**Crystalline solids** represent structures with well-organized patterns and shapes.

Concept #1: Crystalline Solids

Unlike **crystalline solids**, **amorphous solids** represent structures that lack an organized patterns or shapes.

When examining the particles within a crystal you may observe them tightly packed in an organized pattern. The smallest portion of which is termed the **unit cell**.

There are 7 crystal systems and 14 types of unit cells that naturally occur. The **simple** **cubic unit cell **represents one of the simplest types.

Concept #2: Simple Cubic Unit Cell

The **Simple Cubic Unit Cell** is composed of a cube with an atom at each corner. In the **Lattice Diagram** each of the unit cells are combined to form a crystal lattice. In the **Space Filling Unit Cell Diagram** we are shown that the unit cell uses only 1/8 of each of the 8 corner atoms.

The **body-centered cubic unit cell **is composed of a cube with one atom at each of its corners and one atom at the center of the cube.

Concept #3: Body Centered Cubic Unit Cell

The **face-centered cubic unit cell** is composed of a cube with one atom at each of its corners and one atom in the center of each cube face.

Concept #4: Face Centered Cubic Unit Cell

Example #1: Unit Cell Calculations 1

Example #2: Unit Cell Calculations 1

Example #3: Unit Cell Calculations 1

Example #4: Unit Cell Calculations

Example #5: Unit Cell Calculations 2

Example #6: Unit Cell Calculations 2

Example #7: Unit Cell Calculations 2

Example #8: Unit Cell Calculations 3

Example #9: Unit Cell Calculations 3

Example #10: Unit Cell Calculations 3

Aluminum has a face-centered cubic unit structure and a density of 2.716 g/cm3. Calculate the edge length of the unit cell.
a) 4.041 x 10 -8 cm
b) 3.992 x 10 -8 cm
c) 3.615 x 10 -8 cm
d) 3.247 x 10 -8 cm
e) 2.836 x 10 -8 cm

What is the number of nearest neighbors in a body-centered-cubic lattice?
(A) 12
(B) 8
(C) 6
(D) 4

Determine the radius of an Al atom (in pm) if the density of aluminum is 2.71 g/cm 3. Aluminum crystallizes in a face centered cubic structure with an edge length of 2√2 r.
a) 143 pm
b) 227 pm
c) 96 pm
d) 172 pm
e) 193 pm

Which one of the following elements is considered an insulator?
a. Fe
b. Ga
c. N
d. Ge
e. Si

Which of the following statements about crystalline and amorphous solids is TRUE?
A) A crystalline solid is composed of atoms or molecules arranged with long-range repeating order.
B) An example of a crystalline solid is glass.
C) An example of an amorphous solid is table salt (NaCl).
D) An amorphous solid is composed of atoms or molecules with a majority of its volume empty.
E) All of the above statements are TRUE.

Rank the three cubic crystalline structures in order of increasing space between the particles of the crystal.
Note: FCC = face-centered cubic, BCC = Body-centered cubic, and SC = simple cubic.
a) SC < BCC = FCC
b) FCC < BCC < SC
c) BCC < FCC < SC
d) FCC < SC < BCC
e) SC = BCC < FCC

Sodium chloride, NaCl, crystallizes in a face-centered cubic lattice of chloride ions, with the smaller sodium ions occupying holes between the chloride ions. How many Cl – ions are in contact with any single Na+ ions?
a) 4
b) 6
c) 8
d) 12

Which term describes the number of atoms surrounding an atom in a crystal lattice
a) Unit cell
b) Coordination number
c) Crystalline solid
d) Packing efficiency

What is the edge length of a face-centered cubic unit cell made up of atoms having a radius of 128 pm?
A) 181 pm
B) 362 pm
C) 512 pm
D) 1020 pm
E) 81 pm

Vanadium crystallizes in a body centered cubic structure and has an atomic radius of 131 pm. Determine the density of vanadium, if the edge length of a bcc structure is 4r/√3.
A) 3.06 g/cm3
B) 12.2 g/cm3
C) 6.11 g/cm3
D) 2.77 g/cm3
E) 8.46 g/cm3

The edge of a body-centered-cubic unit cell (which contains two atoms per unit cell) of an element Y was found to be 3.16 x 10 –8 cm. The density of the metal is 19.35 g•cm –3. What is the approximate molar mass of Y?
a) 65.4 g•mol –1
b) 92.0 g•mol –1
c) 184 g•mol –1
d) 238 g•mol –1

Which one of the following cannot form a solid with a lattice based on the sodium chloride structure?
A. CuO
B. NaBr
C. LiF
D. CuCl2
E. RbI

Potassium metal crystallizes in a body-centered cubic structure with a unit cell edge length of 5.31 angstroms. The radius of a potassium atom is __________ angstroms.
A. 2.30
B. 2.66
C. 5.31
D. 1.33
E. 1.88

Determine the number of atoms per unit cell for each of the following metals .Polonium

Tausonite, a mineral composed o f Sr, O, and Ti, has the
cubic unit cell shown in the drawing .What is the empirical formula of this mineral?

