Is there any health danger by radioactivity on the use of dimensional stones?

For this study, a wide range of samples were selected regarding the mineralogy and the geological background focussing on ornamental stones but in additon samples which expected higher radiation values were also included. These include acidic, igneous rocks such as granite and a larger variety of metamorphic rocks as well sedimntary rocks. A high organic content in the rock, as can occur in shales and limestones, is also often a source of the relevant radioactive isotopes of uranium, thorium and potassium (Bone et al. 2017; Fuller et al. 2020; Tzortzis et al. 2003; Yang et al. 2012). Based on this finding, a selection of 82 rocks was chosen to measure their radioactivity and calculate the resulting annual equivalent doses and radon exhalation.

For further evaluation (see Table 1), the samples with similar petrographical and geochemical characteristics were divided into eight different rock groups (Fig. 2): (1) the mafic volcanics/magmatites (basalt, gabbro, trachyandesite and ignimbrite) and their metamorphic equivalents (amphibolite and serpentinite) with a total of seven samples (MV), (2) gneisses (gneiss and kinzingite) with 15 samples (GN), (3) the felsic volcanic rocks/magmatites (granite and granodiorite) with 17 samples (FV), (4) limestones (limestone, travertine) with ten samples (KS), (5) marbles with seven samples (MA), (6) quartzite with five samples (QT), (7) sandstones and similar sedimentary rocks (sandstone, greywacke, metaconglomerate and metapsammite) with nine samples (SA) and (8) metamorphic rocks like slates, phyllites and metapelite with 12 samples (SF).

Potassium is most abundant in rock-forming minerals and has an average concentration of 2.09 wt% (Taylor 1964) or 400 Bq kg^–1 (European Commission 1999) in the continental crust. Potassium is geochemically an incompatible LILE (large-ion lithophile element), but occurs as a major component in many minerals, such as feldspars (orthoclase, microcline and sanidine), mica and clay minerals (biotite, muscovite, phlogopite and illite), foids (leucite and nepheline) and salts (sylvin). A substitution process often takes place between potassium and sodium, which have geochemically similar properties, in the minerals. Potassium has three isotopes, of which only ⁴⁰K is radioactive and occurs with a relative abundance of 0.012% (Plant and Saunders 1996) and a half-life of 1.31 Ga (Burch 1953).

Thorium occurs in rocks as a trace element with an average concentration of 9.6 ppm or 40 Bq kg^–1 in the continental crust (European Commission 1999; Taylor 1964). Thorium occurs in higher concentrations in thorite (in the wt% range) but also in higher trace concentrations in monazite, apatite or allanite, etc. (Frondel and Fleischer 1952). There is a close geochemical relationship between uranium and thorium, both of which are HFSE (high field strength element), in which thorium can partially replace uranium in minerals. Unlike uranium (U⁶⁺), thorium is an immobile element. Thorium has only one isotope, ²³²Th, which is relevant for measuring radioactivity (Plant and Saunders 1996) and has a half-life of 14.2 Ga (Chikkur and Umakantha 1977).

Radium is a highly incompatible element in minerals and has a concentration of about 0.9 ppm, or 40 Bq kg^–1 in the continental crust (European Commission 1999; Lide 2008). The radium isotope ²²⁶Ra is an intermediate decay product of the ²³⁸U series with a half-life of 1600 years (Broecker et al. 1967) and is selectively absorbed in clay minerals (e.g. in illite) and metal oxides (Hidaka et al. 2007; IAEA 2014). According to geochemical compatibility, radium is able to substitute in small amounts barium, lead and, to some extent, strontium and calcium, in a crystal lattice. Since in the decay series of ²³⁸U-²⁰⁶Pb the segment beginning with ²²⁶Ra is radiologically the most important, the activity of radium is often measured instead of uranium (European Commission 1999). Thus, uranium-bearing minerals, e.g. uraninite or coffinite, directly control radium concentrations in geological reservoirs (Klepper and Wyant 1957).

The rock samples were crushed by hand to a grain size of < 1 cm and filled into Behroplast wide neck bottles (PET) 250 ml. Depending on the density, between 350.33 and 598.89 g were filled into the bottles at the same volume. The samples were sealed airtight with adhesive tape and stored for 4 weeks until measurement, to establish radioactive equilibrium of Ra-226 and the follow-on products Rn-222, and especially Pb-214 and Bi-214.

The activity of K-40 was measured directly. The other two radionuclides, Ra-226 and Th-232, show only gamma emmisions with low transition probability, which would be partially perturbed by stronger lines of other nuclides. The Ra-226 was determined by the average of the Pb-214 and Bi-214 activities. A secular equilibrium between Ra-226 and Rn-222 is achieved in 23 days (Gehrcke et al. 2012). Similarly, the determination of the activity for Th-232 was calculated by the mean value of Ac-228, Pb-212 and Bi-212. In the two radioactive decay series, the noble gas radon occurs as an intermediate product that can escape from the samples. Because both isotopes of radon have relatively short half-lives (3.82 days for Rn-222 in the uranium decay series and 56 s for Rn-220 in the thorium decay series; Cecil and Green 2000) and the samples were stored in gas-tight beakers, the measured samples are not affected by radon loss. The mean analytical detection limits from all gamma spectrometric measurements were determined as follows: Pb-214 = 1.7091 Bq kg⁻¹, Bi-214 = 1.3103 Bq kg⁻¹, Ac-228 = 2.0377 Bq kg⁻¹, Pb-212 = 0.5281 Bq kg⁻¹, Bi-212 = 6.081 Bq kg⁻¹, K-40 = 6.504 Bq kg⁻¹.

