The Hexagonal Close-Packed (HCP) unit cell can be imagined as a hexagonal prism with an atom on each vertex, and 3 atoms in the center. An element occurs in the body centered cubic lattice with a cell edge of 300 pm. There are no spare bonds. I thought this was mostly unit conversion. Prove that the Voronoi cells induced by the single-nearest neighbor algorithm must always be convex. What is metal X if its density is 1. nearest/neighbor#atoms#in#Ge. . Previous question Next question. The crystal structure of aluminium isQ4. What is the distance between the adjacent Miller planes if the first order reflection from X-rays of wavelength 2. 866a. The calculated lattice constants of bcc V-Mo, bcc V-Ti, and hcp V-Ti solid solution phases are presented in Fig. This is the link • Trick to calculate Nearest neighbour. Calculating nearest neighbor distances. Interplanar distance in FCC and BCC. The total energy for a perfect crystal with N atoms can be written, where p ijR is the distance between an atom i and another atom j and R is the nearest neighbor. Solution (a) The answer can be found by looking at a unit cell of Cu (FCC). 414 * a So, for bcc, d = 1. e. g. "A metal X has a BCC structure with nearest neighbor distance 365. 20 pm. The diagram below shows the conventional birds-eye view of the (110) surface - emphasizing the rectangular. I have also discussed how to find out first,second and third nea. 52 Å. Sodium has a BCC structure with nearest neighbour distance of 365. 9 p m. Sodium has bcc structure with nearest neighbour distance 367. 5 ˚ A and 3. 1 (a), (b), and (c), in comparison. H. b) Distance between next neighbours: The next nearest neighbour of center atom will be the next center atom. 7k points) jee; jee mains; 0 votes. Start learning . There is one at the center of the adjacent cube to our cube. FCC has 6 next-nearest neighbors, and 24 next-next nearest neighbors. For a FCC lattice, the nearest neighbor distance is one-half the diagonal of a face. Its density will be ( K = 39,NA = 6 × 10^23 )An element crystallizes in a BCC lattice nearest neighbours and next nearest neighbours of the elements are respectively 1) 8,8 2)8,6 3)6,8 4)6,6. Asked 5 years, 4 months ago. A solid has 'BCC' structure. The diamond cubic crystal structure has an fcc lattice with a basis of two silicon atoms. The Nearest Neighbor rule is a well-known classification me-thod largely studied in the pattern recognition community, both for its simplicity and its performance. 52 Å. Lattice point per conventional cell: 1=8×1/8 Volume (conventional cell): a 3 Volume (primitive cell) :a 3 Number of nearest neighbors: 6 Nearest neighbor distance: a In the present video I have discussed all the basic necessary details of Body Centered Cubic (BCC)Structure. Class 9; Class 10; Class 11; Class 12; CBSE BoardIn a simple cubic lattice, the coordination number is x and the packing efficiency of BCC is y%. 414). How close-packed structures of spheres can be constructed: In a first layer the spheres are arranged in a hexagonal pattern, each sphere being surrounded by six others (A). Q. (a) the distance of second nearest neighbors. Find atoms/cell and nearest neighbor distance for sc, bcc, and fcc lattices. a. The density of the element is 8. Say you are sitting in the center of a cell. by 12 nearest neighbors in the bulk fcc. Find the perpendicular distance between the two planes indicated by the Miller indices (1 2 1) and (2 1 2) in a unit cell of a cubic lattice with a lattice constant parameter ‘a’. (A) Calculate the total number of atoms found inside the unit cell lattice. 7 Å and 6. This is consistent with the packing density calculations reported in lecture that give FCC as being 74% dense and BCC 68% dense. . • write ri = ρir0, where r0 is nearest neighbour distance,. SO there are EIGHT. Nearest cities. Say you are sitting in the center of a cell. So for BCC let's consider the atom at the body centre, for this atom the atom at the corner are nearest. The analysis algorithms [acna,baa,cspfcc,cspbcc,voro,nda] sort the neighbor. The number of nearest neighbors and the next nearest neighbors are, _______ respectively. Element. Therefore, for a BCC lattice there are eight (8) nearest neighbors for any given lattice point. Sodium has a bec structure with nearest neighbour distance 365. The red rectangles indicate primary cell in each structure and the circles indicate the ranges over which an atom interacts with its neighbors. 