The Structures of Simple Solids: Detailed Notes

Introduction to Solid-State Chemistry

• Solid-state chemistry explores the properties, synthesis, and structure of solid materials. Unlike gases and liquids, solids possess fixed shapes and volumes, arising from the strong interatomic forces that hold their constituent particles (atoms, ions, or molecules) in relatively fixed positions.
• Understanding the arrangement of these particles—their crystal structure—is paramount, as it directly dictates a solid’s macroscopic properties, including its mechanical strength, electrical conductivity, optical behavior, and magnetic characteristics. The goal is to move beyond simple classifications to detailed geometric descriptions.
• This section focuses on the fundamental principles governing the structures of simple solids, primarily metallic, ionic, and covalent network solids, emphasizing concepts like close packing, lattice types, and common crystal structures.

1. Classification of Solids

• Solids can be broadly categorized based on the nature of the forces holding their constituent particles together:
• Metallic Solids: Composed of metal atoms held together by metallic bonds.
  • Characterized by a “sea” of delocalized valence electrons shared among a lattice of positive metal ions.
  • Properties: High electrical and thermal conductivity, malleability, ductility, lustrous appearance.
  • Examples: Copper (Cu), Iron (Fe), Silver (Ag).
• Ionic Solids: Composed of positive and negative ions held together by strong electrostatic forces (ionic bonds).
  • Ions typically arrange themselves to maximize attractive forces and minimize repulsive forces.
  • Properties: High melting points, brittle, poor electrical conductors in solid state (but good conductors when molten or dissolved).
  • Examples: Sodium Chloride (NaCl), Magnesium Oxide (MgO), Calcium Fluoride (CaF2​).
• Covalent Network Solids (or Covalent Solids): Atoms are held together by a continuous network of covalent bonds throughout the entire structure.
  • Essentially one giant molecule.
  • Properties: Very high melting points, extremely hard, typically poor electrical conductors (exceptions like graphite).
  • Examples: Diamond (carbon), Silicon (Si), Silicon Dioxide (SiO2​).
• Molecular Solids: Discrete molecules are held together by weak intermolecular forces (van der Waals forces, hydrogen bonds).
  • The atoms within each molecule are covalently bonded, but the molecules themselves interact weakly.
  • Properties: Low melting points, soft, poor electrical conductors.
  • Examples: Ice (H2​O), Dry Ice (CO2​), Iodine (I2​), Sucrose (C12​H22​O11​).

2. Crystal Lattices and Unit Cells

• Most solids are crystalline, meaning their constituent particles are arranged in a highly ordered, repeating three-dimensional pattern. This ordered arrangement is called a crystal lattice.
• Unit Cell: The smallest repeating unit of a crystal lattice that, when translated in three dimensions, generates the entire lattice. It acts as the fundamental building block of the crystal.
  • The geometry of the unit cell (lengths of its edges and angles between them) defines the shape of the crystal.
• Lattice Points: Imaginary points in space that represent the locations of atoms, ions, or molecules within the crystal structure. Each lattice point has identical surroundings.
• Bravais Lattices: In 1848, Auguste Bravais proved that there are only 14 unique ways to arrange points in three-dimensional space such that each point has identical surroundings. These 14 arrangements are known as Bravais lattices, which are derived from 7 crystal systems.
• The 7 Crystal Systems (and their unit cell parameters):
  1. Cubic: a=b=c, α=β=γ=90∘
     • Contains 3 Bravais lattices: Simple Cubic (SC), Body-Centered Cubic (BCC), Face-Centered Cubic (FCC).
  2. Tetragonal: a=b=c, α=β=γ=90∘
     • Contains 2 Bravais lattices: Simple Tetragonal, Body-Centered Tetragonal.
  3. Orthorhombic: a=b=c, α=β=γ=90∘
     • Contains 4 Bravais lattices: Simple Orthorhombic, Body-Centered Orthorhombic, Face-Centered Orthorhombic, Base-Centered Orthorhombic.
  4. Hexagonal: a=b=c, α=β=90∘, γ=120∘
     • Contains 1 Bravais lattice: Simple Hexagonal.
  5. Trigonal (Rhombohedral): a=b=c, α=β=γ=90∘
     • Contains 1 Bravais lattice: Simple Trigonal (Rhombohedral).
  6. Monoclinic: a=b=c, α=γ=90∘, β=90∘
     • Contains 2 Bravais lattices: Simple Monoclinic, Base-Centered Monoclinic.
  7. Triclinic: a=b=c, α=β=γ=90∘
     • Contains 1 Bravais lattice: Simple Triclinic.