The samples were measured on 3 pure germanium detectors, Canberra N-type with a relative efficiency of about 25%, each for 250,000 s. The electronics with analogue to digital converters were at detector GE1—Ortec Dspec LF, at GE2—Ortec Dspec jr and at GE3—Ortec 92X Spectrum Master.

The obtained raw data were processed with the software Gammavision 8.10 and user interface.

LV is 2.760. Activity calculation from the recorded spectra was performed using the mentioned programs according to DIN 11929 (2020) for determination of detection limit, activity and error.

The background was determined using the same empty sample vessels. The energy and efficiency calibration was performed using the same sample containers filled with quartz sand with a density of 1.6 with added Multi Nuclide Standards.

The activity Index (“I”) proposed in the Eueopean Directive (European Commission 1999) was calculated by the following equation:

To determine the equivalent doses H (for the explanation see Eq. 4), the free software Rad Pro Calculator (version 3.26) by Ray McGinnis was used. For the calculation, the simplified assumption applies that it is a point source of radioactive radiation. This assumption is made in order to obtain dose rate data for the samples that can be compared with the literature and the legal regulations. When calculating the doses, the first step was to calculate the activities via the measured specific activities and the masses of the substances. Since the dose depends on the distance of the radioactive point source, the calculations were carried out for the distances s = 0.01 m, s = 0.05 m and s = 0.1 m. In this way, the doses for all involved substances were calculated. Thus, the doses were determined for all nuclides involved, ⁴⁰K, ²²⁶Ra and ²³²Th, which were finally summed up to a total dose for each sample. For the samples where the specific activity of the three nuclides was below the detection limit, the activity was assumed to be A = 0 Bq for the calculation in order to still obtain a quantified value for the dose.

Rn-222 and Rn-220 exhaled per unit mass were determined simultaneously with the accumulation method following the procedures described in Domingos et al. (2021). The crushed rock samples were placed in beakers with an approximately volume of 0.3 L. The beakers were then placed in stainless steel radon-proof containers with a volume of 5 L and sealed with a lock ring to prevent radon loss. The containers were left to reach equilibrium in the radon ²²²Rn decay series. Rn-222 and Rn-220 were measured simultaneously with an AlphaGuard DF2000 monitor (from Saphymo GmbH) using Tygon standard LMT-55 tubes characterized by low gas permeability to couple the containers to the measuring equipment. The length of the tubes was minimized to increase the efficiency of Rn-222 recovery.

The AlphaGuard DF2000 monitor continuous Rn/Tn measuring protocol was selected to discriminate between Rn-222 and Rn-220 activity concentration using a flowrate of 2 L/min. The detection limits are 15 Bq/m³ for ²²²Rn and 30 Bq/m³ for ²²⁰Rn (Burkin and Villert 2017). These authors also recommend that the activity concentration to be measured over longer periods to increase the accuracy of the mean results computed. Hence, on average, measurements of the activity concentration of the radioisotopes were performed over a 24 h period with previous subtraction of the background (not taken in account for thoron because of its short half-life). The instrument was decontaminated between each measurement by pumping atmospheric air into the ionization chamber.

The Rn-222 and the Rn-220 exhalation rates (in Bq kg⁻¹ h⁻¹) were determined with the following equation:

where * is the isotope, C is the mean activity concentration (in Bq/m³), V is the free volume of the accumulator (in m³), W is the weight of the sample (in kg), and λ is the decay constant (in h⁻¹). The emanation coefficients (EC) of Rn-222 and Rn-220 were computed with following equation, where A is the activity concentration (in Bq/kg) of ²²⁶Ra and ²³²Th, respectively:

Within the rock groups, described different levels of activity are observed in the three nuclides measured. The activities of the radionuclides can be seen in Table 1 and in Fig. 3.

Similarities to the literature (Gehrcke et al. 2012) can generally be observed, as most materials show activities A < 80 Bq kg^-1 for ²²⁶Ra, A < 100 Bq kg^–1 for ²³²Th and A < 400 Bq kg^–1 for ⁴⁰K. Thus, the upper limits of normal activities A < 100 Bq kg^–1 for ²²⁶Ra and ²³²Th and A < 1000 Bq kg^–1 for 40 K for construction materials are also met for most samples (European Commission 1999). Within the discussed sample groups, different intensities of activity are observed regarding the three measured nuclides.