142 nm. 1 Find atoms/cell and nearest neighbor distance for sc, bcc, and fcc lattices. Electrical Engineering. An element crystallizes in bcc lattice. For a simple cubic lattice, it is clear that the nearest neighbor distance is just the lattice parameter, a. (4) (4) a 2. Nearest neighbour distance in bcc unit cell is greater than that of fcc having same edge length. other (distance = 0. = 42× 3a. In bcc: The atoms at the body diagonal touch each other. 1. 538 Å would be absent. x H 2 O is bcc with edge length, a = 1. 2) 2 = 0. So for BCC let's consider the atom at the body centre, for this atom the atom at the corner are nearest. 142 nm), the distance to the first, second and third nearest neighbor atoms are referred to as r 1 = a 0, r 2 = 3 a 0 , and r. 53%. Statement 2: FCC has greater packing efficiency than BCC. of atom touching a particular atom in the given unit cell is known as coordination number and that atoms are known as nearest neighbour. 6802 a fraction a u S 3 4 a radius SC 74% 68% 52%. Calculate its density - (A s s u m e m a s s o f s o d i u m = 2 3 g / m o l) Medium. The nearest neighbour distance dis the same as the distance from. 52 Å`its atomic weight is `39` its density (in kg `m^(-3)`) will be asked Jun 17, 2019 in Chemistry by KumariPrachi ( 90. 7 4 P F B C C = 0 . Hard. 5)^12 + 8 (1/root6)^12 = 8. Number of atom per unit cell = 8 x 1/8 + 1 x 1 = 2 Number of atoms in - 8ghto4gg. Therefore, for a BCC lattice there are eight (8). So for BCC let's consider the atom at the body centre, for this atom the atom at the corner are. The nearest distance is the distance between centre of these atoms. This source says that the interplanar spacing of the (111) ( 111) plane in FCC is a 3√ a 3, which is in agreement with the formula above. Add a comment | 1 Answer Sorted by: Reset to. Let r n be the distance to the nth nearest neighbor expressed as a multiple of the nearest neighbor distance (e. The (110) surface is obtained by cutting the fcc unit cell in a manner that intersects the x and y axes but not the z-axis - this exposes a surface with an atomic arrangement of 2-fold symmetry. 255 nm. View solution > Answer the following questions . The distance between them is diagonal−of−cube 2 = √3a 2 . (Atomic mass of N a = 23) Q. Therefore, for a simple cubic lattice there are six (6) nearest neighbors for any given lattice point. n th nearest neighbor expressed as a multiple of the nearest neighbor distance (for. 0 g cm −3 . Coordination number (CN) is the number of nearest neighbors of a central atom in the structure. Calculate the interionic distance in CsCl. First closest neighbor is eight (molecules at corner)and The Second closest neighbor is six. $ dfrac{{asqrt 3 }}{2} $ = $ 4. The total energy for a perfect crystal with N atoms can be written, where p ijR is the distance between an atom i and another atom j and R is the nearest neighbor. 5× 3)A˚. Show transcribed image text. Then: Your first neighbours are at the corners of the same cell. Adjacent points in this structure are at distance apart in the integer lattice; the edges of the diamond. The reference structure for Na is bcc and that for Sn is fcc. The body-centered cubic (bcc) has a coordination number of 8 and contains 2 atoms per unit cell. Crystal structures: If the nearest neighbor distance is 2 A then calculate the volume of the unit cells in bcc, fcc and sc structures. Therefore, the distance between nearest-neighbor atoms in a BCC lattice is v3 times the lattice constant "a. 5446 Å, with a nearest-neighbor distance of 2. 