OBSIDIAN HYDRATION DATING BY SECONDARY ION MASS SPECTROMETRY-SURFACE SATURATION, SOME APPLICATIONS...

Journal of Radioanalytical and Nuclear Chemistry, Vol. 261, No. 1 (2004) 51–60

0236–5731/2004/USD 20.00 Akadémiai Kiadó, Budapest© 2004 Akadémiai Kiadó, Budapest Kluwer Academic Publishers, Dordrecht

Dating of hydrated obsidian surfaces by SIMS-SS

I. Liritzis,1 M. Diakostamatiou,1 C. M. Stevenson,2 S. W. Novak,3 Ihab Abdelrehim4

1 Laboratory of Archaeometry, Department of Mediterranean Studies, University of the Aegean, 1 Demokratias Avenue, Rhodes 85100, Greece2 Virginia Department of Historic Resources, 2801 Kensington Avenue, Richmond, VA 23221, USA

3 Evans East, 104 Windsor Center, Suite 101, East Windsor, NJ 08520, USA4 Evans Northeast, 10 Centennial Drive, Peabody, MA 01960, USA

(Received July 21, 2003)

A new approach to dating ancient obsidian artifacts based on the modeling of water diffusion profiles is evaluated using multiple archaeological test cases of known age. Hydrogen profiles from hydrated obsidian surfaces have been collected by secondary ion mass spectrometry (SIMS). The H2O concentration versus depth profiles are modeled and diffusion ages have been produced. SIMS based dates for fourteen obsidian specimens of well-known age, ranging from 300–7000 years old, have been compared with radiocarbon ages. The convergence between the two dating methods is excellent and validates the new dating approach.

Introduction

The obsidian hydration dating (OHD) method is based upon modeling the rate of water diffusion into a natural glass surface by establishing a diffusion coefficient for this process. It is accepted that the rate of water diffusion, the diffusion coefficient, depends exponentially on temperature and exhibits an Arrhenius type behavior. A variety of strategies have been developed over the years to calibrate the movement of ambient water into glass. Many of these approaches have developed procedures for controlling the chemical composition of the glass and modeling the environmental history of the artifact context (e.g., temperature, humidity).1–6 However, the development of calibrations to compensate the variation in external variables has proven to be difficult. This has been the major impediment to making OHD a fully chronometric dating method comparable to radiocarbon dating.

We evaluate have a procedure for obsidian age estimation that is based upon the depth and shape of the hydrogen diffusion profile as determined by secondary ion mass spectrometry (SIMS). We have termed this approach SIMS-SS since the primary input variable, which controls the water in the mass of obsidian, is the saturation achieved in the surface layer (SS). This method is similar to ODD-SIMS7,8 but differs in the manner in which profile is modeled. There are three advantages to our new procedure: (1) the final shape of the hydrogen profile incorporates two of the principal external, and highly variable, environmental parameters, those of temperature and humidity, (2) the use of SIMS instrumentation to measure surface hydration layers results in high precision thickness values with an error of 0.02–0.05 µm depending upon the degree of surface roughness, and (3) absolute age estimates may be calculated.

To demonstrate the accuracy of this method, we have selected six case examples from around the world that

incorporate a wide variety of different obsidians and environmental regimes. These examples have been drawn from the literature, as well as new case examples developed by the authors. The archaeological context of each example is discussed with particular attention placed on establishing the integrity of the context and the relationship between the radiocarbon event and the deposition of the obsidian artifact. It is important that both forms of material within the deposit (e.g., carbon, obsidian) reflect, as closely as possible, the same depositional event and depositional history.

Diffusion of water in obsidian

The model of water diffusion in amorphous silicates developed by DOREMUS9a is the most appropriate descriptor of water diffusion in glass at low temperature because it accounts for the patterning in much of the experimental data.9b In a vapor environment molecular water enters the glass network and reacts with the silicon–oxygen network to form SiOH groups:

Si-O-Si + H2O = SiOH + OHSi (1)

Based upon the infrared spectra of the developing obsidian hydration layer,10 it appears that molecular water is the diffusing species that originates on the obsidian surface. As the molecular water moves through the glass the newly formed OH groups remain relatively fixed. It is assumed that the OH group formation lags well behind the movement of mobile water molecules but eventually reaches equilibrium.