A clear contrast is seen between the felsic (FV) and mafic (MV) rocks in terms of Ra activity (FV median = 105.3 Bq kg^–1; MV median = 3.9 Bq kg^–1) and Th activity (FV median = 50.7 Bq kg^–1; MV median = 6.3 Bq kg^–1). This can mainly be attributed to the incorporation of uranium and thorium in the crystal lattices of the minerals. In the Earth’s mantle and mafic rocks, uranium and thorium occur in relatively low concentrations because they are incompatible in the mafic minerals. During partial melting and fractional crystallization, uranium and thorium are enriched in the melt phase, so they occur in greater concentrations in the more highly differentiated rocks. (IAEA 1989; Larsen and Gottfried 1960). In the metamorphic products of the magmatites (especially in MV), no U- or Th-loss is to be expected due to metamorphic processes, but uranium can be mobilized as U⁶⁺ by hydrothermal processes, while thorium behaves immobile (Dostal and Capedri 1978). Kalium is a less incompatible element than uranium or thorium, but behaves similarly to other incompatible elements in magmatic differentiation (Tilling and Gottfried 1969). Thus, the difference in K activities between FV (median = 1003 Bq kg^–1) and MV (median = 125.3 Bq kg^–1) is equally evident. In the mafic rocks, potassium can be incorporated in amphibole, pyroxene or plagioclase in minimal amounts, thus slightly higher activities are also observed for MV (Fig. 3). In the felsic rocks, potassium is incorporated as a major element in mica and potassium feldspar, providing the highest K activities of all groups (Table 1, Fig. 3). In group MV, Trachyandesite from Armenia and Brown Chocolate are characterized by higher Ra, Th and K activities than the rest of the samples. In the FV group, Coral Red has a particularly high activity for Th, whereas Monsoon and Bianco Saviolo have significantly lower Ra activities than the rest of the samples.

In the limestones (KS), the lowest activities are ²²⁶Ra (median = 6.00 Bq kg^–1), ²³²Th (median = 0.81 Bq kg^–1) and ⁴⁰K (median = 9.68 Bq kg^–1). In the marine environment, under oxic conditions, uranium occurs mainly as U⁶⁺ (uranyl), which can be dissolved in water in relatively large amounts. The precipitation of uranium in the larger uranyl-calcium complexes is not excluded, so limestones can have U concentrations in higher trace ranges (Klinkhammer and Palmer 1991). This also explains the variance in the Ra activities of KS. During the formation of travertines, uranium is incorporated as trace from the water into the crystals as soon as the redox conditions change (Schwarcz et al. 1979). Thorium also shows a relatively low activity in the limestones, because thorium is not incorporated into the crystal lattices of the carbonate minerals, but it can be found in the clay or heavy mineral fraction of the limestones (Bayer et al. 1969). Since thorium is an immobile element, it is also not incorporated into the travertines, which allows the dating of travertines using U-Th (Schwarcz et al. 1979). Potassium contents in a limestone are usually low, resulting in relatively low K activities, but they may show some variation. Potassium can be incorporated into the defective sites of the carbonate minerals, between carbonate ions and CaO6-octahedra, especially at higher-salinity waters (Ishikawa and Ichikuni 1984). In the KS group, the black limestone Uttaradit White Grey from Thailand has relatively high Th and K activities compared to the rest of the samples.

Marbles show low activities of ²²⁶Ra (median = 5.76 Bq kg^–1), ²³²Th (median = 0.62 Bq kg^–1) and ⁴⁰K (median = 62.60 Bq kg^–1). Since marble is mineralogically composed mainly of calcite and dolomite, low concentrations of uranium, thorium and potassium and thus low activities of ²²⁶Ra, ²³²Th and ⁴⁰K are to be expected, similar to limestones. It has been reported that uranium can be incorporated into marble in small amounts during metamorphism in secondary phases (Hamdy and Aly 2011). Similarly, other radioactive nuclides besides uranium can be concentrated in marble, by enriched fluids from uranium-bearing rocks (Iqbal et al. 2000). From group MA, the sample Black Fuao shows strongly high activities for the three measured radionuclides.

In the group of sandstones (SA), moderate variance was observed in the activities of ²²⁶Ra (median = 16.37 Bq kg^–1) and ²³²Th (median = 30.69 Bq kg^–1), while ⁴⁰K (median = 304.6 Bq kg^–1) shows marked variations. In the sedimentation of sandstones, the provenance of the sediments plays an important role in their chemical and mineralogical composition. Particularly high uranium concentrations can be measured if the sandstones originate from a felsic magmatic source area (IAEA 1985). Elevated uranium concentrations can also occur in sandstones if reducing components (e.g. organic material, S^2-) are present in the groundwater, so that dissolved uranium is reduced to U⁴⁺ and precipitated as a secondary phase (IAEA 1985; World Nuclear Association 2020). Elevated uranium and thorium contents may be caused by a greater amount of heavy minerals, such as monazite or zircon, in the sandstone, yielding higher Th and Ra activities (Murray and Adams 1958; Rogers and Richardson 1964). Potassium feldspar may occur in sandstones as a major component and is even an important factor in the classification of sandstones (McBride 1963; Pettijohn et al. 1987). Thus, the K content, as well as the activity of ⁴⁰K, in the sandstones can vary greatly between K-poor quartz sandstones and K-rich arkoses. In the group SA, the sample Tambacher Sandstein shows a particularly high activity of K and the sample Terra Indigo an increased activity of Th.

