K–Ar age constraints on the sources of K minerals in bentonites of the Ankara-Çankırı Basin, Central Anatolia, Turkey

Abstract

Many of the bentonite deposits of the Ankara-Çankırı Basin, Central Anatolia, Turkey were found within the Miocene Hancılı Formation, which comprises lacustrine sedimentary and volcaniclastic rocks that interfinger with Uludere pyroclastic rocks of the Miocene Galatean volcanic province. In the present study, the conventional K–Ar geochronological method was used to evaluate the contribution of volcanic materials to the K-bearing components of the bentonite clay fractions. Four dacite samples from near the southern end of the basin were indistinguishable in K–Ar age (average 18.4 Ma, standard deviation 0.3 Ma). K–Ar measurements of feldspar-enriched rock fragments and hydrobiotite separated from andesitic tuff from near the northern end of the basin indicated an age of 17 ± 1 Ma. The K–Ar age values of clay fractions of bentonites, which ranged from 77 ± 5 Ma to 162 ± 5 Ma, indicate that most of the K in the bentonite clay fractions occurs in minerals derived from the Mesozoic basement rocks adjacent to the Miocene basin. The K–Ar age values support field observations indicating that these bentonites are secondary bentonites formed by alteration of volcanic components during or after deposition of volcaniclastic phases. The K-bearing mineral components of these clay fractions consisted mostly of unaltered illitic material of detrital origin whereas the smectitic components were formed by alteration of Miocene pyroclastic materials.

Appendix

Derivation of the K–Ar age value of pre-Miocene clay in a bentonite clay fraction as a function of the proportion of the clay-fraction K that is in Miocene or younger clay

Definitions

Bentonite clay fraction—the part of a bentonite sample separated as grains smaller than 2 µm.

Component 1—those parts of a bentonite clay fraction formed after the beginning of the Miocene Period.

Component 2—those parts of a bentonite clay fraction formed before the beginning of the Miocene Period.

⁴⁰Ar*—radiogenic argon; also used, by convention, for the amount (amount of substance) of radiogenic argon in a material.

⁴⁰K—the radioactive isotope of terrestrial K; also used, by convention, for the amount (amount of substance) of ⁴⁰K in a material.

T—the K–Ar age value of a material.

Λ—the decay constant of ⁴⁰K.

λ_ε—the partial decay constant for the transformation of ⁴⁰K to ⁴⁰Ar (almost entirely by electron capture).

λ_β—the partial decay constant for the transformation of ⁴⁰K to ⁴⁰Ca by β-decay.

K_c—the amount (amount of substance) of potassium in a bentonite clay fraction.

K₁—in a bentonite clay fraction, the amount of potassium from component 1.

K₂—in a bentonite clay fraction, the amount of potassium from component 2.

Derivation

From a general relationship given by Dalrymple and Lanphere (1969, p. 48),

$${}^{40}{\text{Ar}}^{*} = {}^{40}{\text{K}}\frac{{\lambda_{\varepsilon } }}{{\lambda_{\varepsilon } + \lambda_{\beta } }}\left( {{\text{e}}^{{(\lambda_{\varepsilon } + \lambda_{\beta } )t}} - 1} \right),$$

(1a)

three specific relationships may be written,

$${}^{40}{\text{Ar}}_{\text{c}}^{ *} = {}^{40}{\text{K}}_{\text{c}} \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right),$$

(1b)

$${}^{40}{\text{Ar}}_{1}^{*} = {}^{40}{\text{K}}_{1} \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right),$$

(1c)

And

$${}^{40}{\text{Ar}}_{2}^{*} = {}^{40}{\text{K}}_{2} \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right),$$

(1d)

where the subscripts c, 1, and 2 denote the entire clay fraction and components 1 and 2, respectively, and the sum of the partial decay constants, λ_ε and λ_β, has been replaced by the total decay constant λ.