It is also assumed in previous model development that the initial concentration of water in the glass is zero. However, it is well documented that natural glasses contain structural water concentrations that may range up to several tenths of a percent. This will exponentially increase the diffusion coefficient as concentration rises.5,11,12 This is believed to occur because the occurrence of greater amounts of SiOH in the network

I. LIRITZIS et al.: DATING OF HYDRATED OBSIDIAN SURFACES BY SIMS-SS

52

(referred to the intrinsic water molecules which may be present as OH with the silicious network) may weaken the neighboring Si–O–Si bonds, causing them to easily break, and therefore, lower the overall activation energy.13,14

The diffusion rate of water in amorphous silicates is also strongly correlated with the concentration of water within the surface hydration layer15–17 and is referred to as concentration-dependent diffusion. When dealing with a narrow compositional range, the anhydrous component of the glass has little influence on the mobility of water.18 Under ambient temperatures (0–30 °C) the diffusion of water in obsidian is not a steady state diffusion process with a constant D, and cannot be mathematically estimated with Fick’s first law. Instead, as water enters the glass network the structure is depolymerized and allows additional water to enter the glass at a faster rate. This changing diffusion coefficient results in the formation of a characteristic S-shaped concentration-depth profile (Fig. 1).7,16,19 As a result, alternate modeling procedures are required.

SIMS-SS modeling

Theoretical background

The diffusion of environmental water into obsidians depends on the random molecular motion but with the tendency to move in the direction of decreasing water concentration. The rate of this movement also depends on the temperature, relative humidity and the location and arrangement of ions within the obsidian structure.

Fig. 1. Water diffusion in obsidian illustrated by a hydrogen diffusion profile, showing the saturation layer and location of xs and Cs

The result is a sigmoid shape water (hydrogen ions) concentration profile that incorporates all variations of the external parameters into the final profile shape (Fig. 1). Using this end product of diffusion, we have developed a phenomenological model, based on certain initial and boundary conditions and physicochemical mechanisms, that expresses the H2O concentration versus depth profile as a diffusion/time equation. This allows chronometric ages to be calculated.

We model this diffusion process as a one-dimensional phenomena, where water molecules enter a semi-infinite medium in a direction perpendicular to the surface. The model is based on the idea that in the saturated surface (SS) layer encountered near the exterior of the sample (i.e., in the first half of the sigmoid curve), the concentration (C) of molecular water is assumed as constant along a very short distance. Thereafter, C decreases gradually following the trend of the sigmoid curve.

The mathematical theory of diffusion in isotropic substances is based on the observation that the rate of transfer of the diffusing substance, through a unit area, is proportional to the concentration gradient measured normal to the section. It is expressed by:

Fx = –D ∂C/∂x (2)

where Fx is the rate of transfer of water moles per unit area (kmol.m–2.s–1) along the x-direction, C is the concentration gradient of diffusing substance (mass per unit volume) acting as the driving force, x is the distance coordinate measured normal to the section, and the proportionality constant D is called the diffusion coefficient (m2.s–1) or less commonly as molecular mass diffusivity or just mass diffusivity. The negative sign arises because the diffusion occurs in the direction opposite to that of increasing concentration.

For the use of diffusion for dating it is essential to establish the time in which diffusion has occurred. For this, complex dynamic or time-dependent analysis is required rather than simple steady state. Hence, the concept of property balance is introduced, whereas:

input (∂C/∂t) + generation == output (C) + accumulation (∂(D∂C/∂x))

In considering this case of one-dimensional diffusion through an obsidian surface, where there is a concentration gradient along the x-axis, the diffusion coefficient (D), as a function of change in C with time, will be variable, and it is derived from the partial differential equation:

∂C/∂t = ∂ (D∂C/∂x)/∂x (3)

which is a combination of Eq. (2) for non-steady state condition with the balance equation concept for no flow or generation, where t is the time and x is the distance.


53

It denotes the rate of change of C with time (t), which equals a diffusion coefficient by the rate of change of Calong the X-axis. In fact, D relates C(t) with C(x), and has the significance that it is the contribution to the rate of transfer in the x-direction due to the component of Cgradient in this direction.

For constant D, Eq. (1) becomes:

∂C/∂t = D(∂2C/∂x2) (4)

that is, there is a gradient of C only along the x-axis, and the rate of change of C with time (t) equals the rate of transferred water molecules per unit distance (x) times the rate of change of C divided by x. Equations (2) and (4) are usually referred to as Fick’s 1st and 2nd laws of diffusion by direct analogy with the equations of heat conduction.

It has been shown20 that Eq. (4) produces several numerical solutions depending on the system’s initial and boundary conditions. For the present obsidian–water system, an exponential diffusion coefficient is modeled under the constraints (Fig. 1), where:

Initial conditions: C=C0=Ci, where Ci is the initial or structural water concentration of the glass, x equals the diffusion depth, where x>0, for a diffusion time, t=0.

Boundary condition: C=Cs the obsidian surface (saturated) water concentration, for x=0 and t>0.

However, in concentration-dependent diffusion, D is not constant during the hydration process but depends on changes in C. A family of curves that relates concentration-to-distance for an exponential diffusion coefficient during sorption is given in Fig. 2, which, through linear interpolation, are based on those given by CRANK.20 Additional curves have been added (Fig. 3) and developed to accurately estimate k-value (of ek). They represent calculated results for variable diffusion coefficients for non-steady-state conditions. It follows that the form of exponential dependence of the C from Dis given by:

D=Ds exp (kC/Cs) = Dsexp[β(C–Cs)] (5)

where k is a constant, Ds is the diffusion coefficient for C=Cs and β is a constant.