0016 g cm-3? View answer. function of the interatomic distance, (a) Using the Lennard-Jones potential, calculate the lattice constants of the fcc, hcp, and bcc crystals at zero pressure and temperature. ∴ Distance between two atoms. LDHint: In a bcc lattice or body centred unit cell, there is one additional particle present at the centre within the body of the unit cell in addition to the particles at the corners of the unit cell. 912Å at room temperature. The distance between two nearest- neighbor atoms is 0. A rock containing three crystals of pyrite (FeS 2). We must know that in BCC lattice, the packing efficiency is 68%. The nearest neighbor distance is 0. I. Hence, distance between the nearest neighbour atoms; is half the diagonal length of a. The ratio of the distances with the nearest neighbours in a body centered cubic (BCC) and a face centered cubic (FCC) crystals with the same unit cell edge length is: Q. Text Solution. View Solution. ALL ABOUT CUBE :- WITH US ON CHEMISTRY UNTOLD HINDI :- equal to -Z1/2 and the scaled equilibrium nearest-neighbour distance is unity. 564×10−7cm)# # Number#of#atoms#in#the#cubic#unit#cell:# N u =8× 1 8 +6× 1 2 +4=8## (Eightonthecorners,sharedwith8neighbors+6onthefaces,eachonesharedwitha#. 2 Ao. Correct option is B) In bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corners atoms, so the potassium atom will have 8 nearest neighbours. It can also be imagined as stacking 3 close-packed hexagonal layers such that the top layer and bottom layer line up. Reason Bcc has greater packing efficiency than fcc. Q. Numeric vector or matrix containing the nearest neighbour distances for each point. because Statenemt -2: fcc has greater pack. Even with second-nearest neighbors, the deviation from the values of the full analysis remains well over 10 pct. called its nearest neighbors. That will be the nearest neighbour at the next level. Nearest neighbors and next-nearest neighbors of the elements are respectively : Medium. >. Continue reading. The distance between them can be found using the Pythagorean theorem in 3D space: a^2 + a^2 + a^2 = d^2, where d is the nearest neighbor distance. Statement -1:Distance between nearest neighbour in bcc is greater than that of fcc having same edge length. • Rare due to poor packing (only Po [84] has this structure) • Close-packed directions are cube edges. d h k l = a h 2 + k 2 + l 2. BCC 2 4 a radius 3 3 43 2 ( ) 34 0. . Find the number of atoms/unit cell and nearest neighbor distance for (a) sc, (b) bcc, (c) fcc, (d) diamond, and (e) zinc blende unit cells. It is used for classification and regression. Now, for a bcc unit cell, the relationship between r and a (edge-length) is: `r=sqrt3/4a`. Q. In k-nearest neighbor (kNN), the. If a distance between two nearest atoms is 3. Consider a BCC metal with lattice parameter a=4. The (1 1 0) planes are packed in an ABABAB sequence and three {1 1. Solid State Chemistry || Nearest Neighbour Distance || FCC | BCC | SCC. = 23a. Since there are two lattice sites per bcc cubic cell, the density should be. Its relative atomic mass is 39 . Electrical Engineering questions and answers. A corner atom has 6 neighbours at distance a, two per axis : one before, on behind, one left. Question: Crystal structures: If the nearest neighbor distance is 2 A then calculate the volume of the unit cells in bcc, fcc and sc structures. Its density (in kg/ m 3 ) will beHow do I calculate the lattice sums A12 and A6 for a BCC structure? I have calculated the following so far: A12 = 8 (1/1)^12 + 6 (1/root2)^12 + 12 (1/2)^12 + 16 (1/root5. Thus, the nearest-neighbor distance is: d = r * sqrt(2) (b) For the BCC crystal along the [111] direction, there are four atoms per unit cell along this direction. A metal crystallizes in two cubic phases, face centered cubic (fcc) and body centered cubic (bcc) whose unit cell length are 3. The distance between two nearest neighbour in a bcc cell = `1/2xx` the length of body diagonal = `1/2xx4r=2r` `=2xxsqrt3/4a=sqrt3/2a`. Its density will be (K=39,N A=6×10 23) Medium. The nearest neighbors of any apex in FCC are the atoms in the middle of a face. Its atomic mass is 39 g/mole. 9 pm. Calculate its density (atomic mass of sodium = 23) View Solution. 18 16 : 57. g. So for BCC let's consider the atom at the body centre, for this atom the atom at the corner are nearest. The nearest neighbour distance (in pm) is : Medium. 1 CRYSTAL STRUCTURES & CRYSTALLOGRAPHY 6(20) Find the number of atoms/unit-cell and nearest neighbor distance, in terms of the edge length a, for (a) sc, (b) bcc, (c) fcc, (d) diamond, and (e) zinc blende unit-cells. . 9 pm. 216 pm. for the bcc lattice. 