Maturango Museum September 5, HOW DOES OBSIDIAN HYDRATION WORK? A SUMMARY OVERVIEW Alexander K. Rogers, MA, MS, RPA INTRODUCTION

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1 HOW DOES OBSIDIAN HYDRATION WORK? A SUMMARY OVERVIEW Alexander K. Rogers, MA, MS, RPA INTRODUCTION Obsidian hydration, as a technique for constructing archaeological chronologies, dates from the 1960 article by Friedman and Smith (q.v.). Since that time, the technique of obsidian hydration dating (OHD) has gone through periods of great enthusiasm (e.g. Friedman and Long 1976; Hull 2001; Rogers 2007, 2012) and periods of rejection and disillusionment (e.g. Ridings 1995). This paper provides a brief summary of the hydration process in obsidian as it is currently understood, and an overview of measurement techniques. The purpose is to provide a basic understanding of the physical, chemical, and mathematical principles of water diffusion in glass, as an aid to archaeologists. Further remarks expand on the current practice of OHD in the Desert West. Although OHD is inherently highly mathematical, the discussion here avoids mathematics as far as possible; mathematical details can be found in the cited references where necessary. A huge literature has developed on obsidian, including formal publications, gray literature, meeting presentations, and informal papers. This literature unfortunately includes a certain amount of incorrect material, so the old principle of caveat emptor applies. The present overview includes a list of references, including some in the beware category; these are clearly indicated as such in the text. The list of references is not exhaustive, but provides key publications, both classic and recent. OBSIDIAN Mineralogy of Obsidian Obsidian is an alumino-silicate, or rhyolitic, glass, formed by rapid cooling of magma under the proper geologic conditions. Like any other glass, it is not a crystal, and thus it lacks the lattice structure typical of crystals at the atomic level. Glasses do, however possess a matrix-like structure exhibiting some degree of spatial order (Doremus 1994:27, Fig. 2; 2002:59-73). Obsidians are typically about 75% SiO 2 and about 20% Al 2 O 3 by weight, the remainder being source-specific trace elements (Doremus 2002:109, Table 8.1; Stevenson et al. 1998). The minute interstices within the glass matrix, on the order of nanometer in diameter, are where water diffusion takes place. All obsidians also contain small amounts of water, known as intrinsic water or structural water, resulting from the magma formation process; the amount is generally <2% by weight, although cases of somewhat higher concentration are occasionally encountered. Obsidian anhydrous chemistry, or chemical content independent of water, has traditionally been regarded as a major influence on hydration rate (see attempts to determine a chemical index to hydration, e.g. in Friedman and Long 1976). Anhydrous chemistry is controlled by grouping and analyzing the obsidian by source, as determined by trace element composition by X-ray fluorescence or neutron activation analysis. 1

2 However, Stevenson et al. (1998) found no consistent influence of anhydrous chemistry on hydration rate. Zhang and Behrens (2000) and Behrens and Nowak (1997) found the effect of anhydrous chemistry to be negligibly small, although Karsten et al. (1982) reported that Ca 2+ concentration may influence hydration rate to a very slight extent. On the other hand, intrinsic water has a profound affect on hydration rate, much more than that of anhydrous chemistry (Delaney and Karsten 1981; Karsten et al. 1982; Lapham et al ; Stevenson et al. 1998, 2000; Zhang et al. 1991; Zhang and Behrens 2002). Current methods of measuring intrinsic water in obsidian are micro-densitometry, mass loss-on-ignition, IR transmission spectrometry, and IR photo-acoustic spectrometry. All these techniques are costly and are destructive to the artifact, so intrinsic water measurement is not conducted for most practical archaeological investigations in the United States today. The resulting rate variations constitute a source of uncertainty (statistical error) in age analysis. Operationally, it is likely that controlling for source instead functions as a proxy for controlling for intrinsic water (Stevenson et al. 2000), albeit rather poorly (Stevenson et al. 1993; Rogers 2008). Glass is often viewed as an inert material, easy to clean and not subject to corrosion, but this is not true at