In fact, BOLTZMANN21 showed that for certain boundary conditions, provided D is a function of C only, C may be expressed in terms of a single variable and that Eq. (3) may be reduced to an ordinary differential equation by the introduction of a new variable.

Based upon CRANK’s20 numerical solutions of diffusion, and BOLTZMANN’s transformation, the following auxiliary variables are introduced:

ys = x/2(Dst)1/2, (6)

c=(C–Cs)/(Ci–Cs) (7)

where Ci is the initial concentration (pristine water) in obsidian prior to diffusion of water, and

γ = β(Ci–Cs) (8)

Then Eq. (5) becomes:

D = Dieγ (Di at C=Ci) (9)

Substitution of Eqs (6), (8) and (9) into Eq. (3) we obtain:

d(eγdγ/dys)/dys + (2ys)(dγ/dys) = 0 (10)

In view of the boundary condition, Eq. (6), and Eq. (8), the integration of Eq. (10) is to be performed with γ = 0 and ys = 0. Thus, we can use the values of γcalculated from Eq. (10).

Fig. 2. Non-dimensional plot, where K values presented as ek are derived from a family curves (based upon CRANK)20

Fig. 3. Estimation of K-values from family curves of ek versus x/xs for certain C/Cs, produced by interpolation from Fig. 2


54

Fig. 4. Non-dimensional plot for sample DL-93-193

In view of initial condition for C = Ci, the Eq. (7) and Eq. (8), we have:

γ = β(Ci–Cs) = r, ys = ∞ (11)

c = γ/r (12)

Here, it is:

r = log(DC=Ci/DC=Cs) (13)

Indeed, D(C=Ci)=D(C=Cs)exp(β(Ci–Cs))→D(C=Ci)/D(C=Cs)=exp(β(Ci–Cs)), and log[D(C=Ci)/D(C=Cs)]=β(Ci–Cs)=r.

From Eq. (13) and Eq. (5) we define:

r = kC/Cs (14)

Therefore, we use the exponential form:

D(C=Ci) = D(C=Cs)exp(kCi/Cs)

upon which the concentration–distance curves, of Figs 2 and 4, are based (see below, Curve fitting and Age calculation).

Plotting the values of r (i.e., the limiting values of γat y = ∞), as a function of auxiliary parameter g used for the integration of Eq. (10) (for u = eγ), numerical values of c are compiled. Solutions of Eq. (10) from y = –∞ to y = +∞, for the initial conditions, γ = 0, u = 1, y = 0, were obtained for different values of g given by g = (dγ/dy) (for details, see CRANK).20

However, instead of using such plot one may calculate the g values with the aid of the following empirical interpolation formula:

g = (1.128r)/(1–0.177r) (15)

Following BOLTZMANN’s transformation, and using Eq. (6) and Eq. (7), the flux across the surface x = 0 of Eq. (2) becomes:

–Ds(∂C/∂x)x=0 = –1/2(Ds/t)1/2(Ci–Cs)(dc/dys)ys=0 (16)

From g = (dγ/dy), Eq. (12) and Eq. (15), it follows that the dc/dys for ys = 0 is given by:

dc/dys = g/r = 1.128/(1–0.177r) (17)

where, r is calculated from Eq. (13).Equation (16) relates the flux across obsidian’s

surface at x = 0 with the time the flux has occurred, the Cs, the Ci and Ds for Cs.

It is only when, (a) the initial and boundary conditions are expressible in terms of ys alone, (b) the xand t are not involved separately, (c) diffusion occurs in semi-infinite media, and (d) initial water concentrations are uniform (and may be zero) as it occurs in obsidian, that the transformation of Eq. (6) and Eq. (10) can be used.

It is necessary to clarify that the variation of Cduring sorption depends on various factors (environmental, such as, temperature and humidity, atomic structure and chemistry in obsidian, and the chemistry between burial environment and obsidian surface). This variation reflects a respective variation in D. But, the variation of C with distance (hence time) presumably incorporates all these factors. We consider that it is the obtained sigmoid shape of C versus x, that incorporates all these unknown factors as an end product of all processes, which lead the diffusion. It is also assumed that since we are dealing with a compact solid material, the diffusion profile has not changed significantly with time, the material being buried in the natural environment. In this case, the environmental variations are not so radical and so long, in order to cause a significant alteration to the diffusion profile.

Curve fitting and age calculation

In order to model the form of the diffusion profile a value for the constant K must first be determined.