3. Close Packing of Spheres (for Metals and Ionic Compounds)

• Many metallic and ionic structures can be understood by considering the most efficient ways to pack spheres (representing atoms or ions) together to maximize density and coordination number.
• Closest Packed Layers: When spheres are arranged in a single layer, each sphere is surrounded by six others, creating a hexagonal pattern. This generates two types of depressions or “holes”:
  • A-sites: Directly aligned with the centers of spheres in the layer below/above.
  • B-sites: Offset from the centers of spheres.
• Two Common Close-Packed Structures (from stacking layers):
  • Hexagonal Close-Packed (HCP): ABAB… stacking sequence.
    • The third layer (B) sits directly over the first layer (A).
    • Unit cell is hexagonal.
    • Coordination number: 12 (each sphere touches 6 in its layer, 3 above, 3 below).
    • Packing efficiency: 74% (maximum possible for uniform spheres).
    • Examples: Magnesium (Mg), Zinc (Zn), Titanium (Ti).
  • Cubic Close-Packed (CCP) / Face-Centered Cubic (FCC): ABCABC… stacking sequence.
    • The third layer (C) sits over the unoccupied holes of the first layer (A). The fourth layer then sits directly over the first layer (A).
    • Unit cell is face-centered cubic (FCC).
    • Coordination number: 12.
    • Packing efficiency: 74% (same as HCP).
    • Examples: Copper (Cu), Silver (Ag), Gold (Au), Aluminum (Al), Nickel (Ni).
• Coordination Number (CN): The number of nearest neighbors surrounding a central atom or ion in a crystal lattice. In close-packed structures, CN = 12.
• Packing Efficiency: The percentage of space occupied by the spheres in a crystal structure. For both HCP and FCC, it is 74%.
• Other Common Metallic Structures (Not Closest Packed):
  • Body-Centered Cubic (BCC): Each atom is at the center of a cube, with 8 atoms at the corners (or vice versa).
    • Coordination number: 8.
    • Packing efficiency: 68%.
    • Examples: Iron (Fe), Sodium (Na), Potassium (K), Tungsten (W).

4. Holes (Interstitial Sites) in Close-Packed Structures

• When spheres are packed, empty spaces (interstitial sites or “holes”) are created between them. These holes are crucial for understanding the structures of many ionic compounds and alloys.
• Types of Holes in Close-Packed Structures:
  • Tetrahedral Holes: Formed by four spheres, arranged tetrahedrally.
    • Smallest type of hole.
    • Number of tetrahedral holes per sphere: 2 (e.g., in FCC, there are 8 tetrahedral holes per unit cell, and 4 spheres, so 2 holes per sphere).
    • A small cation can fit into a tetrahedral hole if its radius is ≤0.225×radius of anion.
  • Octahedral Holes: Formed by six spheres, arranged octahedrally.
    • Larger than tetrahedral holes.
    • Number of octahedral holes per sphere: 1 (e.g., in FCC, there are 4 octahedral holes per unit cell, and 4 spheres, so 1 hole per sphere).
    • A cation can fit into an octahedral hole if its radius is ≤0.414×radius of anion.