Quartzite (group QT) is a metamorphic product of sandstone, which mineralogically consists predominantly of quartz. Similar to the sandstones, it shows low activities for ²²⁶Ra (median = 10.02 Bq kg^–1) and ²³²Th (median = 10.67 Bq kg^–1), with a higher variance in the activity of ⁴⁰ K (median = 36.41 Bq kg^–1). Equivalent to sandstones, low concentrations of uranium and thorium are usually expected in a quartzite, with elevated amounts of uranium and thorium often associated with the occurrence of heavy minerals (Jain 1972). In exceptional cases, as with other metamorphic rocks, uranium can be enriched in quartzite via hydrothermal processes, often requiring certain changes in redox conditions (Goswami et al. 2019). Quartzites are usually relatively depleted in potassium due to their high quartz content, although certain mineral phases, such as mica or K-containing clay minerals, can provide higher K concentrations, resulting in higher ⁴⁰K activities (Lindeman et al. 2020). In the QT group, the Vasa quartzite sample has a high K activity, and the Masi quartzite sample has very high K and Th activities.

The clayey rocks (group SF) show a very high variance of the activities of ²²⁶Ra (median = 29.92 Bq kg^–1) and ⁴⁰K (median = 591.75 Bq kg^–1), while the activity of ²³²Th (median = 36.90 Bq kg^–1) is less scattered. Clay minerals have the ability to incorporate uranium in different ways. The claystones that form in (deep) marine areas would, like limestones, incorporate relatively little uranium and thorium from the water into the crystal lattice. Uranium has a special affinity for organic material and is thus more enriched in sedimentary layers with a high organic content (Cumberland et al. 2016; Klinkhammer and Palmer 1991). In addition, clay minerals have the ability to efficiently adsorb uranium and, to some extent, thorium on their surfaces, which can also result in an increase in U and Th concentrations (Ames et al. 1983; Syed 1999). The metamorphic products of the mudstones, shales and phyllites are largely composed of different clay minerals, such as illite, vermiculite and chlorite, which may contain high levels of potassium. High initial concentrations of potassium in clay minerals, as well as their ability to exchange with soil potassium, can strongly influence K concentrations in rocks (Inoue 1983; Sawhney 1972). Among the samples of the SF group, the sample of copper shale from the Richtelsdorf Mountains has a very high Ra activity.

The gneisses (group GN) show the broadest spectrum of activities of ²²⁶Ra (median = 17.78 Bq kg^–1), ²³²Th (median = 35.48 Bq kg^–1) and ⁴⁰ K (median = 738.3 Bq kg^–1), because they can form as a metamorphic product of many different rocks under diverse P–T conditions. Thus, the concentrations of uranium, thorium and potassium in the gneiss samples are very dependent on the source rock. Gneisses formed from felsic and intermediate igneous rocks can have high to very high radionuclide activities, similar to the FV group, while gneisses formed from sedimentary rocks tend to have medium to low activities (Heier and Rhodes 1966). Apart from the source rock, the geochemical composition of gneisses also depends strongly on the type of metamorphism, whereby circulating fluids can also influence the concentrations of potassium and uranium. In the GN group, the Shiwakasi sample has a particularly high activity of Ra and the Giallo California sample a high activity of Th.

Using Eq. 1, building materials can first be tested generally for their radiological hazard with I index value (European Commission 1999; Gehrcke et al. 2012; Markkanen 1995). For the solid building materials used, the limits are: I > 1—radiologically hazardous and prohibited (dose of 1 mSv a^–1); I > 0.5 more precise controls are needed (dose of 0.3 mSv a^–1). Since this set of samples concerns building materials that are to be used only superficially in lower thicknesses, these limits are correspondingly I > 6 and I > 2. With the maximum value of I = 1.87 for the Giallo California sample, no analysed sample exceeds the limit for further control.

No general statements about the radiological hazards of different rocks should be made solely on the basis of lithology, but clear differences can be observed for the different rock groups (Fig. 3, Table 1). The majority of the samples from the groups MV, KS, MA and QT are clearly below I = 0.5, while the group SA also exceeds this value with several samples. Groups SF, GN and FV have activity indices mainly in the range 0.5 ≤ I ≤ 1, with individual samples having higher indices up to I = 1.87. In addition, it should be noted that these groups have a very low activity index. In addition, it should be borne in mind that these natural stones are installed in households as thinner cover slabs. Thus, significantly lower activity indices of these analysed building materials are to be expected in reality. Thus, the use of these radiologically analysed products should be permitted by law, without further investigations. The activity indices are clearly controled by the thickness (d = 20 cm) of the building materials, whereby the distribution of the activity indices at lower thicknesses gives the same pattern with systematically lower values (not shown here but see “Discussion” in European Commission 1999 and Bundesamt für Strahlenschutz 2020).

Descriptive statistics are presented for ²²²Rn and ²²⁰Rn exhalation rate and their respective emanation coefficients in Tables 1 and 2. ²²⁰Rn exhalation rate is higher than ²²²Rn exhalation rate by a order of magnitude of 3 due to the shorter half-life of ²²⁰Rn. ²²²Rn exhalation rate ranges from 0.002 to 0.440 Bq kg^–1 h^–1 with a mean of 0.041 Bq kg^–1 h^–1, whereas ²²⁰Rn exhalation rate ranges from 95 to 463 Bq kg^–1 h^–1 with a mean of 98 Bq kg^–1 h^–1. The ²²²Rn emanation coefficient ranges from less than 1 to 40%, averaging 8%, while the ²²⁰Rn emanation coefficient ranges from less than 1 to 31%, averaging 5%. ²²²Rn exhalation rate is more variable than ²²⁰Rn exhalation rate, as shown by the larger coefficient of variation. Conversely, the ²²⁰Rn emanation coefficient is more variable than ²²²Rn emanation coefficient. The ratio between ²²²Rn emanation coefficient and ²²⁰Rn emanation coefficient shows that the first is, on average, two times higher than the later.

