# Improving the Understanding of Chemistry by Using the Right Words: Employing Inorganic Formulas to Convey Chemical Structure

Miguel Reina, Bruno Landeros-Rivera, Gracia Jesuś, Hervé This, Vo Kientza, Antonio Reina

► To cite this version:

Miguel Reina, Bruno Landeros-Rivera, Gracia Jesuś, Hervé This, Vo Kientza, Antonio Reina. Improving the Understanding of Chemistry by Using the Right Words: Employing Inorganic Formulas to Convey Chemical Structure. Journal of Chemical Education, 2025, 10.1021/acs.jchemed.5c00075 . hal-05104222

HAL Id: hal-05104222

https://hal.inrae.fr/hal-05104222v1

Submitted on 9 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
that this new notation system not only clarifies the structural differences between various chemical species but also enhances the overall understanding of chemical structure in educational contexts. By making these distinctions explicit, students and educators can more accurately interpret chemical formulas and their underlying structures.

The addition of precision to this notation, such as the coordination number of each entity, can be very useful for advanced inorganic chemistry courses and, in particular, for solid state chemistry. Herein, we discuss how this novel chemical formula writing can help us gain insights into the structure of crystalline solids, whether there are monoelemental or polyelemental ones, to easily determine the structure and composition of a reticulum. We discuss, as well, the scope and limitations of the proposal.

## PROPOSAL

The notation proposed earlier is based on the addition of slashes (//) to refer to layered structures, understood as a stable and electrically neutral chemical species with a conceptually infinite number of chemical bonds in a two-dimensional network, and brackets ({}), for reticulums, i.e., stable and electrically neutral chemical species with a conceptually infinite number of chemical bonds connecting all the chemical entities within the structure in a three-dimensional network.

To provide deeper structural insights, we suggest including the coordination number of both entities (atoms or ions) within the slashes or curly brackets. In general, the substance /A<sub>m</sub>B<sub>n</sub>/ is a layered structure, and {A<sub>m</sub>B<sub>n</sub>} is a reticulum in which A has a coordination number of *n*, and B has a coordination number of *m*.

### Chemical Formulas for Gaining Insight into Monoelemental Structures

This precision in the notation is useful for monoelemental substances, i.e. substances consisting of atoms of a single element, as demonstrated in the case of carbon diamond {C<sub>4</sub>} and graphite /C<sub>3</sub>/ corresponding to a reticulum where each carbon atom is bonded to four others and to a layered structure where each carbon atom is bonded to three others, respectively (Figure 1).<sup>5–7</sup>

In this regard, it can also be used to refer to metallic substances such as lithium, sodium, potassium, gold, nickel, etc. When used for metals, the crystalline structure of the metal is

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Diamond {C<sub>4</sub>} and graphite /C<sub>3</sub>/ structures. The curly brackets indicate that the chemical system is a reticulum, while the slashes indicate that the system is a layered structure. The numbers 4 and 3 in subscript, correspond to the coordination of carbon in each material (see Figure S1).</figcaption></figure>

<table><caption>**Table 1.** General Structures of Monoelemental Solids</caption><thead><tr><th>Structure</th><th>Formula</th><th>Example</th><th>Reference</th></tr></thead><tbody><tr><td>Simple cubic (cp)</td><td>{Po<sub>6</sub>}</td><td>{Po<sub>6</sub>}</td><td>8</td></tr><tr><td>Body-centered cubic (bcc)</td><td>{M<sub>8</sub>}</td><td>{Li<sub>8</sub>}</td><td>9</td></tr><tr><td>Face-centered cubic (fcc)</td><td>{M<sub>12</sub>}<sub>fcc</sub></td><td>{Au<sub>12</sub>}<sub>fcc</sub></td><td>10</td></tr><tr><td>Hexagonal (hcp)</td><td>{M<sub>12</sub>}<sub>hcp</sub></td><td>{Tl<sub>12</sub>}<sub>hcp</sub></td><td>11</td></tr></tbody></table>