the molecular level. Glass is readily eroded by water, especially deionized water at high temperature and pressure (Stevenson et al. 1998). Furthermore, water diffuses into manufactured glass just as it does in obsidian. The reason we view glass as inert is that the processes of diffusion and erosion are very slow at everyday temperatures. Radical changes can occur to any glass over archaeological or geological time scales. Obsidian Hydration Obsidian hydration, in its most basic aspect, simply describes the process by which water is absorbed by obsidian, and involves both physical and chemical changes in the glass (Doremus 2002; Anovitz et al. 2008). Five steps may be distinguished in the process: 1. When a fresh surface of obsidian is exposed to air, water molecules adsorb on the surface. Since any unannealed obsidian surface exhibits cracks at the nano-scale, the amount of surface area available for adsorption is much greater than the macro-level surface area would suggest, creating a large surface concentration. 2. Some of the adsorbed water molecules, plus others impinging directly from the atmosphere, are absorbed into the glass and diffuse into the interstices in the glass matrix. The diffusion process seems to be driven by two properties of the water molecules: a concentration gradient and osmotic pressure, or chemical potential. Although it has been suggested that chemical reactions play a role (Doremus 2002:108ff.), it is unlikely that they are a major factor below the glass transition temperature (Anovitz et al. 2008). 3. The diffusing molecules stretch the glass matrix, causing an increase in volume in the hydrated region; they also cause an increase in the openness of the glass matrix itself, facilitating further absorption of water. Since the 2

3 hydrated region is expanded and the non-hydrated region is not, a stress region exists between the two. 4. As time passes, the region of increased water concentration progresses into the glass, its rate being a function of the initial openness of the glass, temperature, and the dynamics of the process itself. 5. When the hydrated layer becomes thick enough, typically greater than 20 microns, the accumulated stresses cause the layer to spall off as perlite. MEASUREMENT TECHNIQUES Three general classes of methods have been proposed for measuring obsidian hydration: measurement of water mass uptake or loss vs. time (Ebert et al. 1991; Stevenson and Novak 2011; direct measurement of water profiles vs. depth (Anovitz et al. 1999, 2004, 2008; Riciputi et al. 2002; Stevenson et al. 2004); and observation of the leading edge of the stress zone by optical microscopy (many papers, e.g. Friedman Smith 1960; Friedman and Long 1979). Measurement of Mass Uptake Measurement of the mass of water absorbed or lost by an obsidian sample, per unit obsidian mass, is the most physically fundamental method of measuring hydration, and has a long history. Methods employed for such measurements have been mass loss on heating (e.g. Eberts et al. 1991), IR transmission spectrometry (e.g. Newman et al. 1986), and IR photo-acoustic spectrometry (e.g. Stevenson and Novak 2011). It has been shown that the process of mass uptake is a function of temperature, pressure, and openness of the glass matrix as measured by intrinsic water concentration. Mass gain or loss proceeds proportional to t^n where t is time and n is an exponent lying between approximately 0.5 and 0.6 (Stevenson and Novak 2011). Direct Measurement of Water Profile Water profile measurement is generally performed by Secondary Ion Mass Spectrometry (SIMS) or the electron microprobe. The principle is to measure the concentration of H + ions, as a proxy for water, as a function of depth. The depth of penetration is typically measured by the half-amplitude point, the point where the water concentration has fallen to half its value at the surface. Some data manipulation is generally required to compensate for the presence of a saturated surface layer of water within a few tenths of a micron of the surface. The depth of the half-amplitude point is found to be proportional to t^n, where t is time and n is an exponent lying between approximately 0.6 and 0.7 (Anovitz et al. 1999, 2004; Stevenson and Novak 2011). The half-amplitude measurement is again a function of temperature and openness of the matrix; however, since the measurement is made to a half-amplitude point, i.e. a relative measurement, the technique is not sensitive to the total amount of water present and should not be affected by pressure. Another application of SIMS, although not reported in the literature, is to compute total mass uptake by numerical integration of the area under a SIMS trace. Liritzis and colleagues have developed a technique for SIMS known as SIMS-SS, where SS stands for the saturated surface layer. The principle is to fit a SIMS trace 3