All variables present a positive skewness larger than 1, indicating strongly assymetric distributions. The kurtosis is also larger than the kurtosis of the normal distribution (of 3), indicating strong deviations from the normal distribution. Thus, nonparametric correlation tests such as the Spearman rank correlation coeficient were computed to assess the relationship between ²²²Rn and ²²⁰Rn exhalation rate and their respective emanation coefficients. The results of the Spearman rank correlation indicate a statistically significant correlation between ²²²Rn and ²²⁰Rn exhalation rates (R = 0.40, p value = 0.006, degrees of freedom = 43) and ²²²Rn and ²²⁰Rn emanation coefficients (R = 0.44, p value = 0.002) for a significance level of 0.01.

Data were grouped according to sample groups described in Table 1 and Fig. 3. In Fig. 4, the felsic rocks (FV) present the highest median exhalation rates for both ²²²Rn and ²²⁰Rn, followed by metamorphic rocks (SF) such as slates, phyllites and metapelites (Fig. 4a and b). The lowest exhalation rates are observed in mafic rocks (MV), limestones and travertines (KS). Quartzites also present a low median ²²²Rn exhalation rate compared to other sedimentary rocks and metamorphic rocks (SA and SF groups, respectively); however, their median ²²⁰Rn exhalation rate is similar to sedimentary and metamorphic rocks, namely to the SA and SF sample groups. Marbles also present median ²²²Rn and ²²⁰Rn exhalation rates similar to the SF group. Gneisses present a low median ²²²Rn exhalation rate but high median ²²⁰Rn exhalation rate compared to other groups. ²²²Rn and ²²⁰Rn exhalation rates are highly variable in the GN, FV and SF units, as shown by the range of values in the box and whiskers plot (Fig. 4).

The median ²²²Rn emanation coefficient is only higher than 10% in the SA and QT units. Values for the emanation coefficient generally lower than 30% are in accordance with typical values reported in the literature for a variety of materials (e.g. Sakoda et al. 2011). The lowest median values for the ²²²Rn emanation coefficient are observed in the GN unit, followed by MV, FV, KS, SF and MA units. The median ²²⁰Rn emanation coefficient is fairly similar among sample groups, with median values lower than 10% in all studied units.

The FV unit present the highest variability in terms of both the ²²²Rn and ²²⁰Rn emanation coefficients, and may exceed 30%. Pereira et al. (2017) report median ²²²Rn emanation values ranging from 19 to over 30% in granitic rocks, much higher than the median values reported in the present work for FV. Domingos and Pereira (2018) report median ²²²Rn emanation values of 16% for weathered metamorphic rocks, which are also higher than the median values reported in the present work for the SF unit. However, the increase in the ²²²Rn emanation values reported by Domingos and Pereira (2018) is linked to the high degree of chemical and physical alteration. Sêco et al. (2020) reported median ²²²Rn emanation values lower than 24% for sedimentary rocks outcropping in the Lusitanian Basin (Portugal), similarly to the results obtained in the present study (Fig. 4c). The lowest ²²²Rn emanation values reported by Sêco et al. (2020) correspond to sedimentary rocks presenting a high carbonate fraction, such as limestones, dolostones and dolomitic limestones. In the present study, the lowest ²²²Rn emanation values are also observed in limestones (KS) when compared to other sedimentary rocks (SA).

The set limits of the activity indices correspond to the limits of the effective doses to which people may be exposed to. According to the principles of radiological safety, all building materials that produce a dose of H > 1 mSv a⁻¹ must be comprehensively controlled and may only be used in special cases (European Commission 1999; Markkanen 1995). However, it is recommended that products with a dose of H > 0.3 mSv a⁻¹ also be examined radiologically before use. In Germany, the population may be exposed to a maximum dose of H = 1 mSv in a calendar year (European Commission 1999; Bundesamt für Strahlenschutz 2020), whereas occupationally exposed persons may be exposed to a dose of H = 20 mSv in a calendar year (European Commission 1999; Bundesamt für Strahlenschutz 2020).

Here, the equivalent doses of the samples were determined in the assumed case with the distance s = 1 cm and the exposure time of 8760 h (corresponding to a whole year) for individual radionuclides (Fig. 5a–c), as well as a total sum (Fig. 5d).

