Some may mistake the structure type of CsCl with NaCl, but really the two are different. The packing efficiency is the fraction of crystal or known as the unit cell which is actually obtained by the atoms. Now, the distance between the two atoms will be the sum of twice the radius of cesium and twice the radius of chloride equal to 7.15. of atoms present in one unit cell, Mass of an atom present in the unit cell = m/NA. Which of the following three types of packing is most efficient? Required fields are marked *, \(\begin{array}{l}(\sqrt{8} r)^{3}\end{array} \), \(\begin{array}{l} The\ Packing\ efficiency =\frac{Total\ volume\ of\ sphere}{volume\ of\ cube}\times 100\end{array} \), \(\begin{array}{l} =\frac{\frac{16}{3}\pi r^{3}}{8\sqrt{8}r^{3}}\times 100\end{array} \), \(\begin{array}{l}=\sqrt{2}~a\end{array} \), \(\begin{array}{l}c^2~=~ 3a^2\end{array} \), \(\begin{array}{l}c = \sqrt{3} a\end{array} \), \(\begin{array}{l}r = \frac {c}{4}\end{array} \), \(\begin{array}{l} \frac{\sqrt{3}}{4}~a\end{array} \), \(\begin{array}{l} a =\frac {4}{\sqrt{3}} r\end{array} \), \(\begin{array}{l}Packing\ efficiency = \frac{volume~ occupied~ by~ two~ spheres~ in~ unit~ cell}{Total~ volume~ of~ unit ~cell} 100\end{array} \), \(\begin{array}{l}=\frac {2~~\left( \frac 43 \right) \pi r^3~~100}{( \frac {4}{\sqrt{3}})^3}\end{array} \), \(\begin{array}{l}Bond\ length\ i.e\ distance\ between\ 2\ nearest\ C\ atom = \frac{\sqrt{3}a}{8}\end{array} \), \(\begin{array}{l}rc = \frac{\sqrt{3}a}{8}\end{array} \), \(\begin{array}{l}r = \frac a2 \end{array} \), \(\begin{array}{l}Packing\ efficiency = \frac{volume~ occupied~ by~ one~ atom}{Total~ volume~ of~ unit ~cell} 100\end{array} \), \(\begin{array}{l}= \frac {\left( \frac 43 \right) \pi r^3~~100}{( 2 r)^3} \end{array} \). As a result, particles occupy 74% of the entire volume in the FCC, CCP, and HCP crystal lattice, whereas void volume, or empty space, makes up 26% of the total volume. The calculation of packing efficiency can be done using geometry in 3 structures, which are: CCP and HCP structures Simple Cubic Lattice Structures Body-Centred Cubic Structures Factors Which Affects The Packing Efficiency It means a^3 or if defined in terms of r, then it is (2 \[\sqrt{2}\] r)^3. A vacant Which crystal structure has the greatest packing efficiency? Write the relation between a and r for the given type of crystal lattice and calculate r. Find the value of M/N from the following formula. As a result, atoms occupy 68 % volume of the bcc unit lattice while void space, or 32 %, is left unoccupied. 3. Vedantu LIVE Online Master Classes is an incredibly personalized tutoring platform for you, while you are staying at your home. (8 corners of a given atom x 1/8 of the given atom's unit cell) + (6 faces x 1/2 contribution) = 4 atoms). Packing efficiency refers to space's percentage which is the constituent particles occupies when packed within the lattice. corners of a cube, so the Cl- has CN = 8. Let us take a unit cell of edge length a. P.E = ( area of circle) ( area of unit cell) Therefore, 1 gram of NaCl = 6.02358.51023 molecules = 1.021022 molecules of sodium chloride. The structure must balance both types of forces. Questions are asked from almost all sections of the chapter including topics like introduction, crystal lattice, classification of solids, unit cells, closed packing of spheres, cubic and hexagonal lattice structure, common cubic crystal structure, void and radius ratios, point defects in solids and nearest-neighbor atoms. Therefore, in a simple cubic lattice, particles take up 52.36 % of space whereas void volume, or the remaining 47.64 %, is empty space. Ionic equilibrium ionization of acids and bases, New technology can detect more strains, which could help poultry industry produce safer chickens ScienceDaily, Lab creates first heat-tolerant, stable fibers from wet-spinning process ScienceDaily, A ThreeWay Regioselective Synthesis of AminoAcid Decorated Imidazole, Purine and Pyrimidine Derivatives by Multicomponent Chemistry Starting from Prebiotic Diaminomaleonitrile, Directive influence of the various functional group in mono substituted benzene, New light-powered catalysts could aid in manufacturing ScienceDaily, Interstitial compounds of d and f block elements, Points out solids different properties like density, isotropy, and consistency, Solids various attributes can be derived from packing efficiencys help. Note that