4 with a cubic curve, with the anchor point being the inner edge of the saturated surface layer. Age is computed based on the assumption of an exponential relationship between water concentration and diffusion coefficient. Since the mathematical derivation of the method involves the Boltzmann transformation (z =sqrt(x/dt)), the method inherently assumes that hydration proceeds proportional to t^0.5 (Liritzis and Laskaris 2012, and references cited therein). Observation of Leading Edge of Stress Zone The classical field of OHD is based on measuring the position of the stress zone caused by the diffusion process. Despite its antiquity and phenomenological appeal, it is actually the farthest removed from the physics of hydration. It is, however, the most widely used obsidian hydration dating technique in archaeology today, due to its low cost and apparent simplicity. Near the flaked surface of the obsidian there are three regions to consider: the unhydrated volume, the hydrated volume, and the interface layer between the two. The interface layer, or "hydration front", is a zone of optical contrast when seen under polarized light, due to the phenomenon of "stress birefringence" (Born and Wolf 1980, ). The stress arises because the volume behind the optical hydration front has enlarged due to penetration of the glass matrix by water molecules, while the matrix of the unhydrated glass has not. Measurement in classical OHD is by optical microscopy, using a polarized microscope at a magnification of at least 500X. The same optical phenomenon is sometimes visible in car windows. The rear window of a car often looks mottled when viewed through polarized sunglasses - the lines creating the mottled effect are stress regions enclosing areas of lower stress. In this case it is done deliberately by tempering the glass so that impact causes the glass to break into harmless shards rather than dangerous splinters. The "optical hydration front" in obsidian is a similar stress phenomenon. All experimental evidence, and correlation with archaeological data, indicate that the position of this stress zone, or hydration front, progresses into the obsidian proportional to t^n, where n is approximately 0.5 within limits of experimental error (Stevenson and Scheetz 1989; Stevenson et al. 1998; Rogers and Duke 2011). The agreement with classical diffusion theory, in particular Fick s formulations and the Boltzmann transformation (Crank 1975:105ff.; Rogers 2007, 2012), may be a coincidence or may be due to an as-yet-undiscovered property of the diffusion process itself. FURTHER REMARKS ON CLASSICAL OHD Mass uptake and direct measurement of water profile are appealing techniques, and are the subjects of intensive current research. However, OHD in the Desert West essentially means what is called classical OHD above, so the succeeding remarks here expand on certain issues related to classical OHD. Finally there is a brief discussion of laboratory methods for computing hydration rates, with some cautionary observations. 4

5 Accuracy of Hydration Rim Measurements It is frequently stated by detractors (e.g. Anovitz et al. 1999; Riciputi et al. 2002) that the accuracy achievable in measuring the position of the hydration front in obsidian is limited by the resolution of the microscope employed for the measurement. This resolution is frequently cited as 0.25 microns (Scheetz and Stevenson 1988). However, the notion that resolution limits achievable accuracy is incorrect, and is based on a misunderstanding of the measurement process and the role of resolution. The optical accuracy limit is actually defined, not by resolution, but by a parameter known as vernier acuity; numerous measurements on optical systems have shown this to be approximately one to two orders of magnitude smaller than resolution (Jacobs 1943). Thus, given good laboratory technique, accuracy is not limited by resolution of the microscope to 0.25 microns, but probably lies in the range of microns, which is consistent with data reported by laboratories. In a practical sense, measurement accuracy is more