**4. SEDNORM, SEDMIN, PELNORM and other**

SEDNORM [5] is a method for calculating standard minerals from unconsolidated sediments and coal ash from full chemical analysis. As with the Rittmann standard, different standard variants can be selected depending on the available data (e.g., clay chemistry). According to the authors, SEDNORM is suitable for use on sandstones, shales, and carbonate rocks. The calculation process of SEDNORM is described but is not available online as a program.

SEDMIN [6] is a standard mineral calculation for sediments that focuses on the minerals smectite, chlorite, kaolinite, illite, and ambiguous sericite. Within the full chemical analysis, TiO2 is used to calculate kaolinite. According to the author, SEDMIN is able to predict predominant clay minerals even with atypical sample data. A calculation program for SEDMIN is available online [21].

PELNORM [7] is a calculation method for clay minerals and pelitic rocks from data as in **Table 1**. The procedure differentiates between the variants with missing smectite (A) and existing smectite (B). K2O can be used to determine both orthoclase (Kfeldspar, or) (A1, B1) or illite (ill) (A2, B2) plus orthoclase. According to the authors, the method achieves a good match between normative and modal mineral composition. The calculation steps of PELNORM are described together with program steps in FORTRAN. A computer program is not available online.

## **5. Slatenorm and slatecalculation norm in general**

In a research project from 1989 to 1991, an attempt was made to use a full chemical analysis similar to the CIPW norm for magmatic rocks to make a rather inaccurate norm mineral evaluation for roof and wall slates ([22] and **Table 2** therein). Sericites (muscovite and paragonite), chlorites, quartz, and total carbonates were estimated as the main minerals. Ward and Gómez-Fernandez [23] used the Rietveld method-based Siroquant data processing system for X-ray powder diffraction analysis for the determination of the slate main minerals quartz, feldspar, micas, and chlorites. However, the application of the method was limited to low carbonate Spanish roofing slate. The determined feldspar (albite) values were higher than those of chlorite and likely to be too high. Jung and Wagner [24] created a calculation method similar to the CIPW norm that was ready for practical use. They managed to determine the mineral constituents, and in particular, the content of free quartz with sufficient accuracy for the first time—to some essential practical statements.

The results of such norm calculations have already been used not only in test certificates but also in a manual [25]. Other authors cited such norm calculations together with results of other analyses and found good matches [26]. The results of more than 20 years of application of "slatenorm" [22, 25, 26–30] have shown that the inclusion of additional ore minerals, color-giving minerals, and hydro-micas (especially illite) in the new slatecalculation is reasonable.

The extended method slatecalculation presented here is based on a previous, unpublished program called "slatenorm" [24, 31] (Appendix A and B). The calculations are based on the full chemical analysis (**Table 1**). In the case of slatenorm and slatecalculation norm, a distinction is made between CO2 (= carbonated C) and C (= non-carbonated C, approximate atomic weight = 12.0). In addition, S (approximate atomic weight = 32.1) and not SO3 are being used as a basis. In a first step, the extended algorithm includes the distinction of sulfides. So far, pyrite was the only sulfide calculated in "slatenorm." In many higher metamorphic slates (e.g., slates from Spain), pyrrhotite is predominant and should be included in the calculation because it is more susceptible to oxidation. Therefore, in the first step, the extended algorithm differentiates various sulfides.

The basic calculations of the algorithm, fundamental norm minerals, and chemical formulas are described in a very simplified form below (quoted from [9], detailed flowchart see Appendix A):

$$\text{P}\_2\text{O}\_5 \rightarrow \text{ap} = \text{apatite} = \text{3.3}\text{CaO} \text{ P}\_2\text{O}\_5 \tag{1}$$

S approx*:* Half*;* sofar macroscopically or microscopically determined ! pn pyrrhotite <sup>≈</sup> FeS (2)

$$\text{Residual } \mathbf{S} \to \mathbf{pt.} = \text{pyrite} = \mathbf{FeS}\_2 \tag{3}$$

Fe2O3 and TiO2 ! tm = titanomagnetite = FeO Fe2O3 TiO2, frequently occurring mixture mineral in slates (cf. [22, 32]) At the deficit of FeO in some cases a back calculation (28–31 or 49–51) tm in ru ¼ rutile ¼ TiO2 is needed*:*

$$\text{TiO}\_2 \rightarrow \text{ilm} = \text{ilmenite} = \text{FeOTiO}\_2 \tag{4}$$

$$\text{Fe}\_2\text{O}\_3 \rightarrow \text{he} = \text{hematite} = \text{Fe}\_2\text{O}\_3 \tag{5}$$

$$\mathbf{C} \rightarrow \mathbf{gr} = \mathbf{gr}\\ \text{path} = \mathbf{C} \tag{6}$$

