Determine crystal lattice structure from powder XRD

 P: 34 1. The problem statement, all variables and given/known data Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm) Peak No.------2(theta) 1 -------------38.06 2 -------------44.24 3 -------------64.34 4 -------------68.77 5 -------------73.07 2. Relevant equations $$2dsin\theta = n\lambda$$ $$d = \frac{a}{\sqrt{N}}$$ $$\Delta sin\theta = \left(\frac{\lambda}{4a^{2}}\right)N_{2} - N_{1}$$ $$N= h^{2}+k^{2}+l^{2}$$ 3. The attempt at a solution I've worked out sin theta for each sin theta squared and delta sin theta: Peak------2(theta)------sin theta----sin squared theta---delta sin squared theta 1-----------38.06-------0.32606-------0.10632------------ 2-----------44.24-------0.37655-------0.14179------------0.03547 3-----------64.34-------0.53243-------0.28349------------0.1417 4-----------68.77-------0.56475-------0.31894------------0.03545 5-----------73.07-------0.59531-------0.35440------------0.03549 The only example we've covered is with a primitive cubic structure which I almost knew what I was doing(!) and the only advice that the lecturer gave was to "look for the highest common factor of values in the list delta sin squared theta to find $$\frac{\lambda}{4a^{2}}$$ I obviously noted that the difference between peak 2 and 3 was the same value as Peak 2 but what I'm meant to do with that information I'm not so sure about!!? I know that a fcc structure only has N values of 3,4,8,11 etc but really could do with some advice as where to go from here!!?
 Quote by s_gunn 1. The problem statement, all variables and given/known data Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm) Peak No.------2(theta) 1 -------------38.06 2 -------------44.24 3 -------------64.34 4 -------------68.77 5 -------------73.07 2. Relevant equations $$2dsin\theta = n\lambda$$ $$d = \frac{a}{\sqrt{N}}$$ $$\Delta sin\theta = \left(\frac{\lambda}{4a^{2}}\right)N_{2} - N_{1}$$ $$N= h^{2}+k^{2}+l^{2}$$ 3. The attempt at a solution I've worked out sin theta for each sin theta squared and delta sin theta: Peak------2(theta)------sin theta----sin squared theta---delta sin squared theta 1-----------38.06-------0.32606-------0.10632------------ 2-----------44.24-------0.37655-------0.14179------------0.03547 3-----------64.34-------0.53243-------0.28349------------0.1417 4-----------68.77-------0.56475-------0.31894------------0.03545 5-----------73.07-------0.59531-------0.35440------------0.03549 The only example we've covered is with a primitive cubic structure which I almost knew what I was doing(!) and the only advice that the lecturer gave was to "look for the highest common factor of values in the list delta sin squared theta to find $$\frac{\lambda}{4a^{2}}$$ I obviously noted that the difference between peak 2 and 3 was the same value as Peak 2 but what I'm meant to do with that information I'm not so sure about!!? I know that a fcc structure only has N values of 3,4,8,11 etc but really could do with some advice as where to go from here!!?
 P: 3 Determine crystal lattice structure from powder XRD For Cubic crystal finding hkl (miller indices) is easy note that peak in xrd is a importent factor (1) Identify the peaks. (2) Determine sin2$\theta$ (3) Calculate the ratio sin2$\theta$/ sin2$\theta$min and multiply by the appropriate integers. (4) Select the result from (3) that yields h2 + k2 + l2 as an integer. (5) Compare results with the sequences of h2 + k2 + l2 values to identify the Bravais lattice. (6) Calculate lattice parameters.