likely limited by the material properties of the obsidian. In any case, the accuracy of rim measurement is not a large contributor to the error in computed age in OHD (Rogers 2010). The Hydration Age Equation Determination of an age equation starts from the well-accepted model of diffusion (Doremus 2002) as the description of the obsidian hydration process, and uses the archaeological data to compute the necessary model parameters. The form of the equation is a linear dependence of hydration rim thickness on the square root of time (i.e. r is proportional to t^0.5), which is well-accepted in materials science and geochemistry (e.g. Ebert et al. 1991, Zhang and Behrens 2000 respectively) and has been demonstrated in the laboratory (Stevenson et al. 1989, 1998, 2004; Rogers and Duke 2011). The analysis employs a rigorous correction for effective hydration temperature (EHT), which includes a correction for burial depth. Temperature parameters for the sites are computed by means of regional temperature scaling. The rate is computed by a linear least-squares best fit technique, with t^0.5 as the independent variable and EHT-corrected rim value as the dependent variable (Rogers and Yohe 2011). The rationale for choosing to fit t^0.5 vs. rim instead of the equivalent form of t vs. rim^2 is that the former results in smaller errors in the computed obsidian hydration rate(cvetanovic et al. 1979). Since obsidian is a natural material, it is entirely possible that deviations from t^0.5 occur, particularly at a fine-grained level; however, at the spatial level and accuracy involved in archaeological dating using optical microscopy, t^0.5 appears to be valid for the time scales of interest. Age should be expressed as calendar years before the present, approximately the year Based on these data, t^0.5 is always the functional form of choice. Parameter Optimization vs. Regression Computing a hydration rate is not a regression problem, however, but a problem of parameter optimization. Regression is a technique to estimate the extent to which one variable depends on another. In the present case, however, the degree of dependence is fully known a priori from physics, so the problem is one of optimizing a parameter (the rate) which defines the fit between data and the physical model. Mathematically, the 5

6 formalism used to compute the linear best fit is the same as that used in a regression analyses for a quadratic fit with no linear term and the best-fit line constrained to pass through the origin; the difference lies in the interpretation, since the physical model, and hence the degree of dependence, is known. It follows that, since the form of the hydration equation is known from physics, other forms of the equation must be explicitly avoided, such as linear equations or inclusion of higher-order terms or other exponent values. The situation is rendered more complex since, with virtually any archaeological data set, it is possible to obtain a better fit (measured by residuals) by other forms of the age equation; however, the apparent accuracy thus achieved is entirely spurious. Each data point is a combination of valid data and experimental error, with major errors arising from site formation processes, association between radiocarbon and obsidian, uncertainties in EHT, and unaccounted-for fluctuations in the hydration rate. Therefore, using a different form of the age equation simply provides a better fit to the errors in the current data set; there is no guarantee that the next data point collected will fit. Good practice in numerical analysis is to select the model equation based on the nature of the problem; for obsidian hydration this means the physical or chemical model, which is a linear dependence of hydration rim thickness on the square root of time. Any appeal to another form because of better fit to archaeological data is simply a better fit to error sources and is spurious. But suppose you are faced with a published hydration age equation for a particular source, and it is not of the form t^0.5. What do you do? The recommended procedure is to return to the data set on which the rate is based, compute your own EHT corrections, and compute your own least-squares linear best fit between t^0.5 and EHTcorrected rim. Mathematical details on how to do this are in Rogers and Yohe Of course, it should go without saying that if and when a better model of the hydration process is developed from a physical and chemical standpoint