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Figure 2: Mn and Fe peaks in a pXRF spectrum of urban varnish.
Interpretation of pXRF data
As discussed above, the raw counts data are total counts, or counts per second, in the peaks of the elements of interest. To be useful these data must be converted into physically meaningful quantities. There are several approaches to this.
Mn/Fe counts ratio
The simplest approach to quantification consists of calculating the ratio of Mn counts to Fe counts. This takes advantage of the fact that the Fe content of the bulk sandstone dominates over any Fe content in the varnish, at least in the case of red Triassic sandstone. Hence, the Fe can serve as a 163reference value for normalizing the Mn variations and thus confirms that the varnish has enriched Mn. As shown in Fig. 2, the Fe Ka peaks overlap the Mn peaks. Consequently, the attenuation factors are essentially the same for the two elements, and the counts ratio approximates the mass ratio. This avoids the need to convert the counts into masses. In practice, pXRF spectra are acquired for several points in the varnish along with a similar number of points on the adjacent bare stone for comparison. Fig. 3 presents an example of the application of the Mn/Fe ratio method to an area on the Smithsonian Castle, which shows that the points within varnish patches have significantly elevated levels of Mn.
Figure 3: Plot of Mn/Fe ratios for SW corner of the Smithsonian Castle.
Direct estimate of Mn areal density
The Mn/Fe counts ratio is essentially a qualitative indicator of elevated Mn levels. For a quantitative result the most straightforward approach is to estimate the mass of Mn. To accomplish this, a suitable calibration standard is required. In this project we used a well-characterized set of mudrock (shales, sandstones) samples (HR_01 – HR_65) provided by the manufacturer of the pXRF instrument. To more closely simulate the desert layer structure, McNeill and Cecil prepared a standard consisting of a thin layer of Mn on a glass substrate (McNeil et al. 2009). In either case the result is the total mass of Mn in the beam. This can be normalized to an areal density by dividing the mass of Mn by the beam area. One drawback of this calibration method is that it is valid only for a specific set of instrument settings such as beam current, standoff distance, etc. Thus, these have to be replicated in the field.
Areal density to thickness conversion
Portable XRF is an elemental analysis technique, and consequently the result of the measurements of the varnish is the areal density of the element Mn. However, the conventional literature on desert varnish usually is in terms of layer thickness, because the measurement method is based on optical microscope analysis of cross sections through the varnish (Dorn 2007). Therefore, in order to make comparisons with this literature it is necessary to convert the areal density into an equivalent thickness. However, this gives a nominal or effectiveness thickness that assumes no other minerals are present. This is not directly comparable to desert varnish thicknesses, which usually contains interlayers of clay minerals (Dorn 2007), but it is useful for comparing urban varnish layers on different structures.
Fe/Fe ratio estimate of Mn layer thickness
An alternative approach to estimating the amount of Mn that does not require a calibration standard arises from the overlapping of the Fe and Mn X-ray peaks as illustrated in Fig. 2. A corollary to this relationship is that the two Fe K lines at 6.3 and 7.0 keV bracket the K absorption edge at 6.5 keV in the attenuation factor of Mn. This means that the attenuation of the Fe Kβ is 6 times greater than for the Kα line. This differential attenuation makes it possible to measure very thin layers of Mn on the order of microns on top of the sandstone substrate (Livingston et al. 2020). The Fe X-rays are generated primarily in the bulk of the sandstone, but they are attenuated mainly in the surface layer of Mn. The method requires two pXRF measurements: one on the varnish patch and the other on a nearby area of bare stone. The effective thickness of the Mn layer can be calculated from the decrease of the Fe Kβ/Kα ratio of the varnish point compared to that of the bare stone. This method requires the 164assumption that the Mn is in the form of birnessite. In theory the presence of Fe in the varnish could lead to underestimates of thickness. However, microanalyses of varnish samples have shown that the varnish has very low Fe content (Macholdt et al. 2017b, Sharps et al. 2020). Moreover, sensitivity calculations have shown that the Fe content would have to be greater than 10 % to produce significant error (Livingston et al. 2020).
Field survey design
In order to make the pXRF measurements of urban varnish, it is obviously necessary to find their occurrences. Some have been found simply by random sighting, but there are more systematic approaches. One factor is the type of stone substrate. Most cases have been found on Triassic red sandstone in the United States, occurring in the Newark Supergroup, which is a geological formation that extends from South Carolina to Massachusetts, as shown in the map in Fig. 4.
Figure 4: Map of Newark Supergroup (Grissom et al. 2018).
Triassic building stone can have different local trade names, for instance, Seneca sandstone in the Washington area and Belleville sandstone from New Jersey in the New York City area, but it is essentially the same rock. Lists of buildings constructed with a specific building stone can be found in state geological surveys reports (Merrill and Matthews 1898), histories of local quarries (Peck 2013), architects’ catalogues raisonnés (Ochsner 1982), and architectural preservation studies (Matero and Teutonico 1982). It may be possible to minimize time in field searching for varnish by doing preliminary viewing of candidate buildings online with images from Google Earth.
Preliminary geographical distribution
Selected occurrences of Mn-rich urban varnish identified to date are listed in Table 1. These are divided into two categories: probable, based only on visual appearance; and confirmed, based on XRF detection of elevated Mn levels. In the second category those sites measured by pXRF are indicated in plain font. Asterisk indicate cases where the varnish was sampled and measured using laboratory XRF instruments.
Table 1: Locations with urban rock varnish. * Analyzed by laboratory XRF
| Probable | Confirmed by XRF |
| St. Matthews Cathedral (1895), Washington, DC | Smithsonian Castle (1847–55), Washington, DC |
| Oak Hill Cemetery Gateposts (1865), Washington, DC | Bethesda Fountain Plaza (1864), New York, NY |
| Phillips Collection (c. 1900), Washington, DC | St. James Church (1884), New York, NY |
| Basilica of St. Peter & St. Paul (1864), Philadelphia, PA |
Albany
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