In LIRITZIS and DIAKOSTAMATIOU22 this was fixed by the shape of the experimental curve that closely corresponds to CRANK’s20 theoretical curves. For the non-steady state condition considered here, a collection of sigmoid shaped curves have been produced for non-dimensional distance and concentration that reflect different values of K. In fact, the non-dimensional plot of x/x0 versus C/C0 given by CRANK20 (his Fig. 9.9), includes some curves, where the parameter that defines each curve is the term ek. For a full coverage of the k-values, we have produced intermediate curves by linear interpolation (Fig. 2). Exact estimation of K-values is produced from family curves of ek-versus x/xs for certain C/Cs, by interpolation from Fig. 2 (Fig. 3).

Our SIMS profiles were re-plotted as non-dimensional (standardized to 1) diagrams of C/Cs versus x/xs and were matched to the appropriate profile of our produced curves guided by the end point of C along the


55

x-axis (Fig. 4). This way the k-value can be calculated from any particular sigmoid shape.

A curve is then fitted to the SIMS data (Fig. 5) using TABLECURVE 2D software and takes the form of a polynomial with exponential terms:

C = exp (a+bx+cx2+dx3) (18)

The choice of the fitted curve is important for the age determination of the SS layer, due to the following three criteria: (1) our goal is to achieve the best fitting curve especially for the first portion, or upper half, of the S-like curve. This is a required in order to closely model the shape of the theoretical exponential diffusion curves of the C versus x non-dimensional plots of Fig. 4; (2) theupper half represents the (calculated) gradient of the fitted curve, which corresponds to the surface diffusion coefficient Ds, (i.e., the coefficient for the constant concentration of the saturated layer); and (3) the fitting should be congruent with the tail of the sigmoid curve. Needless to say that this part follows a different diffusion mechanism than the latter part to the end and that in comparing the experimental (Fig. 4) and theoretical (Fig. 2) curves, the initial points near the surface must be discarded.23

To do this, the first points on the SIMS profile, for x>0, are removed gradually and up to the point that concentration ceases to drop, searching for the fitted curve which satisfies the above criteria. When the 3rd degree exponential polynomial curve is found, the SS is defined from the sliding successive linear regressions of the data sets (Table 1). The first linear regression has as the first point that one remaining after the removal of the initial data points and up to the points that approach a constant value. The successive regressions start from the second, third, and so on point, and with data lengths

gradually increasing till the inflection point of the profile. Thereafter, the gradient apparently becomes negative. The smallest gradients (ideally should be a zero gradient within error range of the data points) are met with linear regressions that define the plateau (SS layer) level.

In fact, these appear along a band of less than 10% spread. The successive regressions give almost a stable end point xs for the respective sliding data sets, which corresponds to a constant concentration value, Cs. The SS layer is defined either when the gradient is near zero or changes from positive to negative values, which presumes diffusion within the obsidian (i.e., direction towards decreasing C values). The average ± standard deviation of xs and Cs values within the band define the end of the SS layer, and these are used in the age calculation (Table 2). Occasionally, a second SS layer is obtained, however, with larger gradient values, attributed at present to possible re-use of the tool (i.e., sample DL-1993-193, Table 2).

The exclusion of some initial points to achieve the best fitting with the first half of S-curve is justified from the near surface disturbances due to either sputtering and/or variable environmental effects.6,22

The choice of a 3rd order polynomial, rather than higher order exponential polynomial, was chosen to satisfy the three criteria for fitting of the initial and end points, as well as the first half of the S-curve. Overall, the higher order polynomial fitting seems better but at the expense of the criteria, particularly with the unavoidable presence of more oscillations. This was reinforced in practice during the applied trials and blind tests whereas the 3rd order polynomial gave the best results.

Fig. 5. SIMS hydrogen profile (dots) of obsidian sample DL-93-193 with a fitted curve (line)


56

Tab

le 1

. Gra

dien

t (in

bol

d) c

alcu

latio

ns w

ith th

e sl

idin

g su

cces

sive

reg

ress

ion

anal

ysis

for

sam

ple

DL

-199

3-19

9

Dep

th, c

mC

once

ntra

tion,

gm

ol/c

m3

Dep

thC

once

ntra

tion

6.53

E–0

50.

0002

376.

65E

–05

0.00

0231

9.57

8E–0

50.

0002

126.

78E

–05

0.00

0222

9.06

9E–0

50.

0002

176.

91E

–05

0.00

0221

9.06

9E–0

50.

0002

177.

03E

–05

0.00

0223

9.06

9E–0

50.

0002

177.

16E

–05

0.00

0223

9.06

9E–0

50.

0002

177.

29E

–05

0.00

0221

9.06

9E–0

50.

0002

177.

42E

–05

0.00

022

Slop

e9.

069E

–05

0.00

0217

7.54

E–0

50.

0002

16fr

omSl

ope

9.32

4E–0

50.

0002

147.

67E

–05

0.00

0225

here

from

Slop

e9.

