.005 Outcrop 1, sample 3a. I I I I l I I I I I I I I I l I I I I l I I I I P i u / .- ' E . /. 1 -, ------- ---------------- 4-.-.-- <—-+---: ---------------- - L. ............... 5 ................. 5-.. ..... /'...-. ................. 5 ................ _‘ C 5 II 5 E I I ................ 5-. ...... / 5.. ............... 5 ................. 5 ............... .— ' i / i l 1 I- I / .. . E I ---wo ------------------------------------------- 5 --------------- — >- E O E - L. ............... .5 ................. J ................. J ................. .E ................ .: P J I I I I I I I I I I I I I L I I A I I I 57 Outcrop 1, sample 3b 0.05 If I I I l I I I I l I I I I l I I I I l I I I I l I I r T I I I I I I I I l C § § 3:23.904 0.04 0.03 0 2; Of. 0.02 0.01 ; O I I I I I I J I I I I I I I I I I I I I I I I j J I I I I O 0.05 0.1 0.15 0.2 0.25 0.3 Radius (mm) 58 0.035 0.03 0.025 0.02 Rate 0.015 0.01 0.005 Outcrop 1, sample 4. 1 I I I I f1 fI ' I I I I I I 1 I I I I I T I I I Ti r' : 3 i : i 7 : 5 : : : : * . : ‘55-5% 5 E E I -—-- -------- +-- h I I I I I d I 5 E E E O E 9/ I I I I I I - : : : : ’/:/ u —- ------------ é -------------- a. -------------- 1 --------- o---a.-----------.y-a. ----- + ----- - ' E E = o = ,// : ‘ P n I : :/ " ~ : : : /./ . - = = i ./ i ° * h ooooooooooooo 'r oooooooooooooo 'rcunonobonucuoo .-.,"; ooooooooooooooooooo ‘ ............ d - 5 : . / : ~ : 5 / 50 = 1 I I . 1/ O : . - oooooooooooooooooooooooooo ” oooooooooo foo... oooooooo r .............. f oooooooooooo — - : : ‘ '- l I -I r : : . h- : : cl I I P ............ J------..--.---‘. ....................................................... - r- : - . - . — ............ % .............. J. .............. J .............. J .............. J ............. - u. ' -+ " '1 - . I I I I * I I I I I I I I I I I I #4 I 14 I I I I I I I I I I I J 0.05 0.1 0.15 Radius (mm) 59 0.2 0.25 Rate Outcrop 1, sample 5. 0,03 jIrl I I I I I I ITI TI ' I I I l I TI I II I I I I1 0.025 0.02 0.015 0.01 0.005 r2=61..';% I I I . I I I I I I I I I I I I I I III I I I I+I I I I I O l 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Radius (mm) Outcrop 1, sample 6 .111-1‘11—d111-d4dd‘\+qudqd4*q . - q‘dqd_-ddd 8mm 4 m m m m m M m I . m mo m. m m . w Om m u m m m u . .. ....... u. ........ n. ....... H. ........ H. ........ m. ........ .v ........ v ...... 1 . m m m m m M . . m m. y om m m m . . m a / w. m m m w n "O u/ m. n u u . I ....... m. ........ u. ........ .a ....... H. ........ ”r ........ m. ........ u. ...... 1 n n + u u u u 1 u u u u u u m .. . m. + m m 1 m m . 