Metals - Science topic

Dear all, following a list of interesting books. My Regards

- Fundamentals of Materials Science and Engineering: An Integrated Approach, William D. Callister, David G. Rethwisch, 5th Edt (2015).

- Materials Science and Engineering: An Introduction, 10e WileyPLUS NextGen Card with Loose-Leaf Print Companion Set, Callister Jr., William D., Rethwisch, David G. 10th Edt (2018).

- The Science and Engineering of Materials, Donald R. Askeland, Wendelin J. Wright. 7th Edt (2014).

- Materials Science and Engineering: A First Course, V. Raghavan, (2004).

- Foundations of Materials Science and Engineering, Willaim Smith, Javed Hashemi, 6th Edt (2019).

Many chemicals have several names: trivial and systematic (IUPAC nomenclature, red book), and in this case there can be two nomenclature names - anionic and oxide form. In this case, delafossite is a trivial name (from mineralogy, but it can be from technology, everyday life ...), copper (I) ferrite is an anionic form (there is another copper ferrite CuFe₂O₄ - copper (II) ferrite) and copper oxide (I)-iron(III)) - oxide form of the systematic name.

Harald G. Dill

... If names are not right, words do not fit. If words do not fit, affairs go wrong. ...A gentleman is nowise careless of his words. ... Confucius. Analects XII.3.

Visit kindly the following useful RG link:

Use Wigner-Seitz defect analysis

For predictive simulation of these processes, we use Autodesk Netabb (https://www.autodesk.de/products/netfabb/features), which works great but is cost-intensive. We also use the Simulia Abaqus "AM Modeler" Plugin (https://info.simuleon.com/blog/using-abaqus-to-simulate-additive-manufacturing-printing-an-optimized-hip-implant) which costs less and also delivers good results for this process. These simulations might potentially help you to reduce the thermal and stress-induced defects and deformations in your parts. Further, it might support you to improve your support structure placement (if required for your process).

When considering micro-defects and the quality of the material after manufacturing, you should specify the type of defects that should be "removed". Maybe a simulation would not be appropriate and you should consider an In-Line process monitoring and control for your process, combined with a proper "Design of Experiments". The data achieved by this procedure could be used to improve the simulations mentioned above by considering your materials and machines constraints.

Thank you so much for your post, Prof. Hadi Jabbar Alagealy

Very interesting to know that TB helps in the study & understanding of electron transfer in solid-state devices.

Best Regards.

This paper is related to this thread:

Hi Naveen Kumar

Just came across this question. Slightly unrelated but aligned to re-cycling in the foundry environment.

Please see my paper on recycling waste foundry sand:

The paper also looks at alternative methods of recycling waste foundry sand.

Hope this might be of some use to your overall topic.

Best Regards

Martin

Indeed Dear Ahmed MS Dawelbeit it is a very interesting and subtle question, refer to it as a localization phenomenon is one way since electrons can be seen as wave packets that can be or not well defined within the structure (metal, either metallic polimer).

In general, we have a kinetic criterium with three well-defined regions, the product "l . k_F", since we understand localization as the absence of diffusion of any kind of waves in a disordered medium.

Please check for the case of metallic polymers, the following reference:

Alan J. Heeger, 2003, The Critical Regime of the Metal-Insulator Transition in Conducting Polymers: Experimental Studies. Condensation and Coherence in Condensed Matter, pp. 30-35

it is very instructive

For simulating laser path in Ansys Workbench, download 'Moving Heat Source' extension from the Ansys store.

This video will be helpful:

Dear Ahmed Mousa,

Steel fibers are short discontinues strips of specially manufactured steel. Generally, their inclusion in the concrete improves the mechanical properties of concrete significantly. As the most common matrix, which is now mostly use in construction industry is Reinforced Cement Concrete. Main Reinforcement purpose is to resist bending due to applied load.

Ashish

As you know, hydrogen has good prospects of becoming fuel number one in this World but science & technology have to solve some problems before the switch to hydrogen economy. One problem is finding a "cheap" process for producing H₂ from H₂O " water". Another problem is how to store H₂ adequately since this gas escapes from the best of containers "in terms of materials & designs" and if there is leakage of pressurized H₂ into the air , then a disaster will occur similar to what happened to Space Shuttle Challenger in 1986.

A third problem is the inherent behavior of H₂ in having "annoying" explosive combustion "reaction with oxygen".