given by the formula itself (Table 1, Figure 2). For example, metallic polonium is a substance whose crystalline structure is simple cubic (cp). The formula to represent metallic polonium would then be {Po<sub>6</sub>}, where each polonium atom is bonded to 6 others.<sup>8</sup> On the other hand, metallic lithium shows a body-centered cubic structure (bcc), which can be represented as {Li<sub>8</sub>}, where each lithium atom is surrounded by 8 others.<sup>9</sup> For face-centered cubic (fcc) and hexagonal close-packed (hcp) structures, each atom would be surrounded by 12 others, so we propose to distinguish face-centered cubic gold, {Au<sub>12</sub>}<sub>fcc</sub> from hexagonal thallium, {Tl<sub>12</sub>}<sub>hcp</sub>.<sup>10,11</sup> Table 1 presents the general notations for solid structures, and Figure 2 illustrates those structures.

With the exception of mercury (mp 234.3 K), all metals are solid at room temperature (298 K). However, this can be ambiguous because cesium (mp 301 K) and gallium (mp 303 K) can be liquids.<sup>12</sup> Figure 3 shows the most common crystalline structures of metals at 298 K. As can be seen, body-centered cubic, face-centered cubic, and hexagonal close-packed structures are the most common. Metallic polonium will then be a substance with formula {Po<sub>6</sub>}, tungsten a metal with formula {W<sub>8</sub>}, rhodium will have the formula {Rh<sub>12</sub>}<sub>fcc</sub> and osmium will be noted {Os<sub>12</sub>}<sub>hcp</sub>.

Metals, as well as other reticulums, can show polymorphism. When exposed to variations in temperature and/or pressure, a metal structure can be modified, with each distinct form representing a specific polymorph.<sup>13</sup> For example, iron has a body-centered structure at 25 °C and 1 bar of pressure, resulting in {Fe<sub>8</sub>}. However, at higher temperature, ca. 910 °C, there is a transition to a face-centered structure. Thus, the formula for this substance will be {Fe<sub>12</sub>}<sub>fcc</sub>. Increasing the pressure and temperature enables the transition from {Fe<sub>8</sub>} to {Fe<sub>12</sub>}<sub>hcp</sub> which corresponds to a hexagonal close-packed structure. Our notation enables us to easily distinguish the structure of iron polymorphs, in contrast to the usual notation in which α-Fe, γ-Fe, and ε-Fe represent bcc, fcc, and hcp structures, respectively.<sup>14,15</sup> Figure 4 shows a phase diagram of metallic iron, in which three main structures are present.

### Chemical Formulas for Gaining Insight into Binary Structures

Usually, in inorganic chemistry textbooks, common structures are designated by the name of one of the compounds crystallizing within that structure, since there is not a correspondence to metal arrays such as cp, bcc, fcc, or hcp.<sup>12</sup> It is very common to find sentences like “CsCl type structure” or “rock salt structure”.<sup>12,16,17</sup> Commonly, the structure of binary systems is defined by considering only one of the two chemical entities involved.<sup>17</sup> For example, to visualize the fcc structure of sodium chloride, one should focus only on the chloride or the sodium cation.<sup>17,18</sup> Eight chloride ions form the corners of a cube, and six more are centered in the faces (Figure 5). The arrangement is the same when only the sodium cations are
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Examples of cp, bcc, fcc, and hcp structures with their corresponding formulas. (see Figures S2–S5).</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Structures of metals at 298 K.<sup>12</sup></figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Pressure–temperature phase diagram for iron.<sup>12,13</sup> The proposed notation simplifies and promotes understanding.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Simple cubic and sodium chloride {Na<sub>6</sub>Cl<sub>6</sub>} type structures (see Figure S6). The assumption of a simple cubic structure is an approximation, given that sodium chloride possesses a characteristic rock salt structure.</figcaption></figure>

considered. In some textbooks, the rock salt structure is defined as the interpenetration of two fcc structures, one of sodium cations and one of chloride anions.<sup>12,18</sup> Other manuals consider that sodium chloride structure to be an fcc arrangement of chlorides with sodium cations in octahedral interstitial holes.<sup>19</sup>

However, considering all chemical entities within the structure, not anions or cations merely, the resulting reticulum is similar to a simple cubic-type structure. Chloride and sodium cations alternately occupy the corners of the cube.<sup>20</sup> The notation for this reticulum using our novel formula writing is {Na<sub>6</sub>Cl<sub>6</sub>}, somewhat analogously to monoelemental structures where a simple cubic structure is noted {M<sub>6</sub>}.