each ion is 8-coordinate rather than 6-coordinate as in NaCl. Density of the unit cell is same as the density of the substance. The packing efficiency of simple cubic lattice is 52.4%. Here are some of the strategies that can help you deal with some of the most commonly asked questions of solid state that appear in IIT JEEexams: Go through the chapter, that is, solid states thoroughly. Now, take the radius of each sphere to be r. 6.11B: Structure - Caesium Chloride (CsCl) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. No Board Exams for Class 12: Students Safety First! What type of unit cell is Caesium Chloride as seen in the picture. \(\begin{array}{l} =\frac{\frac{16}{3}\pi r^{3}}{8\sqrt{8}r^{3}}\times 100\end{array} \). As shown in part (a) in Figure 12.8, a simple cubic lattice of anions contains only one kind of hole, located in the center of the unit cell. as illustrated in the following numerical. ), Finally, we find the density by mass divided by volume. An atom or ion in a cubic hole therefore has a . Its packing efficiency is about 52%. Thus, the edge length (a) or side of the cube and the radius (r) of each particle are related as a = 2r. Therefore, these sites are much smaller than those in the square lattice. 4. So,Option D is correct. It must always be seen less than 100 percent as it is not possible to pack the spheres where atoms are usually spherical without having some empty space between them. The constituent particles i.e. The packing fraction of different types of packing in unit cells is calculated below: Hexagonal close packing (hcp) and cubic close packing (ccp) have the same packing efficiency. Instead, it is non-closed packed. This lattice framework is arrange by the chloride ions forming a cubic structure. Let it be denoted by n. Norton. Imagine that we start with the single layer of green atoms shown below. Caesium Chloride is a non-closed packed unit cell. The particles touch each other along the edge. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Chemistry related queries and study materials, Your Mobile number and Email id will not be published. centred cubic unit cell contains 4 atoms. They have two options for doing so: cubic close packing (CCP) and hexagonal close packing (HCP). No. What is the percentage packing efficiency of the unit cells as shown. Example 1: Calculate the total volume of particles in the BCC lattice. Question 1: Packing efficiency of simple cubic unit cell is .. Hence, volume occupied by particles in bcc unit cell = 2 ((23 a3) / 16), volume occupied by particles in bcc unit cell = 3 a3 / 8 (Equation 2), Packing efficiency = (3 a3 / 8a3) 100. Let 'a' be the edge length of the unit cell and r be the radius of sphere. Also, study topics like latent heat of vaporization, latent heat of fusion, phase diagram, specific heat, and triple points in regard to this chapter. These are shown in three different ways in the Figure below . To determine this, we multiply the previous eight corners by one-eighth and add one for the additional lattice point in the center. This clearly states that this will be a more stable lattice than the square one. Unit cell bcc contains 4 particles. When we put the atoms in the octahedral void, the packing is of the form of ABCABC, so it is known as CCP, while the unit cell is FCC. In atomicsystems, by convention, the APF is determined by assuming that atoms are rigid spheres. Substitution for r from equation 3, we get, Volume of one particle = 4/3 (a / 22)3, Volume of one particle = 4/3 a3 (1/22)3. of Sphere present in one FCC unit cell =4, The volume of the sphere = 4 x(4/3) r3, \(\begin{array}{l} The\ Packing\ efficiency =\frac{Total\ volume\ of\ sphere}{volume\ of\ cube}\times 100\end{array} \) The cations are located at the center of the anions cube and the anions are located at the center of the cations cube. The structure of the solid can be identified and determined using packing efficiency. Therefore body diagonalc = 4r, Volume of the unit cell = a3= (4r / 3)3= 64r3 / 33, Let r be the radius of sphere and a be the edge length of the cube, In fcc, the corner spheres are in touch with the face centred sphere. Let us calculate the packing efficiency in different types of, As the sphere at the centre touches the sphere at the corner. One simple ionic structure is: One way to describe the crystal is to consider the cations and anions Let the edge length or side of the