The second & third problems are related. If there is success in the interior design of light-weight containers or storage tanks so that H₂ cannot run away, then there will be avoidance of material loss plus a disastrous outflow of the gas.

To store H₂ in liquefied state, 2 items of equipment are needed (a compressor & a cooler) and these must give a temperature little below -252.87 °C and more than -259.14 °C for sufficient time. Liquefaction of H₂ is cost-intensive & is undesired in practical usage.

Some brainy researchers thought of using metal alloys to store gaseous H₂ (just like using a sponge to hold water) & these alloys, which sandwich the gas, are required to release it slowly. There is some progress in this research but I am not aware of a major "breakthrough".

Finally, some bright researches thought of storing H₂ inside hydrides such as lithium aluminum hydride LiAlH_₄) or sodium borohydride (NaBH₄)or others with finding out ways of slow release of H₂ gas that will proceed with smooth mild burning upon its use as a fuel.

Dear Anouar Jbeli,

I agree with you. The free election density differs in bulk and surface and also on the lattice structure of Fe.

The election density of α-iron and β- iron are different obviously.

Thanks

N Das

About predicting the pH of citric acid ― sodium citrate solutions and buffers for approx. pH < 4.0 ― cf. my post at:

About predicting the pH of citric acid ― sodium citrate solutions and buffers for approx. 4.0 < pH < 5.5 ― cf. my posts at: https://www.researchgate.net/post/Why-the-pH-of-Citrate-buffer-increases-when-diluted-with-water

About predicting the pH of citric acid ― sodium citrate solutions and buffers for approx. 5.5 < pH < 8.0 ― cf. my posts at: https://www.researchgate.net/post/Why-the-pH-of-Citrate-buffer-increases-when-diluted-with-water

About predicting the pH of citric acid ― sodium citrate solutions and buffers for approx. pH > 8.0 ― and for approx. pH > 9.0 ― cf. my posts at: https://www.researchgate.net/post/Why-the-pH-of-Citrate-buffer-increases-when-diluted-with-water

Hi!

Kinematic hardening is only a simplified model that is convenient for describing the Bauschinger effect. More realistic is the combined model that combines isotropic and kinematic hardening.

V.N.

The following publication deserves special attention in this thread:

Pierre Cresson , great paper, I downloaded it early today and then came looking for more info on the conversion subject, and found the author himself :D Thank you!

You might look at the work of Friedrich Hensel. The Clausius–Clapeyron equation is valid, in principle, but the enthalpy of evaporation changes when the vapour phase undergoes the nonmetal/metal transition.

Kiarash Mashoufi, thanks, your answer helped me anyway and I found the meaning of Mr zhilyaev comment by myself!

up

A complete guidance ..

Dear Nikolay A Vinogradov I'm not an expert in this field. However, I thought that the attached article could perhaps give you some useful information. It is entitled "Adsorption of oxygen on clean single crystal faces of aluminium" and was published in Surf. Sci. 1977, 62, 183-196. In this study it was found that thin islands of Al₂O₃-like oxide can form on the (100) face af the single-crystals.

The following link may be useful for you https://www.researchgate.net/publication/222015934_Optical_electrical_and_magnetic_properties_of_Co3O4_nanocrystallites_obtained_by_thermal_decomposition_of_sol-gel_derived_oxalates

I) About iron(III) tartrate; cf. e.g.:

II) About aluminium(III) tartarate; cf. e.g.:

III) About lanthanum(III) tartrate complexes; cf. e.g.:

IV) About indium(III) tartrate; cf. e.g.:

V) On cerium(III) and thulium(III) tartrate complexes; cf.:

I personally use the FPLMTO method, implemented in the Lmtart code (MINDLAB), and I obtained results in very good agreement with those of the experimental work

Refer Raimondo and Boyd chart for same, you can refer my publication

This system works on different frequencies like low-frequency LF (125 – 135 kHz), high-frequency HF (13.65 MHZ) and, Ultra-high frequency (868-928 MHz) according to the requirements and applications.

High-frequency tags work fairly well on objects made of metal and can work around goods with medium to high water content. Typically, HF RFID systems work in ranges of inches, but they can have a maximum read range of about three feet (1 meter).