5. Structures of Ionic Solids (Derived from Packing and Holes)

• Ionic solids are often described by considering the larger ions (usually anions) forming a close-packed (or other) lattice, with the smaller ions (cations) occupying the interstitial holes. The stoichiometry of the compound dictates which and how many holes are filled.
• Radius Ratio Rule: A simple (but often oversimplified) empirical rule used to predict the coordination number of ions in an ionic crystal based on the ratio of the cation radius (r+​) to the anion radius (r−​).
  • r+​/r−​ range for CN:
    • <0.155: CN = 2 (linear, rare)
    • 0.155−0.225: CN = 3 (trigonal planar)
    • 0.225−0.414: CN = 4 (tetrahedral)
    • 0.414−0.732: CN = 6 (octahedral)
    • 0.732−1.000: CN = 8 (cubic)
• Common Ionic Structures:
  • Sodium Chloride (NaCl) Structure (Rock Salt Structure):
    • Anions (Cl−) form an FCC (or CCP) lattice.
    • Cations (Na+) occupy all the octahedral holes.
    • Each Na+ is surrounded by 6 Cl− (octahedral CN), and each Cl− is surrounded by 6 Na+ (octahedral CN).
    • Formula unit per unit cell: 4 NaCl.
    • Examples: NaCl,KCl,MgO,LiF.
  • Cesium Chloride (CsCl) Structure:
    • Anions (Cl−) are at the corners of a simple cubic (SC) lattice.
    • Cations (Cs+) occupy the single cubic hole at the center of the unit cell.
    • Each Cs+ is surrounded by 8 Cl− (cubic CN), and each Cl− is surrounded by 8 Cs+ (cubic CN).
    • Formula unit per unit cell: 1 CsCl.
    • Examples: CsCl,CsBr,TlCl. (Note: anions don’t form a close-packed lattice here).
  • Zinc Blende (ZnS) Structure:
    • Anions (S2−) form an FCC (or CCP) lattice.
    • Cations (Zn2+) occupy half of the tetrahedral holes.
    • Each Zn2+ is surrounded by 4 S2− (tetrahedral CN), and each S2− is surrounded by 4 Zn2+ (tetrahedral CN).
    • Formula unit per unit cell: 4 ZnS.
    • Examples: ZnS (zinc blende form), CuCl,AgI.
  • Fluorite (CaF2) Structure:
    • Cations (Ca2+) form an FCC (or CCP) lattice.
    • Anions (F−) occupy all the tetrahedral holes.
    • Each Ca2+ is surrounded by 8 F− (cubic CN), and each F− is surrounded by 4 Ca2+ (tetrahedral CN). Note the stoichiometry is AB2​.
    • Formula unit per unit cell: 4 CaF2​.
    • Examples: CaF2​,UO2​,ZrO2​.
  • Antifluorite Structure: The inverse of fluorite; anions form the FCC lattice, and cations occupy all tetrahedral holes. (e.g., Li2​O).

6. Covalent Network Solids

• These structures are not typically described by close packing of spheres, as the directional nature of covalent bonds dictates their arrangement.
• Diamond:
  • Each carbon atom is sp3 hybridized and covalently bonded to four other carbon atoms in a tetrahedral arrangement.
  • Forms a giant, three-dimensional network.
  • Properties: Extremely hard, very high melting point, electrical insulator.
• Graphite:
  • Carbon atoms are sp2 hybridized, forming hexagonal layers. Within each layer, carbon atoms are strongly covalently bonded.
  • Layers are held together by weak intermolecular (van der Waals) forces.
  • Properties: Soft, slippery (layers can slide), excellent electrical conductor along layers (due to delocalized π electrons).
• Silicon Dioxide (SiO2) – Quartz:
  • Each silicon atom is bonded to four oxygen atoms, and each oxygen atom is bonded to two silicon atoms.
  • Forms a complex three-dimensional network.
  • Properties: Hard, high melting point, insulator.

7. X-ray Diffraction (XRD): Probing Crystal Structure

• Principle: When X-rays (which have wavelengths comparable to interatomic distances in crystals) interact with the regular, repeating planes of atoms in a crystal, they are diffracted.
• Bragg’s Law: nλ=2dsinθ
  • n: order of diffraction (integer, usually 1)
  • λ: wavelength of X-rays
  • d: interplanar spacing (distance between parallel planes of atoms)
  • θ: glancing angle (angle of incidence equal to angle of reflection)
• By analyzing the diffraction pattern (angles at which constructive interference occurs), crystallographers can determine the dimensions of the unit cell and the arrangement of atoms within it. XRD is the primary experimental technique for elucidating crystal structures.