cube a, and the radius of each particle be r. The particles along face diagonal touch each other. As per the diagram, the face of the cube is represented by ABCD, then you can see a triangle ABC. It can be evaluated with the help of geometry in three structures known as: There are many factors which are defined for affecting the packing efficiency of the unit cell: In this, both types of packing efficiency, hexagonal close packing or cubical lattice closed packing is done, and the packing efficiency is the same in both. The importance of packing efficiency is in the following ways: It represents the solid structure of an object. Both hcp & ccp though different in form are equally efficient. The interstitial coordination number is 3 and the interstitial coordination geometry is triangular. Since chloride ions are present at the corners of the cube, therefore, we can determine the radius of chloride ions which will be equal to the length of the side of the cube, therefore, the length of the chloride will be 2.06 Armstrong and cesium ion will be the difference between 3.57 and 2.06 which will be equal to 1.51 Armstrong. We end up with 1.79 x 10-22 g/atom. The cations are located at the center of the anions cube and the anions are located at the center of the cations cube. Thus the radius of an atom is half the side of the simple cubic unit cell. And the evaluated interstitials site is 9.31%. It is stated that we can see the particles are in touch only at the edges. And so, the packing efficiency reduces time, usage of materials and the cost of generating the products. 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According to Pythagoras Theorem, the triangle ABC has a right angle. The numerator should be 16 not 8. "Stable Structure of Halides. For calculating the packing efficiency in a cubical closed lattice structure, we assume the unit cell with the side length of a and face diagonals AC to let it b. Solution Verified Create an account to view solutions Recommended textbook solutions Fundamentals of Electric Circuits 6th Edition ISBN: 9780078028229 (11 more) Charles Alexander, Matthew Sadiku 2,120 solutions 6: Structures and Energetics of Metallic and Ionic solids, { "6.11A:_Structure_-_Rock_Salt_(NaCl)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11B:_Structure_-_Caesium_Chloride_(CsCl)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11C:_Structure_-_Fluorite_(CaF)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11D:_Structure_-_Antifluorite" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11E:_Structure_-_Zinc_Blende_(ZnS)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11F:_Structure_-_-Cristobalite_(SiO)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11H:_Structure_-_Rutile_(TiO)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11I:_Structure_-_Layers_((CdI_2)_and_(CdCl_2))" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11J:_Structure_-_Perovskite_((CaTiO_3))" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "6.01:_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.02:_Packing_of_Spheres" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.03:_The_Packing_of_Spheres_Model_Applied_to_the_Structures_of_Elements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.04:_Polymorphism_in_Metals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.05:_Metallic_Radii" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.06:_Melting_Points_and_Standard_Enthalpies_of_Atomization_of_Metals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.07:_Alloys_and_Intermetallic_Compounds" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.08:_Bonding_in_Metals_and_Semicondoctors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.09:_Semiconductors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.10:_Size_of_Ions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11:_Ionic_Lattices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.12:_Crystal_Structure_of_Semiconductors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.13:_Lattice_Energy_-_Estimates_from_an_Electrostatic_Model" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.14:_Lattice_Energy_-_The_Born-Haber_Cycle" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.15:_Lattice_Energy_-_Calculated_vs._Experimental_Values" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.16:_Application_of_Lattice_Energies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.17:_Defects_in_Solid_State_Lattices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 