$$\text{CO}\_2 \rightarrow \text{carbonate} \\ \text{(cc} = \text{calcite} = \text{CaO} \text{ CO}\_2 \text{, dol} = \text{dolomite} \tag{7}$$

$$= \text{CaOMgO} \, 2\text{CO}\_2 \, \text{sid} = \text{siderite} = \text{FeOCO}\_2 \, \text{(} \, \text{)}$$

$$\text{Residual CaO} \rightarrow \text{an} = \text{anorthite} = \text{CaO Al}\_2\text{O}\_3 \text{ 2SiO}\_2 \tag{8}$$

$$\text{K}\_2\text{O} \rightarrow \text{mu} = \text{mustkovite} = \text{K}\_2\text{O } \text{\textdegree Al}\_2\text{O}\_3 \text{ \textdegree SiO}\_2\text{ 2H}\_2\text{O} \tag{9}$$

$$\text{Na}\_2\text{O} \rightarrow \text{pa} = \text{paragonite} = \text{Na}\_2\text{O } \text{3Al}\_2\text{O}\_3 \text{ 6SiO}\_2 \text{ 2H}\_2\text{O} \tag{10}$$

The very variable minerals of the chlorite group require more complicated considerations with regard to their composition (see subsection 7).

$$\text{MgO} \rightarrow \text{mc} = \text{\textdegree \text{MgO}} \text{\textdegree 2SiO}\_2 \text{\textdegree H}\_2\text{O} = \text{mc}/\text{\textdegree \text{(srepentre)}} \tag{11}$$

$$\text{FeO} \rightarrow \text{fc} = \text{3FeO } 2\text{SiO}\_2\\\text{2H}\_2\text{O} = \text{fc/3 (greenalite)}\tag{12}$$

$$\text{MgO and Al}\_2\text{O}\_3 \rightarrow \text{mac} = 2\text{MgO Al}\_2\text{O}\_3\\\text{SiO}\_2\text{2H}\_2\text{O} = \text{mac}/2\text{ (amesite)}\tag{13}$$

$$\text{FeO and Al}\_2\text{O}\_3 \rightarrow \text{fac} = 2\text{FeO Al}\_2\text{O}\_3 \text{ SiO}\_2 \text{ 2H}\_2\text{O} = \text{fac}/2 \text{ (daphinite)} \tag{14}$$

With the negative rest of Al2O3 ! (ab, or) = feldspars:

$$\text{instead of pa Na}\_2\text{O} \rightarrow \text{ab} = \text{altitude} = \text{Na}\_2\text{O Al}\_2\text{O}\_3 \text{ 6SiO}\_2 \tag{15}$$

$$\text{instead of } \text{mu} \to \text{K}\_2\text{O} \to \text{or} = \text{orthochastic} = \text{K}\_2\text{O Al}\_2\text{O}\_3 \text{ éSiO}\_2 \tag{16}$$

In case of high Al2O3 – contents the calculation of chloritoid might be necessary:

$$\begin{aligned} \text{instead of } \mathbf{f} \mathbf{a} \mathbf{c} &\to \mathbf{c} \mathbf{t} = \text{chlloritoid} \\ &= \mathbf{F} \mathbf{e} \mathbf{O} \mathbf{A}\_2 \mathbf{O}\_3 \mathbf{S} \mathbf{O}\_2 \mathbf{H}\_2 \mathbf{O} \mathbf{R} \mathbf{s} \text{d} \mathbf{d} \mathbf{u} \mathbf{d} \mathbf{S} \mathbf{O}\_2 \to \mathbf{q} \mathbf{z} \\ &= \mathbf{q} \mathbf{u} \mathbf{r} \mathbf{z} = \mathbf{S} \mathbf{i} \mathbf{O}\_2 \mathbf{R} \mathbf{s} \text{d} \mathbf{d} \mathbf{d} \mathbf{H}\_2 \mathbf{O} \to \mathbf{w} \mathbf{t} \mathbf{r} \to \mathbf{a} \mathbf{q} \end{aligned} \tag{17}$$

The remaining H₂O = aq may have a positive or negative value, and this is the basis for an extended algorithm determining hydro-micas. In the input data, carbon compounds (e.g., CO2 and organic C) and elementary sulfur (S) are not included in the glow loss (or loss of ignition (LOI), but rather subtracted. Furthermore, in the case of predominant FeO compounds, the description of the total amount of Fe as Fe2O3 leads to an unrealistic oxidation gain at the expense of the LOI. Only a carefully corrected LOI can be incorporated in the norm calculation as H₂O = aq but will still be less precise. Thus, the calculated data will have a higher range of variation.