This notation implies that each sodium cation is surrounded by 6 chlorides and vice versa. Strictly speaking, describing sodium chloride as having an fcc-type or simple cubic-type structure is an approximation. In reality, sodium chloride possesses a unique sodium chloride structure (or rock salt structure), which is distinct from fcc, cp, or any other metal arrangement. However, based on this notation proposal, we can generalize that all sodium chloride-type compounds will follow a formula of the type {A<sub>6</sub>B<sub>6</sub>}.

Cesium chloride, classically written CsCl, is well-known for its primitive (simple) cubic lattice.<sup>17,21</sup> However, this classification considers two interpenetrating simple cubic arrays in which the corner of one cell sits at the body-center of the other (Figure 6).

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Body-centered cubic and cesium chloride {Cs<sub>8</sub>Cl<sub>8</sub>} type structures (see Figure S7). The assumption of a body-centered cubic structure is an approximation, given that cesium chloride possesses a characteristic structure.</figcaption></figure>

The resulting reticulum, considering every chemical entity, is similar to a bcc-like crystalline structure, where each cesium cation is surrounded by 8 chlorides and each chloride is surrounded by 8 cesium cations. In fact, Partington stated that cesium chloride crystallizes within a bcc-type structure.<sup>20</sup> Using our proposed notation, cesium chloride formula will be {Cs<sub>8</sub>Cl<sub>8</sub>}, analogously to bcc metallic lattices noted {M<sub>8</sub>}.
Similar to the previous case, describing cesium chloride as having a simple cubic or body-centered cubic structure is an approximation. In reality, it adopts a unique cesium chloride-type structure. Based on our formulation, we can generalize that all cesium chloride-type compounds will follow a formula of the type {A<sub>8</sub>B<sub>8</sub>}.

Zinc sulfide, ZnS, crystallizes in two polymorphs, zinc blende and wurtzite. Zinc blende has an fcc-like structure in which zinc atoms are placed in the corner of a cube and in the center of the faces, while sulfur atoms are placed in the tetrahedral interstitial holes (Figure 7). Each zinc atom is surrounded by 4 sulfur atoms and vice versa, resulting in a diamond-type structure ({C<sub>4</sub>}) (See Figure 1 vs Figure 7).<sup>12,22</sup> Wurtzite has a hexagonal structure where sulfur atoms form a hexagonal close-packed structure, and zinc atoms occupy half of the tetrahedral voids. Each sulfur atom is tetrahedrally bonded to 4 zinc atoms, and vice versa (Figure
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Zinc blende {Zn₄S₄}fcc and wurtzite {Zn₄S₄}hcp type structures (see Figures S8 and S9).</figcaption></figure>

7).¹²,²³ The notation for both structures would then be {Zn₄S₄}. However, as stated above, we can distinguish between fcc and hcp structures, thus zinc blende would then be {Zn₄S₄}fcc and wurtzite {Zn₄S₄}hcp.

It is important to note that, although every wurtzite-like structure will have the same notation {A₄B₄}hcp, this is not the case for every hexagonal close-packed structure. For example, nickel arsenide has a hexagonal structure in which both nickel and arsenic atoms are surrounded by 6 arsenic or nickel atoms, respectively,²⁴ resulting in the notation {Ni₆As₆}hcp (see Figure S10).

Using this notation system, it is possible to determine the most common crystalline structures for binary inorganic solids from their chemical formula, enabling the identification of sodium chloride-, cesium chloride-, fluorite-, zinc blende-, wurtzite-, β-cristobalite-, and rutile-type structures (Table 2, Figure 8).