and published, it should be used instead of t^0.5. Range of Validity It is important to state explicitly the range of validity of the age equation, which is the range of rim values and ages spanned by the original data set. Remember that the original data set always includes zero rim at zero time, based on physics; you get this data point for free! Use of the resulting equation to compute ages within the original range of values is a process of interpolation, which suppresses errors; use outside the range of the original data is extrapolation, which may amplify errors. Thus, the age equation is most trustworthy within this range of validity, and any analyst who uses the age equation needs to know the range of values encompassed by the original data. Finally, since this problem is an optimization rather than a regression, use of Pearson s R as a sole criterion of goodness of fit is inappropriate. It is ineffective at best and misleading at worst. A better measure is the standard deviation of hydration rate, which affects the predictive accuracy of the age equation. EHT Computation Archaeological temperatures vary over time, both annually and diurnally, and hydration rate of obsidian is temperature-dependent. The effect of this varying 6

7 temperature is summarized by the concept of Effective Hydration Temperature (EHT), which is defined as a constant temperature which yields the same hydration results as the actual time-varying temperature over the same period of time. Due to the mathematical form of the dependence of hydration rate on temperature, EHT is always greater than or equal to the mean temperature. For the general case, computation of EHT requires numerical integration of a mathematical model of the hydration rate over a mathematically-modeled temperature history. Fortunately, some simple algebraic equations have been developed for archaeological use (Rogers and Yohe 2011), which are valid over temperature ranges of archaeological interest and are easily implemented with a calculator or MS Excel. Computation of EHT requires three parameters: annual average temperature, annual variation (July mean minus January mean), and mean diurnal variation. Ancient peoples were seldom considerate enough to place their sites in close proximity to current meteorological stations. As a result, temperature parameters for computing EHT must generally be estimated by analysis of data from a number of nearby weather stations. All should represent 30 years of meteorological data, which is the standard length of time employed by meteorologists for establishing seasonal norms. Meteorological data are for air temperatures, while obsidian on the surface is affected by surface temperatures, which can be significantly higher in areas devoid of vegetation. However, for surfaces which have intermittent foliage coverage, the air temperatures are, on average, a good approximation to surface temperatures. Details of computation, with additional references, are in Rogers 2012 and Rogers and Yohe It is important to include the effects of burial depth on EHT. Burial does not affect the annual average temperature, but it does affect the annual (month-to-month) variation of the mean and the diurnal variation, the latter significantly. This dependence of temperature variation on depth is well attested in physics, geology, and soil science (e.g. Carslaw and Jaeger 1959). Even in the presence of site turbation, a correction for burial depth yields improved results on the average. Implementation details are again in Rogers and Yohe Parenthetically, the Lee equation (Lee 1969) does not give correct values of EHT, nor can EHT differences between sites be reliably computed from it. It was developed for crop science to be applied over the length of a growing season, and only includes two parameters, a mean temperature and a range. Description of temperature variation on an annual basis requires three parameters, as described above. The issues involved in use of the Lee equation are discussed at length in Rogers The Lee equation should not be used in obsidian analyses (as in Fredrickson et al. 2006). Accuracy of Rate Determination There are limits to the accuracy that can currently be expected in computing a hydration rate based on obsidian-radiocarbon association. Minor error sources, which are generally negligible, are hydration rim measurement in the laboratory, radiocarbon measurement in the laboratory, radiocarbon calibration, and humidity history. Major error sources are association errors between the obsidian and radiocarbon data, uncertainties in temperature history (i.e. errors in EHT), and uncontrolled variations in intrinsic water within a given obsidian source (leading to uncontrolled variations in hydration rate). Note 7