324E

–05

0.00

0214

7.8E

–05

0.00

0215

–8.2

82he

refr

omSl

ope

Mea

n9.

171E

–05

0.00

0216

7.92

E–0

50.

0002

11–5

.706

7–3

.131

here

from

Slop

eSt

and.

dev

.:1.

687E

–06

1.97

E–0

68.

05E

–05

0.00

0224

–0.7

582

3.39

939.

9301

here

from

Slop

e8.

18E

–05

0.00

0211

–1.5

863

0.07

830.

0412

–9.8

48he

refr

omSl

ope

8.31

E–0

50.

0002

19–0

.731

10.

6098

0.85

71–1

.895

6.05

7he

refr

omSl

ope

8.43

E–0

50.

0002

17–0

.506

20.

4627

0.55

21–0

.977

2.28

68–1

.483

here

from

Slop

e8.

56E

–05

0.00

021

–0.8

373

–0.2

4–0

.414

–1.7

18–0

.457

4–3

.544

–5.6

037

here

from

Slop

e8.

69E

–05

0.00

0209

–0.9

717

–0.5

57–0

.773

–1.7

61–1

.021

9–2

.847

–3.0

697

–0.5

3568

here

from

Slop

e8.

82E

–05

0.00

0211

–0.8

905

–0.5

5–0

.71

–1.3

98–0

.784

1–1

.784

–1.3

639

0.61

804

1.77

1772

1he

refr

omSl

ope

8.94

E–0

50.

0002

21–0

.455

5–0

.096

–0.1

19–0

.488

0.21

04–0

.125

0.79

112.

8595

44.

7384

528

7.70

5133

here

from

Slop

e9.

07E

–05

0.00

0217

–0.3

090.

0116

0.01

45–0

.242

0.34

290.

1413

0.84

062.

1013

92.

6617

698

2.26

6208

–3.1

7272

here

from

Slop

e9.

2E–0

50.

0002

06–0

.501

–0.2

66–0

.314

–0.5

85–0

.206

–0.4

94–0

.176

60.

3249

2–0

.049

4436

–1.6

0283

–5.9

9517

–8.8

1761

here

from

9.32

E–0

50.

0002

14–0

.433

1–0

.224

–0.2

57–0

.468

–0.1

416

–0.3

52–0

.077

50.

3090

30.

0541

612

–0.8

3643

–2.6

494

–1.3

597

6.09

8217

here

9.45

E–0

50.

0002

04–0

.562

6–0

.402

–0.4

57–0

.666

–0.4

353

–0.6

62–0

.517

8–0

.337

96–0

.704

8709

–1.5

5161

–2.9

2546

–2.4

1864

–0.6

3864

–7.3

755

9.58

E–0

50.

0002

12–0

.509

5–0

.363

–0.4

05–0

.574

–0.3

661

–0.5

39–0

.399

1–0

.232

8–0

.481

6862

–1.0

2273

–1.7

6234

–0.9

930.

6098

22–0

.803

59.

71E

–05

0.00

0203

–0.5

924

–0.4

74–0

.526

–0.6

88–0

.529

5–0

.701

–0.6

158

–0.5

2616

–0.7

8492

68–1

.266

52–1

.864

47–1

.385

62–0

.580

97–1

.883

9.83

E–0

50.

0002

03–0

.642

3–0

.544

–0.5

98–0

.748

–0.6

207

–0.7

8–0

.721

9–0

.667

88–0

.903

2355

–1.3

041

–1.7

6195

–1.3

9063

–0.8

5587

–1.7

471

9.96

E–0

50.

0002

–0.7

076

–0.6

28–0

.685

–0.8

27–0

.727

2–0

.879

–0.8

451

–0.8

2062

–1.0

4095

8–1

.389

19–1

.764

21–1

.486

28–1

.131

64–1

.817

70.

0001

010.

0002

12–0

.605

–0.5

23–0

.562

–0.6

73–0

.566

2–0

.676

–0.6

182

–0.5

6259

–0.7

0320

14–0

.926

71–1

.134

23–0

.778

07–0

.335

03–0

.597

50.

0001

020.

0001

96–0

.682

8–0

.616

–0.6

61–0

.771

–0.6

885

–0.8

–0.7

664

–0.7

3986

–0.8

8610

84–1

.102

85–1

.304

66–1

.053

82–0

.770

52–1

.076

20.

0001

030.