The equivalent doses were calculated using specific software, assuming radioactive point sources randomly distributed. A remarkable observation is that with this method the dose values of the nuclide ²³²Th are several orders of magnitude lower than the doses of ²²⁶Ra and ⁴⁰K. As with the activities, clear differences are observed between the different groups, whereby a generalization by rock type on the basis of the equivalent doses is also not correct, since the data within the groups partly show a strong variance. In the distribution of equivalent doses of the individual nuclides, the patterns of the activity distributions (Fig. 3) can be found again. The proportionality of the doses to the activities has also been reported by Markkanen (1995). For the dose of ²²⁶Ra, the MV, KS, MA and QT groups have the lowest values, with the SA group having slightly higher doses and the FV, GN and SF groups having very high scatter and highest doses. For the doses of ²³²Th, the MV, KS, MA and QT groups also have the lowest values, with SA and SF having slightly higher values with moderate scatter and GN and FV having high doses with strong variance. At ⁴⁰K, the KS group has the lowest doses, with MV showing slightly increased doses with smaller variance, and the MA, QT and SA groups showing slightly increased doses with greater variance. The groups FV, GN and SF have the highest dose values with the highest variances. The equivalent doses, calculated on s = 1 cm spacing, have assumed values between 0 and 2.61 mSva^–1, with a total of 24 samples showing a critical dose of H > 1 mSv a^–1 (three samples of which, Shiwakashi, Branco Micaela and Waldstein Granite with doses H > 2 mSv a^–1) and theoretically should not be used. As already mentioned, the equivalent dose is strongly dependent on the distance to the radioactive point source, so that the maximum doses of the sample set decrease for s = 5 cm to Hmax = 0.10 mSv a^–1 and for s = 10 cm to Hmax = 0.03 mSv a^–1. The dependence of the equivalent dose on the distance from the radioactive source is exemplified for the sample Shiwakashi in Fig. 6, which showed the highest equivalent doses from the whole sample set. The equivalent dose decreases in a quadratic relation to the distance, so that already at s = 20 cm hardly any radiation dose is to be expected. The distance s = 1 cm was chosen for Fig. 6 because this represents the minimum distance in the calculations at which a number of samples exceeded the legal dose limit of H = 1 mSv a^–1. Since no human being is in this proximity to the slabs and tiles made of these natural stones throughout the year, the radiation from these samples poses no danger and they may be used legally without restrictions.

The samples from the different rock groups classified in Table 1 were compared with the corresponding analytical results from the existing literature and presented in Tables 3, 4, 5, 6, 7, 8, 9, 10. The presented data given in Tables 3, 4, 5, 6, 7, 8, 9, 10 refer to the following references: [1] Bundesamt für Strahlenschutz (2020), [2] Deutscher Naturwerkstein-Verband (2019), [3] Gehrcke et al. (2012), [4] Yalcin et al. (2020), [5] Ahmed et al. (2006), [6] Örgün et al. (2007), [7] El Aassy et al. (2011), [8] Marocchi et al. (2011), [9] Kovler et al. (2002), [10] Madruga et al. (2019), [11] Shohda et al. (2018), [12] Weng (1996), [13] Mohamed et al. (2016), [14] Rafique et al. (2014), [15] Turhan et al. (2009), [16] Aykamis and Kilic (2011), [17] Iqbal et al. (2000), [18] Pereira et al. (2013), [19] Zeghib et al. (2016).

These literature values should only serve as a general classification of the samples used in this study. These literature values do not represent typical activities for the individual rock types. For the comparison, in most cases the median values of the activities A of the individual groups (calculated from Table 1) were determined.

Radiological studies of granites from different locations are very common in the literature, as they often have amount of radiological components and are often used as natural stone slabs (Myatt et al. 2010; Tzortzis et al. 2003). The activities of the granites of ²²⁶Ra from the literature range from 39 to 133.31 Bq kg^–1, and the median from the granites from this project is located at 105.35 Bq kg–1. The literature values for ²³²Th activity range from 11.7 to 210 Bq kg^–1, while the median of the granites of this project is 50.67 Bq kg^–1. In the literature, there is also a wide variation in the activities of ⁴⁰K between 762.5 and 2012.03 Bq kg^–1, with the median value of the studied granites in this project being 1003 Bq kg–1. This comparison of the granites is shown in Table 3.

Gneisses have also been investigated for their radioactive properties in several studies. The gneisses from the literature have ²²⁶Ra activities in the range of 9.70 Bq kg^–1 and 352 Bq kg^–1, while the median for gneisses from this project is 17.78 Bq kg^–1. The activities of ²³²Th from the literature vary in the range of 8.94–100 Bq kg^–1, and the median for gneisses from this project is also 35.55 Bq kg^–1. The activities of ⁴⁰K of the gneisses from the literature ranged from 490 to 1569.46 Bq kg^–1, whereas the median of the gneiss analyses in this project is 738 Bq kg^–1. Marocchi et al. (2011) analysed the natural stone Kashmir White (Table 1). The measured values of this sample only partially agree with the literature data, especially large discrepancies are observed in the activities of ²²⁶Ra and ⁴⁰K. The comparison of the gneisses is given in Table 4.

The rocks of the MV group given in Table 1 have generally not often been examined for their radiological character in the literature. The basalt Vietnam Black has significantly lower activities in all three measured nuclides than the other basalts from the literature. The Virginia Black sample has ²³²Th activity in the same order of magnitude of the literature data, with ²²⁶Ra activity slightly lower and ⁴⁰K activity far lower than is the case for the metagabbro samples from the literature. The trachyandesite from Armenia also has significantly lower activities in the three radionuclides than the literature data. The Verde Malenco sample has significantly lower activities in the measured radionuclides (all below the detection limit) than the other serpentine samples from the literature. The amphibolite sample, Via Lattea, has similar activities to the amphibolite analyses from the literature. For the comparison of the mafic rocks and their metamorphic products, see Table 5.