<table><caption>**Table 2.** General Structures of Binary Systems</caption><thead><tr><th>Structure</th><th>Formula</th><th>Example</th><th>Structure</th></tr></thead><tbody><tr><td>sodium chloride-like</td><td>{A<sub>6</sub>B<sub>6</sub>}</td><td>{Na<sub>6</sub>Cl<sub>6</sub>}</td><td>18</td></tr><tr><td>cesium chloride-like</td><td>{A<sub>8</sub>B<sub>8</sub>}</td><td>{Cs<sub>8</sub>Cl<sub>8</sub>}</td><td>21</td></tr><tr><td>fluorite-like</td><td>{A<sub>4</sub>B<sub>8</sub>}</td><td>{Ca<sub>4</sub>F<sub>8</sub>}</td><td>25</td></tr><tr><td>zinc blende-like</td><td>{A<sub>4</sub>B<sub>4</sub>}fcc</td><td>{Zn<sub>4</sub>S<sub>4</sub>}fcc</td><td>22</td></tr><tr><td>wurtzite-like</td><td>{A<sub>4</sub>B<sub>4</sub>}hcp</td><td>{Zn<sub>4</sub>S<sub>4</sub>}hcp</td><td>23</td></tr><tr><td>β-cristobalite-like</td><td>{A<sub>2</sub>B<sub>4</sub>}</td><td>{Si<sub>2</sub>O<sub>4</sub>}</td><td>26</td></tr><tr><td>rutile-like<sup>a</sup></td><td>{A<sub>3</sub>B<sub>6</sub>}</td><td>{Ti<sub>3</sub>O<sub>6</sub>}</td><td>27</td></tr></tbody></table>

## Some Limitations Unresolved by This Notation—Nor by Any Other

As with any other model, this proposal has some limitations that should be discussed. Let us focus on titanium oxide, the most widely used white pigment. Titanium oxide can be found in three different structures: rutile, anatase and brookite; which all have a composition of Ti:O = 1:2, resulting in the formula TiO₂ (Figure 9). Our proposed model is unable to establish the

<figure><img src="image_9.png" /><figcaption>**Figure 9.** Rutile, anatase, and brookite {Ti₃O₆} structures.</figcaption></figure>

differences among them because they would all be noted {Ti₃O₆}. This is because they have the same composition and connectivity, with three titanium atoms around each oxygen atom and six oxygen atoms around each titanium atom. The oxygen atoms around the titanium atom form a distorted octahedron.²⁸ Rutile, anatase, and brookite structures vary in terms of the degree of distortion.²⁹ To be fair, none of the actual models allows for this distinction.

More complicated crystalline structures can cause problems in terms of notation. Pyrite (FeS₂) is an interesting material with semiconducting properties.³⁰ Pyrite has a characteristic structure in which each iron atom is bonded to six sulfur atoms, while each sulfur atom is bonded to three iron atoms and a sulfur atom. There are, indeed, S-S bonds within the structure (Figure 10).³¹ In this context, the notation derived from our model, {Fe₃S₆}, fails to transmit the information about S-S bonds. The alternative {Fe₄S₆} gives the correct coordination number, but fails into giving the correct composition, which would be an unacceptable notation. This problem can be overcome if the formula is written as {Fe₆(S-S)₆}. Using this notation, both the structure and composition (Fe:S = 1:2) are respected and communicated. Pyrite-like structures are found

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Most common binary structures (see Figures S6–S13).</figcaption></figure>

<footnote>aSee discussion in *Some Limitations Unresolved by This Notation*.</footnote>
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Pyrite {Fe₆(S-S)₆} structure (see Figure S14).</figcaption></figure>

for several substances such as nickel(II) sulfide and cobalt(II) selenide, which would be noted as {Ni₆(S-S)₆} and {Co₆(Se-Se)₆}, respectively.³²

The magnetic alloy FePd₃, is described as having a simple cubic structure, with iron atoms located at the corners of the cube and palladium atoms at the centers of the faces, resulting in an fcc-like structure (Figure 11).³³,³⁴ Each iron atom is

<figure><img src="image_12.png" /><figcaption>**Figure 11.** Face-centered type and palladium–iron alloy {FePd₃} structures (see Figure S15).³³</figcaption></figure>

surrounded by 12 palladium atoms. Taking into account the alloy composition, the notation should be {Fe₄Pd₁₂}. When examining the structure, each palladium atom is indeed bonded to four iron atoms.³³ However, in the crystalline structure, there are Pd–Pd bonds that would not be described by this notation. Each palladium atom is bonded to eight other palladium atoms.