8 that site formation processes, including bioturbation and geologic covering/exposure, play a major role in the first two of these. These errors and their affects have been exhaustively analyzed (Rogers 2010). To summarize, hydration rates can be reliably estimated by least-squares techniques applied to obsidian-radiocarbon data with errors of about 4-5%, while rates estimated by leastsquares techniques applied to time-sensitive artifacts are somewhat worse, with about 8-10% errors. Rates determined from laboratory techniques (induced hydration) are somewhat more accurate, with about 2-3% error. Accuracy of Age Estimates Similar error sources affect age estimates. Association errors between the obsidian and radiocarbon data are not an issue, but the other sources of uncertainty still apply, notably uncertainties in EHT and intra-source variations in hydration rate due to uncontrolled variations in intrinsic water. Analysis of errors shows that it is unrealistic to expect age errors much less than 15-20% in obsidian hydration dating (Rogers 2010). Given such uncertainties in the computed ages, great caution must be used in inferring duration of site use based on OHD. Laboratory Hydration Methods Quantitative measurement of hydration rate by laboratory methods (sometimes known as induced hydration ) has an equivocal history in archaeology. The temperature dependence of hydration rate is well known, and attempts have been made in the past to measure hydration rate in the laboratory (e.g. Friedman and Long 1976; Stevenson et al. 1998). However, rates measured in the laboratory often have not agreed well with archaeological data (see, for example, the pointed observations in Hall and Jackson 1989:32), and are generally not used by practicing archaeologists today. The method has, however, recently been demonstrated to work in the case of Topaz Mountain obsidian from Utah (Rogers and Duke 2011). The hydration rate of obsidian is strongly temperature-dependent, so that if hydration is allowed to proceed at elevated temperatures, measurable hydration rims develop in days rather than years. The temperature dependence of the hydration rate has a well-attested mathematical form, so the principle of laboratory hydration is to hydrate a set of obsidian samples at elevated temperatures, determine the activation energy and diffusion constant, and then compute the hydration rate for temperatures of archaeological interest. Two points must be made about this technique, one mathematical and the other procedural. Mathematically the procedure depends on a least-squares best fit to the logarithmic Arrhenius equation (see Stevenson and Scheetz 1989; Rogers and Duke 2011). This best fit must include data-point weighting as described by Cvetanovic et al. 1979, because the dependent variable has a logarithmic form; otherwise the activation energy and diffusion constant will be in error. Details of the process and rationale are given in Rogers and Duke The procedural point involves lab techniques. Because of erosion of obsidian by hot deionized water, the hydration must either be performed in vapor phase or using water which is buffered by dissolved silicon. Otherwise the erosion of the surface can exceed the growth of the hydration rim (Rogers and Duke 2011; Stevenson et al. 1998). 8

9 This was not known when Michels performed his extensive early program of laboratory measurements, which unfortunately resulted in seriously incorrect hydration rates. His MOHLAB hydration rates should not be used today without careful verification from other sources. A final point involves scaling of laboratory measurements. It is not valid to argue that obsidian A hydrates 10% faster than obsidian B at high temperature, therefore obsidian A will also hydrate 10% faster than obsidian B at archaeological temperatures. The scaling is actually a complex function of the two hydration rates and their activation energies. In general, scaling requires knowledge of both the activation energy and diffusion constant of the obsidian source in question. CONCLUDING REMARKS The process of hydration in glasses is very complex, involving chemistry, physics, and mathematical modeling. By comparison, the