— Interplanar spacing implies the magnitude of the distance between two adjacent and parallel planes of atoms.

The interplanar spacing is a function of the, Miller indices (h,k and /) as well as the lattice parameter(s).

Interplanar spacing with a given set of Miller indices is a useful bit of information.

Planes with large interplanar spacing have low indices and a high density of lattice points, whereas the reverse is true for planes of close spacing.

— If we consider the simple cube shown in Fig. 35.26, it is obvious that, in this case, the most widely spaced atomic planes are those spaced at intervals equal to the lattice parameters, i.e., the (100) planes. The spacing is

d_{100} = a …(i)

The dodecahedral planes (110) bisect the face diagonal for a spacing of

D_{110} =( ½)√(a^{2}+a^{2})= a/√2 …(ii)

The octahedral planes (111) trisect the body diagonal for a spacing of

d_{111}=(1/3)√(a^{2}+a^{2}+a^{2})=a/√3 …(iii)

— General equations for interplanar spacing for various unit cells can be written in terms of the Miller indices; namely:

Cubic : 1/d^{2}_{hkl} = (h^{2}+k^{2}+l^{2}) / a^{2} …(iv)

Tetragonal: 1/d^{2}_{hkl} = (h^{2}+k^{2})/a^{2} +( l^{2} )/ c^{2} …(v)

Orthorhombic: 1/d^{2}_{hkl} = (h^{2})/a^{2} + k^{2}/b^{2} + (l^{2}) / c^{2} …(vi)

Hexagonal: 1/d^{2}_{hkl} = (4/3)(h^{2}+hk+k^{2}) / a^{2} +l^{2}/c^{2}…(viii)

N.B.: a is lattice parameter and c/a is axial ratio in HCP crystal structure (refer Fig. 35.11). From (iv) above, for a cubic crystal, the interplanar spacing d_{hkl} = a√/(h^{2}+k^{2}+l^{2}) and so on for tetragonal, orthorhombic and hexagonal structures.

Derivation of interplanar spacing of cubic crystal

—The interplanar spacing or distance ‘d_{hkl}‘ between adjacent planes of Miller indices (hkl) is defined as the spacing between the first such plane and a parallel plane passing through the origin.

—Refer Fig. 35.27 ais the lattice constant. Let h, k, and l are the Miller indices for a plane ABC. An equation is to be derived for interplanar distance‘d’ of plane ABC from a plane parallel to it

and passing through ‘o’ (origin) in terms ofh,k,land a. OD is the normal from O on plane ABC. OD – d = interplanar distance. The intercepts of the plane ABC on the three axis i.c.,X, Y and Z axis are OA, OB and OC respectively.

Now, OA=a/h, OB=a/k,OC=a/l …(i)

Also, cos α=OD/OA= d/(a/h) =dh/a …(ii)

cos β= OD/OA= d/(a/k)= dk/a …(iii)

cos γ=OD/OC = d/(a/l) = dl/a …(iv)

Since, cos^{2} α+ cos^{2}β + cos^{2}γ = 1. therefore

(dh/a)^{2} +(dk/a)^{2} + (dl/a)^{2} = 1

d^{2}h^{2}/a^{2 }+ d^{2}k^{2}/a^{2 + } d^{2}l^{2}/a^{2} = 1

d^{2}(h^{2} + k^{2}^{ + } l^{2}) =a^{2}

d^{2}=a^{2 }/(h^{2} + k^{2}^{ + } l^{2})

d= a^{2 }/√(h^{2} + k^{2}^{ + } l^{2})

I need help solving this problem.

Potassium iodide has an interplanar spacing

of 0.139 nm. A monochromatic x-ray beam

shows a first-order diffraction maximum when

the angle of incidence is 5.4◦.

Calculate the x-ray wavelength.

Answer in units of nm.