1 m m. m /W,o + m 1 , ....... H. ........ u. ........ .. ........ m... a ........ .. ........ H. ...... 1 . W m m m m M m . . % m m m u m m . J n u m m u u ........ ........ ........ W ........ w ........ ........ ...... .. . m m M m m m m . . m m m M m m . Phpb—nnbhhbbbhmh-nn—nbhb—bhhb_F-hp—-n- 4 5 3 5 2 5 .I. 5 0 0 3 0. 2 0. 1 0 O 0 O. 0 O. O O. 0 0. O 0 O 0 0.25 0.2 0.15 0.1 0.05 Radius (mm) 61 Outcrop 1, sample 8. ddfid - h p n b n n P _ --..-.....--. f .-.......-.--.--- u1dd—J-114d O .,.------..--..-.. 0 ‘..----....---...-~-........ hhb hL-n _ 0.03 0.02 *—--.---.--....-. 2am _ 1 d d d n o u u u p o a n o a u c -‘ ....... o u n u n o c u u u u‘ n u c u o u u u - u c m h b p b 1 o 0 0.25 0.2 0.15 0.1 0.05 Radius (mm) 62 0.04 0.035 0.03 0.025 0.02 Rate 0.015 0.01 0.005 Outcrop 1, sample 10. O 0.05 0.1 0.15 0.2 Radius (mm) 63 0.25 0.3 0.04 0.035 0.03 0.025 Rate 0.02 0.015 0.01 0.005 Outcrop 1, Sample 11a. I I f I I I I I 1 I I I I j I T I I I I T I I I I I C I I I I I .l +— ------------ + ------------- + -------------- :9 -------------- z» ------------ 2r ------------ - : E r‘5-6% S 05 i 1 . : II o: : - —""""""' """""""""" * """"""" i """"""" i """"""" i """"""" '- : : : : : 2 P : I O .I I ”/- - : :o : If-" . I I . 9 5 : O 6 i I — ------------- 5- -------------- ro ------------ “Luna-«If. -------------- l ------------ J : : ' 0 : 9 : E 1 l. i i . . i i d . : : : : a - """""" '2' """"""" ' """"""" 2' """"""" 2' """"""" 2' """""" " I a s a a l — ------------ i -------------- a -------------- -§- ------------- -:- -------------- ------------- - C— ............ E .............. . .............. .5 .............. I .............. 4' ............. .— - : : : d I I I I I I I I I I I I I L 14 I I I I I I I I I J I I I I I I 0.1 0.15 Radius (mm) 0.2 0.25 Rate 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 Outcrop 1, sample 11b. I I I I I I I I I I - i = 0 j n I I I _ . : . .: .4 l I I I I I l d I - OOOOOOOOOOOO or oooooooooooooo r oooooooooooooo .rocoo. ........ .r -------------- r ............ fl _ I I I .1 I I I I. I I I q . : : o : . I p I I I I - I I l I — ...... q .............. fl .............. - ............................ _ I I I .. . . : .1 _ I I I cl I I I I- I I a II I I u q n I I I b. oooooooooooo ‘ oooooooooooooo ‘. .............. 1' OOOOOOOOOOOOOO 4 .............. { CCCCCCCCCCCCC - n ' ' ' all I I I - : : : l P l l l . : “ d r- L I I I I I 4 I I I I I I I I I I I I I I I I I I l I I I 0.15 Radius (mm) 65 0.2 0.25 0.3 Rate 0.035 0.03 0.025 0.02 0.015 0.01 0.005 Outcrop 1, sample 13a. I I I I E I I I I ! I I I I I I I I I I I T I I l I I I I I I I | I I I I I I I I I I I I I I J 14 I I J J_I4I L I I I I I I H 0.05 0.1 0.15 0.2 0.25 Radius (mm) 0.3 Rate Outcrop 1, Sample 13b. 0.026 1:.g.:Ig.1juxrg...!...ga..:rt'w 0.024 0.022 0.02 0.018 0.016 — --------- ;~ ------- / ’ ----------- ---------- --------- - .. / 1 i " - I// 05 o o 5 o . 