Determine the coordination number for each structure.

Calculate the packing efficiency of the face-centered cubic unit cell.

Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.Suppose you dope that 1 - cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).What is the coordination number of each aluminum atom?

Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).Calculate the density of aluminum metal.

Determine the number of atoms per unit cell for each of the following metals .Nickel

Consider the face-centered cubic structure shown below .What is the length of the line (labeled c) that runs diagonally across one of the faces of the cube in terms of r (the atomic radius)?

Consider the face-centered cubic structure shown below .Use the answer to part a and the Pythagorean theorem to derive the expression for the edge length (l) in terms of r.

A face-centered tetragonal lattice is not one of the 14 three-dimensional lattices. Show that a face-centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.

Aluminum metal crystallizes in a face-centered cubic unit
cell.How many Aluminum atoms are in a unit cell?

Aluminum metal crystallizes in a face-centered cubic unit
cell.What is the coordination number of each Aluminum atom?

Aluminum metal crystallizes in a face-centered cubic unit
cell.Estimate the length of the unit cell edge, a, from
the atomic radius of Aluminum (1.43
Å).

An increase in temperature causes most metals to undergo
thermal expansion, which means the volume of the metal
increases upon heating.How does thermal expansion affect
the unit cell length? What is the effect of an increase in temperature on the density of a metal?

Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic, with an edge length of 809 pm.How many atoms of Al are in the unit cell?

Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic, with an edge length of 809 pm.How many atoms of Mg are in the unit cell?

The unit cells for cesium chloride and barium chloride are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.
barium chloride

Consider the rock salt structure in the figure:
What type of structure would result if all the anions were somehow removed, leaving only cations?

Why are X-rays used for crystallography? Why not use some other, more accessible type of electromagnetic
radiation such as ultraviolet light?

Platinum has a cubic crystalline lattice structure.Platinum has what type of cubic lattice structure?

The structures of CsCl, NaCl, and ZnS. Each structure type can be generated by the combination of a two-atom motif and the appropriate lattice.
CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in the following figure.Use ionic radii, Cs+ (r=1.81) and I- (r=2.06), to predict with which structure CsI will crystallize.

Does the following diagram best describe a crystalline solid, a liquid,
or a gas?

Two patterns of packing for two different are shown here.
Determine the two-dimensional unit cell for (i).

Two patterns of packing for two different are shown here.
Determine the two-dimensional unit cell for (ii).

A tetrahedral site in a close-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a close-packed arrangement the spheres are in contact and if the spheres have a radius r, the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube.Find the length of the body diagonal of this cube.

Melting and boiling points for benzene, toluene, and phenol.In which substance do the molecules pack more efficiently?

Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain 90 .
What kind of primitive lattice have you made?

The volume of a unit cell of diamond is 0.0454 nm3, and the density of diamond is 3.52 g/cm3.Find the number of carbon atoms in a unit cell of diamond.

Which arrangement of atoms in a lattice represents
close-packing?

Determine the coordination number for each structure.

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice?

Consider the body-centered cubic structure shown below: .Use the Pythagorean theorem to derive an expression for the length of the line (labeled b) that runs diagonally across one of the faces of the cube in terms the edge length (l).

The density of solid Ag is 10.5 g/cm3.a. How many atoms are present per cubic centimeter of Ag?b. As a solid, Ag adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Ag?c. What is the volume of a unit cell of this metal?d. What is the edge length of a unit cell of Ag?

Consider a body-centered cubic unit cell as shown here.a. How many corner atoms (orange) are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube? c. How many body atoms shown in this image? d. What fraction of each body atom is inside the boundaries of the cube? e. If you sum all the fractions of atoms, how many atoms are actually inside a body-centered cubic unit cell?