0002

06–0

.648

5–0

.585

–0.6

22–0

.717

–0.6

373

–0.7

3–0

.691

4–0

.658

38–0

.772

0963

–0.9

3795

–1.0

7865

–0.8

3232

–0.5

6137

–0.7

527

0.00

0105

0.00

0199

–0.6

732

–0.6

18–0

.655

–0.7

43–0

.674

4–0

.761

–0.7

306

–0.7

0658

–0.8

1156

73–0

.959

37–1

.081

71–0

.876

95–0

.663

38–0

.836

8


57

Table 2. Basic data by sample for age calculation

Sample Ref. No. Xav±sd, cm Cav±sd, gmol/cm3 K r Ds, cm2/y Age, years BP

CHO024 7E-05±8.02E-06 0.1246±0.00114 5.298 0.9447 3.60E-11 1021+105/-78DL-1993-74 9.55E-05±7.48E-07 5.34E-04±1.05E-05 0.693 0.0965 1.83E-12 542+20/-19DL-1993-76 5.06E-05±2.65E-06 6.23E-04±6.23E-04 3.91 0.378 1.44E-12 416+46/-39DL-1993-82 6.06E-05±7.79E-07 4.11E-04±3.95E-06 2.996 0.789 8.68E-13 543+33/-30DL-2000-149 2.787E-04±5.927E-06 6.053E-04±3.2191E-06 1.609 0.512 9.79E-13 6610+81/-88DL-2000-150 1.093E-04±3.42E-06 2.14E-04±2.2E-06 3.91 1.353 7.0334E-13 6980+175/-174DL-2000-144 1.006E-0±1.94E-06 7.73E-04±4.81E-06 4.554 0.421 1.849E-12 4290+120/-118DL-1983-101 1.21E-04±1.716E-06 2.896E-04±1.922E-06 3.4 0.000315 1.52E-13 2100+200/-160DL-1983-100 8.49E-05±1.95E-06 2.63E-04±2.16E-06 4.554 0.000894 5.75E-13 2130+77/-82DL-1993-153 5.78E-05±1.30E-06 3.46E-04±2.51E-06 5.298 0.000452 1.36E-12 1280+57/-54DL-1993-199 9.17E-05±1.69E-06 2.16E-04±1.97E-06 1.609 0.000195 4.22E-13 1020+7/-11DL-1993-129* 1.547E-04±6.53E-06 1.33E-02±1.98E-04 3.912 0.2018 2.71E-11 1150+63/-47DL-1993-184 9.65E-05±2.46E-06 2.134E-04±1.72E-06 0.693 0.0182 1.06E-12 645+22/-23DL-1993-193(two gradients indicating re-use)1st layer

2nd layer

6.82E-05±4.77E-06

1.073E-04±5.15E-06

3.195E-04±2.16E-06

2.985E-04±4.07E-06

4.094

2.30

0.000585

0.000352

1.11E-12

4.55E-13

695+102/-88

1486+138/-155

* The gradients do not form a band but a cone shape. The band is dispersed and the outliers above and below this band may indicate re-use; the calculated dates being 2934 BP and 840 BP.

As a first approach in the earlier publication,22 the gradient dC/dx, or the tangent at a certain point of the fitted curve, or from another point of view, the rate of change, was attributed to the diffusion coefficient:

dC/dx = (b+2cx+3dx2) exp (a+bx+cx2+dx3) (19)

and D was found and expressed from the calculated data of Eq. (19).

For C = Cs and x = xs then we set D = Ds as shown below.

From Eq. (16) the age is calculated:

T = [(Ci–Cs)2 (1.128/(1–0.177kCi/Cs)

2]//[4Ds(b exp(a))2] (20)

where Ci and Cs (both in gram moles of water per cm2), as well as xs (in cm) are measured parameters, while Ds(=flux/gradient,) and k are calculated, and a and b are constants. In the first work,22 Ds was defined as = dC/dxfor C = Cs, x = xs, in cm2/unit of time, where unit of time of 1012 years was used as an empirical adjustment. In fact according to Fick’s law Ds is the inverse of gradient × 10E-11 years, assuming the flux is constant and taken as unity.23 In the calculation of D the 10E-11 is been done in order to convert the units of D from the calculated µm2/1000 years to cm2/year, which is the units used in SIMS-SS.

We now evaluate the ability of our model to estimate the ages of prehistoric artifacts using SIMS profiles recorded from ancient samples. To do this, the water diffusion coefficient at any particular moment is expressed by the first derivative of the hydrogen profile.

This is the apparent hydration rate. The average xs and Cs obtained from the determination of the SS layer gives the overall error attached to the SIMS-SS ages.

Secondary ion mass spectrometry

SIMS analyses were conducted at two different laboratories. At the commercial laboratory of Evans East, East Windsor, NJ, the profiles were collected using PHI Model 6300 and 6600 quadrupole-based secondary ion mass spectrometers. A 5.0 keV Cs+ primary ion beam with an impact angle of 60° with respect to surface normal was used and negative secondary ions were detected. Charge build up during profiling was compensated for by the use of an electron beam. The ion signal was maximized by using the electron beam resulting in the least amount of charging. The measurements were performed using a 300×300 µm2 ion beam raster, which results in very little visual disruption to the sample surface. Generally, the SIMS depth scale accuracy is within 5–10%. This translates into an estimated error of ±0.05 µm. This value is not equivalent to the ±0.01–0.03 µm standard deviation usually associated with SIMS because of the irregular surface topography present on naturally cleaved samples.