I guess oxygen plasma would work. I am also looking for making tungsten hydrophilic. If it has not worked for you, i shall try along with oxygen plasma little bit of argon and let you know the result. I wish to coat Ba and Sr Carbonates on tungsten. I have prepared the solution by mixing the powders with water. Solution seems to be consistent. I am unable to coat this solution on tungsten wire. I heated the wire to more than 2000 degrees by passing current into that, then tried to coat the paste, did not work.

Did you try etching it by HF acid ? I am going to try this. If I get results I shall post it here.

Dear Ali:

Dr. Mandal is correct - this was the dilemma that faced the early engineers studying the first recognized fatigue failures in the mid 1800s - how could a component fail at stresses below the yield strength? The answer of course is local stress concentrations particularly at the surface, i.e., from microstructural defects, inclusions, pre-existing microcracks, notches - and often tensile residual stresses, all of which generate locally high stresses (exceeding the yield strength) to promote dislocation activity in the form of cyclic plasticity to initiate and grow fatigue cracks. Since stress is the most important factor promoting fatigue failures - the fatigue lifetime is invariably a function of the stress raised to a high power - lowering the far-field (applied) stresses has to be combined with considerations of design, e.g., by minimizing the presence of notches (the first commercial jet airlines, the De Havilland Comets in the 1950s, failed by fatigue cracks in the fuselage which initiated at the corners of the plane's square windows), reducing the presence of inclusions and other microstructural defects, smoothing the surface of the component to try and remove nicks, scratches, cracks, and ideally putting in beneficial compressive residual stresses - by such processes as shot-peening, laser-shocking, burnishing, cold rolling, etc. - and/or hardened surface layers - by the same types of procedures.

The notion of an ideal surface without imperfections is naturally purely hypothetical. However, if you can polish a surface together with imparting beneficial surface residual stresses, it is possible to suppress the initiation of fatigue cracks at the surface, which transitions the initiation process to occur from sub-surface cracks. As internal cracks have to be essentially twice as large to surface cracks to have the same effect (all other things being equal) and that the initial growth of such internal cracks will not be subjected to external environmental effects, i.e., they will initially grow in vacuo (these sub-surface initiated fatigue cracks are often referred to as "fisheyes"), the fatigue life of the component can be dramatically extended.

Just a final note, whereas metal fatigue is dominated by the role of dislocation plasticity, ceramics can also fatigue by an entirely different process which has nothing to do with dislocations. The effect is much smaller - more subtle may be a better description - but can occur in toughened ceramics and their composites by the cyclic loading induced degradation of their toughening mechanisms, specifically from crack-tip shielding by such mechanisms as crack bridging. If this is of interest, the attached article can provide further details.

ROR

Be careful with TCEP.

It does have a mild cysteine directed side-reaction proteolytic activity that may be a problem in some cases.

Ref:

https://doi.org/10.1016/j.jasms.2010.01.016

Title:

A Tris (2-Carboxyethyl) Phosphine (TCEP) Related Cleavage on Cysteine-Containing Proteins

Introduced in the late 1980s as a reducing reagent, Tris (2-carboxyethyl) phosphine (TCEP) has now become one of the most widely used protein reductants. To date, only a few studies on its side reactions have been published. We report the observation of a side reaction that cleaves protein backbones under mild conditions by fracturing the cysteine residues, thus generating heterogeneous peptides containing different moieties from the fractured cysteine. The peptide products were analyzed by high performance liquid chromatography and tandem mass spectrometry (LC/MS/MS). Peptides with a primary amine and a carboxylic acid as termini were observed, and others were found to contain amidated or formamidated carboxy termini, or formylated or glyoxylic amino termini. Formamidation of the carboxy terminus and the formation of glyoxylic amino terminus were unexpected reactions since both involve breaking of carbon–carbon bonds in cysteine.

----

Dear Alaa Eldin

Your answer looks pretty neat, I only would suggest adding a few words about the skin effect for AC currents. Skin depth decreases AC conductivity in metals.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/skineffect.html

Please go to this link:

Hello Dennis, Check out https://doi.org/10.1021/acs.est.9b07657

Hey!

I had a query along similar lines though I have been working with the Python meep wrapper for a while now, I keep facing a problem with metallic components say thin films of metal. The field intensity blows up near a metallic film and hence when you run a Meep code for something as simple as calculating the transmittance of the said film the code shows an error because of Inf field intensities.