0m“ f’ """"" 5 """""" i """"" f ""3”“; """"" '3' """"" """"" ‘ .- 1 Q . E 1 3 i i 0.012 4L I I f L I I I I I I4 I I I41 I l I I I I I I I I I L I I I 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Radius (mm) 67 0.025 0.02 0.015 Rate 0.01 0.005 Outcrop 2, sample 25. l- I E E E II P : o 5 E E - _ : r'Z-l/o : : : q k ---------------- ----- + --------------- — Z 5 E E E o 1 - ' E i i + - ---------------- r ----------------- g- ----------------- g-«o ------- o----!o--+ --------- —- : ' E fyM. : . E o 95 E . r-P ---------------- ~:----+ ---------- ~:- --------------- — ' s 0 E i ‘ I E E0 E I h. 000000000000000 J OOOOOOOOOOOOOOOOO ‘: OOOOOOOOOOOOOOOOO ‘: IIIIIIIIIIIIIIIII JE OOOOOOOOOOOOOOOO - L E E E ‘ . : : : .4 " ' : : i 1 I I I I I I I I I I I I I I J I L I 68 0.025 0.02 0.015 Rate 0.01 0.005 Outcrop 3, sample 27. I 1 I I ! I I I I ! I I I I l' I I I I I I I I I I I I I I I I I b ’ 1 L . I '1 I I D . d I n : q I b. nnnnnnnnnnnn J uuuuuuuuuuuuuu J. uuuuuuuuuuuuuu J .............. J oooooooooooooooooooooooooooo _ I l- . d F d h cl P d IIIIIIILIIIIIIIIIIIIIIIIIJIII 0.05 0.1 0.15 0.2 0.25 Radius (mm) 69 Rate Outcrop 4, sample 31. 0.03 I I I I I I I I I I If I I I I I I I f I I I 0.025 - -------------------- ---------------------- --------------------- $ ------------------- — 0.02 — -------------------- é ---------------------- é- ---------------- «-4 ----- ,9/- --------- — i + . 0.015 — -------------------- '- --------------------- 4-, ------- o+-------§--o ---------------- - 0.01 —- -------------------- .~ ---------------------- o ------------------- -------------------- - I 0005 I I 1 I I L I I I I I I I I I I 1 41 I C 70 0.025 0.02 0.015 Rate 0.01 0.005 Outcrop 4, sample 32. . s a s - F : : 9 : . . 2 : o o : E . ___________ r _=14.1% a + i z / ’ i : /./.V' * s . s / = ‘ v- I I / ' : Ii __ E O O O :// O : ‘ ' 5% 5° 5 - _ ................ . ................. g. .............. a ................. ; ............... _ ' : o 5 E ‘ P : : : - — --------------------------------- {ac-"mun":- ---------------- -§- --------------- — - . E E q r- : i 4 . 