Archaeological samples and contexts

Chalco, Mound 65, Mexico

The prehistoric site of Chalco was located on the shore of Chalco Lake within the Basin of Mexico, Mexico.


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Table 3. Obsidian hydration ages and radiocarbon dated contexts

Sample Location Reference SIMS-SS age Calibrated 14C age

CH0024 Chalco, Mexico(Otumba source)

ANOVITZ et al. (1999)RICIPUTI et al. (2002)

1021 BP* 1280–740 BP

DL-1993-74 Easter Island, Chile Site 10-241, F.26 Evans EastSTEVENSON (2000)

542 BP 526–301 BP


416 BP 526–301BP


543 BP 522–310 BP

DL-2000-149 Mykonos (Ftelia), Greece(Melos source)

Evans EastSTEVENSON et al. (2002)

6610 BP 7050–6450 BP

DL-2000-150 Mykonos (Ftelia), Greece(Melos source)


6980 BP 7050–6450 BP

DL-2000-144 Melos (Phylakopi), Greece(Melos source)


4290 BP 4450–3950 BP

DL-1983-101 Hopewell Site, USA Evans East 2100 BP 2150–1450 BP**DL-1983-100 Hopewell Site, USA Evans East 2130 BP 2150–1450 BPDL-1993-153 Xaltocan, Mexico Evans East

STEVENSON et al. (2000)1280 BP 1330–835 BP

DL-1993-199 Xaltocan, Mexico Evans EastSTEVENSON et al. (2000)

1020 BP 1255–955 BP

DL-1993-129 Xaltocan, Mexico ANOVITZ et al. (1999) 1150 BP 1160–785 BPDL-1993-184 Xaltocan, Mexico Evans East

STEVENSON et al. (2000)645 BP 655–480 BP

DL-1993-193 Xaltocan, Mexico Evans EastSTEVENSON et al. (2000)

695 BP 655–480 BP

* The BP for SIMS-SS is year 2000, while for 14C is 1950. See the text for age derivation.** Age estimates for the Hopewell site represent the time span of this cultural period.

The city was occupied from the Early PostClassic (200–750 AD) through the Late Postclassic (1200–1521 AD) and emerged as one of the larger urban centers in the region. Within this urban setting test excavations were conducted at Mound 65, a stratigraphically complex deposit with up to 20 cultural levels that included patios and living floors. Ceramic associations and radiocarbon dates revealed that the mound was initially formed during the Epiclassic (750–950 AD) with later occupation within the Aztec I–III periods (1150–1519 AD). An occupational hiatus occurred from 900–1100 AD.8 We have utilized one published SIMS profile from ANOVITZ et al.7 Sample CH0024 (Table 3) is from Level 24. The stratigraphically closest calibrated 14C date lies between layers 18 and 30 or 670–1210 AD (1280–740 BP).8

Easter Island, Site 10-241, Chile

Easter Island (Rapa Nui) is a small island in the south-central Pacific that supported a prehistoric Polynesian population from approximately 1150–90 BP. The island was intensively farmed and habitation sites such as 10–241 are associated with remote inland field systems. Excavations at this site identified numerous cooking, storage and processing features. Three pit features were radiocarbon dated and demonstrated that the site was occupied in the 14th and 16th centuries.24

Three obsidian samples were taken from two of the dated pit features. DL-1993-74 and DL-1993-76 were recovered from the fill of Feature 26. The calibrated radiocarbon date had a 2σ age range of 526–301 BP. Sample DL-1993-82 was taken from pit Feature 41. It produced a similar 2σ age range of 522–310 BP.

Ftelia and Philakopi, Greece

Melos island hosts the most important obsidian source in the Aegean, comprised of at least two sub-sources, Adamas and Demenegaki.6,25 The sample from the Philakopi settlement on Melos island is of Early Bronze Age III period (2000–2500 BC, 4450–3950 BP) and derives from an excavated trench within the site boundaries. Two samples come from the Ftelia Neolithic settlement on the Cycladic island of Mykonos were derived from living floors encountered during trenching operations.26 The age span of this settlement is 4500–5100 BC (7050–6450 BP) calibrated C14 years.

Hopewell Site, Ohio, USA

The obsidian artifacts from the eastern United States come from the Hopewell Site near Chillicothe, OH. They originated from within a large 136-kg obsidian cache placed within an earthen mound. Excavation of this mound27 resulted in the identification of a cremated


59

person associated with pearl beads, mica and copper artifacts. The cache was located away from the cremation pit and appeared not to have been effected by the burning of the individual. Two obsidian flakes were removed from the cache for SIMS analysis. The mound, or any of the interior features, have never been chronometrically dated but can be securely assigned to the Middle Woodland Period (200 BC–500 AD, 2150–1450 BP).