Yes Dear Prof. Prasad Sarangapani

Electron-phonon interaction in normal metals leads to a sound attenuation effect in normal metals (by contrast to metals below the transition temperature which leads to a different calculation)

1. The classical work to study electron-phonon scattering in normal metals using physical kinetics (what you call transport) is:

Course Of Theoretical Physics Volume 10 Physical Kinetics

L. P. Pitaevskii & E.M. Lifshitz. Pergamon 1981. For normal metals see ch. IX- & 79. pp. 334.

2. The classical work about sound attenuation in normal metals is:

Theory of Ultrasonic Attenuation in Metals and Magneto-Acoustic Oscillations

Proc. R. Soc. Lond. A. B. Pippard, 1960.

(without & with magnetic field)

hot solution 4% HNO3 is available

Dear Thomas Anthony Troszak ,

if you use extensions of the same material and connect them under the same conditons, the additional thermovoltages rule out. But you must ever be sure, what you exactly do. Let me give an example used in practice:

Thermocouples are used in vacuum container to determine temperatures. Lets say, you want to bake out a recipient or you want to heat a sample holder to a certain temperature. You fix your thermocouple to the corresponding point the temperature T you want to control. It can be that the couple is not long enough. Furthermore, you have a feedthrough you must connect your wires with it. Then you have almost different metals. On the outside you must use a special plug which contains a contact of the identical material combination. The material combinations are standardized (example type K). The outer contact lies at room temperature. With a control unit which measures the T you control the heater. Of course, if you have more extensions, the contacts between different materials can be different (oxidation, lubrication). Therefore, it is important, if you want exact results, to control the measurement of T.

First test: The thermovoltage must be zero, if both contacts have the same T (room temperature). If there are any contact potentials then you see them.

Second test: You put your "hot contact" into a reference liquid (boiling point must be known). Then you must get the right temperature difference.

With Regards

R. Mitdank

Dear Franklin,

You will get these graphs in many literature. But it is not possible to get these graphs upto 1000 degree celsius for all materials.

Anyway, I think it is better to get these results by your own Experiments because standard data always doesn't match with your working material due to impurities and difference in microstructures.

If anything you want regaring the Experimental details for these I can tell you ( but upto 600 degree Celsius)

Love and Regards

N Das

Dear Loren,

Here is your answer for determination of physical or chemical sorption from Temkin isotherm.

From Temkin isotherm, you got the value of two constants i.e. Temkin isotherm equilibrium binding constant (L/g) (= A) and Constant related to heat of sorption (J/mol) (= B). After getting heat of sorption value, you have to convert it kcal/mol from J/mol. If heat of sorption value is less than 1.0 kcal/mol, then physical adsorption is occurs. And its value 20-50 kcal/mol, then chemical adsorption is occurs. If heat of sorption value is in-between (1 - 20 kcal/mol), than both physical and chemical adsorptions are involved in the adsorption.

I think this answer may be helpful to your research.

With Regards,

Dr. Himanshu Patel

Dear Yixian,

I have just developed a toolkit for elastic constant calculation using the stress-strain method combined with VASP.

http://www.matdesign.cn/elastool/

ElasTool is an automated toolkit for calculating the second-order elastic constants (SOECs) of any crystal systems belonging to two- and three-dimensional. It can utilize three kinds of strain-matrix sets, the high-efficiency strain-matrix sets (OHESS), the universal linear-independent coupling strains (ULICS) [2] and the all single-element strain-matrix sets (ASESS) to calculate the SOECs automatically. In an automatic manner, ElasTool can deal with both zero- and high-temperature elastic constants.

Best,

Zhongli

You're welcome. I just noted a typing error in my answer. 0.786 g AgNO3 is of course 4.63 mmole, not 6.63 mmole. It must be the same as the mmole amount of Ag.