How many atoms are in one body-centered cubic unit cell of a metal?
A) 1
B) 2
C) 3
D) 4

Rank the crystal lattice structures in order of decreasing efficiency of space in the structure.Simple cubic, Body centered cubic, Face centered cubic, Hexegonal close packed

The structure of manganese fluoride can be described as a simple cubic array of manganese ions with fluoride ions at the center of each edge of the cubic unit cell. What is the charge of the manganese ions in this compound?

a. The density of solid Fe is 7.87 g/cm3. How many atoms are present per cubic centimeter of Fe? b. As a solid, Fe adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of Fe? c. What is the volume of a unit cell of this metal? d. What is the edge length of a unit cell of Fe?

Lithium crystallizes in a body centered cubic unit cell. What is the mass of one unit cell? Report answer in grams.

Determine the number of atoms per unit cell for each of the following metals.a. Tungstenb. Nickel

Metallic copper crystallizes in a face-centered cubic lattice, with one Cu atom per lattice point. If the edge length of the unit cell is found to be 362 pm, what is the metallic radius of Cu in pm?

The coinage metals—copper, silver, and gold—crystallize in a cubic closest packed structure. Use the density of copper (8.95 g/cm3) and its molar mass (63.55 g/mol) to calculate an approximate atomic radius for copper.

Argon has a cubic closest packed structure as a solid. Assuming that argon has a radius of 190. pm, calculate the density of solid argon.

The structure of the compound K 2O is best described as a cubic closest packed array of oxide ions with the potassium ions in tetrahedral holes. What percent of the tetrahedral holes are occupied in this solid?

A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead.

What fraction of the total volume of a cubic closest packed structure is occupied by atoms? ( Hint: Vsphere = 4/3 πr3.) What fraction of the total volume of a simple cubic structure is occupied by atoms? Compare the answers.

A certain metal fluoride crystallizes in such a way that the fluoride ions occupy simple cubic lattice sites, while the metal ions occupy the body centers of half the cubes. What is the formula of the metal fluoride?

The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69). Given that the density of cesium chloride is 3.97 g/cm3, and assuming that the chloride and cesium ions touch along the body diagonal of the cubic unit cell, calculate the distance between the centers of adjacent Cs+ and Cl- ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of Cs+ is 169 pm, and the ionic radius of Cl - is 181 pm.

Polonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm3, a radius of 167 pm, and a molar mass of 209 g/mol.Use these data to estimate Avogadros number (the number of atoms in one mole).

Calcium crystallizes in a cubic closest packed structure. If the atomic radius of calcium is 197 pm, find the density of the solid.

An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. What is the mass of a unit cell?

An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. Calculate an approximate atomic mass for the element.

Ni3Al is used in the turbines of aircraft engines because of its strength and low density. Nickel metal has a cubic close-packed structure with a face-centered cubic unit cell, whereas Ni3Al has the ordered cubic structure shown in the figure below. The length of the cubic unit cell edge is 3.53 Ni3Al for nickel and 3.56 Ni3Al for Ni3Al. Use these data to calculate and compare the densities of these two materials.Give the calculated density of pure nickel (FCC with an edge length of 3.53 Å).

Ni3Al is used in the turbines of aircraft engines because of its strength and low density. Nickel metal has a cubic close-packed structure with a face-centered cubic unit cell, whereas Ni3Al has the ordered cubic structure shown in the figure below. The length of the cubic unit cell edge is 3.53 Ni3Al for nickel and 3.56 Ni3Al for Ni3Al. Use these data to calculate and compare the densities of these two materials.Give the calculated density of the Ni3Al alloy (ordered structure shown in the image with an edge length of 3.56 Å).

Alabandite is a mineral composed of manganese(II) sulfide (MnS). The mineral adopts the rock salt structure. The length of an edge of the MnS unit cell is 5.223 Å at 25˚C. Determine the density of MnS in g/cm3 m g/cm^3.

An ideal quantum dot for use in TVs does not contain any cadmium due to concerns about disposal. One potential material for this purpose is InP, which adopts the zinc blende (ZnS) structure (face-centered cubic). The unit cell edge length is 5.869If the quantum dot is shaped like a cube, how many of each type of atom are there in a cubic crystal with edge length of 3.00 nm?

An ideal quantum dot for use in TVs does not contain any cadmium due to concerns about disposal. One potential material for this purpose is InP, which adopts the zinc blende (ZnS) structure (face-centered cubic). The unit cell edge length is 5.869 Suppose one nanoparticle has an edge length of 3.00 nm and another has an edge length of 5.00 nm. If one of the nanoparticles emits blue light and the other emits orange light, which color is emitted by the crystal with the 3.00 nm edge length? With the 5.00 nm edge length?