414). View solution > Sodium metal crystallizes in a body-centered cubic lattice with a unit cell edge of 4. The distance between the two nearest neighour is The distance between the two nearest neighour is ASince the number of atoms in a single unit cell of Zn and S is the same, it is consistent with the formula ZnS. Interstitial Sites in the Basic Crystal Structures (SC,. The nearest neighbor distance in a BCC (Body-Centered Cubic) structure can be calculated using. In BCC, the nearest atom from one corner is at the body center, at a distance of √(3a/2). Simulation resultsFor bcc structure, the nearest neighbor distance is 3 a 2/ , thus R= 3 a 4/. View Solution. 141 pm. Xenon crystallizes in the face-centred cubic lattice and the edge of the unit cell is `620` pm. In crystallography, the cubic (or isometric) crystal system is a. Nearest Neighbors in BCC Metals. ) [1]. 23 26 Metallic is explained by Diffusion of ions (O Excitation of free electrons Oscillation of positive ions Existence of bcc al I attic. 5. The calculated lattice constants of bcc V-Mo, bcc V-Ti, and hcp V-Ti solid solution phases are presented in Fig. Nearest neighbors and next-nearest neighbors of the elements are respectively : Medium. In a BCC unit cell, there are 8 atoms at the corner of a cube and 1 atom at the centre. . Its density will be. Question: Crystal structures: If the nearest neighbor distance is 2 A then calculate the volume of the unit cells in bcc, fcc and sc structures. Then the value of 6y 17x is: View Solution. 214 Å. Therefore, for a simple cubic lattice there are six (6) nearest neighbors for. Potassium has a bcc structure with nearest neighbour distance 4. Visualise this by imagining each lattice site of be the centre of an atom, whose radius is a 2 r. READ: What is the relation between. Solution. Say you are sitting in the center of a cell. For cubic materials, there are equations in which to calculate nearest neighbor (NN), second nearest neighbor, etc. 0k points) class-12Sodium has a bcc structure with the nearest neighbor distance 3 6 5. ##Recall#that#1#nm=# 1×10−7#cm. View solution > The number of close neighbours in a body-centred cubic lattice of identical spheres is:. The integrated unit conversion calculator can quickly convert a value to the units that you need. Nearest neighbour to an atom (say at origin) is the atom present is the centre of theat point P and the position of P can be =The correct answer is: = The positions of number of nearest neighbours in a unit cell of bcc structure is given by:a)b)c)d)None of theseCorrect answer is. Medium. 0. The packing efficiency in BCC and FCC are as follow: P F F C C = 0 . First we have to calculate the edge length of unit cell. Can this be done with tetragonal crystal structures? I want to calculate NN, 2NN, and 3NN of $ce{TiO2}$ rutile with a tetragonal crystal structure but am unsure how to do it. Reason Bcc has greater packing efficiency than fcc. First of all, the structural characteristics of BCC lattice is examined. Engineering. Usage. Calculate the distance between the query-instance and all the training. View solution. Solution. For a simple cubic lattice, the nearest neighbor distance is the lattice constant. 707 a$. ) Assume that a hypothetical BCC Pt crystal has the same mass density as FCC Pt. The correct answer is: a Sodium has bcc packing. 1. How many atoms are in the primitive unit cell of graphite? 5. The distance between two nearest neighbors can be found by considering a right triangle formed by the side length (a) and the body diagonal (d). 2 Equilibrium SeparationA 4Å A B A B A A B A 4Å A B Note: The atoms are the same size and touch each other by the hard sphere approximation. 9 pm. Option 2) 6, 12. The. Now put all the given values in this formula, we get :Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Potassium has a bcc structure with nearest neighour distance `4. And in a 3D packing a unit cell will be sitting on the top of our unit cell. In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the BCC crystal structure along the [110] direction. = 42× 3a. The centres of four vertical faces are another nearest lattice points. BCC 8; FCC 12; HCP 12 . e. On the picture below a a is shown. Question: 3. Its atomic mass is 39 g/mole. Potassium had body centred cubic structure with the nearest neighbour distance 2 6 0 3 p m. 03:44. The distance would be 'a' = size of cube in the lattice. 