fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics

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1 Solid Stte Physics JEST-0 Q. bem of X-rys is incident on BCC crystl. If the difference between the incident nd scttered wvevectors is K nxˆkyˆlzˆ where xˆ, yˆ, zˆ re the unit vectors of the ssocited cubic lttice, the necessry condition for the scttered bem to give Lue mximum is () hkl even (b) h k l (c) hkl,, re ll distinct (d) h kl odd Solution: In BCC bsis 0, 0, 0,,, Crystl structure fctor F is defined s neff ihu n kvn l n F f S f e n i h k l 0 i f e e f e ih k l F0 f I f, F 0 I 0, F00 f I f Thus, if hkl even, then plne will be present. If h k l odd, then plne will be bsent. Q. The second order mximum in the diffrction of X-rys of 0.0 nnometer wvelength from simple cubic crystl is found to occur t n ngle of thirty degrees to the crystl plne. The distnce between the lttice plnes is () ngstrom (b) ngstrom (c) ngstrom (d) 8 ngstrom Solution: d sin n d sin dsin d m 0.0 m 0 m 9 0 o o 9 Q. The Dulong Petit lw fils ner room temperture (00 K) for mny light elements (such s boron nd beryllium) becuse their Debye temperture is () >> 00 K (b) ~ 00 K (c) << 00 K (d) 0 K m H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com

2 JEST-0 Q. flt surfce is covered with non-overlpping disks of sme size. Wht is the lrgest frction of the re tht cn be covered? 5 6 () (b) (c) (d) 6 7 Solution: In closed pcked hexgonl lttice, neff nc nf ni 6 nd r Now, lrgest frction of re i.e., pcking frction 6 n eff 6 r r Q5. metl suffers structurl phse trnsition from fce-centered cubic FCC to the ns. : () simple cubic SC structure. It is observed tht this phse trnsition does not involve ny chnge of volume. The nerest neighbor distnces d fcc nd d sc for the FCC nd the SC d fcc structures respectively re in the rtio [Given.6] dsc ().09 (b). (c).7 (d).0 Solution: Nerest neighbour in SC is nd CN. 6 Nerest neighbour in FCC is nd CN. d fcc d. sc H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com

3 JEST-0 Q6. Circulr discs of rdius m ech re plced on plne so s to form closely pcked tringulr lttice. The number of discs per unit re is pproximtely equl to () 0.86 m (b) 0. Solution: For closely pcked tringulr lttice, r, r m (c) neff nc nf nl 6 n eff 0 0 n eff n eff Occupncy m 0.9 m (d) 0.m Q7. n idel gs of non-reltivistic fermions in -dimensions is t 0K. When both the number density nd mss of the prticles re doubled, then the energy per prticle is multiplied by fctor () / (b) (c) Solution: / (d) E F n t T 0 K m / / / n n nd m m E F n n m m Q8. When two different solids re brought in contct with ech other, which one of the following is true? () Their Fermi energies become equl (b) Their bnd gps become equl (c) Their chemicl potentils become equl (d) Their work functions become equl / Closely pcked hexgonl H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com

4 JEST-05 Q9. Wht is the re of the irreducible Brillouin zone of the crystl structure s given in the figure? () (b) o (c) 60 B B (d) Solution: re of the Brillouin zone cn be relted to the re of norml cell s re of B.Z. re of cell B B B sin sin 60 0 re of Brillouin zone Q0. For - dimensionl honeycomb lttice s shown in the figure, the first Brgg spot occurs for the grzing ngle, while sweeping the ngle from 0 o. The next Brgg spot is obtined t given by o o () sin sin (b) sin sin 0 0 B o 0 (c) sin sin (d) sin sin Solution: ccording to Brgg s lw, the condition for first Brgg spot nd second spot is dsin n nd dsin n B 0 60 B H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com

5 d dsin dsin sin sin d For - dimensionl honeycomb lttice, the lttice constnt nd interplnr spcing d is linked s d d sin sin nd d k E sin 0, where E 0 nd re constnts nd is the lttice prmeter. Wht is the group velocity of n electron t the Q. Given the tight binding dispersion reltion k E second Brillouin zone boundry? () 0 (b) h Solution: Group velocity is defined s, Since E E0 sin k v g de dk (c) h (d) de k k sin cos sin k dk 0 K In one dimension, the Brillouin zone boundry is The st Brillouin zone boundries lie t The nd Brillouin zone boundries lie t Thus, the group velocity t the second Brillouin zone boundry is vg sin sin v 0 g h 0 60 d H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com 5

6 Q. The totl number of N nd Cl ions per unit cell of NCl is, () (b) (c) 6 (d) 8 Solution: Totl number of N nd Cl ions per unit d is N Cl nc nf, NN ne ni 8 where nc number of ions t corner number of ions t fce n f ne number of ions t edges n number of ions inside i N NCl NN Q. For non-intercting Fermions in E d d dimensions, the density of sttes E. The Fermi energy E F of n N prticle system in will scle respectively s, Cl N D vries s, nd dimensions () N, N /, N (b) N /, N, N (c) / N, N, N (d) N /, N, N H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com 6

7 JEST-06 Q. If k is the wvevector of incident light ( k, is the wvelength of light) nd G is reciprocl lttice vector, then the Brgg s lw cn be written s: () k G 0 (b) kg. G 0 (c) kg. k 0 (d) kg. 0 ns. : (b) Solution: By mens of Ewrd construction, we cn write the Brgg s lw in vector form K B G OB, K O G For diffrction it is necessry tht vector K G K, tht is vector B O be equl in mgnitude to the vector K or K G K K GG 0 Q5. The number of different Brvis lttices possible in two dimensions is: () (b) (c) 5 (d) 6 ns. : (c) Solution: Five Brvis lttices in D re: (i) Squre lttice (ii) Rectngulr P lttice (iii) Rectngulr C lttice (iv) Hexgonl lttice (v) Oblique lttice H.No. 0 D, Ground Floor, Ji Sri, Ner IIT, Huz Khs, New Delhi 006 Phone: / Website: Emil:.physics@gmil.com 7

QUB XRD Course. The crystalline state. The Crystalline State

QUB XRD Course. The crystalline state. The Crystalline State QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by