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Reciprocal lattice, X-Ray diffraction & Fe3O4 SynthesisPoint of attractionsX-Ray diffraction Fe3O4 Pulsed laser deposition Fe3O4 on MgOLattice matching

-Moinuddin CNS&NT Punjab University

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Real lattice and Reciprocal lattice

H = hb1+kb2+lb3

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X ray Diffraction in Real and Rec. lattice

Real latticeReciprocal latticeA0BCAC=ABAB= dSinAC=dsin BA+AC= Path difference= 2dsin So for the constructive interference should be in integer multiple.So n= 2dsin

Direction of S and S0 are in inclined and reflected direction unit vector.For reciprocal orientation the incident vector has value of

OD=S/

Hhkl= [S- S0 ]/ Phase diffrence =-2[S- S0 ]/ *OA

Single crystal diffraction

Ewald sphere

kkEach time k = G, a reciprocallattice vector, you get a Bragg reflection. This is a point of intensity at some 2 angle, and some angle in spaceBragg reflections

So by finding in between the X-ray source and Detector We can find the value the Hhkl . Which i.e Base to defind the orientation of the crystal structure

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Wigner Seitz CellA 3D space where Distance of root atom lattice is less than nearest lattice ( here 8 nearest lattice point).

a1a2

Brillouin Zones

Point D in reciprocal space

GD

Wigner-Seitz cell

Therefore, the Brillouin Zone exhibits all wavevectors, k, which can be Bragg-reflected by a crystal

A Brillouin Zone is defined as a Wigner-Seitz primitive cell in the reciprocal lattice.To find this, draw the reciprocal lattice.Then, use the same algorithm (done in animation) as for finding the Wigner-Seitz primitive cell in real space (draw vectors to all the nearest reciprocal lattice points, then bisect them. The resulting figure is your cell).The nice result of this is that it has a direct relation to the diffraction condition:

k (1/2 G) = (1/2 G)2

BRAGG PLANE and Brillouin Zones

Is the perpendicular bisector to the line joining the origin of reciprocal space to any reciprocal lattice point.

BRAGG PLANE Brillouin Zones

1st Brillouin zone2nd Brillouin zone 3rd Brillouin zone Every zone have equal volume of space in R.L1st Brillouin zone

Reciprocal lattice to SC lattice

a1 a2a1 a2 a3a1 a2 a3a1 a2 a3a2 a3a3 a1b2 2b3 2b1 2The primitive translation vectors of any simple cubic lattice are:a1 = a xa2 = a ya3 = a zUsing the definition of reciprocal lattice vectors:

We get the following primitive translation vectors of the reciprocal lattice:

b1 = (2/a)xb2 = (2/a)yb3 = (2/a)z

This is another cubic lattice of length 2/a

Reciprocal lattice to SC lattice

The boundaries of the first Brillouin zone are the planes normal to the six reciprocal lattice vectors +/- b1, +/- b2, +/- b3 at their midpoints:+/- (/a)The length of each side is 2/a and the volume is (2/a)3

2/a

Primitive cellWigner Seitz Cell

Deposition method -Pulsed laser deposition

Pulsed laser deposition(PLD) is aphysical vapor deposition(PVD) technique.high-power pulsedlaserbeambackground gas-1- ultra high vacuum2- Oxygen for Oxides

High vaccuum parameter -> 10-7 ~10-9

PLD Process-Laser ablation of the target material and creation of a plasma:Ablation of the target material upon laser irradiation removal of atoms, vaporization of the bulk at the surface regionDynamic of the plasmaScattering and interference of plasma ion and background gas.Deposition of the ablation material on the substrateion bombarding the substrate surfaceDamage could occur at this point; by sputtering of plasma at substrate Nucleation and growth of the film on the substrate surfaceGrowth and nucleation is dependent on these parameterLaser parametersSurface temperatureSubstrate surfaceBackground pressure

Growth mode in PLDStep flow growthLayer by layer growth3D growth ( all at same time)

Kinetics of PLDDistance and masking in between substrate and target plays a important role in the term of layer growth,

Figure (b) has the highest probability to deposit dense and uniform layer of sample.

Flexible, easy to implement Growth in any environmentExact transfer of complicated materials (YBCO)Variable growth rate Epitaxial at low temperatureResonant interactions possible (i.e., plasmons in metals, absorption peaks in dielectrics and semiconductors) Atoms arrive in bunches, allowing for much more controlled depositionGreater control of growth (e.g., by varying laser parameters)

Uneven coverageHigh defect or particulate concentrationNot well suited for large-scale film growthMechanisms and dependence on parameters not well understood

Advantages of PLDDisadvantages of PLD

Reference-Pulse laser deposition US patent/Mayer, Frederick J. "Pulsed laser microfabrication." U.S. Patent No. 4,752,455. 21 Jun. 1988.NPTEL- Material Science engineering 1) Tiwari, Shailja, et al. " Journal of Physics: Condensed Matter19.17 (2007): 176002.2) Shvets, Igor, Sunil Arora, and Sumesh Sofin Ramakrishna Pillai. " U.S. Patent Application No. 11/078,416.3) Chaudhary R.J, et al. "Oriented growth of Fe3O4 thin film on crystalline and amorphous substrates by pulsed laser deposition."Journal of Physics D: Applied Physics40.16 (2007)4) Cao, X., et al. "Synthesis of pure amorphous Fe2O3."Journal of materials research12.02 (1997): 402-406.Klug, Harold Philip, and Leroy Elbert Alexander.X-ray diffraction procedures. Vol. 2. New York: Wiley, 1954.