packing efficiency of csclpacking efficiency of cscl

Some examples of BCCs are Iron, Chromium, and Potassium. The chapter on solid-state is very important for IIT JEE exams. 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. As per our knowledge, component particles including ion, molecule, or atom are arranged in unit cells having different patterns. The centre sphere and the spheres of 2ndlayer B are in touch, Now, volume of hexagon = area of base x height, =6 3 / 4 a2 h => 6 3/4 (2r)2 42/3 r, [Area of hexagonal can be divided into six equilateral triangle with side 2r), No. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Let us calculate the packing efficiency in different types of, As the sphere at the centre touches the sphere at the corner. Packing efficiency is a function of : 1)ion size 2)coordination number 3)ion position 4)temperature Nb: ions are not squeezed, and therefore there is no effect of pressure. What type of unit cell is Caesium Chloride as seen in the picture. Credit to the author. Ionic compounds generally have more complicated It is an acid because it increases the concentration of nonmetallic ions. , . There is no concern for the arrangement of the particles in the lattice as there are always some empty spaces inside which are called void spaces. This is a more common type of unit cell since the atoms are more tightly packed than that of a Simple Cubic unit cell. By substituting the formula for volume, we can calculate the size of the cube. Now, in triangle AFD, according to the theorem of Pythagoras. Packing Efficiency of Simple Cubic of atoms present in 200gm of the element. In the same way, the relation between the radius r and edge length of unit cell a is r = 2a and the number of atoms is 6 in the HCP lattice. Example 3: Calculate Packing Efficiency of Simple cubic lattice. Quantitative characteristic of solid state can be achieved with packing efficiencys help. Find the number of particles (atoms or molecules) in that type of cubic cell. 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. Both hcp & ccp though different in form are equally efficient. Length of body diagonal, c can be calculated with help of Pythagoras theorem, \(\begin{array}{l} c^2~=~ a^2~ + ~b^2 \end{array} \), Where b is the length of face diagonal, thus b, From the figure, radius of the sphere, r = 1/4 length of body diagonal, c. In body centered cubic structures, each unit cell has two atoms. Diagram------------------>. The packing efficiency of body-centred cubic unit cell (BCC) is 68%. These are two different names for the same lattice. Click on the unit cell above to view a movie of the unit cell rotating. 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. Put your understanding of this concept to test by answering a few MCQs. Now we find the volume which equals the edge length to the third power. Assuming that B atoms exactly fitting into octahedral voids in the HCP formed Find the number of particles (atoms or molecules) in that type of cubic cell. Your email address will not be published. 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. Volume occupied by particle in unit cell = a3 / 6, Packing efficiency = ((a3 / 6) / a3) 100. In this lattice, atoms are positioned at cubes corners only. Let 'a' be the edge length of the unit cell and r be the radius of sphere. always some free space in the form of voids. Unit Cells: A Three-Dimensional Graph . of atoms in the unit cellmass of each atom = Zm, Here Z = no. The volume of the cubic unit cell = a3 = (2r)3 Put your understanding of this concept to test by answering a few MCQs. Different attributes of solid structure can be derived with the help of packing efficiency. 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 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. The numerator should be 16 not 8. Simple, plain and precise language and content. Now correlating the radius and its edge of the cube, we continue with the following. It is usually represented by a percentage or volume fraction. Moment of Inertia of Continuous Bodies - Important Concepts and Tips for JEE, Spring Block Oscillations - Important Concepts and Tips for JEE, Uniform Pure Rolling - Important Concepts and Tips for JEE, Electrical Field of Charged Spherical Shell - Important Concepts and Tips for JEE, Position Vector and Displacement Vector - Important Concepts and Tips for JEE, Parallel and Mixed Grouping of Cells - Important Concepts and