5 5 4 —. --------------- J ----------------- J nnnnnnnnnnnnnnnnn IE ooooooooooooooooo IE ---------------- -I L E E I I I I I I— I I _I I I I I I 14L I L LI 4 71 APPENDIX B Overgrth Thickness and Radius Thin Section Measurements for All Samples 72 0N _ M00 000N0.0 000N0.0 000N0.0 005 .00 000 .0.0 050 _0.0 050 _ 0.0 0330.0 0mNN0.0 000N0.0 005 .0.0 0nNN0.0 000 .00 000.000 000N0.0 00NN0.0 0230.0 000M0.0 005 _0.0 000 _ 0.0 mthod 0N _ No.0 0mNN0.0 0N0 _ 0.0 000 .0.0 000mm .0 000 _ m0 0000m .0 0000N.0 0000?.0 0000N.0 0000?.0 0000m.0 000010 0000n.0 00va.0 0000m.0 000 _ m.0 000mm.0 0000N.0 000MN.0 009330 0000m.0 000Nn.0 000Nm.0 0033.0 000NN.0 0093.0 000NN.0 0000 _ .0 000NN.0 0000m0 000m0.0 0mNh _ .0 0530.0 0mNhN.0 000N0.0 03.0 _ .0 03. _0.0 0000 _ .0 000 _0.0 000N_.0 0020.0 03k. _ .0 000N0.0 0033.0 0330.0 003. _ .0 000N0.0 0000 _ .0 000N0.0 00mm _ .0 0mNN0.0 00mm _ .0 0330.0 000— _.0 050 .0.0 03% _ .0 000 _ 0.0 0me _ .0 0mm. _ 0.0 000s. _ .0 000 _0.0 0000 — .0 000N0.0 000N _ .0 0N0_0.0 00th.0 mm _ N00 000 _ N0 0053.00 0000 — .0 000 _0.0 A55 305. 055 85. a. 295m 030 _ .0 330.0 0000 _ .0 0330.0 0000 _ .0 03.0.0 033 _ .0 30 _0.0 030 _ .0 0030.0 0300.0 000 _0.0 03K. _ .0 0330.0 030 _ .0 0030.0 0000 _ .0 330.0 000v _ .0 00030.0 003 _ .0 0030.0 0000 _ .0 00030.0 000 _ .0 0030.0 0000 _ .0 0030.0 03. _ .0 00030.0 0033.0 3030.0 030 _ .0 00030.0 003.. _ .0 03 _ 0.0 0000. .0 0008.0 033.0 0008.0 00000.0 03 _ 0.0 030. .0 0030.0 0003.0 0330.0 030 _ .0 038.0 9.5 3.5. :85 32 gm 28% 8888 F888 8N _ 8 338.8 828 588.8 89.8 named 838 8588 omfimd 838 828 828 8?. _ .o 8m .8 8de 8m 58 8:8 828 8R8 305.8 89.8 828 88 8 m8 _ 8 82.8 8.88 82 _ .o 84. .8 8m :3 8.0.8.8 c828 888 89.8 828 8mm; 28 5.8 888 3:8 828 888 8&8 m3 :3 82.8 8888 8m _ no 888.8 888 888.8 8m _ 8 808.8 82 _.o 888 A55 8:81 850 35. mm 208% A55 3:5. 0:5 as. N 28% 73 0000 . .0 0008.0 0000 . .0 0030.0 0000 . .0 00.. .00 0000 . .0 000 .00 030 . .0 038.0 000. 0.0 330.0 00003.0 0008.0 0000 . .0 038.0 0000 . .0 0030.0 030 . .0 0008.0 0083.0 038.0 000 . 3.0 000 .00 0003.0 0030.0 00003.0 038.0 0003.0 0008.0 0000.0 038.0 0003.0 0008.0 0000 . .0 038.0 0303.0 038.0 000 . 0.0 038.0 033.0 0030.0 00003.0 0008.0 030 . .0 038.0 00003.0 0030.0 0800.0 000 . 0.0 0000 . .0 038.0 0000 . .0 3.8.0 000 . 3.0 3.8.0 008 . .0 0008.0 0003.0 0008.0 :55 8:5. 055 25. 0. 283m 00033.0 00030.0 030 . .0 000.00 030.0 00300.0 0000. .0 030000 0000. .0 00030.0 0000.0 00300.0 000 .30 00000.0 0000. .0 00030.0 0003.0 030.0.0 0000.0 03.300 00303.0 03.300 0000 .0 00030.0 0030.0 00000.0 0000.0 00030.0 0003 . .0 00000.0 000 .30 03030.0 0030.0 00000.0 000 .30 000 .00 0000.0 00300.0 0030.0 00030.0 0000.0 000.00 00033.0 00300.0 0000.0 00000.0 0000.0 003.00 0000. .0 000.00 .580 9.03. :55 25. 0 28am 0000.0 000.0.0 0000 .0 03.300 000. 3.0 03000.0 000v . .0 00030.0 0000.0 00030.0 0000.0 000.0.0 0003 . .0 000 . 