Plastics can show two types of deformations, ductile or brittle. Thermoset plastic will show brittle failure because of the high crosslinking density of the log and stiff polymeric chain, hyperbranched structures and what not while the thermoplastics show elongation as in their strain is high under stress. The length and area of the thermoplastic are bound to change. While ceramics are exclusively brittle, hence, after a very to very low elastic response, the ceramics rupture without showing any form of deformation. As in the shape of ceramics do not change rather they undergo fracture soon after a small elastic region. The above analogy is for monolithic materials without any secondary dispersed phase. Composites, on the other hand, are multiphase materials and hence, their deformation is dependent largely on the reinforcement. A fiber-reinforced composite offers multi-step deformation, in this case, matrix fails first followed by fiber failure which is not a catastrophic failure rather than the fiber failure occurs in steps giving you a fine warning about the future failure. Composites always give you warning before they fail and hence, their deformation is largely categorized as brittle or ductile along with fiber pullout, and fiber bridging. If the fiber-matrix bonding is too strong expect a single step failure without any deformation or change in shape or size, while in case of weak fiber-matrix bonding, the fiber pullout a fiber bridging offer a bit of reformation and high toughness which is categorized as a ductile fracture. Matrix also plays an important role. Composite can't be generalized, you can design and modify the properties as per your needs. Hence, not all composite show same deformation or mechanical, thermal, physical response.

Liu Wei did we calculated normally? Or there is another aproach?

You have raised a very attractive querry.You may get clarification and understanding on some points raised in your querry by approaching prof b s murty, director iit hyderabad. He has a book on high entropy alloys and is an ex-student of eminent metallurgist&material scientist Prof.S Ranganathan of iisc bangalore.

Please check this RG discussion:

Dear Adhidesh,

Unfortunately, you can not predict those tie lines that you see in ternary phase diagrams, they are experimentally determined by different techniques depending on what kind of sample you have (NMR spectroscopy, low-angle x-ray scattering and etc...). Usually, when the two phases region is determined, the tie lines are determined as well. I think your question was: can i draw the tie limes (by geometry or any other mathematical means) if i know the limits of the two phases region? The answer is no, those lines are experimentally determined by analyzing the composition of the two phases.

For example, if you know the limits of the two phases, what you do is take many samples inside the two phases region and determine analytically the composition of each phase: if you have one phase with 25% of A, 50% of B and 25% of C and the other phase with 60% of A, 30% of B and 10% of C, you now have two points that can be connected to form one tie line.

Once you have sufficiently tie lines inside your two phases region, other tie lines can be predicted (conjugate lines).

Best,

Thiago.

Hi. How about 1,3-diketone ?

Such as -----> Tris(acetylacetonato) iron(III)

Erkan Yersel I also would like to know that!

Usually, what a customer is willing to pay for an alloy is determined by its properties, not its chemistry. That is, one may assume that customers buy the cheapest alloy that meets their needs. Of course, properties are determined by the specific combination of chemisty, processing, and microstructure. For example, most Al alloys are over 90% Al; and therefore, on a commodity basis they should all cost about the same. However, the processing and heat treatments required to get the properties required for aircraft alloys has a strong influence on their final price. However, let us suppose one only wants to look at the cost of the elemental constituents for some analysis. What level of purity should one use for each element in this calculation? That is, the cost of an element in "pure form" can vary greatly with the degree of purity. An element can be very inexpensive at a commercial purity of 99.8%, but orders of magnitude more expensive at 99.9998%. The 0.2% could be elements that ruin the properties of a high tech alloy, but are perfectly acceptable in a low tech alloy. These requirements will be a significant factor in determining the price of the commodities required to make an alloy.

Hi we routinely do EBSD of Aerospace Alloys and our final mechanical polish is with a soft silk cloth using 0.25micron. We then always ion beam mill usually at 8kV for 15min at 4degrees followed by 2kV at 5degrees for another 8min. Finally 400V at 5degrees for 5minutes. This consistently produces good results on the bulk Al and intermetallics.

Thank you for the references sir!

Hi Afza,

there are just two things you hve to be aware of the liquid should wet the sample and should not react with it. It should not evaporate quickly. The sample has to be completely immersed how deep the sample is in the liquid does not matter. You should control the temperature of the liquid (accuracy +/- 0.1 °C to have the correct density, for water you can find reliable density data.

We measure ceramics with an accuracy of 0.001 g/cm² if samples have a weight of ~ 10g. The bigger the sample the better the accuracy.

best regards

Frank

It is dependent to Fe and Ti phases. If these elements are in sulfide or oxide form, the most simple way to remove iron is using Iron and Sulfur oxidizing micro-organisms such as acidithiobacillus ferrooxidans and acidithiobacillus thiooxidans. These microorganisms produce sulfuric acid and dissolve the Fe by providing an oxidizing environment.

However, if Fe and Ti are in silicate phase using fungi (Such as aspergillus niger) can be better. These microorganisms decompose the silicate structures by producing organic acids which results to Fe dissolution.

as per standards u can take 2.5 mm radius of circle. However you have to take ratio of original dimension and final dimension of circle, you can go for 5 mm radius of circle as well. This will not affect ur results.

