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I. A Vacuum X-Ray Diffractometer for High Temperature Studies. II. An Investigation of the Allotropic Transformation of Titanium

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Diffusion of mercury through the cold trap in the room can be difficult in two ways.; the butt. Fluor.c:ent scattering, can usually be emitted by choosing the proper radiation or pulae heilht dberlmination and.the Compton .catterinl usually zero .because the atomic numbers are high and x-ray photon enerlle. A IS tnikron aluminum foU (Z), which covers. open the oven for the x-ray beam, .erves.

Provialon la made to pump re,10n containing. connect the heater, re!111 it with the arion, and then •• disconnect it from the vacuum chamber. With this configuration, most of the lisht resulting from the absorption of an X-ray photon by the Na 1 crystal (T-e.) reaches the photocathode of the photomultiplier. The re,ions wbere .tep .cannin, 1a to appear can be chosen to any quarter of the de,ree interval between 0° and 1750 • Interval.

TABLE  OF  CONTENTS
TABLE OF CONTENTS

EVALUATION OF ERRORS LIMITING THE ACCURACY OF THE DIFlta..ACTOMETER

Convolutions (Faltungs) of functions with a pure diffraction profile have been thoroughly investigated using the superposition theorem (60). The first two factors, the approximation of a natural plate and the penetration of X-rays into the sample, lead to asymmetric broadening and & shift of the center of gravity towards low 0 values. The derivation of the above equation is true when the vertical diversonco ia limited by the SoUer collimating suta.

If the aource is asymmetric, there is no shift if the deviation anal Zg ia measured from the center of srayity of the source to the sravity center of the diffraction peak and the center of ,ravity of tb.e source pa •• •• above the axis of rotation of the spectrometer Consider a diffraction peak f(Zg), where Zg 1a measured from the center of the iravity of the X-ray beam around the axis of rotation of the spectrometer. fifth factor, the width of recelvln, .IU, i.e. a symmetrical folding and will not move tbe center of aravity.

The la.t factor which can affect the location of the center of ,ravity of a diffraction peak 11 of the milalignm,nta diffractometer. The centen of Ipechnen, llit recelving and lource are not in the lame horbontal plan. If the center of radiation of the beam does not lie pa.1 above the axis of rotation, there is 10 a, a constant extension of the location a of the center of radiation of the diffraction peak.

Due to the fact that the above expression 11 is linear with respect to I, a vertical rotation of Ipecimen with respect to the source. A rotation of the receiving sUt relative to the source also DOt set the center of the Iravlty, but only broadens the peak. The angular dependence of the ajatematic error, neslecUna the vertical divergence, may be very clearly represented by a four.

4.4). where a . o1 b the extrapolated value of the lattice parameter corresponding to the extrapolation function flCg). Because of the inverae triaometrlc behavior of "1 and the nature of the terms in the sums, no simple method could be found for summiDl seri.s lor f. To determine the oreier of the magnitude and nature of the above coefficients, it was decided to i evaluated them for a specific material and radiation.

Figure  22.  Convolution  of  a  step  scanning  slit  with  a  symmetrical  diffraction  peak
Figure 22. Convolution of a step scanning slit with a symmetrical diffraction peak

600XIO~ I

EXPERIMENTAL PR.OCEDUR.E AND RESULTS

A typical extrapolation of the five highest angle reflections with the sample at 410 °C, against the Nelson-Riley function, is shown in F1lur. The coefficients of thermal expansion of X-rays as determined by Spreadborouah and ChriaUan (38) and Berry and Raynor (39) are Cl.

Figure  35.  Calibration  of  the  Pt-Pt  100/0  Rh  thermocouple.
Figure 35. Calibration of the Pt-Pt 100/0 Rh thermocouple.

DISCUSSION

The lethal energy of metals consists of the electrostatic attraction between a free electron. Near the bottom of tbe band, this dependence can be represented by a formula like Equation 6.17, but with m i8 replaced by tn., effectively ma.s. Between the two extreme cases is the perturbation of almost free electrons with a periodic potential.

The boundaries of the regions are entirely determined by the point and spatial symmetries of the crystal lattice. In the reduced region scheme, it should be emphasized that there are not necessarily 2N states between the energy discontinuities because the structure factor can eliminate. The thermal, electrical and magnetic properties of free electrons in a metal depend only on those states that are very close to the Fermi energy.

The electron contribution to the free energy for one unfilled band can be estimated using the following formula. Greater than copper and higher than any element in the first transition era, (3) paramagnetic susceptibility and (~) high electron specific heat (79). The eatemate can be made by the following auumptlon.i (1) the free energy of the lower band can be represented.

Although the results are very approximate, it is clear from the above that the contribution of the electron.

Figure  37.  The  temperature  varia tion  of  the  free  energy  of  a  Debye  solid
Figure 37. The temperature varia tion of the free energy of a Debye solid

CONCLUSIONS

The experimental procedure for worm ear calibration requires the use of two worm ears • one of which may be a dummy ear. The relative rotation can be measured very accurately by chan,tn, frin,e pattern between optical flat. On the other hand, a comparison can be made with autocollimatol'l, which will measure relative rotation about a live axis with an accuracy of 0.1 arcsecond.

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TABLE  OF  CONTENTS
Figure 1. The high temperature x-ray diffractometer installation.
Figure  2.  Schematic  of  the  high  temperature  x - ray  diffractometer  installation
72" 0.0. VACUUM CHAMBER  o LICUID  NITROGEN  COLD TRAP  r.;.r-B" I.P.S. VACUUM LINE  CONSOLIDATED MHG 900 I 5  DIFFUSION-PUMP ~,  KINNEY KS-47  Figure 4
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