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Department Library

1978

Ralph Watson Young (PhD Dissertation, December 1978, Advisor: Howard Vanfleet )

Abstract

The dehancement of Au diffusivity in Pb due to the concentration of the Au was measured as a function of temperature and pressure. Temperatures ranged from 160-352ºC, and three pressures were used: 1 atm, 20 kbars, and 35 kbars. A new self-dehancement technique was based on an integral solution to the nonlinear diffusion equation was employed. This solution allows the diffusion coefficient to be concentration dependent, and makes possible the use of a single pure host sample in making each dehancement measurement. Saturation solubilities as a function of temperature and pressure were also determined in the course of the experiment. The dehancement and solubility data were shown to be consistent with a model in which the Au forms doublet clusters as well as singlets when dissolved in the Pb. The data predicts that an Au doublet and an Au singlet each occupy approximately the same volume in the lattice, a volume of about .7 or .8 atomic volumes of Pb. This result is consistent with a model of Au doublets in Pb in which two Au atoms occupy a single substitutional site.

1975

James Doug Jorgensen (PhD Dissertation, April 1975, Advisor: Howard Vanfleet )

Abstract

The diffusion of mercury in solid lead has been measured at hydrostatic pressures to 38 kilobars using a radioactive tracer and sectioning technique. High pressures were produced by a 400 ton ram capacity hexahedral anvil press. The data were analyzed assuming a single effective mechanism of diffusion and using reaction rate theory. The measured diffusion coefficient, activation energy and activation volume at zero pressure and 600oK are: D = 5.71±0.55x10-9 cm2/sec, ΔH = 23.06±0.12 kcal/mole, and ΔV = 0.514±0.026 atomic volumes. Even though the activation energy is near that for lead self-diffusion, the activation volume is too small t oeb consistent with a vacancy mechanism. However, the results can be explained either in terms of a double mechanism, if the interstitial component is assumed to have a relatively large activation energy, or in terms of an interstitial solute-vacancy pair mechanism.

1974

John Douglas Schmutz (Masters Thesis, January 1974, Advisor: Howard Vanfleet )

Abstract

The diffusion of cadmium in solid lead is measured by a radioactive tracer and sectioning technique. Diffusion coefficients are obtained over a pressure range of zero to 42 kbars and a temperature range of 250oC to 500oC. The activation energy is found to increase from 19.53 kcal/mole at zero pressure to 23.44 kcal/mole at 40 kbar. The activation volume is calculated to be .36 ± .05 atomic volumes. Do is found to have a value of .074 ± .032 cm2/sec at zero pressure and 327oC. The three mechanism diffusion model proposed by Miller and generalized to include all solutes in lead by Decker is presented and compared with the results of this experiment. It is concluded that cadmium probably fits the model, but due to the great uncertainty in the pressure calibration, the fit is not as good as expected. The results of this work strongly suggest that the form of the pressure calibration which fits a tetrahedral anvil press does not apply to the cubic press used in this study.

1971

Calvin T Candland (PhD Dissertation, August 1971, Advisor: Howard Vanfleet )

Abstract

The diffusion of copper in lead has been investigated using radioactive racer and sectioning techniques. Diffusion coefficients have been obtained within the largest hydrostatic pressure range (0-56 kb) and temperature range (218-530 C) ever reported for diffusion in solid lead. The activation energy was found to increase from a value of 5.6 ± .5 kcal/mole at zero pressure, to 7.8 ± .5 kcal/mole at 56 kb. The activation volume was calculated to be .04 ± .03 atomic volumes. The small activation volume and activation energy diffusion of silver in head and gold in lead, indicate that copper diffuses in lead primarily by the interstitial mechanism. The results of previous high pressure studies of the diffusion of silver in lead and gold in lead were explained in terms of double diffusion (interstitial and substitutional) mechanisms. Frank and Turnbull’s dissociative double mechanism solution is compared to an exact solution which is introduced in this work. Significant changes in hydrostatic cell pressure due to heating were measured in this study.

Howard Roy Curtin (PhD Dissertation, August 1971, Advisor: Howard Vanfleet )

Abstract

The diffusion of lithium in p-type germanium has been investigated in the temperature range 300oC to 550oC using a p-n junction depth technique, and at room temperatures through the determination of the relaxation times for the Ga-, Li+ ion-pairing reaction. These measurements, which covered a pressure range of 0 to 50 kbar resulted in D (T, P) = .00153 exp(-.025P) exp(-11.33-.0078P-.00085P2) /RT (D in cm2/sec., T in oK, P in kbar). This result is compared with Weiser’s model for interstitial diffusion in the diamond lattice. The ambient temperature and pressure values, calculated from this result, for; D, the activation energy (Q), and the activation volume (∆V); are: Do = .00145 ± .00006 cm2/sec., Q = 11.33 ± .04 kcal/mole, ∆V/Vo = .039 ± .010. A limited theoretical and experimental investigation of the pressure variation of the solid solubility of lithium in germanium was made. This study indicated that, in the temperature range 300 to 500oC, the solubility of Li+ in Ge varies by less than 50 percent from the ambient pressure solubility when the pressure is varied in the range 0-45 kbar.