40 Multiple Choice Questions from Selected Text

1. What is the defining characteristic of solids, as stated in the introduction? a) They are compressible. b) They possess fixed shapes and volumes. c) Their particles are in constant random motion. d) They have weak interatomic forces.Answer: b) They possess fixed shapes and volumes. Explanation: The “Introduction to Solid-State Chemistry” states: “Unlike gases and liquids, solids possess fixed shapes and volumes, arising from the strong interatomic forces that hold their constituent particles…”
2. According to the introduction, what directly dictates a solid’s macroscopic properties? a) Its temperature b) Its mass c) Its crystal structure d) Its reactivityAnswer: c) Its crystal structure Explanation: The “Introduction to Solid-State Chemistry” states: “Understanding the arrangement of these particles—their crystal structure—is paramount, as it directly dictates a solid’s macroscopic properties…”
3. Metallic solids are characterized by a “sea” of: a) Localized electrons b) Delocalized valence electrons c) Positive metal ions only d) Covalently bonded atomsAnswer: b) Delocalized valence electrons Explanation: The “Metallic Solids” section states they are “Characterized by a ‘sea’ of delocalized valence electrons shared among a lattice of positive metal ions.”
4. Which property is not characteristic of metallic solids according to the text? a) High electrical conductivity b) Brittleness c) Malleability d) Lustrous appearanceAnswer: b) Brittleness Explanation: The “Metallic Solids” section lists “malleability, ductility” as properties, which are opposite of brittleness. Brittleness is listed as a property of ionic solids.
5. In ionic solids, how do ions typically arrange themselves? a) Randomly b) To maximize attractive forces and minimize repulsive forces c) In a continuous covalent network d) In discrete molecular unitsAnswer: b) To maximize attractive forces and minimize repulsive forces Explanation: The “Ionic Solids” section states: “Ions typically arrange themselves to maximize attractive forces and minimize repulsive forces.”
6. Which type of solid typically has low melting points and is soft? a) Metallic solids b) Ionic solids c) Covalent network solids d) Molecular solidsAnswer: d) Molecular solids Explanation: The “Molecular Solids” section states: “Properties: Low melting points, soft, poor electrical conductors.”
7. What is the smallest repeating unit of a crystal lattice? a) Crystal system b) Lattice point c) Unit cell d) Bravais latticeAnswer: c) Unit cell Explanation: The “Unit Cell” section defines it as: “The smallest repeating unit of a crystal lattice that, when translated in three dimensions, generates the entire lattice.”
8. In 1848, who proved there are only 14 unique ways to arrange points in three-dimensional space such that each point has identical surroundings? a) Svante Arrhenius b) G.N. Lewis c) Auguste Bravais d) Ralph PearsonAnswer: c) Auguste Bravais Explanation: The “Bravais Lattices” section states: “In 1848, Auguste Bravais proved that there are only 14 unique ways to arrange points…”
9. Which crystal system has unit cell parameters a=b=c and α=β=γ=90∘? a) Cubic b) Tetragonal c) Orthorhombic d) HexagonalAnswer: b) Tetragonal Explanation: The “7 Crystal Systems” list specifies this for “Tetragonal.”
10. How many Bravais lattices are contained within the Orthorhombic crystal system? a) 1 b) 2 c) 3 d) 4Answer: d) 4 Explanation: The “Orthorhombic” entry under “The 7 Crystal Systems” states: “Contains 4 Bravais lattices.”
11. What is the stacking sequence for a Cubic Close-Packed (CCP) structure? a) ABAB… b) ABCABC… c) AAAA… d) ABCA…Answer: b) ABCABC… Explanation: The “Cubic Close-Packed (CCP) / Face-Centered Cubic (FCC)” section states: “ABCABC… stacking sequence.”
12. What is the coordination number of atoms in a Hexagonal Close-Packed (HCP) structure? a) 6 b) 8 c) 10 d) 12Answer: d) 12 Explanation: The “Hexagonal Close-Packed (HCP)” section states: “Coordination number: 12”.
13. What is the packing efficiency for both HCP and FCC structures? a) 52% b) 68% c) 74% d) 100%Answer: c) 74% Explanation: The “Packing Efficiency” section states: “For both HCP and FCC, it is 74%.”
