scholarly journals MATHEMATICAL EQUATION FOR IMPURITY DISTRIBUTION AFTER SECOND PASS OF ZONE REFINING

2021 ◽  
Vol 27 (1) ◽  
pp. 32-35
Author(s):  
Milan Skrobian ◽  
Rudolf Pernis
Keyword(s):  
Linear Trend ◽  
Exponential Model ◽  
Impurity Distribution ◽  
Molten Zone ◽  
Mathematical Tool ◽  
Zone Refining ◽  
Mathematical Equation ◽  
Simplified Approach ◽  
First Pass ◽  
Complex Models

A mathematical equation has been derived that describes impurity distribution in ingot after second pass of zone refining. While an exponential impurity distribution is calculated by a simplified model after first pass, second pass is described by mixed linear - exponential model. Relationship of transformed impurity concentration is constant over whole length of semi-infinite ingot for first pass. However, it has linear trend for second pass. Last part of molten zone at infinity solidifies differently and can be described mathematically as directional crystallization. A mathematical tool devised for second pass of zone refining can be tried to be used for derivation of functions of more complex models that would describe impurity distribution in more realistic way compared to simplified approach. Such models could include non-constant distribution coefficient and/or shrinking or widening molten zone over a length of ingot.

scholarly journals Simplification of a Molten Zone Refining Formula

JOM ◽  
1955 ◽  
Vol 7 (7) ◽  
pp. 838-838
Author(s):  
Keith S. Milliken
Keyword(s):  
Molten Zone ◽  
Zone Refining

Prediction of Drilling Mud Rheology Using a Simplified Herschel-Bulkley Model

1977 ◽  
Vol 99 (3) ◽  
pp. 485-490 ◽  
Author(s):  
M. Zamora ◽  
R. Bleier
Keyword(s):  
Power Law ◽  
Drilling Mud ◽  
Simplified Approach ◽  
Complex Models ◽  
Drilling Muds

Drilling muds are rheologically complex. Models presently used to characterize their behavior are those of Bingham and Ostwald-deWaele (power law). The Herschel-Bulkley model is shown in this paper to be superior, but more difficult to implement with theoretic exactness. However, a simplified approach suitable for field use is developed and compared to rigorous solutions.

scholarly journals Characterization and Interpretation of the Aluminum Zone Refining through Infrared Thermographic Analysis

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2039
Author(s):  
Xiaoxin Zhang ◽  
Semiramis Friedrich ◽  
Bernd Friedrich
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
High Purity ◽  
Refining Process ◽  
Crystal Growth Rate ◽  
Molten Zone ◽  
Zone Refining ◽  
Ir Camera ◽  
Zone Length ◽  
Thermographic Analysis

High purity metals are nowadays increasingly in demand to serve in electronic, photovoltaic, and target materials industries. The zone refining process is the most common way to achieve high purity in the final step of metal purification. Zone length and crystal growth rate are the main parameters that control the zone refining process. To determine these values, information about temperature profiles in the molten zone is necessary due to its direct correlation with these values. As the determination of this profile is not practically achievable in the present, the novel approach of applying an infrared (IR) camera during the zone refining of 2N8 aluminum is the focus of the investigation in this work. The whole temperature profile of the region near the molten zone was recorded by IR camera during the entire running process. The zone length and the crystal growth rate at each thermographic image shooting moment were successfully extracted by thermographic analysis. Results showed that both factors varied significantly, which is in contrast to the assumption in literature about their stability while running under constant input power and heater movement velocity, though noticeable purification took place in all of these experiments. However, the impurity concentration during refinement fluctuated remarkably. This was well-demonstrated by the tendency of variation in crystal growth rate attained in this work. These results provide a better understanding of the mechanisms of zone refining with an inductive heater and contributes to the optimization of the process.

scholarly journals Prediction of CPI in Saudi Arabia: Holt’s Linear Trend Approach

2020 ◽  
Vol 11 (6) ◽  
pp. 302
Author(s):  
Anis Ali ◽  
Ayman Mahgoub
Keyword(s):  
Saudi Arabia ◽  
Linear Model ◽  
Linear Trend ◽  
Consumer Price Index ◽  
Exponential Model ◽  
Market Basket ◽  
Goods And Services ◽  
Low Weight ◽  
Double Exponential Smoothing ◽  
The Cost

The Consumer Price Index (CPI) indicates and measures price level changes in an economy based on total purchased goods and services. CPI is calculated by dividing the cost of the market basket in a given year by the cost of the market basket in a Base Year and multiplied by 100. CPI is subject to the Classification of Individual Consumption by Purpose (COICOP) in Saudi Arabia. Home expenditure items, such as housing, water, electricity, gas, and other fuels, food, and beverages are considered high while weight, health, education, recreation, and culture are given low weight in the COICOP in Saudi Arabia. Holt’s linear model based on three equations and popularly known as double exponential smoothing or linear exponential model and the most commonly used method in forecasting data based on internal trends. Holt’s linear model is composed of three equations relating to smoothing, trend, and forecast. In this paper, the CPI data were taken monthly from the General Authority for Statistics, Saudi Arabia for the period from May 2019 to July 2020 with 15 realizations. The CPI for Saudi Arabia is predicted for the next twelve months and as observed from the trend of CPI, the prices of total purchased goods will increase in the next eleven months.

scholarly journals Medico-economic impact of robot-assisted lung segmentectomy: what is the cost of the learning curve?