Xaltocan, Mexico

The Postclassic (Aztec) site of Xaltocan is situated on a small island within Lake Xaltocan in the Valley of Mexico, Mexico. Test excavations conducted by Elizabeth BRUMFIEL, Albion College, were completed at nineteen locations.28 Five obsidian samples were selected for analysis (Table 3).

(1) Sample DL-1993-129 was taken from Operation G, Level 16, located on the North side of the island. At a depth of 1.68 m below the surface, a room was encountered with two superimposed living floors. The latest floor contained a fire-related feature interpreted as a hearth. Charcoal fragments from this feature returned a 14C calibrated age of 880±80 AD (Beta-41911) or a 2σrange of AD 790–1165 (1160–785 BP). The obsidian sample was recovered the same level as the dated hearth.

(2) Sample DL-1993-153 was recovered in Operation I, Level 34. Operation I was a large platform mound with 11 superimposed plaster floors. Excavations proceeded systematically through these floor levels and provided carbon samples that bracket the obsidian sample. In Level 32, this strata containing Aztec I ceramics was 14C dated to 830±30 AD (695–1045 AD, 1150–1115 AD, I = 960) (1255–835 BP). This was followed by carbon date from Level 46 with an age of 570±80 AD (620–695 AD, I = 660) (1330–1255 BP) (all dates calibrated).

(3) Sample DL-1993-184 was taken from Operation R, Level 4 and sample DL-1993-193 was recovered from Level 6. Excavations within a surface concentration of ceramics at the base of a mound resulted in the identification of a large refuse pit with Aztec III–IV ceramics, obsidian, bone, shell and stone. Carbon from this feature was dated to 1410±70 AD (1295–1470 AD, 655–480 BP). The two obsidian artifacts were from this feature.

(4) Sample DL-1993-199 was excavated from Operation T, Level 15, a low mound located near the center of Xaltocan. The upper part of the unit contained a refuse pit with Aztec IV ceramics that extended to a depth of 1.2 m. This was separated from deeper deposits by a low artifact density fill layer. Below a depth of 1.3 m a second midden deposit was found with obsidian, bone and corn cobs. This context containing only Aztec I ceramics was dated to 770±60 AD (695–995, I = 880) (1255–955 BP). The obsidian sample came from within this lower midden deposit.

Discussion and conclusions

The ages for the fourteen obsidian samples were calculated using Eq. (20) and compared with radiocarbon dates from the same or adjacent occupation layers (Table 3, Fig. 6). The obsidian dates are in very good agreement with the radiocarbon determinations in all but three cases (DL-1993-74, DL-1993-82, DL-1993-193). In each of these cases the mean SIMS-SS dates occur outside of the 2σ 14C age range and are earlier by 16–40 years. These are not large outliers and their standard deviations overlap the limit of the radiocarbon age range in each case. The obsidian dates also appear to be randomly distributed within the radiocarbon age ranges with no consistent bias for the upper or lower part of the range.

Fig. 6. SIMS-SS age versus archaeological/mean radiocarbon age


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Obsidian hydration dating based upon SIMS hydrogen profiling of the surface saturated layer is emerging to be a reliable chronological dating method for archaeological applications. The errors involved are less than 5% with some cases between 5–10%, which is a very high level of precision, equivalent to, or less than, that of conventional calibrated radiocarbon dating. An additional advantage is that SIMS-SS does not suffer from the problem of alternate age ranges like those generated by multiple intercepts on the radiocarbon calibration curve. More often than not, the probabilities assigned to the alternate outcomes of 14C ages, coupled with site context information, can alleviate this problem, but it is often a concern. Furthermore, SIMS-SS age determinations have the potential for to produce age determinations within the last centuries and thus useful for historic investigations. However, the SIMS-SS is a new approach and will require additional refinements in the modeling process. We expect that a larger number of analyses and comparisons with dated contexts will demonstrate the utility of this approach.

*

The authors thank the Municipality of Rhodes and Silver & Byrites Ore Mining Co. for partial funding of the project, A. SAMPSON

for providing the Aegean samples, and The Ministry of Culture, Athens, Greece for granting permission to analyze the samples from Mykonos and Melos. An award from the International Association for Obsidian Studies (IAOS) contributed toward the successful completion of this project. We are grateful to Prof. M. TOMOZAWA and Prof.R. BRODKEY for their constructive comments.

References

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Obsidian Studies: Method and Theory, M. S. SHACKLEY (Ed.), Advances in Archaeological and Museum Science, Vol. 3, New York, Plenum Press, 1998, p. 181.

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OBSIDIAN HYDRATION DATING BY SECONDARY ION MASS SPECTROMETRY-SURFACE SATURATION, SOME APPLICATIONS...

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