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 Å. The atom in the center of the face is in contact with the corner atoms, as shown in the drawing.Calculate the atomic radius of an iridium atom.

Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium.

A metallic solid with atoms in a face-centered cubic unit cell with an edge length of 392 pm has a density of 21.45 g/cm3. Calculate the atomic mass and the atomic radius of the metal. Identify the metal.

Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. ( Hint: In a body-centered arrangement of spheres, the spheres touch across the body diagonal.)

Calculate the fraction of empty space in cubic closest packing to five significant figures.

What is the formula for the compound that crystallizes with a cubic closest packed array of sulfur ions, and that contains zinc ions in 1/8 of the tetrahedral holes and aluminum ions in 1/2 of the octahedral holes?

Rhodium crystallizes in a face-centered cubic unit cell. The radius of a rhodium atom is 135 pm.Determine the density of rhodium in g/cm3.

The unit cell of MgO is shown below.Does MgO have a structure like that of NaCl or ZnS? If the density of MgO is 3.58 g/cm3, estimate the radius (in centimeters) of the O2- anions and the Mg2+ cations.

Palladium crystallizes with a face-centered cubic structure. It has a density of 12.0 g/cm3, a radius of 138 pm, and a molar mass of 106.42 g/mol.Use these data to calculate Avogadro's number.

KF has the same type of crystal structure as NaCl. The unit cell of KF has an edge length of 5.39 Å. Find the density of KF.

What is the number of atoms per unit cell for Silver, Ag?

Platinum nanoparticles of diameter ~2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å.Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is (4/3)πr3large{left( {frac{4}{3}} ight)pi r^3}. Recall that 1 Å = 1 x 10–10 m and 1 nm = 1 x 10–9 m.

Platinum nanoparticles of diameter ~2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å.Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4πr2) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 Å.

Platinum nanoparticles of diameter ~2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å.Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is (4/3)πr3. Recall that 1 Å = 1 x 10–10 m and 1 nm = 1 x 10–9 m. Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4πr2) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 Å.Using your results, calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle.

Platinum nanoparticles of diameter ~2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å.Estimate how many platinum atoms would fit into a 2.0-nm sphere; the volume of a sphere is (4/3)πr3. Recall that 1 Å = 1 x 10–10 m and 1 nm = 1 x 10–9 m. Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere (4πr2) and assuming that the "footprint" of one Pt atom can be estimated from its atomic diameter of 2.8 Å.Using your results, calculate the percentage of Pt atoms that are on the surface of a 5.0-nm nanoparticle.

Calculate the volume in Å3 of each of the following types of cubic unit cells if it is composed of atoms with an atomic radius of 1.81 Å .face-centered cubic

Zinc oxide adopts the zinc blende crystal structure (figure below). How many Zn 2+ ions are in the ZnO unit cell?

What is the coordination number of an aluminum atom in the face-centered cubic structure of aluminum?

Calcium sulfide adopts the sodium chloride crystal structure (figure below). How many S 2− ions are in the CaS unit cell?

Aluminum (atomic radius = 1.43 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face-centered cubic unit cell and the density of aluminum.

Zinc selenide (ZnSe) crystallizes in the zinc blende structure and has a density of 5.42 g/cm3. What is the mass of a unit cell?

An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. How many atoms are in each unit cell?

Clausthalite is a mineral composed of lead selenide (PbSe). The mineral adopts a NaCl-type structure. The density of PbSe at 25 oC is 8.27 g/cm3.Calculate the length of an edge (a) of the PbSe unit cell.

The unit cell of a compound containing potassium, aluminum, and fluorine is shown here.What is the empirical formula?

The unit cell of a compound containing potassium, aluminum, and fluorine is shown here.What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)?

The unit cells for lithium oxide and silver iodide are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.a) lithium oxideb) silver iodide

Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.Describe the
shape of the coordination environment for the sodium
ion.

Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic, with an edge length of 809 pm.How many atoms of O are in the unit cell?

Explain why the chemically similar alkali metal chlorides NaCl and CsCl have different structures, whereas the chemically different NaCl and MnS have the same structure.

You may want to reference (Pages 460 - 462) Section 11.7 while completing this problem.Which of the following statements are true?(a) The liquid crystal state is another phase of matter, just like solid, liquid, and gas.(b) Liquid crystalline molecules are generally spherical in shape.(c) Molecules that exhibit a liquid crystalline phase do so at well-defined temperatures and pressures.(d) Molecules that exhibit a liquid crystalline phase show weaker-than-expected intermolecular forces.(e) Molecules containing only carbon and hydrogen are likely to form liquid crystalline phases.(f) Molecules can exhibit more than one liquid crystalline phase.