David L Wheeler (Masters Thesis, August 1971, Advisor: Howard Vanfleet )

Abstract

A study was made of the feasibility of measuring the diffusion of Sb into Ge at high pressures. A tetrahedral press was used to obtain the high pressures. The diffusion constant was determined by measuring the depth of a p-n junction formed by diffusing Sb into p-type Ge. An interference technique was used to measure the depth of the p-n junction. NaI was an adequate pressure transmitting medium at 700oC to pressures of 20 kbar, while nothing was found which gave satisfactory results above 20 kbar at the high temperatures required for diffusion measurements. Preliminary measurements at 15 kbar indicate an activation energy greater than 5 eV and a possible change of diffusion mechanisms. It is felt that meaningful diffusion measurements can be made at pressures less than 20 kbar.

1969

Jack A. Weyland (PhD Dissertation, January 1969, Advisor: Howard Vanfleet )

Abstract

The diffusion of gold in lead has been investigated using radioactive tracer techniques in a temperature range within 250oC of the melting point of lead for four pressures between 15 and 40 kbar. The activation energy was found to increase monotonically with pressure, from a value of 12.2± 1.1 kcal/mole at 17.6 kbar, to 16.3 ± 1.7 kcal/mole at 39.3 kbar. The activation volume was within experimental error nearly a constant at 0.36 atomic volumes over the pressure range investigated as the temperature decreased from 693°K. A consistent mechanism for the diffusion of gold in lead is shown to be one in which the solute dissolves and diffuses both interstitially and substitutionally with the interstitial mechanism being the main contributor to the measured diffusion constant. Previous results for the diffusion of silver in lead from atmospheric pressure to 40 kbar are used to discuss the properties of the diffusion of the noble metals in lead. Results for both silver and gold diffusing in lead seem consistent with a two-component mechanism. For this interstitial-substitutional diffusion mechanism, the expected curvature of plots of ln D versus P is shown to be positive or negative, depending upon the magnitude of csDs/ciDi.

1965

Rondo N. Jeffery (Masters Thesis, August 1965, Advisor: Howard Vanfleet )

Abstract

A method for measuring ultra-high pressures is presented along with experimental results obtained at pressures up to 100,000 atmospheres. The method is based on measuring the compression of sodium chloride with the x-ray diffraction tetrahedral press and comparing with the theoretical equation of state for NaCl calculated by Decker to obtain the pressure. The calibration of the apparatus is shown to vary by several percent from run to run. The shape of the calibration curve near the origin is shown as well as direct observation of apparatus hysteresis. Intrinsic hysteresis in certain sample materials is also shown apart from apparatus hysteresis. The calibration of certain fixed point transition pressures is determined. A new pressure scale is proposed based on the calibration of the fixed points Bi I-II = 25.0 ± 0.5 kbar, T1 II-III = 35.6 ± 1.3 kbar, Yb I-II = 38.1 ± 1.3 kbar, Ba I-II = 54.5 ± 1.5 kbar, and Bi III-V = 76.5 ± 2.0 kbar. The actual values of the NaCl compression at the transitions were found to be: ∆ a/ao= 0.0285 ± .0005 for Bi I-II, 0.0378 ± 0.0007 for T1 II-III, 0.0398 ± 0.0007 for Yb I-II, 0.0518 ± 0.0008 for Ba I-II, and 0.0653 ± 0.0006 for Bi III-V. These determinations constitute a significant contribution to the pressure calibration field aside from specific reference to theoretical compression curves.

Nalini R. Mitra (PhD Dissertation, January 1965, Advisor: Howard Vanfleet )

Abstract

"By using the tetrahedral anvil press the melting curves of silver, copper, and platinum have bene investigated to a pressure of 70 kilobars. The melting temperatures were detected by sharp increase in resistivity. The pressure correction due to heating of the sample chamber has been worked out in detail. The raw melting data have been temperature-corrected for the error in locating the thermocouple junction, and then the pressure has been applied. The melting curves of the three metals are represented by the Simon equations (P/119 ) = (T/1234) 1.75 -1 Silver (P/327) = (T/1356.2) -1 Copper

1964

Vern E. Bean (Masters Thesis, January 1964, Advisor: Howard Vanfleet )

Abstract

Howard Roy Curtin (Masters Thesis, August 1964, Advisor: Howard Vanfleet )

Abstract

Diffusion constants associated with the diffusion of Ag110 into Pb at pressures to 38 kilobars, and temperatures in a 150℃ range below the melting point of lead, have been determined by annealing silver-plated lead single crystals in high viscosity silicone oil—the high pressure anneals being conducted in a Tetrahedral-Anvil press. The activation energy (Q) was determined at six pressures and shown to vary from 15.8 kcal/mole at atmospheric pressure to 21.0 kcal/mole at 38 kb. Corresponding values of Do varied from .160 cm2/sec at atmospheric pressure to .051 cm2/sec at 38 kb. A plot of the log of the diffusion constant versus the ratio of the melting temperature™ to the anneal temperature revealed that the ratio Q/Tm was very nearly independent of pressure (≈26.4 cal/mole °K) for pressures to 38 kb. The molar ratio of the activation volumes, calculated from results below 23 kb, ranged from .428 at 556oK to .454 at 769oK. These values are considerably less than those reported for self-diffusion (≈.65). Calculated values of the geometric constant in the Dushman-Langmuir equation varied by a factor of two with pressure, indicating that this equation is over-simplified. On the other hand, calculated values of the entropy of activation vary from 13.22 cal/moleoK at atmospheric pressure to 11.14 cal/mole oK at 38 kb. showing satisfactory agreement with Zener’s theory of Do.