Another limitation of this model arises from the discussion of ternary systems. Wollastonite is a calcium inosilicate mineral (with formula CaSiO₃) with a triclinic structure. In the structure, each calcium is bonded to six oxygens, each silicon is bonded to four oxygens, and oxygens can be bonded in two ways: (i) to three calcium and one silicon; or (ii) to two silicon and one calcium, within the same structure (Figure 12).³⁵ Using the proposed notation, assigning the coordination number of oxygen and silicon corresponding to calcium would not be possible, and therefore the notation would not allow to account for the wollastonite structure. In any case, we propose to write the formula in slashes to denote that wollastonite is a layered

<figure><img src="image_13.png" /><figcaption>**Figure 12.** Wollastonite /CaSiO₃/ and perovskite {CaTiO₃} structure (see Figures S16 and S17).</figcaption></figure>

compound: /CaSiO₃/.¹ Writing the formula for ternary substances can clearly become complicated. Perovskite (CaTiO₃), an example of a double oxide, does not contain TiO₃²⁻ anions, as the formula might imply. Actually, there are Ca²⁺ and Ti⁴⁺ cations. Each calcium is bonded to 12 oxides, while each titanium is bonded to six oxides (Figure 12).¹² Each oxygen is bonded to two titanium cations and to four calcium cations, resulting in {Ca₄Ti₂O₁₂⁻₆}.³⁶ However, this notation does not reflect the composition in the substance, thus, we propose to write only {CaTiO₃}.

The model can only account for substitutional alloys, in which atoms of the solute occupy sites in the lattice of the solvent metal, or for interstitial alloys, in which atoms occupy the interstitial holes, but only in the case of stoichiometric alloys. In the cases in which the amount of solute with regard to the solvent metal is very low, 0.01 to 10%, this notation would not be very useful. However, this type of mixture does not correspond to typical classroom study cases.

## Activities with Students

The activities conducted with the students were the same as those conducted with the professors. Both groups completed a preliminary questionnaire (Figure 13) before being presented

1.- Determine the coordination number of each atom or ion in the following systems.

<table><tr><td>Pre-test</td><td>{NaCl}</td><td>{ZnS}</td><td>{CaF<sub>2</sub>}</td><td>{Po}</td><td>/C<sub>graphite</sub>/</td><td>{C<sub>diamond</sub>}</td></tr><tr><td>Post-test</td><td>{Na<sub>4</sub>Cl<sub>6</sub>}</td><td>{Zn<sub>4</sub>S<sub>4</sub>}<sub>fcc</sub></td><td>{Ca<sub>4</sub>F<sub>8</sub>}</td><td>{Po<sub>6</sub>}</td><td>/C<sub>3</sub>/</td><td>{C<sub>4</sub>}</td></tr></table>

2.- Write the chemical formula of the following systems.

<figure><img src="image_14.png" /></figure>

3.- Determine the structure of the following metals.

<table><tr><td>Pre-test</td><td>{K}</td><td>{Ti}</td><td>{Cu}</td><td>{Cr}</td><td>{Po}</td><td>{Ba}</td></tr><tr><td>Post-test</td><td>{K<sub>8</sub>}</td><td>{Ti<sub>12</sub>}<sub>ncp</sub></td><td>{Cu<sub>12</sub>}<sub>fcc</sub></td><td>{Cr<sub>8</sub>}</td><td>{Po<sub>6</sub>}</td><td>{Ba<sub>8</sub>}</td></tr></table>