Tips for JEE, Find Best Teacher for Online Tuition on Vedantu. The fraction of void space = 1 - Packing Fraction % Void space = 100 - Packing efficiency. The constituent particles i.e. Test Your Knowledge On Unit Cell Packing Efficiency! Definition: Packing efficiency can be defined as the percentage ration of the total volume of a solid occupied by spherical atoms. Packing efficiency of simple cubic unit cell is .. The calculation of packing efficiency can be done using geometry in 3 structures, which are: Factors Which Affects The Packing Efficiency. They will thus pack differently in different "Binary Compounds. corners of its cube. The Packing efficiency of Hexagonal close packing (hcp) and cubic close packing (ccp) is 74%. (3) Many ions (e.g. The packing efficiency of both types of close packed structure is 74%, i.e. The cations are located at the center of the anions cube and the anions are located at the center of the cations cube. The cubic closed packing is CCP, FCC is cubic structures entered for the face. ". Why is this so? 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%. Treat the atoms as "hard spheres" of given ionic radii given below, and assume the atoms touch along the edge of the unit cell. The formula is written as the ratio of the volume of one, Number of Atoms volume obtained by 1 share / Total volume of, Body - Centered Structures of Cubic Structures. Let it be denoted by n, Find the mass of one particle (atoms or molecules) using formula, Find the mass of each unit cell using formula, Find the density of the substance using the formula. Solution Show Solution. This page is going to discuss the structure of the molecule cesium chloride (\(\ce{CsCl}\)), which is a white hydroscopic solid with a mass of 168.36 g/mol. The void spaces between the atoms are the sites interstitial. 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. Below is an diagram of the face of a simple cubic unit cell. The structure must balance both types of forces. Examples are Magnesium, Titanium, Beryllium etc. A three-dimensional structure with one or more atoms can be thought of as the unit cell. Face-centered Cubic (FCC) unit cells indicate where the lattice points are at both corners and on each face of the cell. Required fields are marked *, \(\begin{array}{l}(\sqrt{8} r)^{3}\end{array} \), \(\begin{array}{l} The\ Packing\ efficiency =\frac{Total\ volume\ of\ sphere}{volume\ of\ cube}\times 100\end{array} \), \(\begin{array}{l} =\frac{\frac{16}{3}\pi r^{3}}{8\sqrt{8}r^{3}}\times 100\end{array} \), \(\begin{array}{l}=\sqrt{2}~a\end{array} \), \(\begin{array}{l}c^2~=~ 3a^2\end{array} \), \(\begin{array}{l}c = \sqrt{3} a\end{array} \), \(\begin{array}{l}r = \frac {c}{4}\end{array} \), \(\begin{array}{l} \frac{\sqrt{3}}{4}~a\end{array} \), \(\begin{array}{l} a =\frac {4}{\sqrt{3}} r\end{array} \), \(\begin{array}{l}Packing\ efficiency = \frac{volume~ occupied~ by~ two~ spheres~ in~ unit~ cell}{Total~ volume~ of~ unit ~cell} 100\end{array} \), \(\begin{array}{l}=\frac {2~~\left( \frac 43 \right) \pi r^3~~100}{( \frac {4}{\sqrt{3}})^3}\end{array} \), \(\begin{array}{l}Bond\ length\ i.e\ distance\ between\ 2\ nearest\ C\ atom = \frac{\sqrt{3}a}{8}\end{array} \), \(\begin{array}{l}rc = \frac{\sqrt{3}a}{8}\end{array} \), \(\begin{array}{l}r = \frac a2 \end{array} \), \(\begin{array}{l}Packing\ efficiency = \frac{volume~ occupied~ by~ one~ atom}{Total~ volume~ of~ unit ~cell} 100\end{array} \), \(\begin{array}{l}= \frac {\left( \frac 43 \right) \pi r^3~~100}{( 2 r)^3} \end{array} \). Hence they are called closest packing. 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. Packing faction or Packingefficiency is the percentage of total space filled by theparticles. There is one atom in CsCl. The packing fraction of the unit cell is the percentage of empty spaces in the unit cell that is filled with particles. In 1850, Auguste Bravais proved that crystals could be split into fourteen unit cells. One of our favourite carry on suitcases, Antler's Clifton case makes for a wonderfully useful gift to give the frequent flyer in your life.The four-wheeled hardcase is made from durable yet lightweight polycarbonate, and features a twist-grip handle, making it very easy to zip it around the airport at speed. Volume of sphere particle = 4/3 r3. One simple ionic structure is: One way to describe the crystal is to consider the cations and anions The volume of the unit cell will be a3 or 2a3 that gives the