0.0 0003.0 000.0.0 00000.0 000 .00 0000 .0 00300.0 0000. .0 00030.0 0000.0 030.00 0003 . .0 00030.0 0000.0 000.0.0 0000.0 00030.0 0003.0 00030.0 000 .30 00030.0 0030.0 030.0.0 0000.0 000.0.0 0000. .0 00000.0 0000. .0 00030.0 0000.0 000 . 0.0 000.3.0 000.0.0 0030 . .0 00000.0 .88. 8.8.0 055 23. 0 2950 0000.0 000.0.0 000 .30 00030.0 0000 .0 000 30.0 00303.0 00030.0 0000 .0 00030.0 0003.0 030.0.0 000. .0 000.0.0 0000.0 0030.0 000. .0 003.0.0 0000.0 00030.0 0000.0 00030.0 00033.0 00030.0 000.10 000.0.0 0000.0 00330.0 0030.0 00330.0 0000.0 000 .00 000. .0 000.0.0 00000.0 000 .00 003.30 00030.0 00303.0 00330.0 00003.0 00030.0 0000.0 000 .00 0000 .0 000 .00 Es. £3... :55 23. 0 295m 74 0000.0 003.0.0 0000.0 00030.0 000v . .0 000 .00 00003.0 000300 0000 . .0 000 .00 0003.0 030.00 0000.0 000 .00 0003.0 003.00 000. .0 000 .00 0030.0 00030.0 0000 .0 000.00 0000.0 03.300 0000.0 03. 30.0 0000.0 000.00 0000 . .0 000300 0000 . .0 00330.0 000M . .0 000 . 0.0 0000.0 000.0.0 0000.0 000 .00 000.. . .0 000 .00 00003.0 00330.0 0000.0 00030.0 0000.0 00030.0 0000 . .0 00030.0 0000.0 003.0.0 000. .0 000.0.0 App-:0 03.00”. A80 35.. 0: 0.950 0030 . .0 038.0 000. . .0 3 . 8.0 0000. .0 03030.0 0008.0 0030.0 00.. . 3.0 00030.0 00033.0 0030.0 0003 . .0 00030.0 0000 . .0 0008.0 0000 . .0 0030.0 0003 . .0 3 . 30.0 00003.0 00030.0 003.0 03.0.0 030 . .0 00030.0 00000.0 00330.0 0000 . .0 00330.0 00003.0 0030.0 0000 . .0 0008.0 0000 . .0 00030.0 0000. .0 00.. .00 0000 . .0 0008.0 000.. . .0 00030.0 0003 . .0 03.0.0 080 . .0 0008.0 000.. . .0 00330.0 000. ..0 3.8.0 0000. .0 0008.0 0003.0 0008.0 .55 03.05. 0:5 83. 00. 0.0800 00003.0 00030.0 00003.0 03 . 30.0 0000.0 003.0.0 0000.0 00330.0 0000.0 000.00 0000.0 000.0.0 0000 .0 00030.0 0000.0 000 .00 0003.0 00030.0 00000.0 00030.0 0000.0 00030.0 0000. .0 00 030.0 0000.0 00030.0 00033.0 03030.0 00003.0 00030.0 0000 .0 030 .00 0000.0 003.0.0 00030 003000 0000. .0 000 .00 0000. .0 00030.0 0000.0 00000.0 00003.0 003.0.0 0000. .0 00030.0 000. 3.0 000000 0000. .0 00030.0 0000. .0 00030.0 000.. . .0 00000.0 0000.0 000.00 .55 03.5. .55 38. 0: 0.850 0000 . .0 038.0 030 . .0 3 . 30.0 00003.0 0008.0 0000. .0 00330.0 00003.0 00330.0 000.. . .0 00030.0 000 . 3.0 03. 8.0 00003.0 00030.0 000 . 3.0 3 . 8.0 0000. .0 038.0 000.. . .0 000 .00 0000. .0 00.. .00 00003.0 00030.0 00003.0 000 00.0 0000. .0 00030.0 00003.0 0030.0 0000. .0 03 . 8.0 0000. .0 00030.0 00003.0 00330.0 0000 . .0 0008.0 0000. .0 00.. .0.0 0000. .0 00030.0 0000. .0 00030.0 0000.0 00030.0 030.0 3.8.0 000. . .0 000 .0.0 0000 . .0 03030.0 0000. .0 00030.0 055 3.05. .EE. 0.5. 