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


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.

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This present study was supported financially by the Scientific Research Projects Fund of Eskişehir Osmangazi University in the framework of Projects 2014–656. Use of the K–Ar facility at Georgia State University, USA, was supported with funds from the Faculty International Partnership Engagement (FIPE) Grant ID # FIPE-16-446 to W. Crawford Elliott in cooperation with Selahattin Kadir.

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Correspondence to W. Crawford Elliott.



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


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.

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

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

Kc—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.


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

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

three specific relationships may be written,

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


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

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, λε and λβ, has been replaced by the total decay constant λ.

By definition,

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

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

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

Dividing (3) by 40Kc,

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

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

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

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

Dividing (1b) by 40Kc,

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

Equating the two expressions for 40Arc*/40Kc in (5) and (6),

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

By definition,

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

so by subtraction of K1,

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

Dividing (9) by Kc,

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

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

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

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

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

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

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

Adding 1 to (13),

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

Taking the natural logarithms,

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

Dividing (15) by λ and reversing,

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

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Elliott, W.C., Wampler, J.M., Kadir, S. et al. K–Ar age constraints on the sources of K minerals in bentonites of the Ankara-Çankırı Basin, Central Anatolia, Turkey. Int J Earth Sci (Geol Rundsch) 109, 2353–2367 (2020).

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  • Ankara-Çankırı Basin
  • Bentonite
  • K–Ar age
  • Volcaniclastics
  • Turkey