Sands and sandstones have often been studied radiologically in the literature, as they are the most common sediments on Earth. The activity of ²²⁶Ra varies in the literature data between 3.1 and 104.23 Bq kg^–1, with a median of 16.37 Bq kg^–1 for the sandstones from this project. The activity of ²³²Th is in the range of 3.7 Bq kg^–1 and 180.4 Bq kg^–1 in the literature data, whereas the median from this project is also 30.69 Bq kg^–1. ⁴⁰K has activities ranging from 39.82 to 1421 Bq kg^–1 in the literature data, with the median of the sandstones from this project being 305 Bq kg^–1. The comparison of the sandstones is shown in Table 6.

The pelitic rocks and their metamorphic products, schist and phyllite, have been studied for their radioactive characteristics in some papers. In the literature data, these rocks have ²²⁶Ra activities ranging from 7.52 to 68.2 Bq kg^–1 and the median for the clayey rocks from this project is 29.92 Bq kg^–1. The activities of ²³²Th for these clayey rocks from the literature range from 31.74 and 65.3 Bq kg^–1, a range where the median from this project 37.89 Bq kg^–1 is included. The activities of ⁴⁰K vary in the literature data between 246.03 and 1016 Bq kg^–1, the median from this project is in this range with 592 Bq kg^–1. The comparison of these rocks is shown in Table 7.

Even if the limestones and travertines are not particularly dangerous radiologically, there is published work on their radioactive character. The activity of ²²⁶Ra of limestones from the literature varies between 5 and 135.97 Bq kg^–1, whereas the median of the carbonates from this project is 8.04 Bq kg^–1. The ²³²Th activities from the literature take values in the range of 3.1 Bq kg^–1 and 32.28 Bq kg^–1, whereas the median of the current project is somewhat lower at 0.90 Bq kg^–1. The activities of ⁴⁰K from the literature range from 20 to 251.31 Bq kg^–1, whereas the median from this project is also lower at 18.50 Bq kg^–1. The comparison of the carbonate rocks is shown in Table 8.

Besides limestone, quartzite is another lithology that has been studied less frequently due to its radiological insignificance. The activities of ²²⁶Ra from the literature data vary between 6.94 and 77.5 Bq kg^–1, with the median from this project being 10.28 Bq kg^–1. The activity of ²³²Th from the literature ranges from 6.3 to 10.54 Bq kg^–1 and the median from this project is 12.35 Bq kg^–1. The ⁴⁰K activities from the literature data take values from 140 to 226.4 Bq kg^–1, with the median from the current project being 165 Bq kg^–1. The comparison of the data from quartzite can be seen in Table 9.

Among “granites” in the international trade, the petrographic description is often not correctly denominated; therefore, sometimes marbles are also described as granitoges. Thus, radiological data of marbles can also be found in numerous works. The activities of ²²⁶Ra from literature data vary from 2 to 95.17 Bq kg^–1, with the median from this project being 9.43 Bq kg^–1. The activities of ²³²Th from the literature range from 0.1 to 110.73 Bq kg^–1, whereas the median from this project is 2.01 Bq kg^–1. The activities of ⁴⁰K in the literature range from 0.8 to 1054.65 Bq kg^–1, with the median from this project being 62.6 Bq kg^–1. The comparison of the marbles is shown in Table 10.

The potential radiation exposure for humans can be calculate by very complex models (e.g. Markkanen 1995; Myatt et al. 2010). For this purpose, an array of different parameters is important and needs to be considered, such as the radiation activity of the natural stone used, the total volume of the installed stone, the cumulative daily and yearly duration of residence of a person in the observed room as well as their average distance to the walls (Zeghib et al. 2016).

To constrain our results in the context of everyday life, the potential annual equivalent doses were calculated using two extreme, hypothetical approaches. The first model, “Small room”, describes a square room, where the floor, ceiling and walls are covered by 3-cm-thick stone tiles. The dimensions of the room are 2 × 2 × 2 m and there are no further objects (doors, windows etc.) inside the room. It is assumed that the room is completely shielded from the external radiation; therefore, the effects of the background radiation (cosmic and terrestrial radiation) are not considered. The radioactive dose for the centre of the room is calculated. Since the origin of the measured activities are point sources, it is necessary to alternatively recalculate the activities for a surface. Therefore, a volume of 1 cm³ is assumed for each single point source. In such a manner, a total of 40,000 point sources are quantified for the total of a 6 × 4 m² (24m²) wall surface area for each side with the thickness of 1 cm. Subsequently, there are three 1-cm-thick “layers” defined from the assumed total tile thickness of 3 cm. So the total amount of point sources adds up to 120,000 for the wall in total. Since the two rear layers are covered by the layers of point sources in front of them, an effect of attenuation is generated for the reference point in the middle of the room. To calculate this effect of attenuation, a shielding calculator from the DAMP engineering office (Ingenieurbüro DAMP) was used to determine the attenuation factors (SF) for the rear (SF₃) and the middle layer (SF₂) in the wall; it is not necessary for the front layer (SF₁), as there is no shielding material between it and the reference point. From the selection of materials for the calculator, normal concrete was chosen as shielding material, since it best represents the shielding parameters of the natural stones. Since each radionuclide has a characteristic equivalent dose rate constant Γ_H [nSv qm h⁻¹ GBq⁻¹], they also possess distinct attenuation factors (Table 11). The following equation (Eq. 4):

is applied as a basis for the calculation of the equivalent dose rate H [μSv h⁻¹], where A is the activity of the respective nuclides (²²⁶Ra, ²³²Th, ⁴⁰K) in GBq and r is the distance from the radiation source in metre (m) using the inverse-square law. For the assumed case that a 2-m-tall person is in the centre of the room, the average distance of the wall surfaces to the centre of the room is calculated with the equation:

For the application of this model, Eq. (5) was modified to Eq. (6).