Rubidium iodide crystallizes with a cubic unit cell that contains iodide ions at the corners and a rubidium ion in the center. What is the formula of the compound?

NaH crystallizes with the same crystal structure as NaCl. The edge length of the cubic unit cell of NaH is 4.880 Å.(a) Calculate the ionic radius of H−. (The ionic radius of Li+ is 0.0.95 Å.)

At room temperature and pressure RbI crystallizes with the NaCl-type structure. Use ionic radii to predict the length of the cubic unit cell edge. Use this value to estimate the density.

A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(a) What is the empirical formula of this compound? Explain your answer.

Boron nitride (BN) exists in two forms. The first is a slippery solid formed from the reaction of BCl 3 with NH 3, followed by heating in an ammonia atmosphere at 750 ˚C. Subjecting the first form of BN to a pressure of 85,000 atm at 1800 ˚C produces a second form that is the second hardest substance known. Both forms of BN remain solids to 3000 ˚C. Suggest structures for the two forms of BN.

CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in the following figure.Use ionic radii, Na+(r = 1.61 Å) and I–(r = 2.06 Å), to predict with which structure NaI will crystallize.

The ionic substance strontium oxide, SrO, forms from the direct reaction of strontium metal with molecular oxygen. The arrangement of the ions in solid SrO is analogous to that in solid NaCl and is shown here.The experimental density of SrO is 5.10 g/cm3. Based on the ionic radii in the figure below, predict the length of the side of the cube in the figure. Given your answer, what is the number of formula units of SrO that are contained in the cube in the figure?

Which compound is most likely to crystallize in the zinc blende structure?(a) RbCl (Rb+ radius = 148 pm; Cl– radius = 181 pm)(b) MgCl2 (Mg2+ = radius 65 pm; Cl– radius = 181 pm)(c) CuI (Cu+ radius = 96 pm; I– radius = 216 pm)

Identify the coordination number for each structure.

Identify the structure of each of the two unit cells shown for lithium oxide and silver iodide shown here as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

Cadmium sulfide, sometimes used as a yellow pigment by artists, crystallizes with cadmium, occupying one half of the tetrahedral holes in a closest packed array of sulfide ions. What is the formula of cadmium sulfide? Explain your answer.

A compound of cadmium, tin, and phosphorus is used in the fabrication of some semiconductors. It crystallizes with cadmium occupying one-fourth of the tetrahedral holes and tin occupying one-fourth of the tetrahedral holes in a closest packed array of phosphide ions. What is the formula of the compound? Explain your answer.

What is the formula of the magnetic oxide of cobalt, used in recording tapes, that crystallizes with cobalt atoms occupying one-eighth of the tetrahedral holes and one-half of the octahedral holes in a closely packed array of oxide ions?

Calculate the packing efficiency of the two-dimensional lattice shown here:

Two patterns of packing two different spheres are shown here.Determine
whether the lattice vectors are of the same
length or of different lengths for the structure (i).

Two patterns of packing two different spheres are shown here.Determine the type of two-dimensional lattice for the structure (i).

Two patterns of packing two different spheres are shown here.Determine the type of two-dimensional lattice for the structure (ii).

The unit cell of nickel arsenide is shown here. What type of lattice does this crystal possess?

What type of two-dimensional lattice describes the structure of a single layer of close-packed atoms?Close packing of equal-sized spheres. Close packing of equal-sized spheres. Hexagonal (left) close packing and
cubic (right) close packing are equally efficient ways of packing spheres. The red and yellow
dots indicate the positions of depressions between atoms.

Imagine you generate a three-dimensional lattice by taking a and b vectors that form a two-dimensional square lattice. Then add a third vector, c, that is of different length and perpendicular to the first two. Which of the seven three-dimensional lattices results?

Make a drawing of each unit cell: simple cubic, body-centered cubic, and face-centered cubic.

An oxide of titanium crystallizes with the following unit cell (titanium = gray; oxygen = red).What is the formula of the oxide?

The unit cells for lithium oxide and silver iodide are shown below.Show that the ratio of cations to anions in each unit cell corresponds
to the ratio of cations to anions in the formula of each
compound.