Students, n = 113

Professors, n = 18

<caption>**Figure 13.** Pre- and post-test activities with students (n = 113) and teachers (n = 18). The original questions were administered in Spanish.</caption>

with the core concepts. The presentation highlighted several key points covered in this manuscript, including the use of coordination numbers as a useful tool for advanced inorganic chemistry courses, metallic lattices, the most common binary systems structures, and the limitations of the model. Following the presentation, a discussion was held with the students and faculty members to address their questions and gather feedback. Subsequently, a second questionnaire was administered to both groups (Figure 13). The only difference between the pretest and post-test questionnaires was the inclusion of our proposed formula notation in the latter. Below, we provide both the questionnaires and the results obtained. Both, students and professors involved were familiar with our previous contribution, and thus, the use of slashes and curly brackets.¹ The 113 students who participated in the activity were mainly third-semester students enrolled in one of six majors (Chemistry, Chemical Engineering, Biological Pharmaceutical Chemistry, Food Chemistry, Metallurgical Chemical Engineering, and Chemistry of Materials) at the Facultad de Quimica, UNAM. The professors, from the Inorganic and Nuclear Chemistry
Students

<figure><img src="image_15.png" /><figcaption>Q2: Write the chemical formula of the following systems.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Q3: Determine the packed structure of the following metals.</figcaption></figure>

<figure><img src="image_17.png" /></figure>

Professors

<figure><img src="image_18.png" /><figcaption>Q2: Write the chemical formula of the following systems.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Q3: Determine the packed structure of the following metals.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 14.** Results of the pre- and post-test activities with students (n = 113) and teachers (n = 18).</figcaption></figure>

Department at the same institution, were currently teaching General Chemistry I, General Chemistry II, and/or Inorganic Chemistry I. Additional information about these groups is available in the *Supporting Information*.

Concerning the first question, almost no student or professor could determine the coordination number of atoms or ions within the structures (Figure 14). Some of them, based on prior experience, knew the coordination number of sodium cations and chlorides in NaCl or the coordination number of carbon in diamond. This result highlights that the chemical structure of a reticulum or a layered structure is very difficult to predict using the minimal formula, and knowledge of this topic relies solely on experience. In contrast, the results of the post-test evaluation showed a clear and significant increase in the mean grade of both populations (4.63 increment for students, and 3.66 increment

for professors), indicating the importance and usefulness of our proposal.

The second question identified an important feature. When the chemical structure is presented, both students and professors could write the minimal formula of the substance. In addition, it is probable that they already knew the chemical formulas of the substances showed: titanium oxide (TiO₂), cesium chloride (CsCl), silicon oxide (SiO₂), and cadmium iodide (CdI₂). In the post-test, both populations were able to write the chemical formulas introduced by us and use them to describe the chemical systems. Using the coordination numbers, the key aspect was to count the number of oxygens around titanium and vice versa to write the formula {Ti₃O₆}. Nevertheless, in the post-test, we observed that determining the chemical formulas of cesium chloride {Cs₈Cl₈} and cadmium iodide /Cd₃I₆/ was more intricate than the formulas of titanium oxide {Ti₃O₆} and silicon
oxide {Si₂O₄}. The results before and after the activity were similar, highlighting the importance of displaying the chemical structure.

In the third question, as expected, neither the students nor the professors achieved good grades in the pretest because it is not possible to predict the structure of metals. However, using the notation proposed by us, both populations were able to identify and distinguish between simple cubic, body-centered cubic, and closed-packed structures: face-centered cubic and hexagonal structures. As a result, in the post-test, the outcomes were exceptional, with an average grade of 5.29 for students and 5.28 for professors out of 6.

Data collection from all participants, including students and teachers, adhered to an ethical consent process. All individuals consented to share their personal academic information, and the authors of this article committed to using the data exclusively for its intended purpose—namely, the evaluations and perspectives discussed herein.

## ■ CONCLUSIONS

In conclusion, we have demonstrated how a slight refinement in our chemical formula proposal,¹ can be very useful for obtaining deeper insights in the chemical structure of substances, in particular for reticulums and layered structures. By including the coordination number of the entities involved, it becomes easy to determine the structure of metals, the structure of commonly found ionic solids, their relation to structures, and even the determination of the chemical formula from the unit cell. We are confident that this new chemical formula notation will be very useful, particularly in advanced inorganic chemistry courses. We also discuss the limitations of our proposal. Although this notation does not help distinguish between rutile, brookite, and anatase, this limitation is shared by the current models. Additionally, although the new chemical formulas allow for the depiction of more complex systems, such as pyrite {Fe₆(S–S)₃}, they are less effective for ternary systems like wollastonite /CaSiO₃/ and perovskite {CaTiO₃}. The effectiveness of this proposal was tested with 18 professors and 113 undergraduate students at the Facultad de Química, UNAM, with exceptional results. In our view, adopting this new chemical formula notation for advanced inorganic courses will enhance students' and educators' understanding of chemical structures, enabling them to better connect composition and structure directly from the formula.