result of 8a3. Thus if we look beyond a single unit cell, we see that CsCl can be represented as two interpenetrating simple cubic lattices in which each atom . Since a face The importance of packing efficiency is in the following ways: It represents the solid structure of an object. Packing efficiency The hcp and ccp structure are equally efficient; in terms of packing. The main reason for crystal formation is the attraction between the atoms. Press ESC to cancel. Packing efficiency is defined as the percentage ratio of space obtained by constituent particles which are packed within the lattice. Like the BCC, the atoms don't touch the edge of the cube, but rather the atoms touch diagonal to each face. Thus the In crystallography, atomic packing factor (APF), packing efficiency, or packing fractionis the fraction of volumein a crystal structurethat is occupied by constituent particles. as illustrated in the following numerical. Therefore a = 2r. In atomicsystems, by convention, the APF is determined by assuming that atoms are rigid spheres. It is common for one to mistake this as a body-centered cubic, but it is not. Copyright 2023 W3schools.blog. They have two options for doing so: cubic close packing (CCP) and hexagonal close packing (HCP). (Cs+ is teal, Cl- is gold). 4. #potentialg #gatephysics #csirnetjrfphysics In this video we will discuss about Atomic packing fraction , Nacl, ZnS , Cscl and also number of atoms per unit cell effective number in solid state physics .gate physics solution , csir net jrf physics solution , jest physics solution ,tifr physics solution.follow me on unacademy :- https://unacademy.com/user/potentialg my facebook page link:- https://www.facebook.com/potential007Downlod Unacademy link:-https://play.google.com/store/apps/details?id=com.unacademyapp#solidstatesphysics #jestphysics #tifrphysics #unacademyAtomic packing fraction , Nacl, ZnS , Cscl|crystallograpy|Hindi|POTENTIAL G Thus, packing efficiency in FCC and HCP structures is calculated as 74.05%. CsCl has a boiling point of 1303 degrees Celsius, a melting point of 646 degrees Celsius, and is very soluble in water. Question 4: For BCC unit cell edge length (a) =, Question 5: For FCC unit cell, volume of cube =, You can also refer to Syllabus of chemistry for IIT JEE, Look here for CrystalLattices and Unit Cells. of spheres per unit cell = 1/8 8 = 1, Fraction of the space occupied =1/3r3/ 8r3= 0.524, we know that c is body diagonal. Apart from this, topics like the change of state, vaporization, fusion, freezing point, and boiling point are relevant from the states of matter chapter. Suppose edge of unit cell of a cubic crystal determined by X Ray diffraction is a, d is density of the solid substance and M is the molar mass, then in case of cubic crystal, Mass of the unit cell = no. The Unit Cell contains seven crystal systems and fourteen crystal lattices. No Board Exams for Class 12: Students Safety First! 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. Therefore, in a simple cubic lattice, particles take up 52.36 % of space whereas void volume, or the remaining 47.64 %, is empty space. Try visualizing the 3D shapes so that you don't have a problem understanding them. In a simple cubic unit cell, atoms are located at the corners of the cube. Therefore, the ratio of the radiuses will be 0.73 Armstrong. The packing efficiency of simple cubic lattice is 52.4%. Summary was very good. 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For the most part this molecule is stable, but is not compatible with strong oxidizing agents and strong acids. For detailed discussion on calculation of packing efficiency, download BYJUS the learning app. Atoms touch one another along the face diagonals. The packing efficiency is the fraction of crystal or known as the unit cell which is actually obtained by the atoms. The packing efficiency is the fraction of crystal or known as the unit cell which is actually obtained by the atoms. Also, study topics like latent heat of vaporization, latent heat of fusion, phase diagram, specific heat, and triple points in regard to this chapter. small mistake on packing efficiency of fcc unit cell. Let us take a unit cell of edge length a. Its packing efficiency is about 68% compared to the Simple Cubic unit cell's 52%. The particles touch each other along the edge as shown. = 1.