At standard temperature and pressure the molar volumes of Cl2 and NH3 gases are 22.06 and 22.40 L, respectively.On cooling to 160 K, both substances form crystalline solids. Do you expect the molar volumes to decrease or increase on cooling the gases to 160 K?

The structures of some common crystalline substances are shown below. Show that the net composition of each unit cell corresponds to the correct formula of each substance.

A tetrahedral site in a close-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a close-packed arrangement the spheres are in contact and if the spheres have a radius r, the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube.Find the radius of the tetrahedral hole.

Assume the two-dimensional structure of an ionic compound, M xAy, isWhat is the empirical formula of this ionic compound?

Which arrangement of cations (yellow) and anions (blue) in a lattice is the more stable?

Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of the tantalum compound whose unit cell is depicted below:

Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of the tantalum compound whose unit cell is depicted below:

As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:What is the change in unit cell?

An oxide of rhenium crystallizes with the unit cell depicted here (where rhenium = gray and oxygen = red).What is the formula of the oxide?

Of the five major types of crystalline solid, which does the following form, and why: Ni?

The memory metal, nitinol, is an alloy of nickel and titanium. It is called a memory metal because after being deformed, a piece of nitinol wire will return to its original shape. The structure of nitinol consists of a simple cubic array of Ni atoms and an inner penetrating simple cubic array of Ti atoms. In the extended lattice, a Ti atom is found at the center of a cube of Ni atoms; the reverse is also true. Describe the unit cell for nitinol.

Of the five major types of crystalline solid, which does the following form, and why: F2?

The memory metal, nitinol, is an alloy of nickel and titanium. It is called a memory metal because after being deformed, a piece of nitinol wire will return to its original shape. The structure of nitinol consists of a simple cubic array of Ni atoms and an inner penetrating simple cubic array of Ti atoms. In the extended lattice, a Ti atom is found at the center of a cube of Ni atoms; the reverse is also true. What is the empirical formula of nitinol?

In the unit cell drawing on the right, why do we see eight Sm atoms and nine Co atoms if the empirical formula is SmCo5?

Which one of these unit cells would
you expect to represent the densest
packing of spheres?

Materials containing the elements Y, Ba, Cu, and O that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductor would have the structure shown in part (a) of the following figure.What is the formula of this ideal perovskite material?

Consider the two-dimensional square lattice of the figure below. The "packing efficiency" for a two-dimensional structure would be the area of the atoms divided by the area of the unit cell, times 100%. What is the packing efficiency for a square lattice for atoms of radius large{frac {a}{2}} that are centered at the lattice points?

Calculate the packing efficiency of the body-centered cubic unit cell.

One of the most important enzymes in the world—nitrogenase, the plant protein that catalyzes nitrogen fixation—contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell (d of Mo = 10.28 g/cm3). Determine the edge length of the unit cell.

Tantalum (Ta; d = 16.634 g/cm3 and ℳ = 180.9479 g/mol) has a body-centered cubic structure with a unit-cell edge length of 3.3058 Å. Use these data to calculate Avogadro’s number.

What is the edge length of a body-centered cubic unit cell made up of atoms that each has a radius of 168 pm?

Barium is the largest nonradioactive alkaline earth metal. It has a body-centered cubic unit cell and a density of 3.62 g/cm3. What is the atomic radius of barium? [Volume of a sphere: V = 4/3(πr3).]

The densities of the elements K, Ca, Sc, and Ti are 0.86, 1.5, 3.2, and 4.5 g/cm3, respectively. One of these elements crystallizes
in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure.Which one crystallizes in
the body-centered cubic structure?

Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3.Use this information and Avogadros number (NA = 6.022 1023) to estimate the atomic radius of sodium.

Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3.If it didnt react so vigorously, sodium could float on water. Use the answer from Part A to estimate the density of Na if its structure were that of a cubic close-packed metal.

Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3.Would it still float on water?

Calcium crystallizes with a body-centered cubic structure.Estimate the length of the unit cell edge, a, from the atomic radius (r) of calcium, 1.97 Å .

Calcium crystallizes with a body-centered cubic structure.Estimate the density of Ca metal based on the unit cell properties you determined in the previous parts.

Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium.

The unit cell for nickel arsenide is shown below. What is the formula of this compound?

Barium has a density of 3.59 g/cm3 and crystallizes with a body-centered cubic unit cell. Calculate the radius of a barium atom.

What is the number of atoms per unit cell for Polonium, Po?

Chromium adopts the body-centered cubic unit cell in its crystal structure. If the density of chromium is 7.14 g/cm3, find its atomic radius.