86 g/cm3. FCC Neighbors: 1st, 2nd and 3rd. 1x of. Baskes, 2,† Hanchul Kim, 1 and Yang Koo Cho 1You should ensure the appropriate nearest neighbors of an atom are found within the cutoff distance for the presumed crystal structure (e. for a three-dimensional microstructure) in space, and then allows random movements of these impenetrable particles in the simulation space. C. In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. Hence, there are three groups of four lattice points lying in three perpendicular face planes, that also lie at this distance from any given lattice point. Its atomic mass is 39 g/mole. 2 2 nm. Here a is the lattice constant of the bcc lattice and R is the radius of the sphere. because Statenemt -2: fcc has greater packing than bcc. 12. Hence, the nearest atoms are the one which presnt at the face centres when the reference atom is at corner. Then: Your first neighbours are at the corners of the same cell. in terms of the atomic radius, r, determine the distance between the centers of adjacent atoms (nearest-neighbor distance) for the following directions and monoatomic crystal structures: (a) for the FCC crystal along the [100] direction; b) for the BCC crystal along the [111] direction; (c) for the BCC crystal along the [110] direction. 3 33 = = ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ⎟⎟ = ⎠ ⎞ ⎜⎜⎝ ⎛ × πR a π π. Packing fraction in face-centered cubic unit cell is :1 denotes the number of nearest neighbors. Plan Your Route allows you to enter a start and end destination and receive the shortest route (as determined by Google) with step-by-step instructions. The distance would be 'a' = size of cube in the lattice. 732 = 542. First three nearest neighbour distance for body centred cubic lattice are respectively:Introduction of edge length and Calculation of coordination no. example, in simple cubic, r 11, r 21. Range of parameter space to use by default for radius_neighbors queries. Each radial cutoff distance was set to a value larger than the second nearest neighbor distance in each system. Note that the nearest-neighbor distance corresponds to the atomic bond length. Calculate its density. give a relationship between nearest neighbour distance(d),radius of atom(r), edge of unit cell(a), for fcc and BCC crystal. it is estimated to be 0. In bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corners atoms, so the pottassium atom will have 8 nearest neighbours. Radius of curvature at the point when satellite is at a distance 2 R is n R, here n is (Answer upto two decimal places)Electrical Engineering. Show transcribed image text. sc: atoms/cell = 8 18 = 1 ##### nearest neighbor distance = a. Interplanar distance in FCC and BCC. Coordination Number (CN) is the number of nearest neighbors that each atom has. 29 A. Its density would be ((5. Then: Your first neighbours are at the corners of the same cell. Its density (in kg/ m 3 ) will beThe calculations for the Cu-Co and Cu-Mo systems were performed with a radial cutoff distance of 3. Threfore there are three groups of four lattice points lying in three perpendicular face planes. Second nearest-neighbor modified embedded atom method potentials for bcc transition metals Byeong-Joo Lee, 1, * M. 27, has a distorted close-packed structure. It could be seen that the SIA (atom D) deviates from its original interstitial site at the GB, and atom A moves to position A′ by 1. Join / Login >> Class 12. potential energy A=Rn acting only between nearest neighbors. Thus, the nearest-neighbor distance is: d = r * sqrt(4) = 2r (c) For the BCC crystal along the [110] direction, there are two atoms per unit cell along this direction. These are the nearest neighbours for the atom at the center. What is the lattice constant of silicon? Correct option is B) In bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corners atoms, so the potassium atom will have 8 nearest neighbours. 15 it indicates the settlement pattern? “The Nearest Neighbour Analysis will always generate a result between 0 and 2. 