Frank’s rule

Sir Frederick Charles Frank (1911-1998) received his Ph.D. in 1937 from Oxford University, followed by a postdoctoral position at the Kaiser Wilhelm Institut fiir Physik in Berlin. During World War II, Frank was involved with the British Chemical Defense Research Establishment, and because of his keen powers of observation and interpretation, he was later transferred to Scientific Intelligence at the British Air Ministry. In 1946, Frank joined the H. H. Wills Physics Laboratory at the University of Bristol under its director, Nevill Mott, who encouraged him to look into problems concerned with crystal growth and the plastic deformation of metallic crystals. A stream of successes followed, establishing his scientific fame, as evidenced by many eponyms the Frank-Read source, the Frank dislocation, Frank s rule, Frank-Kasper phases. His theoretical work has been the foundation of research by innumerable scientists from around the world. Frank was awarded the Order of the British Empire (OBE) Medal in 1946, elected a Fellow of the Royal Society (FRS) in 1954, and was knighted in 1977. 

FIGURE 12.3 Diagram used for proving Frank s rule for conservation of b. 

However, the (100) product dislocations in Eq. (16) are both perfect dislocations and are perpendicular to one another. Frank s rule indicates that, to first order, such a reaction would not lead to reduction in the dislocation line energy, whether it occurs by glide or climb. Of course, if the screw/edge character of the (110) dislocation is taken into account, then Eq. (16) will be favorable for an edge dislocation and unfavorable for a screw dislocation. 

Kharasch s earliest studies in this area were carried out in collaboration with graduate student Frank R. Mayo. Mayo performed over 400 experiments in which allyl bromide (3-bromo-1-propene) was treated with hydrogen bromide under a variety of conditions, and determined the distribution of the "normal" and "abnormal" products formed during the reaction. What two products were formed Which is the product of addition in accordance with Markovnikov s rule Which one corresponds to addition opposite to the rule ... 

The court s ruling passes the question of marijuana s medical future to Congress, which would have to rewrite current laws to allow it to be used therapeutically. In response, Rep. Barney Frank (D-Mass.) introduced a bill to reclassify marijuana as a Schedule II drug, which would permit physicians to prescribe it for their patients if state law permitted its use. 

In order to compute the partial autocorrelation function, assume that the process of interest can be modelled as a r-order autoregressive process. Note that it does not matter what model the true process has. Setup the r-order Yule-WaUcer equation in the form given by Eq. (5.76). It can be shown that the partial autocorrelation of lag t is equal to a, that is, the final parameter that is estimated (Franke et al. 2011)." Practically, rather than computing all the parameters, it is easier to simply compute the final desired value using Cramer s rule, that is,... 

Should you memorize Woodward s rules Frankly, we think not—although there are those who strongly disagree, and some of these people write examination questions. These rules were an important part of structure determination but are restricted in utility to relatively simple polyenes. You should know they exist, know what systems they apply to, and look them up when you need them. If you wind up in steroid research, you ll learn them. 

Frequently, an approximate value of the optimum exit-water ten Derature is all that is required, and a rule-of-thumb will be satisfactory. Table 4.4 hsts the approach tenperature difference, which is the difference between the two terminal temperatures of two passing streams, for several heat exchangers. Several approach temperature differences were taken from Uhich [8], For refrigerants, Ulrich s range of 10 to 50°C is on the high side. Frank [7] recommends a range of 3 to 5°C whereas Walas [3] recommends a value of 5.6 C or less. 

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