Potassium adopts the body-centered cubic unit cell in its crystal structure. If the atomic radius of potassium is 227 pm, find the edge length of the unit cell.

Molybdenum crystallizes with a body-centered unit cell. The radius of a molybdenum atom is 136 pm. Calculate the density of molybdenum.

Chromium crystallizes with a body-centered cubic unit cell. The radius of a chromium atom is 125 pm. Calculate the density of solid crystalline chromium in grams per cubic centimeter.

The unit cell of a compound containing Co and O has a unit cell shown below. The Co atoms are on the corners, and the O atoms are completely within the unit cell.What is the empirical
formula of this compound?

What is the coordination number of a chromium atom in the body-centered cubic structure of chromium?

The unit cell of a compound containing Co and O has a unit cell shown below. The Co atoms are on the corners, and the O atoms are completely within the unit cell.What is the oxidation state of
the metal?

Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 Å.(b) Calculate the density of tungsten.

Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms
at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.What is the coordination number of strontium in the perovskite structure?

The unit cells for cesium chloride and barium chloride are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 Å. The atom in the center of the face is in contact with the corner atoms, as shown in the drawing.Calculate the density of iridium metal.

Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.The unit cell edge length is 5.55 Å . Determine the density of Na2O.

The density of solid Ni is 8.90 g/cm3. How many atoms are present per cubic centimeter of Ni?_____ atoms/cm3As a solid, Ni adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Ni?_____ unit cells/cm3What is the volume of a unit cell of this metal?_____ cm3What is the edge length of a unit cell of Ni?_____ cm

An unknown metal is found to have a density of 7.8748 g/cm3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is found to be 0.28864 nm .Calculate the atomic mass of the metal.

Iridium (Ir) has a face-centered cubic unit cell with an edge length of 383.3 pm. Calculate the density of solid iridium.

As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:Which crystal structure has the greater packing efficiency?

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. Which structure(s) corresponds to the densest packing of atoms?

Compare the crystal structure of diamond (C) and zinc blende (ZnS). What are the key similarities and
differences between the two structures?

Show how the zinc blende unit cell contains a cation-to-anion ratio of 1:1.

The unit cell of nickel arsenide is shown here. What is the empirical formula?

Show how the cesium chloride and sodium chloride unit cells each contain a cation-to-anion ratio of 1:1.

Calculate the number of atoms per unit cell in each type of cubic unit cell.Enter three integers separated by commas (e.g., 1, 2, 3) in the following order: primitive cubic, body-centered cubic, and face-centered cubic.

The unit cells for lithium oxide and silver iodide are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

An oxide of uranium crystallizes with the following unit cell (uranium = gray; oxygen = red) What is the formula of the oxide?

Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å(b) Calculate the density of barium.

The substance lithium is found to crystallize in a cubic lattice, with an edge length of 346.0 pm. If the density of solid lithium is 0.5565 g/cm3, how many Li atoms are there per unit cell?

Lithium crystallizes in a body-centered cubic unit cell. What is the mass of one unit cell in grams?

One of the most important enzymes in the world—nitrogenase, the plant protein that catalyzes nitrogen fixation—contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell (d of Mo = 10.28 g/cm3). Calculate the atomic radius of Mo.

An element crystallizes in a face-centered cubic lattice. The
edge of the unit cell is 4.078×10−8 cm, and the density of the crystal is 19.30 g/cm3. Calculate the atomic weight of the element.

Copper crystallizes in a face-centered cubic lattice. If the edge of the unit cell is 351 pm, what is the radius of the copper atom?

Gold crystallizes in a face-centered cubic structure. What is the edge length of the unit cell if the atomic radius of gold is 144 pm?a) 204 pmb) 288 pmc) 333 pmd) 407 pm

Polonium, the Period 6 member of Group 6A(16), is a rare radioactive metal that is the only element with a crystal structure based on the simple cubic unit cell. If its density is 9.142 g/cm3, calculate an approximate atomic radius for polonium.

MnO has either the NaCl type structure or the CsCl type structure. The edge length of the MnO unit cell is 4.47 x 10-8 cm and the density of MnO is 5.28 g/cm 3. Assuming that the ionic radius of oxygen is 140. pm, estimate the ionic radius of manganese.

Cobalt metal crystallizes in a hexagonal closest packed structure. What is the coordination number of a cobalt atom?

Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing .To see
the full coordination environment of the other ions,
we have to consider neighboring unit cells. How many oxygens are coordinated to strontium?