0 ˚ A respectively. Calculate its density - ( A s s u m e m a s s o f s o d i u m = 2 3 g / m o l ) MediumIf the distance of the closest approach between the two atoms is 1. Nearest neighbours in FCC= a √ 2 (Face center to Body corner) Thus, the nearest neighbour distance in BCC unit cell is greater than the FCC. 1,683. The lattice parameter a = 4r/ 3–√ a = 4 r / 3 and the spacing of atoms along 110 110 directions is a 2–√ a 2. 866 a$. If the distance of nearest approach between two atoms is 1. Cesium chloride (CsCl) (a = 4. In bcc: The atoms at the body diagonal touch each other. The reference structure is BCC for Cr, Fe, Mo, FCC for Al, Ni, and HCP for Co, Ti, respectively. For cube of length a and atomic radius r, we have. Nearest Neighbor Distance Ratio: The nearest neighbor distance ratio (NNDR), or ratio test, finds the nearest neighbor to the feature descriptor and second nearest neighbor to the feature descriptor and divides the two. algorithm {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, default=’auto’ Algorithm used to compute the nearest neighbors: ‘ball_tree. In a BCC unit cell, there are 8 atoms at the corner of a cube and 1 atom at the centre. The ionic radius for Zn 2+ is 74pm and for S 2-is 190pm. >. 0 Å, respectively. centred cubic (BCC) and face-centred cubic (FCC). as in this crystal structure the first-nearest-neighbour distance is only slightly smaller than the second-nearest-neighbour distance and. r = nearest neighbor distance. This is incorrect. 52 A o. Potassium has a bcc structure with nearest neighbour distance 4. . Who are the experts?Bihar Board. Fill in the blank. How long does. When you are looking for the smallest nearest neighbour distance this means that you are looking for the smallest a a in an FCC or HPC packing. how many nearest and next nearest neighbours respectively each potassium has in BCC lattice What is the distance between next nearest Neighbour in BCC unit cells? For a body centered cubic (BCC) lattice, the nearest neighbor distance is half of the body diagonal distance, 23 a . the calculation of GB structures [12], GB and surface energies 11,. If the nearest neighbour distance is x then calculate the volumes of the unit cells in bcc, fcc, & sc structures in terms of x. In transition metals, small foreign atoms usually sit on interstitial sites. The distance between two nearest neighbour in a bcc cell = `1/2xx` the length of body diagonal = `1/2xx4r=2r`. Distance between Victoria and Clearwater in miles and kilometers. 2)^2 = 0. 1 How many atoms are in a body-centered cubic (BCC) lattice? 2 What is the number of nearest-neighbor atoms for an atom in a body-centered cubic (BCC) lattice? 3 3 What is the nearest-neighbor atom distance for a body-centered cubic (BCC) lattice? {av2 a ja13. 10. g. (a) the distance of second nearest neighbors. All. Since each fluoride ion has four nearest-neighbor calcium ions, the coordination in this structure is described as (8:4). Q2. In bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corners atoms, so the potassium atom will have 8 nearest neighbours. Solution The correct option is A √3 2 Nearest neighbour distance in BCC crystal (r+r−) = √3 a 2 Nearest neighbour distance in FCC crystal (r+r−) = √2 a 2 Given: Edge length. 4. In the N a C l type structure shortest distance between two nearest neighbours is 100 pm, then the distance between two next nearest neighbours in the same unit cell will be: View Solution Q 5Let rn be the distance to the. a 1, a 2, a 3, a 4 are coefficients of any 4 consecutive terms in the expansion of (1 + x) n, then a 1 a 1 + a 2 + a 3 a 3 + a 4 =Thus, the nearest-neighbor distance is: d = r * sqrt(2) (b) For the BCC crystal along the [111] direction, there are four atoms per unit cell along this direction. So for BCC let's consider the atom at the body centre, for this atom the atom at the. All calculations were done with the LAMMPS [18] and an in-house MD code, KISSMD [19]. How many next nearest neighbours does each Li have ? View Solution. 9 p m. The face-centered cubic (fcc) has a coordination number of 12 and contains 4 atoms per unit cell. 540 A° in FCC-iron. The nearest neighbor distance is 0. First closest neighbor is eight (molecules at corner)and The Second closest neighbor is six. Q3. This is the nearest distance in fcc. R eq values are also needed in the computation of a eq, the equivalent lattice parameters. Option 4) 8, 12.