14. Which of the following metals is an example of a Body-Centered Cubic (BCC) structure according to the notes? a) Copper (Cu) b) Magnesium (Mg) c) Iron (Fe) d) Silver (Ag)Answer: c) Iron (Fe) Explanation: The “Body-Centered Cubic (BCC)” examples include “Iron (Fe).”
15. What type of holes are formed by four spheres arranged tetrahedrally in close-packed structures? a) Octahedral holes b) Cubic holes c) Trigonal holes d) Tetrahedral holesAnswer: d) Tetrahedral holes Explanation: The “Tetrahedral Holes” section states they are “Formed by four spheres, arranged tetrahedrally.”
16. How many octahedral holes are there per sphere in an FCC lattice? a) 1 b) 2 c) 4 d) 8Answer: a) 1 Explanation: The “Octahedral Holes” section states: “Number of octahedral holes per sphere: 1 (e.g., in FCC, there are 4 octahedral holes per unit cell, and 4 spheres, so 1 hole per sphere).”
17. What is the maximum radius ratio (r+​/r−​) for a cation to fit into an octahedral hole? a) ≤0.155 b) ≤0.225 c) ≤0.414 d) ≤0.732
    Answer: c) ≤0.414 Explanation: The “Octahedral Holes” section states: “A cation can fit into an octahedral hole if its radius is ≤0.414×radius of anion.”
18. In the Sodium Chloride (NaCl) structure, where do the cations (Na+) occupy positions? a) Half of the tetrahedral holes b) All of the tetrahedral holes c) Half of the octahedral holes d) All of the octahedral holesAnswer: d) All of the octahedral holes Explanation: The “Sodium Chloride (NaCl) Structure” section states: “Cations (Na+) occupy all the octahedral holes.”
19. What is the formula unit per unit cell for the Cesium Chloride (CsCl) structure? a) 1 CsCl b) 2 CsCl c) 4 CsCl d) 8 CsCl
    Answer: a) 1 CsCl Explanation: The “Cesium Chloride (CsCl) Structure” section states: “Formula unit per unit cell: 1 CsCl.”
20. In the Zinc Blende (ZnS) structure, what proportion of the tetrahedral holes do the cations (Zn2+) occupy? a) All b) Half c) One-quarter d) One-eighthAnswer: b) Half Explanation: The “Zinc Blende (ZnS) Structure” section states: “Cations (Zn2+) occupy half of the tetrahedral holes.”
21. Which ionic structure features cations forming an FCC lattice and anions occupying all the tetrahedral holes? a) Sodium Chloride (NaCl) structure b) Cesium Chloride (CsCl) structure c) Zinc Blende (ZnS) structure d) Fluorite (CaF2) structureAnswer: d) Fluorite (CaF2) structure Explanation: The “Fluorite (CaF2) Structure” section describes this arrangement.
22. The Antifluorite structure is the inverse of which common ionic structure? a) Sodium Chloride b) Cesium Chloride c) Zinc Blende d) FluoriteAnswer: d) Fluorite Explanation: The “Antifluorite Structure” section states: “The inverse of fluorite…”
23. Which of the following is a characteristic property of diamond? a) Soft and slippery b) Electrical conductor c) Very high melting point d) Forms hexagonal layersAnswer: c) Very high melting point Explanation: The “Diamond” section states: “Properties: Extremely hard, very high melting point, electrical insulator.”
24. What is the hybridization state of carbon atoms in graphite? a) sp b) sp2 c) sp3 d) sp3dAnswer: b) sp2 Explanation: The “Graphite” section states: “Carbon atoms are sp2 hybridized, forming hexagonal layers.”
25. What holds the layers of carbon atoms together in graphite? a) Strong covalent bonds b) Ionic bonds c) Metallic bonds d) Weak intermolecular (van der Waals) forcesAnswer: d) Weak intermolecular (van der Waals) forces Explanation: The “Graphite” section states: “Layers are held together by weak intermolecular (van der Waals) forces.”
26. Which type of solid is exemplified by Silicon Dioxide (SiO2​) – Quartz? a) Metallic solid b) Ionic solid c) Covalent network solid d) Molecular solidAnswer: c) Covalent network solid Explanation: The “Silicon Dioxide (SiO2) – Quartz” section classifies it as a Covalent Network Solid.
27. What is the principle behind X-ray Diffraction (XRD)? a) X-rays are absorbed by the crystal. b) X-rays are emitted from the crystal. c) X-rays are diffracted by the regular planes of atoms in a crystal. d) X-rays cause the crystal to fluoresce.Answer: c) X-rays are diffracted by the regular planes of atoms in a crystal. Explanation: The “Principle” of X-ray Diffraction states: “When X-rays… interact with the regular, repeating planes of atoms in a crystal, they are diffracted.”
