Rate of growth

Studies have been made on the rate of growth of oxide films on different crystal faces of a metal using ellipsometric methods. The rate was indeed different for (100), (101), (110), and (311) faces of copper [162] moreover, the film on a (311) surface was anisotropic in that its apparent thickness varied with the angle of rotation about the film normal. 

Another important appHcation of LEFM is the rate of growth of a fatigue crack under cycHc loading. This is also controlled by the stress intensity factor through an equation of the following form (110) ... 

Modem cancer therapy has been primarily dependent upon surgery, radiotherapy, chemotherapy, and hormonal therapy (72) (see Chemotherapeutics,anticancer Hormones Radiopharmaceuticals). Chemotherapeutic agents maybe able to retard the rate of growth, but are unable to eradicate the entire population of neoplastic cells without significant destmction of normal host tissue. This serious side effect limits general use. More recentiy, the immunotherapeutic approach to cancer has involved modification and exploitation of the cellular and molecular mechanisms in host defense, regulation of tissue proliferation, tissue differentiation, and tissue survival. The results have been more than encouraging. 

Domestic production of methyl methacrylate from 1971 to 1992 has shown a 5.7% annualized rate of growth ... 

Economic Aspects. Capacity for sodium thiocyanate in the United States is substantially the same as that for ammonium thiocyanate because both products can be made in the same plants, but production is estimated at only slightly over 1000 t. The rate of growth is slight. The price on a 100 wt % basis in 1995 was 2.10/kg. Most sodium thiocyanate is sold as the solution. Potassium thiocyanate is a much lower volume product. 

Size of GNP and rate of growth Are plant sites readily available ... 

Size of market for your products rate of growth Degree of skill and disciphne at all levels... 

Size of population rate of growth Tranquillity of labor relations... 

Per capita income rate of growth Presence or absence of militant or Communist-dominated unions... 

Rate of Growth Crystal growth is a layer-by-layer process, and since growth can occur only at the face of the crystal, material must be transported to that face from the bulk of the solution. Diffusional... 

If L is a charac teristic dimension of a ciystal of selected material and shape, the rate of growth of a ciystal face that is perpendicular to L is, by definition,... 

Rate of growth (low deformahility) Increase rate of nuclei formation... 

Increase residence time Rate of growth (high deformahility) Decrease hinder viscosity... 

Either the and the two e s diffuse outward through the film to meet the 0 at the outer surface, or the oxygen diffuses inwards (with two electron holes) to meet the at the inner surface. The concentration gradient of oxygen is simply the concentration in the gas, c, divided by the film thickness, x and the rate of growth of the film dx/dt is obviously proportional to the flux of atoms diffusing through the film. So, from Pick s Law (eqn. (18.1)) ... 

Since the mid-1970s, the rate of growth of per capita gasoline consumption has slowed. An important factor in causing this moderation in demand was the trend to improve automobile fuel economy that was initiated by worldwide fuel shortages. Fuel economy hovered around 14.1 mpg between 1955 and 1975 it rose sharply over the next 15 years, reaching around 28.2 mpg in 1990. 

When a solid metal is attacked by oxygen gas, the product of the reaction is the metal oxide which, if it is not volatile, builds up as a surface layer on the metal. The oxide layer may be protective or non-protective. A non-protective layer does not inhibit the continued access of oxygen to the unchanged metal the rate of growth of such an oxide layer is independent of its thickness X and the law of growth is AX/At =. On integration this gives the linear law... 

If Q is the volume of the oxide per metal atom, the rate of growth, dA /d/, is equal to / Q. Thus from equation 1.179 we derive the parabolic law... 

If K = 1 K, a = 0.25 nm, and z = 3, X = 30nm at 300 K, so that for a film 1 nm thick, the field increases the rate of growth by a factor of about 10 The term in the growth law due to the field, namely exp (K/X), is large only when X is small. Because of this a thin oxide film can form even at low temperatures where the ordinary rate of entry of ions into the oxide, is negligible. As the film thickens, the factor exp /X) decreases rapidly, and the rate of growth soon falls to such a low value that, for practical purposes, oxidation has ended. 

In certain circumstances even the parabolic rate law may be observed under conditions in which the oxide is porous and permeated by the oxidising environment". In these cases it has been shown that it is diffusion of one or other of the reactants through the fluid phase which is rate controlling. More usually however the porous oxide is thought to grow on the surface of a lower oxide which is itself growing at a parabolic rate. The overall rate of growth is then said to be paralinear - and may be described by the sum of linear and parabolic relationships (see equations 1.197 and 1.198). 

It can be seen from equation 2.14 that the ratio of iron corroded to iron in the form of sulphide should be 4 1, but values from 0.9 to 48 are commonly obtained experimentally. Subsequently it was shown by Booth and his co-workers that the ratios of the corrosion products were dependent on the particular strain of Desulphovibrio and on their rates of growth. Later the activity of the enzyme hydrogenase which bring about the reaction ... 

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