I calculated these answers and they turned up wrong

.0131nm

.00131nm

.00655nm

Physicists please help

Ekaterina, your answer came out wrong too. thanks for giving it a shot though

The distance between consecutive (101) planes in a cubic crystal is 4A.

Determine the lattice parameter.

In a tetragonal crystal, the lattice parameters are a=b=2A and c=3A.

Deduce the interplanar spacing between consecutive (101) planes.

Thanks guys.

if the x-ray(wavelength(Y) = 0.159nm) angle of diffraction for the (211) set of planes on BCC crystal of is 75.99 degrees; compute the interplanar spacing for this set of planes.

problem states that this is a first order reflection, so n=1

(n being a integer number of wavelengths)

Y being wavelength

d being distance between planes

Q being angle of reflection

my book says nY=2dsinQ

but when i insert given Q, N, Y, and

solve for d, i get d= 0.0855nm but the book says d=0.13nm

please help! this book is crap, there is only one super easy example with a simple cubic crystal!

jon bon clammy: they are the same angles. at least in this case.

X-ray of wavelength 4.225 Å are reflected from a crystal having interplanar spacing of 1.549 Å. what is the order of diffraction maxima?

im aware that d =

a

—————————–

(h^2 + k^2 +a^2)

A wavelength of 0.134 nm characterizes K(beta) X-rays from zinc. When a beam of these X-rays is incident on the surface of a crystal whose structure is similar to that of NaCl, a first-order maximum is observed at 3.43 degrees. Calculate the interplanar spacing based on this information.

Answer in units of nm.

(Wickipedia) “As of 2009, graphene appears to be one of the strongest materials ever tested. Measurements have shown that graphene has a breaking strength 200 times greater than steel, a bulk strength of 130GPa.[99]“. And…” Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm, which means that a stack of 3 million sheets would be only one millimeter thick.”

X rays from a copper X-ray tube ( = 1.54 Å) were diffracted at an angle of 14.22 degrees by a crystal of silicon. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in silicon?

X rays from a copper X-ray tube (1.54A) were diffracted at an angle of 14.22 degrees by a crystal of silicon. Assuming first order diffraction (n=1 in the Braggs equation), what is the interplanar spacing in silicon?

please show work

im aware that d = a

—————————–

(h^2 + k^2 +a^2)

but how do we calculate a?

I can’t figure out how to put the image here but basically they give me a graph of the x-ray diffraction pattern for tungsten where the y-axis is intensity and the x-axis is diffraction angle (2 theta). Also given is: tungsten has a BCC crystal structure and monochromatic x-radiation having a wavelength of 0.1542 nm was used. They ask for a) Index (i.e., give h, k, and l indices) for the first peak. b) Determine the interplanar spacing for the first peak. and c) For the first peak, determine the atomic radius for W.

PLEASE HELP!!!

Do both of these involve nearly full time field work ?

Are the working conditions generally risky ?

I can’t figure out how to put the image here but basically they give me a graph of the x-ray diffraction pattern for tungsten where the y-axis is intensity and the x-axis is diffraction angle (2 theta). Also given is: tungsten has a BCC crystal structure and monochromatic x-radiation having a wavelength of 0.1542 nm was used. They ask for a) Index (i.e., give h, k, and l indices) for the first peak. b) Determine the interplanar spacing for the first peak. and c) For the first peak, determine the atomic radius for W.

PLEASE HELP!!!

1. consider a one-dimensional collision at relativistic speeds between two particles with mass m1 and m2. particle 1 is initially moving with a speed of 0.7c and collides with particle 2, which is initially at rest.After the collision, particle 1 recoils with speed 0.5c, while particle 2 starts moving with speed of 0.2c. What is the ratio of m1/m2?

2. for BBC iron, compute the interplanar spacing and the diffraction angle for the (220) set of planes.The lattice parameter for Fe is 0.2866 nm. Also, assume that monochromatic radiation having a wavelength of 0.1790 nm is used, and the order of reflection is 1.