6.11B: Structure - Caesium Chloride (CsCl), [ "article:topic", "showtoc:no", "license:ccbyncsa", "non-closed packed structure", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FInorganic_Chemistry%2FMap%253A_Inorganic_Chemistry_(Housecroft)%2F06%253A_Structures_and_Energetics_of_Metallic_and_Ionic_solids%2F6.11%253A_Ionic_Lattices%2F6.11B%253A_Structure_-_Caesium_Chloride_(CsCl), \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), tice which means the cubic unit cell has nodes only at its corners. corners of its cube. The packing efficiency of body-centred cubic unit cell (BCC) is 68%. Put your understanding of this concept to test by answering a few MCQs. between each 8 atoms. Particles include atoms, molecules or ions. Packing efficiency is the proportion of a given packings total volume that its particles occupy. In addition to the above two types of arrangements a third type of arrangement found in metals is body centred cubic (bcc) in which space occupied is about 68%. The steps below are used to achieve Body-centered Cubic Lattices Packing Efficiency of Metal Crystal. The higher coordination number and packing efficency mean that this lattice uses space more efficiently than simple cubic. Also, 3a=4r, where a is the edge length and r is the radius of atom. Packing Efficiency of Simple Cubic crystalline solid is loosely bonded. There is one atom in CsCl. Assuming that B atoms exactly fitting into octahedral voids in the HCP formed The packing efficiency of the body-centred cubic cell is 68 %. This misconception is easy to make, since there is a center atom in the unit cell, but CsCl is really a non-closed packed structure type. \[\frac{\frac{6\times 4}{3\pi r^3}}{(2r)^3}\times 100%=74.05%\]. Press ESC to cancel. This is the most efficient packing efficiency. The percentage of the total space which is occupied by the particles in a certain packing is known as packing efficiency. b. It is a dimensionless quantityand always less than unity. Now we find the volume which equals the edge length to the third power. Common Structures of Binary Compounds. Summary of the Three Types of Cubic Structures: From the The higher are the coordination numbers, the more are the bonds and the higher is the value of packing efficiency. How many unit cells are present in a cube shaped? If any atom recrystalizes, it will eventually become the original lattice. Therefore, the formula of the compound will be AB. This is obvious if we compare the CsCl unit cell with the simple Get the Pro version on CodeCanyon. Note: The atomic coordination number is 6. We all know that the particles are arranged in different patterns in unit cells. Therefore, if the Radius of each and every atom is r and the length of the cube edge is a, then we can find a relation between them as follows. Thus 26 % volume is empty space (void space). taking a simple cubic Cs lattice and placing Cl into the interstitial sites. Thus, the percentage packing efficiency is 0.7854100%=78.54%. When we see the ABCD face of the cube, we see the triangle of ABC in it. of spheres per unit cell = 1/8 8 = 1 . What is the packing efficiency of BCC unit cell? Thus the radius of an atom is 3/4 times the side of the body-centred cubic unit cell. The calculated packing efficiency is 90.69%. Out of the three types of packing, face-centered cubic (or ccp or hcp) lattice makes the most efficient use of space while simple cubic lattice makes the least efficient use of space. Hence, volume occupied by particles in FCC unit cell = 4 a3 / 122, volume occupied by particles in FCC unit cell = a3 / 32, Packing efficiency = a3 / 32 a3 100. One cube has 8 corners and all the corners of the cube are occupied by an atom A, therefore, the total number of atoms A in a unit cell will be 8 X which is equal to 1. The lattice points in a cubic unit cell can be described in terms of a three-dimensional graph. CsCl has a boiling point of 1303 degrees Celsius, a melting point of 646 degrees Celsius, and is very soluble in water. Therefore, face diagonal AD is equal to four times the radius of sphere. What is the coordination number of Cs+ and Cl ions in the CSCL structure? It is an acid because it increases the concentration of nonmetallic ions. , . Packing efficiency = Volume occupied by 6 spheres 100 / Total volume of unit cells. Regardless of