process of beta decay, on which radiocarbon dating is based, is relatively straight-forward. In addition, glass science has not had the benefit of a Manhattan Project to lay the physics ground-work (although much good science on hydration has been done under the Nuclear Waste program). Obsidian hydration has the added handicap in terms of a chronometric tool that the measured results depend strongly on post-formation processes, like opticallystimulated luminescence and unlike radiocarbon or dendro. Three basic methods for measuring hydration are currently being pursued: water mass uptake, water profile measurement (either by 50% point or by SIMS-SS), and optical measurement of the hydration rim or stress zone. A basic point of physics is that in each case, two fundamental equations are involved: an age equation of some type; and a temperature dependence equation, which is usually of the Arrhenius form. Since the physical phenomena being measured differ, the age equations differ slightly as well, in particular the exponent of the time (age) variable. It is likely that the parameters of the Arrhenius equation are slightly different as well, although investigations of this point have not yet been reported; at any rate, it would be incautious to apply, say, an activation energy determined from water mass uptake to the optical case without careful study. Despite the fact that the optical technique (classical OHD) is furthest removed from the basic physics of hydration, it is the most widely used. Despite criticism by advocates of other techniques (e.g. Anovitz et al. 1999; Liritzis and Laskaris 2012), it works well for construction of coarse chronologies. It is especially useful in the Desert West, where other sources of chronometric data are frequently lacking. When used with the mathematical techniques discussed in this paper, it is capable of reliably placing obsidian artifacts in the correct archaeological period, and generally the qualifying descriptions of early, middle, or late can be safely attached to the period name as well. Probably the greatest needs at present are for (1) a cheap, accurate, and nondestructive method for determining intrinsic water content of a specimen, to permit adjusting the hydration rate, and (2) a similarly cheap and non-destructive laboratory method to characterize the temperature history of an artifact. 9

10 References Cited Anovitz, Lawrence M., J. Michael Elam, Lee R. Riciputi, and David R. Cole 1999 The Failure of Obsidian Hydration Dating: Sources, Implications, and New Directions. Journal of Archaeological Science 26(7): Isothermal Time-Series Determination of the Rate of Diffusion of Water in Pachuca Obsidian. Archaeometry 42(2): Anovitz, Lawrence M., David R. Cole, and Mostafa Fayek 2008 Mechanisms of Rhyolitic Glass Hydration Below the Glass Transition. American Mineralogist 93: Behrens, H., and M. Nowak 1997 The Mechanisms of Water Diffusion in Polymerized Silicate Melts. Contributions to Mineralogy and Petrology 126: Born, Max, and Emil Wolf 1980 Principles of Optics, 6 th ed. Pergamon Press: New York. Carslaw, H. S., and J. C. Jaeger 1959 Heat Conduction in Solids, 2 nd ed. Clarendon Press: Oxford. Crank, J The Mathematics of Diffusion. Oxford: Oxford University Press. Cvetanovic, R. J., D. L. Singleton, and G. Paraskevopoulos 1979 Evaluations of the Mean Values and Standard Errors of Rate Constants and their Temperature Coefficients. Journal of Physical Chemistry 83(1): Delaney, J. R., and J. L. Karsten 1981 Ion Microprobe Studies of Water in Silicate Melts: Concentration- Dependent Water Diffusion in Silicon. Earth and Planetary Science Letters 52: Doremus, R. H Glass Science. New York: Wiley Interscience Diffusion of Reactive Molecules in Solids and Melts. New York: Wiley Interscience. Ebert, W. L., R. F. Hofburg, and K. K. Bates 1991 The Sorption of Water on Obsidian and a Nuclear Waste Glass. Physics and Chemistry of Glasses 32(4): Fredrickson, D., J. Lloyd, T. Jones, A. Schroeder, and T. Origer 2006 The Coso-Casa Diablo Conundrum. Proceedings of the Society for California Archaeology 19: Friedman, Irving, and William Long 1976 Hydration Rate of Obsidian. Science 191(1): Friedman, Irving, and R. Smith 1960 A New Method of Dating Using Obsidian; Part 1, the Development of the Hall, M. C., and Jackson, T. L Obsidian Hydration Rates in California, pp , In: Current Directions in California Obsidian Studies, Richard C. Hughes, ed., Contributions of the University of California Archaeological Research Facility No. 48, Dec Berkeley: University of California. 10