## ■ ASSOCIATED CONTENT

### ■ Supporting Information

The Supporting Information is available at https://pubs.acs.org/doi/10.1021/acs.jchemed.5c00075.

The different questions and results of the students' and professors' quiz (PDF)

## ■ AUTHOR INFORMATION

### Corresponding Authors

Miguel Reina – Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México;
● orcid.org/0000-0003-4959-4105; Email: mreina@quimica.unam.mx

Bruno Landeros-Rivera – Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad

Nacional Autónoma de México, 04510 Ciudad de México, México; Email: brunolanderos@quimica.unam.mx

Jesús Gracia Mora – Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México;
● orcid.org/0000-0001-8067-1215; Email: jgracia@quimica.unam.mx

Hervé This – Université Paris-Saclay, INRAE AgroParisTech, 75005 Paris, France; Group of Molecular Gastronomy, Inrae-AgroParisTech, F-75005 Paris, France; Email: herve.this@agroparistech.fr

Antonio Reina – Departamento de Química Inorgánica y Nuclear, Facultad de Química, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México;
● orcid.org/0000-0001-7527-7176; Email: antonio.reina.0711@quimica.unam.mx

Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.jchemed.5c00075

### Notes

Every participant granted permission for the collected data to be used for academic purposes. The authors used an ethical consent procedure approved according to procedures established by the Facultad de Química, UNAM.

The authors declare no competing financial interest.

## ■ ACKNOWLEDGMENTS

The authors thank the meaningful discussions with all the faculty members and students, especially with Karla Salas-Martin (FQ, UNAM).

## ■ REFERENCES

(1) Reina, M.; Landeros-Rivera, B.; Gracia-Mora, J.; This, H.; Reina, A. Improving the Understanding of Chemistry by Using the Right Words: Transforming Inorganic Formulas for Chemical Structure Insight. *J. Chem. Educ.*, 2024, DOI: 10.1021/acs.jchemed.5c00074.

(2) Reina, M.; This, H.; Reina, A. Improving the Understanding of Chemistry by Using the Right Words: A Clear-Cut Strategy to Avoid Misconceptions When Talking about Elements, Atoms, and Molecules. *J. Chem. Educ.* **2022**, *99* (8), 2999–3006.

(3) Reina, M.; This, H.; Reina, A. Reply to Using the Right Words in the Right Way: Atom, Molecule, Element and Compound. *J. Chem. Educ.* **2023**, *100* (1), 7–9.

(4) Reina, M.; This, H.; Reina, A. Improving the Understanding of Chemistry by Using the Right Words: Why Is Talking about Compounds so Messy? *J. Chem. Educ.* **2024**, *101* (1), 39–48.

(5) The Materials Project, C, mp-66 (visited on May 2024). 2024, https://next-gen/materialsproject.org/materials/mp-66.

(6) Geim, A. K.; Novoselov, K. S. The rise of graphene. *Nat. Mater.* **2007**, *6*, 183–191.

(7) Umar, E.; Ikram, M.; Haider, J.; Nabgan, W.; Imram, M.; Nazir, G. 3D graphene-based material: Overview, perspective, advancement, energy storage, biomedical engineering and environmental applications a bibliometric analysis. *J. Environ. Chem. Eng.* **2023**, *11* (5), 110339.

(8) The Cambridge Crystallographic Data Centre (CCDC). Crystal structure of polonium. https://www.ccdc.cam.ac.uk/elements/polonium/.

(9) The Materials Project, 2024. Li, mp-567337 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-567337?formula=Li.

(10) The Materials Project, Au, mp-81 2024. (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-81?formula=Au.

