4.2: Classroom Activity
- Page ID
- 46408
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Mineral Identification of Calcite and Quartz Using X-Ray Diffraction Data
Figure \(\PageIndex{1}\): Multimodal compositional analysis of ancient Roman concrete. EDS maps of a freshly fractured surface (A) and polished cross-section (D) are quantified, and each pixel is replotted as a relative ratio of calcium, silicon, and aluminum on a ternary diagram (B and E), with the most Ca-rich phases shown in red and denoted by the red circle near the Ca vertex in (B). Pixels in the ternary diagrams (B and E) and phase maps (C and F) were colored on the basis of the cluster of EDS data to which they belong. Surrounding each of the lime clasts is a clear rim of a compositionally unique phase (the hydration rim), which is denoted by the light blue zones in (F) and is shown at higher magnification at right with color-coded text for additional clarity. Powder XRD of a relict lime clast (G) and its surrounding matrix (H) confirms the presence of calcite and quartz and suggests the presence of vaterite among other phases [e.g., halite (*) and volcanic minerals (diopside, leucite, etc.) (+)] in the mortar. (From Seymour et al. 2023.)
In this activity, we will use XRD data to identify calcite and quartz minerals. In subplot G of Fig. \(\PageIndex{1}\) above, the XRD spectra for calcite and quartz are shown. In XRD, X-ray photons are incident on the sample crystals and are scattered by the atoms in the crystal; the angles of the scattered X-rays are related to the orientation of the sets of atomic planes in the crystal. Bragg's law relates the lattice spacing \(d \) of a set of atomic planes and the diffraction angle \(\theta \):
\[2d\sin\theta = n\lambda\]
where \(\lambda=0.154\ \rm nm \) is the wavelength of the X-rays from copper emission used in the experiments. By identify the several sets of atomic planes, one can finger print the identify of the mineral. For example, the strongest diffraction peak in the calcite spectrum (red) occurs at the angle of \(2\theta = 29.2^\circ \). From Bragg's law, one can determine the lattice spacing to be \(d=0.305\ \rm nm \); this distance matches the spacing of the (104) atomic planes of calcite.
- Locate the four strongest diffraction peaks for calcite (red) in subplot G. From the angle of diffraction of these peaks, use Bragg's law to identify the corresponding atomic plane lattice spacing \(d \). Verify that all four lattice spacings belong to the crystal calcite.
- Locate the four strongest diffraction peaks for quartz (blue) in subplot G. From the angle of diffraction of these peaks, use Bragg's law to identify the corresponding atomic plane lattice spacing \(d \). Verify that all four lattice spacings belong to the crystal quartz.
Supplemental Materials:
Libretexts: X-ray diffraction identification of minerals.