11 Hull, Kathleen L Reasserting the Utility of Obsidian Hydration Dating: A Temperature- Dependent Empirical Approach to Practical Temporal Resolution with Archaeological Obsidians. Journal of Archaeological Science 28: Jacobs, D. H Fundamentals of Optical Engineering. New York: McGraw-Hill. Karsten, J. L., J. R. Holloway, and J. R. Delaney 1982 Ion Microprobe Studies of Water in Silicate Melts: Temperature- Dependent Water Diffusion in Obsidian. Earth and Planetary Science Letters 59: Lapham, K. E., J. R. Holloway, and J. R. Delaney 1984 Diffusion of H 2 O and D 2 O in Obsidian at Elevated Temperatures and Pressures. Journal of Non-Crystalline Solids 67: Lee, R Chemical Temperature Integration. Journal of Applied Meteorology 8: Liritzis, Ioannis, and Nickolaos Laskaris 2012 The SIMS-SS Obsidian Hydration Dating Method, pp In: Obsidian and Ancient Manufactured Glasses, Ioannis Liritzis and Christopher Stevenson, eds. University Of New Mexico Press: Albuquerque. Newman, S., E. M. Stolper, and S. Epstein 1986 Measurement of Water in Rhyolitic Glasses: Calibration of an Infrared Spectroscopic Technique. American Mineralogist 71: Riciputi, Lee R., J. Michael Elam, Lawrence M Anovitz, and David R. Cole 2002 Obsidian Diffusion Dating by Secondary Ion Mass Spectrometry: A Test using Results from Mound 65, Chalco, Mexico. Journal of Archaeological Science 29(10): Ridings, Rosanna 1996 Where in the World Does Obsidian Hydration Dating Work? American Antiquity 61(1): Rogers, Alexander K Effective Hydration Temperature of Obsidian: A Diffusion-Theory Analysis of Time-Dependent Hydration Rates. Journal of Archaeological Science 34: Obsidian Hydration Dating: Accuracy and Resolution Limitations Imposed by Intrinsic Water Variability. Journal of Archaeological Science. 35: Accuracy of Obsidian Hydration Dating based on Obsidian-Radiocarbon Association and Optical Microscopy. Journal of Archaeological Science 37: Temperature Correction for Obsidian Hydration Dating, pp In: Obsidian and Ancient Manufactured Glasses, Ioannis Liritzis and Christopher Stevenson, eds. University Of New Mexico Press: Albuquerque. 11

12 Rogers, Alexander K., and Daron Duke An Archaeologically Validated Protocol for Computing Obsidian Hydration Rates from Laboratory Data. Journal of Archaeological Science 38: Rogers, Alexander K., and Robert M. Yohe II 2011 An Improved Equation for Coso Obsidian Hydration Dating, based on Obsidian-Radiocarbon Association. Proceedings of the Society for California Archaeology, vol. 25 (2011). Available on-line. Scheetz, Barry E., and Christopher M Stevenson 1988 The Role of Resolution and Sample Preparation in Hydration Rim Measurement: Implications for Experimentally-determined Hydration Rates. American Antiquity 53(1): Stevenson, C. M., and B. E. Scheetz 1989 Induced Hydration Rate Development for Obsidians from the Coso Volcanic Field: A Comparison of Experimental Procedures, pp in: Current Directions in California Obsidian Studies, Contributions of the University of California Archaeological Research Facility No. 48. University of California: Berkeley. Stevenson, C. M, E. Knaus, J. J. Mazer, and J. K. Bates 1993 Homogeneity of Water Content in Obsidian from the Coso Volcanic Field: Implications for Obsidian Hydration Dating. Geoarchaeology 8(5): Stevenson, C. M., J. J. Mazer, and B. E. Scheetz 1998 Laboratory Obsidian Hydration Rates: Theory, Method, and Application. In: Archaeological Obsidian Studies: Method and Theory. Advances in Archaeological and Museum Science, Vol. 3, M. S. Shackley, ed., pp New York, Plenum Press. Stevenson, Christopher M., Mike Gottesman, and Michael Macko 2000 Redefining the Working Assumptions for Obsidian Hydration Dating. Journal of California and Great Basin Anthropology 22(2): Stevenson, Christopher M., Ihab. M. Abdelrehim, and Steven W. Novak 2004 High Precision Measurement of Obsidian Hydration Layers on Artifacts from the Hopewell Site Using Secondary Ion Mass Spectrometry. American Antiquity 69(4): Stevenson, Christopher M., and Steven W. Novak 2011 Obsidian Hydration Dating by Infrared Spectroscopy: Method and Calibration. Journal of Archaeological Science 38: Zhang, Y., and H. Behrens 2000 H 2 O Diffusion in Rhyolitic Melts and Glasses. Chemical Geology 169: Zhang, Youxue, E. M. Stolper, and G. J. Wasserburg 1991 Diffusion of Water in Rhyolitic Glasses. Geochimica et Cosmochimica Acta 55(2):