the packing method, there are always some empty spaces in the unit cell. Question no 2 = Ans (b) is correct by increasing temperature This video (CsCl crystal structure and it's numericals ) helpful for entrances exams( JEE m. The Unit Cell refers to a part of a simple crystal lattice, a repetitive unit of solid, brick-like structures with opposite faces, and equivalent edge points. Put your understanding of this concept to test by answering a few MCQs. Packing efficiency is defined as the percentage ratio of space obtained by constituent particles which are packed within the lattice. In triangle ABC, according to the Pythagoras theorem, we write it as: We substitute the values in the above equation, then we get. The formula is written as the ratio of the volume of one atom to the volume of cells is s3., Mathematically, the equation of packing efficiency can be written as, Number of Atoms volume obtained by 1 share / Total volume of unit cell 100 %. How may unit cells are present in a cube shaped ideal crystal of NaCl of mass 1.00 g? 1.1: The Unit Cell is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. 8 Corners of a given atom x 1/8 of the given atom's unit cell = 1 atom To calculate edge length in terms of r the equation is as follows: 2r Anions and cations have similar sizes. The coordination number is 8 : 8 in Cs+ and Cl. For every circle, there is one pointing towards the left and the other one pointing towards the right. Therefore, the ratio of the radiuses will be 0.73 Armstrong. It must always be less than 100% because it is impossible to pack spheres (atoms are usually spherical) without having some empty space between them. Although it is not hazardous, one should not prolong their exposure to CsCl. Where, r is the radius of atom and a is the length of unit cell edge. The reason for this is because the ions do not touch one another. !..lots of thanks for the creator Caesium chloride dissolves in water. Its packing efficiency is about 52%. Let us suppose the radius of each sphere ball is r. Solved Examples Solved Example: Silver crystallises in face centred cubic structure. What is the pattern of questions framed from the solid states chapter in chemistry IIT JEE exams? Assuming that B atoms exactly fitting into octahedral voids in the HCP formed, The centre sphere of the first layer lies exactly over the void of 2, No. If you want to calculate the packing efficiency in ccp structure i.e. unit cell. Since a body-centred cubic unit cell contains 2 atoms. Show that the packing fraction, , is given by Homework Equations volume of sphere, volume of structure 3. This problem has been solved! In the Body-Centered Cubic structures, 3 atoms are arranged diagonally. Mass of unit cell = Mass of each particle x Numberof particles in the unit cell, This was very helpful for me ! efficiency of the simple cubic cell is 52.4 %. Face-centered Cubic (FCC) unit cells indicate where the lattice points are at both corners and on each face of the cell. It is also possible to calculate the density of crystal lattice, the radius of participating atoms, Avogadro's number etc. (Cs+ is teal, Cl- is gold). Thus, the statement there are eight next nearest neighbours of Na+ ion is incorrect. The atomic coordination number is 6. Question 2: What role does packing efficiency play? The Packing efficiency of Hexagonal close packing (hcp) and cubic close packing (ccp) is 74%. Packing efficiency of face-centred cubic unit cell is 74%your queries#packing efficiency. In crystallography, atomic packing factor (APF), packing efficiency, or packing fractionis the fraction of volumein a crystal structurethat is occupied by constituent particles. Try visualizing the 3D shapes so that you don't have a problem understanding them. The Unit Cell contains seven crystal systems and fourteen crystal lattices. Touching would cause repulsion between the anion and cation. It is the entire area that each of these particles takes up in three dimensions. As we pointed out above, hexagonal packing of a single layer is more efficient than square-packing, so this is where we begin. Silver crystallizes with a FCC; the raidus of the atom is 160 pm. For the most part this molecule is stable, but is not compatible with strong oxidizing agents and strong acids. Body-centered Cubic (BCC) unit cells indicate where the lattice points appear not only at the corners but in the center of the unit cell as well.