Metal cations like Na, K, Ca, Mg and Li (some 1000 to 10 mg/kg) can be found in dependance of geochemical composition. Their origin is from salts (e.g. Muschelkalk in the Molasse basin).

I second Dimitar's answer And add that you more than likely will need a femtosecond laser specifically. With longer pulse width, especially close to nanosecond, you might end up having melt zones near your machined edges. These melt edges may be in the form of microscopic bumps. I would try to avoid such artifacts for a nanostencil application.

Thanks Dear Prof. yes, my mistake, I confused the statistical operator \hat{\rho}={{e}^(\beta(\Omega -\hat(H}+ \mu \hat(N)) with the thermodynamical potential \Omega used in statistical physics, and as you stated is not an operator, but a real number, deduced from the Helmholtz free energy . \Omega does not have a hat, inside the statistical operator \hat{\rho}. The potential \Omega_o can be calculated as the trace of the operators (\hat(H}_o - \mu \hat(N)) for the case of quantum statistics. But still, I read from the previous answers, that the Fermi energy is a fundamental scale and the Debay frecuency play an important rol as the cut-off frequency? Thanks Dear Prof Baldomir and Dear Ilias Serifi as well.

You can read Callister reference "Materials Science and Engineering

An Introduction"

Dear find attached.

By processes implying low temperature (i.e. Pvd or electrodeposotion) you can obtain alloys not predicted by phase diagrams (that are constructed for equilibrium conditions). These alloys are not thermodynamically stable. So if you increase the temperature, they can decrease their excess of energy and you obtain a thin film exactly composed of the phases predicted by the phase diagram of the bulk material. It happens at ambiant temperature with thin film of gold deposited on copper. With ageing, the copper and gold diffuse and at the end your (cheap) watch becomes pink.

Dear Ali,

As you know, we say CDRX because there is not distinct steps of nucleation and growth. During CDRX, whole of the microstructural evolution is continuous. So, it can be occurred by transformation of LAGBs to HAGBs, fragmentation, GDRX, etc. You can consider the GDRX and fragmentation mechanism as some types of CDRX. The term "fragmentation" some times has been used instead of CDRX in literature.

Please note that in most cases it is very hard to distinguish the different restoration mechanisms. For example, it is well developed that CDRX does not inherit the deformation texture. However, I found in my research that the existence of deformation textures in the material can not always be the sign of CDRX.

I think the story of dynamic restoration mechanisms have not been completed, yet.

It is not possible to model all three classes together. The all have different chemical properties (adsorption, photolysis, concentration range) and you will have serious problems to get data for validation. In addition you will also have to take care of sediment/water/plant interactions. Check out your data set, lab facilities and then focus on a few substances.

Hi Ronak, there is an interesting article for you. It is accessible online: Atzori S, Salvi S (2014) SAR Data Analysis in Solid Earth Geophysics: From Science to Risk Management, DOI: 10.5772/57479

By reduction of Nitro group in aromatic compound to amine group by using

H₂/ Pd or Ni as a catalyst .

Regards

Hello Ali

read the artical in link

Hi Sergio, thanks for the question! By anomalously low, I mean the case when the Young's modulus value of a composite is about 2 or more times lower as compared with the modulus value of its component exhibiting the lowest modulus value.

You are welcome Julia Lucchese

As far as I know there is no analytical solution for this problem (but I might be wrong). In such cases I would use two different Maxwell-solver for example an FDTD-based like FDTD solutions and a second one like a finite-element-based like the one that is used in COMSOL. If both solutions converge for decreasing mesh sizes you can consider yourself to be fairly safe. On a second thought, how about carrying out the corresponding experiment?... ;-)

The connection between diffusivity and mobility M=D/kT is known as The Einstein- Nern

st equation in the absence of the chemical factor, which may be easily derived from the drift-diffusion equation in the presence of the additional driving force, which is a gradient of the applied external field at the steady state considerations,only!!!.

Kindly read this article

Xionghui Ji Saihua LiuHuang Juan John Jiang Ailan HeElena Bocharnikova Vladimir Matichenkov

How about Frontiers -they published Review with max. length 12'000 words and 15 Figures and/or tables .

Thanks a lot for your answer