(11) The Materials Project, 2024. Tl, mp-82 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-82?chemsys=Tl.
(12) Housecroft, C. E.; Sharpe, A. G. *Inorganic Chemistry*, 3rd ed.; Prentice Hall: 2008.

(13) Pepperhoff, W., Acet, M. The structure of iron. In: *Constitution and Magnetism of Iron and its Alloys. Engineering Materials*; Springer: 2001. DOI: 10.1007/978-3-662-04345-5_1.

(14) Mathon, O.; Baudelet, F.; Itié, J. P.; Polian, A.; d'Astuto, M.; Chervin, J. C.; Pascarelli, S. Dynamics of the Magnetic and Structural α-ε Phase Transition in Iron. *Phys. Rev. Lett.* **2004**, 93, 255503.

(15) Okamoto, H.; Schlesinger, M. E.; Mueller, E. M. (1992) *Alloy Phase Diagrams*. ASM Handbook. Vol. 3. ASM International, 2.210, 4.9.

(16) Galasso, F. S. *Structure and properties of inorganic solids*, 1st ed.; Pergamon Press: 1970.

(17) Huheey, J. E. *Inorganic Chemistry: principles of structure and reactivity*, 4th ed.; Pearson: 1993.

(18) The Materials Project, NaCl, 2024, mp-22862 (visited on May 2024). https://next-gen/materialsproject.org/materials/mp-22862?formula=NaCl.

(19) Wilson, J. G.; Newall, A. B. *General and Inorganic Chemistry*; Cambridge University Press: 1968.

(20) Partington, J. R. *A Text-book of Inorganic Chemistry*; Macmillan: 1950.

(21) *The Materials Project*, 2024, CsCl, mp-22865 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-22865?chemsys=Cs-Cl.

(22) *The Materials Project*, 2024, ZnS, mp-561286 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-561286?chemsys=Zn-S.

(23) *The Materials Project*, 2024, ZnS, mp-554820 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-554820?chemsys=Zn-S.

(24) The Materials Project, 2024, NiAs, mp-590 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-590?chemsys=Ni-As.

(25) The Materials Project, 2024, CaF₂, mp-2741 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-2741?formula=CaF2.

(26) The Materials Project, 2024, SiO₂, mp-8352 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-8352.

(27) The Materials Project, 2024, TiO₂, mp-390 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-390?formula=TiO2.

(28) Davis, K. A. Titanium dioxide. *J. Chem.* **1982**, *59* (2), 158-159.

(29) Reyes-Coronado, D.; Rodríguez-Gattorno, G.; Espinosa-Pesqueira, M. E.; Cab, C.; de Coss, R.; Oskam, G. Phase-pure TiO₂ nanoparticles: anatase, brookite and rutile. *Nanotechnology* **2008**, *19*, 145605.

(30) Macpherson, H. A.; Stoldt, C. R. Iron Pyrite Nanocubes: Size and Shape Considerations for Photovoltaic Application. *ACS Nano* **2012**, *6* (10), 8940-8949.

(31) The Materials Project, 2024, FeS₂, mp-226 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-226?chemsys=Fe-S.

(32) Stillwell, C. W. Crystal chemistry. IV. The structure of AX₂, A₂X₃, AX₃, AX₄ compounds. Summary. *J. Chem. Educ.* **1936**, *13* (12), 566-575.

(33) Kvashnin, Y. O.; Khmelevskyi, S.; Kudrnovsky, J.; Yaresko, A. N.; Genovese, L.; Bruno, P. Noncollinear magnetic ordering in compressed FePd₃ ordered alloy: A first principles study. *Phys. Res. B* **2012**, *86*, 174429.

(34) The Materials Project, 2024, FePd₃, mp-21845 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-21845?chemsys=Fe-Pd.

(35) The Materials Project, 2024, CaSiO₃, mp-4429 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-4429?chemsys=Ca-Si-O.

(36) The Materials Project, 2024, CaTiO₃, mp-4019 (visited on June 2024). https://next-gen/materialsproject.org/materials/mp-4019?chemsys=Ca-Ti-O.