2019 ◽  
Author(s):  
Constance Le Gac ◽  
Henri Gondé ◽  
André Gillibert ◽  
Marc Laurent ◽  
Jean Selim ◽  
...  
Keyword(s):  
Learning Curve ◽  
Linear Trend ◽  
Operating Time ◽  
Exponential Model ◽  
Cost Of Care ◽  
Robot Assisted ◽  
Cost Study ◽  
Cumulative Sum Analysis ◽  
Significant Difference ◽  
Medico Economic

Abstract OBJECTIVES The objective of this study was to assess the learning curve (LC) of robot-assisted lung segmentectomy and to evaluate hospital-related costs. METHODS We conducted a retrospective study of Robot-assisted thoracic surgery (RATS) segmentectomies performed by 1 surgeon during 5 years. Perioperative and medical device data were collected. The LC, based on operating time, was assessed by Cumulative SUM analysis and an exponential model. Cost of care was estimated using the French National Cost Study method. RESULTS One hundred and two RATS segmentectomies were included. The LC was completed at ∼30 procedures according to both models without significant difference in patients’ characteristics before or after the LC. Mean operative time decreased from 136 min [95% confidence intervals (CI) 124–149] for the first 30 procedures to 97 min (95% CI 88–107) for the last 30 procedures. Mean length of stay decreased non-significantly (P = 0.10 for linear trend) from 8.1 days (95% CI 6.1–11.0) to 6.2 days (95% CI 4.9–7.9). The overall costs for the last 30 procedures as compared with the first 30 did not significantly decrease in the primary economic analysis but significantly decreased (P = 0.02) by €1271 (95% CI −2688 to +108, P = 0.02 for linear trend) after exclusion of 1 outlier (hospitalization-related costs > €10 000). After exclusion of this outlier, costs related to EndoWrist® instruments significantly decreased by €−135 (95% CI −220 to −35, P = 0.004), whereas costs related to clips decreased non-significantly (P = 0.28). CONCLUSIONS The LC was completed at ∼30 procedures. Inexperienced surgeons may have higher procedure costs, related to consumable medical devices and operating time.

Limiting impurity distribution during zone refining

2014 ◽  
Vol 40 (6) ◽  
pp. 460-461 ◽  
Author(s):  
V. I. Bochegov ◽  
A. S. Parakhin
Keyword(s):  
Impurity Distribution ◽  
Zone Refining

Embedding Procedure for Water Swollen Samples

1970 ◽  
Vol 28 ◽  
pp. 504-505
Author(s):  
Ann M. Thomas ◽  
Virginia Shemeley
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Ion Exchange ◽  
Structural Changes ◽  
Cross Linking ◽  
Ion Exchange Resins ◽  
Transmission Electron ◽  
First Pass ◽  
Exchange Resins

Those samples which swell rapidly when exposed to water are, at best, difficult to section for transmission electron microscopy. Some materials literally burst out of the embedding block with the first pass by the knife, and even the most rapid cutting cycle produces sections of limited value. Many ion exchange resins swell in water; some undergo irreversible structural changes when dried. We developed our embedding procedure to handle this type of sample, but it should be applicable to many materials that present similar sectioning difficulties.The purpose of our embedding procedure is to build up a cross-linking network throughout the sample, while it is in a water swollen state. Our procedure was suggested to us by the work of Rosenberg, where he mentioned the formation of a tridimensional structure by the polymerization of the GMA biproduct, triglycol dimethacrylate.

High-resolution EM investigation about effect of stress on formation of ω-phase crystals in β-tttanium alloys

1996 ◽  
Vol 54 ◽  
pp. 1006-1007
Author(s):  
E. Sukedai ◽  
M. Shimoda ◽  
A. Fujita ◽  
H. Nishizawa ◽  
H. Hashimoto
Keyword(s):  
High Resolution ◽  
Titanium Alloys ◽  
High Resolution Electron Microscopy ◽  
Dark Field ◽  
Zone Refining ◽  
Ω Phase ◽  
Α Phase ◽  
Nucleation Sites ◽  
Resolution Electron ◽  
Bcc Structure

ω-phase particles formed in β-titanium alloys (bcc structure) act important roles to their mechanical properties such as ductility and hardness. About the ductility, fine ω-phase particles in β–titanium alloys improve the ductility, because ω-phase crystals becomes nucleation sites of α-phase and it is well known that (β+α) duplex alloys have higher ductility. In the present study, the formation sites and the formation mechanism of ω-phase crystals due to external stress and aging are investigated using the conventional and high resolution electron microscopy.A β-titanium alloy (Til5Mo5Zr) was supplied by Kobe Steel Co., and a single crystal was prepared by a zone refining method. Plates with {110} surface were cut from the crystal and were pressured hydrostatically, and stressed by rolling and tensile testing. Specimens for aging with tensile stress were also prepared from Ti20Mo polycrystals. TEM specimens from these specimens were prepared by a twin-jet electron-polishing machine. A JEM 4000EX electron microscope operated at 400k V was used for taking dark field and HREM images.

Sign in / Sign up

Export Citation Format

Share Document