Hence, the equivalent dose rate H is calculated in three separate terms, as different attenuation factors are effective for each respective cladding with the tiles. The summed up terms are divided by the volume of the sample box (V_B), as the activity units are given in GBq kg⁻¹ rather than in Bq per sample. The certified volume of 250 ml for the vessels is referred to a normal fill level. A volume of 280 ml was adopted for the calculations, since the sample boxes were completely filled. The volume of 280 ml was estimated by filling a single sample box with water. Additionally, the calculated equivalent dose rate is multiplied by the number of walls and the units are converted from nSv h⁻¹ to mSv a⁻¹.

For the second model, “Coffin”, Eq. 5 was adjusted to room dimensions of 1.8 × 0.8 × 0.4 m. Thereby, two surfaces with 1.44 m², two with 0.72 m² and two with 0.32 m². The average distances to the centre of the room of 0.73 m (r_min), 0.8 m and 0.97 m (r_max), respectively, were assumed. The background radiation was neglected in this model as well.

The calculated annual dose rates for the models 1 and 2 are displayed in Fig. 5. The activity values of at least one of the measured radionuclides laid below the limit of detection for the total of 15 out of 82 investigated samples. For the affected nuclides in these samples, an activity of A = 0 Bq was set for the further calculations. The calculated equivalent dose rates from the model 1 vary from  < 0.01 to 0.79 mSv a⁻¹ (for the sample Giallo California). Thus, no measured sample exceeds the annual dose rate of 1 mSv a⁻¹, which is set as the maximal value for the German regulations. The annual dose rate for a total of 24 samples was calculated to be in the critical region of 0.3 to 1 mSv a⁻¹ and should therefore not be installed as stone tiles prior to further investigations. It is noticeable that the annual dose rates calculated based on the model 2 are significantly higher than for the model 1. For the model 2, the annual dose rates vary between < 0.01 and 1.29 mSv a⁻¹, calculated for the sample Giallo California. An annual dose rate exceeding the limit of 1 mSv a⁻¹ was calculated for a total of 16 samples, whereas for another 34 samples the determined annual dose rate was in the critical area of 0.3–1 mSv a⁻¹. The higher annual dose rates from the second model are derived from the smaller distance of the radioactive sources to the centre of the room (inverse-square law), as the goal of this model was to enclose a person as close as possible with stone tiles from all sides. Even though the approach “what equivalent dose rate affects a person when enclosed in a coffin for a year” is not entirely realistic, it is shown that even when enclosed with material with the highest dose rate values (here Giallo California) of 1.29 mSv a⁻¹, a dose far below the maximum dose of 20 mSv a⁻¹ is experienced, which is set for people with occupational radiation exposure in Germany (Bundesamt für Strahlenschutz 2020).

The contribution of the building materials to the indoor radon can be simulated on the basis of the data obtained for the exhalation rate of the same materials. For this goal, the radon concentration (C_Rn) can be calculated from the following equation (Eq. 7) taken also in account the ventilation rate:

were E_m is the exhalation rate by mass (in Bq kg⁻¹ h⁻¹), M is the mass of the stone used as building material (in kg), λo is the radon decay rate (0.0076 h⁻¹), λv is the ventilation rate (in h⁻¹), and V is the volume of the room (in m³). M is the product of the density of the material by the volume of the tiles used. The product of E_m * M is designated also as the radon entry (in Bq h⁻¹).

The radon concentration is calculated for a room with the dimensions of 4 × 3 × 2.5 m, including a window of 1 × 1 m and a door with 2 × 1 m. Tiles of stone materials with different thickness (variable between 0.01 and 0.2 m) cover all the walls and the floor (Fig. 7). It is assumed no other contribution to indoor radon beside the stone material. Different ventilation rates is allowed and tested, assuming a value of λv = 0.2 h⁻¹ as representative of a poorly ventilated room and 0.5 h⁻¹ as of the opposite case.

The results related to the worst situation in what concern to radon exposure in the room, considering a low ventilation rate, is shown in Fig. 8 for the different lithological groups. In the first case (tiles with a thickness of 1 cm), all the stone materials comply with the european legislation, with modelled maximum indoor radon less than 100 Bq m⁻³. For tiles with thickness of 3 cm the same scenario is forecasted, despite the general increase in the radon concentrations; the highest averages are related with the FV group (granites), followed by the gneisses (GN group).

For higher tiles thickness, and for poorly ventilated spaces, some of the building materials can induce indoor radon concentrations above the action limit, as expected all included in the FV group (Fig. 7). This is the case of the Waldstein, the Flossenburger, the Amarelo Real, for 10-cm-thick tiles, but for higher thickness (20 cm) others show the same behaviour, as the case of the Coral Red and, in less extend, the Branco Micaela and the Kuperscheifer types; this last rock is the only one not included in the FV group (SF).

The ventilation is a crucial parameter to control the indoor radon concentrations, as expected, and for higher rates (λv = 0.5 h⁻¹) only the more problematic rocks (Waldstein, the Flossenburger, the Amarelo Real) are able to increase the indoor radon concentrations up to the action limit (Fig. 8).