### Izochronowa kontrola i interpretacja wyników oznaczeń wieku bezwzględnego K-Ar

#### Abstract

ISOCHRONOUS CONTROL AND INTERPRETATION OF RESULTS OF K-Ar ABSOLUTE AGE DETERMINATION

Summary

In the geochronology laboratory of the Geological Institute, where volumetric measurements of radiogenic argon are made, a precise method of separation and cleaning of argon from minerals has been worked out. The method guarantees in a maximum way the purity of the radiogenic argon produced, and highly decreases the possibility of contamination with atmospheric argon (T. Depciuch - paper in print). Mathematical method of interpretation of the results obtained has also been elaborated; the method allows us to ascertain and to take into consideration all systematic error. The principles of this method are based on the main elements of isotope geochronology. If a mineral in study makes a closed system from the moment of its formation, then the amount of the constant isotope Np, originated from a given amount of the radioactive isotope No in time *t*, is given in the following formula: Np=No(e* ^{λt}*-1) where:

*λ*- radioactive isotope constant; e - base of natural logarithm. It results from this formula that the ratio Np/No is also a constant value for each moment of time

*t*. Thus, in the mineral of a given age the ratio radiogenic argon Ar

^{40}– potassium represents a constant value (as compared with the constant isotope relations of the contemporaneous potassium). In this way the samples of minerals of the same age and with different amounts of potassium will reveal various quantities of radioactive argon, but will be always in a constant relation to potassium. When in the coordinate system we present the values of argon amounts on the X-axis, and the values of potassium amounts - on the Y-axis, the points corresponding to the same ratio of these two values will make a straight line that begins at the zero point of the system with the following formula: Ar

^{40}=

*b*K, where:

Ar^{40} - amount of radiogenic argon in grammes; K - amount of potassium in grammes; *b* - tg of an angle between the straight line am Y-axis. The coefficient *b* expresses the radiogenic argon - potassium ratio. Seeing that t = 1/*λ *ln (1 + Ar^{40}/K^{40} · (1 + *R*)/*R*), where: *t* - age in mill. of years, *λ* - general radioactive potassium constant *λ _{k} +*

*λ*, R -

_{β}*λ*/

_{k}*λ*ratio, the straight line is an isochrone of samples of the same age, but with various content of potassium. Using special tables and coefficient

_{β}*b*we may read off the isochronous age of a given geological object. In the case when the results of determinations are charged with a systematic error due to the presence of constant but not considered background of the instrument, or due to some constant losses of argon, the isochrone takes the following form: Ar

^{40}= ±

*a*+ b K. Coefficient

*a*, expressed in grammes, reflects an intarsection point of isochrones and X-axis, and quantitatively determines the constant surplus or insufficiency of argon. In the case of isochronous interpretation of K-Ar results we use, according to the character of the samples examined, a different scheme of determinations: a - if the samples include a series of potassium-bearing minerals, where potassium content ranges considerably (e.g. rock with amphibole, potassium feldspar, biotite and muscovite) - determinations of argon are made using similar amounts of rock samples; b - if potassium amounts in samples are approximate, the weights of the individual samples should be chosen in a way allowing us to comprise the greatest interval of values; c - having at our disposal only one sample of mineral, we make a series of argon determinations taking various weights of sample. On the basis of analytical data, the isochrone is calculated by means of the method of least squares. Below, there are given two examples of age calculation and of control of determinations of argon using isochronous method for biotite samples from the Karkonosze granites (T. Depciuch, J. Lis - paper in print) and for one sample from the Strzelin granite (T. Depciuch, J. Lis, 1970). The following isochrone has been obtained for the Karkonosze granites: Ar

^{40}= 8,9·10

^{-9}+ 23,008·10

^{-7}K. The ratio Ar

^{40}/K

^{40}= 23,008·10

^{-7}corresponds to an age of 299·10

^{6}years. The arithmetic mean of ages for samples, on the basis of which the isochrone has been calculated, amounts to 301,8·10

^{6}years. Thus, the difference between the arithmetic mean of ages and the isochronous age amounts approximately to 3 mill. years. The difference illustrates that the results of determinations were charged with positive systematic error of about 1%. As concerns the sample of the Strzelin granite from Gęsiniec, the isochrone is as follows:

Ar^{40} = 14,0·10^{-9} + 20,488·10^{-7 }K, and this corresponds to an isochronous age equal to 269·10^{6} years. The difference between the isochronous age and arithmetic mean of the individual determinations amounts to 3 mill. years, too. In this case the results are also charged with a positive error of about 1%. The two examples are illustrated in Figs. 1 and 2. In the normal analytical practice the points making the isochrone do not lie precisely on a straight line, but they constitute a probability ellipse, as it may be seen on Fig. 1. The estimation of such a dispersal is made by calculation of linear correlation coefficient. It results from the practice of our laboratory that this coefficient is of higher values for an isochrone calculated on the basis of the determinations of the same sample (ca 0.999) than in the case of various samples of the same geological object. It appears that in any case it cannot be lower than 0,99. A considerably high dispersal of points round the isochronous straight line for rocks, most probably of the same age, may demonstrate either an incorrectness of analyses, or an unstable potassium-argon balance due to the activity of certain natural processes. In this case, this may be an advice for further research on the nature of these phenomena. The method of calculation of isochronous age and of control of determinations of radiogenic argon may be used in determinations of argon by means of both volumetric method and isotope dilution method.