28. What does λ represent in Bragg’s Law (nλ=2dsinθ)? a) Order of diffraction b) Wavelength of X-rays c) Interplanar spacing d) Glancing angleAnswer: b) Wavelength of X-rays Explanation: The “Bragg’s Law” section defines λ as “wavelength of X-rays.”
29. What is the coordination number of Na+ in the NaCl (rock salt) structure? a) 4 b) 6 c) 8 d) 12Answer: b) 6 Explanation: The “Sodium Chloride (NaCl) Structure” section states: “Each Na+ is surrounded by 6 Cl− (octahedral CN)…”
30. Which crystal system has a=b=c but α=β=γ=90∘? a) Cubic b) Hexagonal c) Monoclinic d) Trigonal (Rhombohedral)Answer: d) Trigonal (Rhombohedral) Explanation: The “7 Crystal Systems” list specifies this for “Trigonal (Rhombohedral).”
31. In the context of close packing, what are “holes” or “interstitial sites”? a) The atoms themselves. b) Empty spaces created between packed spheres. c) The bonding regions in a covalent solid. d) Defects in the crystal lattice.Answer: b) Empty spaces created between packed spheres. Explanation: The “Holes (Interstitial Sites) in Close-Packed Structures” section defines them as “empty spaces (interstitial sites or ‘holes’) are created between them.”
32. The radius ratio rule is described as: a) A precise quantum mechanical calculation. b) A simple (but often oversimplified) empirical rule. c) A method for determining electron density. d) Applicable only to molecular solids.Answer: b) A simple (but often oversimplified) empirical rule. Explanation: The “Radius Ratio Rule” section describes it as “A simple (but often oversimplified) empirical rule…”
33. Which radius ratio range corresponds to an octahedral coordination number (CN=6)? a) 0.155−0.225 b) 0.225−0.414 c) 0.414−0.732 d) 0.732−1.000
    Answer: c) 0.414−0.732 Explanation: The “Radius Ratio Rule” table shows this range for CN=6.
34. A crystal lattice is described as a highly ordered, repeating three-dimensional pattern of: a) Gases only b) Liquids only c) Constituent particles d) Disordered atomsAnswer: c) Constituent particles Explanation: The “Crystal Lattices and Unit Cells” section defines a crystal lattice as where “their constituent particles are arranged in a highly ordered, repeating three-dimensional pattern.”
35. Which of the following is an example of a covalent network solid? a) Sodium (Na) b) Sucrose (C12​H22​O11​) c) Silicon (Si) d) Magnesium Oxide (MgO)Answer: c) Silicon (Si) Explanation: The “Covalent Network Solids” section lists Silicon (Si) as an example.
36. In the Fluorite (CaF2​) structure, how many F− ions surround each Ca2+ ion? a) 4 b) 6 c) 8 d) 12Answer: c) 8 Explanation: The “Fluorite (CaF2) Structure” section states: “Each Ca2+ is surrounded by 8 F− (cubic CN)…”
37. What is the unit cell of the Cubic Close-Packed (CCP) structure? a) Simple Cubic b) Body-Centered Cubic c) Face-Centered Cubic (FCC) d) HexagonalAnswer: c) Face-Centered Cubic (FCC) Explanation: The “Cubic Close-Packed (CCP) / Face-Centered Cubic (FCC)” section explicitly states: “Unit cell is face-centered cubic (FCC).”
38. Which type of hole in close-packed structures is larger, octahedral or tetrahedral? a) Tetrahedral holes are larger. b) Octahedral holes are larger. c) They are the same size. d) Size depends on the specific atom.Answer: b) Octahedral holes are larger. Explanation: The “Octahedral Holes” section states: “Larger than tetrahedral holes.”
39. What are “Lattice Points” defined as in crystal lattices? a) The actual atoms or ions. b) Imaginary points in space representing particle locations with identical surroundings. c) The center of the unit cell. d) The boundaries of the crystal.Answer: b) Imaginary points in space that represent the locations of atoms, ions, or molecules within the crystal structure. Each lattice point has identical surroundings. Explanation: The “Lattice Points” section defines them as “Imaginary points in space that represent the locations of atoms, ions, or molecules within the crystal structure. Each lattice point has identical surroundings.”
40. What is the common coordination number for ions in the Cesium Chloride (CsCl) structure? a) 4 b) 6 c) 8 d) 12Answer: c) 8 Explanation: The “Cesium Chloride (CsCl) Structure” section states: “Each Cs+ is surrounded by 8 Cl− (cubic CN), and each Cl− is surrounded by 8 Cs+ (cubic CN).”