0. . 0.0800 75 0000.0 00030.0 000.30 000 .00 0000.0 030.0.0 0003.0 000.0.0 0000.0 000.0.0 0000 .0 030 . 0.0 0003.0 000.0.0 0003 . .0 000 .00 0030 . .0 000000 0000.0 000 .00 000. .0 003.0.0 00000.0 000.0.0 0000.0 03. .00 0003.0 03. .00 000.10 003.0.0 0030 . .0 000 .00 0000 .0 00030.0 0000 .0 000 .00 0003 . .0 000 .00 00033.0 000 .00 0003.0 000 .00 00003.0 00030.0 00003.0 030 . 0.0 0000 .0 000.0.0 0000 .0 003 . 0.0 0000 .0 80.0.0 0030.0 003.0.0 0.5.5 03.05. App-:0 85. 00033.0 000 .00 0000 .0 030.0.0 0000 .0 000 _ 0.0 000v . .0 03.300 000. .0 000 . 0.0 000v . .0 030 . 0.0 000. .0 00000.0 0000 . .0 000 .00 0000 .0 000 .00 0000. .0 00330.0 000v. .0 000 .00 0000 .0 003 . 0.0 0003.0 03.300 0000. .0 000 .00 0000. .0 000 . 0.0 0003 . .0 000 .00 0003.0 000.0.0 000. .0 030.0.0 0033. .0 00030.0 0003 . .0 030 .00 .55 3.3. .5... as. 30 0.950 0000. .0 000 .00 0003.0 03.300 00000.0 00 3 . 0.0 0000 . .0 00030.0 0003 . .0 00330.0 0030 . .0 000 .00 0000 _ .0 000 .00 0030.0 003—0.0 0000. .0 003.0.0 0003 . .0 000 . 0.0 00000.0 000 . 0.0 0000 .0 00030.0 0000. .0 000 . 0.0 0000.0 000 . 0.0 0000.0 030.0.0 0003.0 000.0.0 0000.0 000300 00030 000.0.0 00000.0 003 . 0.0 0000. .0 030 . 0.0 0;... £3. .5... as. .0 2950 03 2950 0000.0 000 .00 0000. .0 000 . 0.0 0000 .0 00000.0 0000.0 000.0.0 0000 .0 00000.0 000.30 000 .00 00033.0 003 . 0.0 00303.0 000 .00 0000.0 003 . 0.0 0000. .0 000 . 0.0 0000.0 003.0.0 0003 . .0 00030.0 00033.0 00000.0 00003.0 000 . 0.0 0003.0 003.0.0 00003.0 003 . 0.0 0033.0 03. .00 000?. .0 03. .00 0000.0 00000.0 0000. .0 00000.0 00033.0 000 .00 050 9.05. 050 «5. 03 0.00.00 76 APPENDIX C Overgrowth Thickness and Radii Measurements for Two Sample T-Test 77 00000... 0003.... 8000.. 0.53.... 000.0... 0033.... ........3... 03.3.... 0803... 03.3.... 2.000... 0030.... ......33... 000...... 00033... 000 .0... 00000.. 0003.... 000...... 03.3.... 00000... 000 .0... 00000.. 0033.... 00030... ....0 .0... 00003.. 000 .0... 000...... 0033.... 00030... 0008... 00000... 0003.... 00003... 0003.... 00030.. 0033.... 00000... 0003.... 00033.. 000...... 00000... 03.3.... 00003... 03.3.... 00030.. 0033.... 8033... 03.3.... 05:. 8.3. as. .. 2950 00003.0 000000 0030. .0 00030.0 00303.0 00030.0 0000 . .0 000 .00 0000. .0 000 .00 0003. .0 000 .00 0000.0 00030.0 00003.0 00030.0 0000. .0 00030.0 0000. .0 000 30.0 0000.0 00330.0 0030.0 00030.0 000. .0 000 .00 0000. . .0 000 . 0.0 0030.0 000 .00 0000. .0 000 .00 0000. .0 000 30.0 0003.0 030 .00 00003.0 03.300 000 . 3.0 00030.0 0000. .0 000 .00 0F... 00.05. 0:5 85. .. 