= 2.571021 unit cells of sodium chloride. These unit cells are given types and titles of symmetries, but we will be focusing on cubic unit cells. How can I solve the question of Solid States that appeared in the IIT JEE Chemistry exam, that is, to calculate the distance between neighboring ions of Cs and Cl and also calculate the radius ratio of two ions if the eight corners of the cubic crystal are occupied by Cl and the center of the crystal structure is occupied by Cs? 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. We always observe some void spaces in the unit cell irrespective of the type of packing. Three unit cells of the cubic crystal system. This is probably because: (1) There are now at least two kinds of particles The Percentage of spaces filled by the particles in the unit cell is known as the packing fraction of the unit cell. Dan suka aja liatnya very simple . Example 1: Calculate the total volume of particles in the BCC lattice. Ignoring the Cs+, we note that the Cl- themselves Packing efficiency = volume occupied by 4 spheres/ total volume of unit cell 100 %, \[\frac{\frac{4\times 4}{3\pi r^3}}{(2\sqrt{2}r)^3}\times 100%\], \[\frac{\frac{16}{3\pi r^3}}{(2\sqrt{2}r)^3}\times 100%\]. Free shipping for many products! Regardless of the packing method, there are always some empty spaces in the unit cell. Let the edge length or side of the cube a, and the radius of each particle be r. The particles along the body diagonal touch each other. This is the most efficient packing efficiency. These types of questions are often asked in IIT JEE to analyze the conceptual clarity of students. Common Structures of Binary Compounds. We all know that the particles are arranged in different patterns in unit cells. We can therefore think of making the CsCl by To packing efficiency, we multiply eight corners by one-eighth (for only one-eighth of the atom is part of each unit cell), giving us one atom. There are two number of atoms in the BCC structure, then the volume of constituent spheres will be as following, Thus, packing efficiency = Volume obtained by 2 spheres 100 / Total volume of cell, = \[2\times \frac{\frac{\frac{4}{3}}{\pi r^3}}{\frac{4^3}{\sqrt{3}r}}\], Therefore, the value of APF = Natom Vatom / Vcrystal = 2 (4/3) r^3 / 4^3 / 3 r. Thus, the packing efficiency of the body-centered unit cell is around 68%. powered by Advanced iFrame free. And the evaluated interstitials site is 9.31%. The packing efficiency of a crystal structure tells us how much of the available space is being occupied by atoms. 2. Question 1: Packing efficiency of simple cubic unit cell is .. It is a common mistake for CsCl to be considered bcc, but it is not. Let us take a unit cell of edge length a. of Sphere present in one FCC unit cell =4, The volume of the sphere = 4 x(4/3) r3, \(\begin{array}{l} The\ Packing\ efficiency =\frac{Total\ volume\ of\ sphere}{volume\ of\ cube}\times 100\end{array} \) Note: The atomic coordination number is 6. The structure of CsCl can be seen as two interpenetrating cubes, one of Cs+ and one of Cl-. Simple Cubic Unit Cell image adapted from the Wikimedia Commons file "Image: Body-centered Cubic Unit Cell image adapted from the Wikimedia Commons file ". Click 'Start Quiz' to begin! Atomic coordination geometry is hexagonal. The percentage of the total space which is occupied by the particles in a certain packing is known as packing efficiency. 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. It is a salt because it is formed by the reaction of an acid and a base. Also, the edge b can be defined as follows in terms of radius r which is equal to: According to equation (1) and (2), we can write the following: There are a total of 4 spheres in a CCP structure unit cell, the total volume occupied by it will be following: And the total volume of a cube is the cube of its length of the edge (edge length)3. Mass of unit cell = Mass of each particle x Numberof particles in the unit cell, This was very helpful for me ! Packing paling efficient mnrt ku krn bnr2 minim sampah after packing jd gaberantakan bgt. An example of this packing is CsCl (See the CsCl file left; Cl - yellow, Cs + green). Further, in AFD, as per Pythagoras theorem. Cesium Chloride is a type of unit cell that is commonly mistaken as Body-Centered Cubic. And the packing efficiency of body centered cubic lattice (bcc) is 68%. "Stable Structure of Halides. If we compare the squares and hexagonal lattices, we clearly see that they both are made up of columns of circles.
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