Calcium crystallizes with a body-centered cubic structure.How many Ca atoms are contained in each unit cell?

A particular form of cinnabar (HgS) adopts the zinc blende structure shown. The length of the unit cell side is 5.852 Å. Calculate the density of HgS in this form.

One of the various manganese oxides crystallizes with a cubic unit cell that contains manganese ions at the corners and in the center. Oxide ions are located at the center of each edge of the unit cell. What is the formula of the compound?

When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68 % of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube in terms of r.

Platinum (atomic radius = 1.38 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face-centered cubic unit cell and the density of platinum.

What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?

The density of solid Cr is 7.15 g/cm 3. How many atoms are present per cubic centimeter of Cr? in atoms/cm3As a solid, Cr adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of Cr? in unit cells/cm3What is the volume of a unit cell of this metal? in cm 3What is the edge length of a unit cell of Cr? in cm

Nickel has a face-centered cubic unit cell. The density of nickel is 6.84 g/cm 3. Calculate a value for the atomic radius of nickel.

Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is 139 pm .Calculate the edge length of the unit cell.

Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms
at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.If the edge length of the unit cell is 3.905 Å, calculate the density of perovskite in g/cm3 m g/cm^3.

Nickel metal crystallizes in a cubic closest packed structure. What is the coordination number of a nickel atom?

Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is 139 pm.Calculate the density of platinum in g/cm3.

The density of an unknown metal is 12.3 g/cm3 and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal.

Perovskite is a mineral containing calcium, titanium, and oxygen. Two different representations of the unit cell are shown below. Show that both these representations give the same formula and the same number of oxygen atoms around each titanium atom.

In solid KCl the smallest distance between the centers of a potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride.

Calcium crystallizes with a body-centered cubic structure.How many nearest neighbors does each Ca atom possess?

Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 Å.(a) What is the atomic radius of tungsten in this structure?

The density of aluminum is 2.7 g/cm3; that of silicon is 2.3 g/cm3. Explain why Si has the lower density even though it has heavier atoms.

Cobalt fluoride crystallizes in a closest packed array of fluoride ions with the cobalt ions filling one-half of the octahedral holes. What is the formula of this compound?

Iron has a density of 7.86 g/cm3 and crystallizes in a body-centered cubic lattice. Show that only 68% of a body-centered lattice is actually occupied by atoms, and determine the atomic radius of iron.

An atom located on a face of a unit cell is shared equally between ____ unit cells.23468

The radius of gold is 144 pm, and the density is 19.32 g/cm3. Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?

Consider a simple cubic (a.k.a, primitive cubic) unit cell as shown here.(i) How many atoms are shown in this image?(ii) What fraction of each atom is inside the boundaries of the cube?(iii) If you sum all (the fractions of atoms, how many atoms are actually inside a simple cubic unit cell?

The density of solid W is 19.3 g/cm3. a) How many atoms are present per cubic centimeter of W? b) As a solid, W adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of W? c) What is the volume of a unit cell of this metal? d) What is the edge length of a unit cell of W?

Consider a face-centered cubic unit cell as shown here.a. How many corner atoms are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube?c. How many face atoms are shown in this image?d. What fraction of each face atom is inside the boundaries of the cube?e. If you sum all the fractions of atoms, how many atoms are actually inside a face-centered cubic unit cell?

Arrange the three common unit cells in order from least dense to most dense packing.

The radius of tungsten is 137 pm and the density is 19.3 g/cm3. Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?

An atom has radius of 138
pm and crystallizes in a body-centered cubic unit cell. What is the volume of the
unit cell?

A particular form of cinnabar (HgS) adopts the zinc blende structure shown. The length of the unit cell side is 5.852 Å. The mineral tiemmanite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell side in this mineral is 6.085 Å. What accounts for the larger unit cell length in tiemmanite?

The unit cell for a pure xenon fluoride compound is shown below. What is the formula of the compound?

Consider the body-centered cubic structure shown below: .What is the length of the line (labeled c) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of r (the atomic radius)?

At room temperature and pressure RbI crystallizes with the NaCl-type structure.At high pressure the structure transforms to one with a CsCl-type structure. Use ionic radii to predict the length of the cubic unit cell edge for the high-pressure form of RbI. Radius of Rb+ is 1.52 Å and I- is 2.20 Å

Rhodium has density of 12.43 g/cm3 and crystallizes with the face-centered cubic unit cell.Calculate the radius of a rhodium atom.