By definition,

$${}_{{}}^{40} {\text{Ar}}_{{ {\text{c}}}}^{*} = {}_{{}}^{40} {\text{Ar}}_{ 1}^{*} + {}_{{}}^{40} {\text{Ar}}_{ 2}^{*} .$$

(2)

Substituting in (2) the expressions for ⁴⁰Ar*₁ and ⁴⁰Ar*₂ from (1c) and (1d),

$${}^{40}{\text{Ar}}_{\text{c}}^{*} = {}^{40}{\text{K}}_{1} \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) + {}^{40}{\text{K}}_{2} \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(3)

Dividing (3) by ⁴⁰K_c,

$$\frac{{{}^{ 4 0}{\text{Ar}}_{{ {\text{c}}}}^{ *} }}{{{}^{ 4 0}{\text{K}}_{\text{c}} }} = \frac{{{}^{ 4 0}{\text{K}}_{ 1} }}{{{}^{ 4 0}{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) + \frac{{{}^{ 4 0}{\text{K}}_{ 2} }}{{{}^{ 4 0}{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(4)

By convention, ⁴⁰K/K in natural terrestrial materials is considered equal to 0.001167 (Steiger and Jäger 1977), so a ratio of ⁴⁰K amounts in two different natural materials is the same as the ratio of K amounts in those two materials. It follows from (4) that

$$\frac{{{}^{ 4 0}{\text{Ar}}_{\text{c}}^{ *} }}{{{}^{ 4 0}{\text{K}}_{\text{c}} }} = \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) + \frac{{{\text{K}}_{ 2} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right),$$

(5)

where the subscripts c, 1, and 2 continue to denote the entire clay fraction and components 1 and 2, respectively.

Dividing (1b) by ⁴⁰K_c,

$$\frac{{{}^{ 4 0}{\text{Ar}}_{\text{c}}^{ *} }}{{{}^{ 4 0}{\text{K}}_{\text{c}} }} = \frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right).$$

(6)

Equating the two expressions for ⁴⁰Ar_c*/⁴⁰K_c in (5) and (6),

$$\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right) = \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) + \frac{{{\text{K}}_{ 2} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(7)

By definition,

$${\text{K}}_{1} + {\text{K}}_{2} = {\text{K}}_{\text{c}} ,$$

(8)

so by subtraction of K₁,

$${\text{K}}_{ 2} = {\text{K}}_{\text{c}} - {\text{K}}_{1}$$

(9)

Dividing (9) by K_c,

$$\frac{{{\text{K}}_{ 2} }}{{{\text{K}}_{\text{c}} }} = 1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}.$$

(10)

Replacing $\frac{{{\text{K}}_{ 2} }}{{{\text{K}}_{\text{c}} }}$ in (7) with its equivalent from (10),

$$\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right) = \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) + \left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(11)

Subtracting the first right-hand term from (11),

$$\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{c} }} - 1} \right) - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right) = \left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(12)

Dividing (12) by $\left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }$,

$$\frac{{\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{c} }} - 1} \right) - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right)}}{{\left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }}} = \left( {{\text{e}}^{{\lambda t_{2} }} - 1} \right).$$

(13)

Adding 1 to (13),

$$\frac{{\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right) - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right)}}{{\left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }}} + 1 = {\text{e}}^{{\lambda t_{2} }} .$$

(14)

Taking the natural logarithms,

$$\ln \left\{ {\frac{{\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right) - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right)}}{{\left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }}} + 1} \right\} = \lambda t_{2} .$$

(15)

Dividing (15) by λ and reversing,

$$t_{2} = \frac{1}{\lambda }\ln \left\{ {\frac{{\frac{{\lambda_{\varepsilon} }}{\lambda }\left( {{\text{e}}^{{\lambda t_{\text{c}} }} - 1} \right) - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}\frac{{\lambda_{\varepsilon } }}{\lambda }\left( {{\text{e}}^{{\lambda t_{1} }} - 1} \right)}}{{\left( {1 - \frac{{{\text{K}}_{ 1} }}{{{\text{K}}_{\text{c}} }}} \right)\frac{{\lambda_{\varepsilon } }}{\lambda }}} + 1} \right\}.$$

(16)