2950 00033.0 000300 0030 . .0 0003.0 0030.0 003000 0000. .0 030000 0000. .0 00030.0 0000.0 00300.0 000 .30 00000.0 0000. .0 000 30.0 0003.0 030.0.0 0000.0 03.300 00303.0 03.300 0000. .0 000300 0030 . .0 000 000 0000.0 00030.0 0003. .0 00000.0 000 .30 030300 0030.0 00000.0 000 .30 000 .00 0000.0 00300.0 0030.0 000300 0000.0 000.00 00033.0 00300.0 0000. .0 00000.0 0000.0 003.0.0 0000. .0 000 .00 0:5 00.05. 0:5 0.5. 0 0.0.5.0 0000.0 00030.0 00033.0 000 30.0 0003.0 30.0.0 030 . .0 00000.0 0000. .0 000 .00 000 .30 00030.0 0000. .0 000.00 0000.0 030.0.0 0000.0 00030.0 003... .0 00030.0 0000. .0 000 .00 030.0 000.00 000 33.0 00330.0 0030.0 00000.0 000 33.0 03. 00.0 0000 . .0 0030.0 0030 . .0 00000.0 0000. .0 0 00 30.0 0000.0 00030.0 0000. .0 0330.0 .5... £3. .55 as. 0 2.050 78 000 .00 00003.0 000 .0.0 000. 0.0 000 .00 00003.0 000 .00 00003.0 000.00 0000.0 03 .300 00030 .0 000 .0.0 0000.0 00030.0 00030.0 00330.0 00000.0 000 .00 00000.0 000 .00 00033.0 00030.0 0000.00 00000.0 00003.0 000 .00 00003.0 000 .00 0000.0 003 .00 00000.0 0 00 .00 00003.0 003 .00 00003.0 00030.0 000. 0.0 000 .00 000.030 03 0.00.00 0000.0 00030.0 000 . 3.0 000 .00 0000. .0 030 .00 000v. .0 000 .00 0000.0 000 .00 0000 .0 030 .00 0003.0 000 .00 0003 . .0 000 .00 0030 . .0 00000.0 0000. .0 000 .00 000 . .0 003 .00 00000.0 000 .00 0000. .0 03. .00 0003 . .0 03. .00 000v. .0 003 .00 0030 . .0 000 .00 0000 .0 00030.0 0000. .0 000 .00 0003 . .0 000 .00 00033.0 000 .00 000v . .0 000 .00 00003.0 00030.0 00003.0 030 .00 0000 .0 000 .00 0000 .0 003 .00 0000. .0 000 .00 0030.0 003.0.0 03 0.95.0 79 REFERENCES CITED Bjorkum, RA, 1996, How Important is Pressure Solution of Quartz in Sandstones?, Journal of Sedimentary Research, v. 66, p. 147-154. Burley, S.D., 1992, Thin Section and S.E.M Textural Criteria for the Recognition of Cement-Dissolution Porosity in Sandstones, Sedimentology, v. 33, p. 587- 604. Burton, W.K., Vabrera, N., and Frank, RC, 1951, The Growth of Crystals and the Equilibrium Structure of Their Surfaces, Philosophical Transaction of the Royal Society of London, Mathematical and Physical Sciences, v. 243, p. 299-358. Carlson, W.D., 1989, The Significance of Intergranular Diffusion to the Mechansisms and Kinetics of Porphyroblast Crystallization, Contributions to Mineralogy and Petrology, v. 103, p. 1-24. Carlson, W.D., 1991, Competetive Diffusion Controlled Growth of Porphyorblast, Mineralogical Magazine, v. 55, p. 317-330. Chayes, F., 195 6, Petrographic Modal analysis: An elementary statistical appraisal, John Wiley and Sons, Inc., 113 pp. Eberl, D.D., Drits. V.A., and Srodon, J., 1998, Growth Mechanisms of Mineral from the Shapes of Crystal Size Distributions, American Journal of Science, v. 298, p. 499-533. Garside, J ., and Jancic, S.J., 1978, Prediction and Measurements of Crystal Size Distribution for Size-Dependent Growth, Chemical Engineering Science, v. 33, p. 1623-1630. Hoholick, J .D., Metarko, T., and Potter, P.E., Regional Variations of Porosity and Cement: St. Peter and Mount Simon Sandstones in Illinois Basin, v. 68, p.753— 764. Kessels, L.A., Interpreting Crystal Grth Kinetics of Ancient Dolomites, Ph.D. Dissertation, Michigan State University, 251 pp. 80 Klein, C., and Hulbert, Jr. CS, 1985, Manual of Mineralogy afier J.D. Dana, John Wiley and Sons, Inc., 681 pp. Kretz, R., 1973, Kinetics of the Crystallization of Garnet at Two Localities Near Yellowknife, The Canadian Mineralogist, v. 12, p. 1-20. Kretz, R., 1974, Some Models for the Rate of Crystallization of Garnet in Metamorphic Rocks, Lithos, v. 7, p. 123-131. Mendenhall, W., 1993, Beginning Statistics A to Z, Wadsworth Publishing Company, 525 pp. Mitrivic, M.M., and Ristic, KL, 1991, Growth Rate Dispersion of Small MnClz 4H20 Crystals 1. Growth Without a Magnetic Field, Journal of Crystal Growth, v. 112, p. 160-170. Nielsen, A.E., 1964, Kinetics of Precipitation, Pergamon Press, 151 pp. Nordeng, SH, and Sibley, DR, 1996, A Crystal Rate Equation for Ancient Dolomites: Evidence for Millimeter-Scale Flux-Limited Growth, Jomnal of Sedimentary Research, v. 66, p. 477-481. Ohara, M., and Reid, RC, 1973, Modeling Crystal Growth Rates from Solution, Prentice-Hall, 272 pp. Randolph, A.D., and Larson, M.A., 1971, Theory of Particulate Processes, Academic Press, 251 pp. Runkel, A.C., McKay, R.M., and Plamer, A.R., 1998, Origin of a Classic Craton Sheet Sandstone: Stratigraphy Across the Sauk II-Sauk IH Boundary in the Upper Mississippian Valley, Geological Society of America Bulletin, v. 110, p. 1 88-210. Russ, J ., 1986, Practical Stereology, Plenum Press, 185 pp. Sippel, R.F., 1968, Sandstone Petrology, Evidence From Luminescence Petrography, Journal of Sedimentary Petrology, v. 38, p. 530-554. 81 Swan, A.R.H., and Sandilands, M., 1995, Introduction to Geological Data Analysis, Blackwell Science Ltd., 446 pp. White, E.T., Bendig., LL, and Larson, M.A., 1976, The Effect of Size on the Growth Rate of Potassium Sulfate Crystals, American Institute of Chemical Engineers, v. 72, p. 41-47. Wilson, T.V., and Sibley, DR, 1978, Pressure Solution and Porosity Reduction in Slmllow Buried Quartz Arenite, The American Association of Petroleum Geologist Bulletin, v. 62, p. 2329-2334. 82 ”llllllllllllllll