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机械工程英语试题及答案一、单项选择题（每题2分，共20分）1. The term "mechanical engineering" refers to the field of study that involves the application of principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems.A. TrueB. False答案：A2. Which of the following is not a sub-discipline of mechanical engineering?A. RoboticsB. ThermodynamicsC. Civil EngineeringD. Materials Science答案：C3. The process of converting a design into a physical object is known as:A. PrototypingB. DesignC. AnalysisD. Manufacturing答案：D4. In mechanical engineering, what does the acronym "CAD" stand for?A. Computer Aided DesignB. Computer Aided DraftingC. Computer Aided DevelopmentD. Computer Aided Drawing答案：A5. What is the primary function of a bearing in a mechanical system?A. To reduce frictionB. To increase frictionC. To absorb shockD. To generate heat答案：A6. The study of heat transfer, thermal energy storage, and the effects of temperature on materials is known as:A. ThermodynamicsB. Fluid MechanicsC. Heat TransferD. Materials Science答案：C7. What is the SI unit for power?A. WattB. JouleC. NewtonD. Pascal答案：A8. A gear system that uses two or more gears to transmit motion and force is called:A. GearboxB. Pulley systemC. Cam mechanismD. Lever system答案：A9. In mechanical engineering, what does the term "stress" refer to?A. Force per unit areaB. Strain per unit forceC. Force per unit volumeD. Strain per unit volume答案：A10. Which of the following is a type of energy storage device used in mechanical systems?A. SpringB. BatteryC. CapacitorD. Inductor答案：A二、填空题（每题2分，共20分）1. The ________ of a material is its ability to resist deformation under applied force.答案：stiffness2. The ________ of a material is its ability to resist breaking under stress.答案：strength3. In a four-stroke internal combustion engine, the ________ stroke is where the fuel-air mixture is compressed.答案：compression4. A ________ is a mechanical device that converts rotational motion into linear motion.答案：screw5. The ________ of a system is the total energy required to produce the system.答案：embodied energy6. A ________ is a type of simple machine consisting of a wheel and a rope wrapped around it.答案：pulley7. The ________ of a system is the energy required to operate the system over its lifetime.答案：operational energy8. A ________ is a type of energy storage device that uses the elastic properties of materials to store energy.答案：spring9. The ________ of a material is its ability to resist deformation under stress.答案：ductility10. A ________ is a type of energy storage device that uses the potential energy of a raised mass to store energy.答案：gravity storage system三、简答题（每题10分，共40分）1. Explain the difference between static and dynamic equilibrium in mechanical systems.答案：Static equilibrium refers to a state where all forces and moments acting on a system are balanced, resulting in no acceleration. Dynamic equilibrium occurs when the net force and net moment on a system are zero, allowing the system to move with constant velocity.2. Describe the function of a flywheel in a mechanical system. 答案：A flywheel is a rotating mechanical device that stores rotational kinetic energy. It smooths out fluctuations in the power delivery of an engine or motor, providing a moreconstant output.3. What is the purpose of a heat exchanger in a mechanical system?答案：A heat exchanger is a device used to transfer heat between two or more fluids without mixing them. Its purposeis to either cool a hot fluid or heat a cold fluid, improving the efficiency of the system.4. Explain the concept of a control system in mechanical engineering.答案：A control system in mechanical engineering is a system that regulates the behavior of other systems or processes. It uses feedback to compare the actual output with the desired output and makes adjustments to minimize the difference, ensuring the system operates as intended.。
不同频率飞秒激光脉冲序列加工炸药过程安全性的数值计算伍俊英，刘嘉锡，杨利军，李姚江，吴姣姣，陈朗（北京理工大学爆炸科学与技术国家重点实验室，北京100081）摘要：为了研究飞秒激光加工炸药技术的安全性，建立了飞秒激光脉冲序列加工炸药的计算模型，考虑了炸药在受热条件下的自热反应。
采用数值计算的方法对飞秒激光脉冲序列烧蚀炸药（TNT ，TATB 和HMX ）的过程进行了计算，分析了飞秒激光脉冲序列加工炸药过程的安全性。
计算结果表明，飞秒激光脉冲序列频率、炸药自热反应放热量和热扩散系数会显著影响加工过程的安全性。
在这三种炸药中，HMX 自热反应的放热量最大，热扩散系数最小，因此热累积效应最明显，在三种不同频率（1×103Hz ，1×105Hz 和2×105Hz ）的飞秒激光脉冲序列作用下均发生了点火；相反，TATB 的热累积效应最弱，在三种不同频率的飞秒激光脉冲序列作用下均未发生点火；TNT 的热累积效应介于HMX 和TATB 之间，因此只在频率较高的飞秒激光脉冲序列作用下才发生点火。
在实际加工过程中，特别是对自热反应放热量较大和热扩散系数较小的炸药，为保证加工过程的安全性，应尽量选用频率较低的飞秒激光脉冲序列对其进行加工。
关键词：飞秒激光；脉冲序列；激光加工；炸药；数值计算中图分类号：TJ55文献标志码：ADOI ：10.11943/CJEM20201831引言具有高精度结构的炸药部件对提升武器的毁伤性能十分重要。
由于炸药自身具有一定的危险性，所以对炸药进行高安全、高精度的切削加工一直是一个技术难题。
飞秒激光加工炸药技术是利用高功率的飞秒激光，把其聚焦区内的炸药瞬间变成高温高压等离子体来实现对炸药的烧蚀去除。
在飞秒激光加工物质的过程中，加工物质形成等离子体的时间尺度远小于飞秒激光能量传递到被加工区域周围的时间尺度，因此被加工区域周围的物质不易受到热传导的作用，这使得飞秒激光与物质作用的过程不同于长脉冲激光（皮秒、纳秒和毫秒激光），从而从根本上消除了长脉冲激光加工过程中存在的热影响和热损伤现象，实现了对材料的“冷加工”［1-3］。
热力学专业英语作文Title: Thermodynamics in EnglishThermodynamics is the branch of physics that deals with the relationships between heat, work, energy, and temperature.It is one of the fundamental sciences that help us understand and predict the behavior of systems.In this essay, we will explore some key concepts and terms related to thermodynamics in English.Firstly, let"s talk about the laws of thermodynamics.There are four laws of thermodynamics, but the first and second laws are the most fundamental.The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another.The second law of thermodynamics states that in a closed system, the total entropy always tends to increase over time, meaning that processes tend to become more disordered.ext, let"s discuss some common units of measurement in thermodynamics.The joule (J) is the unit of energy in the International System of Units (SI), while the calorie (cal) is a non-SI unit of energy commonly used in nutrition.The watt (W) is the unit of power, which is the rate at which work is done or energy is transferred.The kilowatt-hour (kWh) is a common unit of energy consumption, often used in the context of electricity usage.Thermodynamic properties are characteristics of a system that can be used to describe its state and predict its behavior.Some common thermodynamic properties include temperature, pressure, volume, and internal energy.Temperature is a measure of the average kinetic energy of the particles in a system, while pressure is a measure of the force exerted by the particles on the walls of the container.Volume is the amount of space occupied by the system, and internal energy is the total energy of the system, including both kinetic and potential energy.ow, let"s talk about some thermodynamic processes.An isothermal process is a process in which the temperature of the system remains constant.A reversible process is one that can be undone by a small change in the system"s state, while an irreversible process is not reversible and may involve a large change in the system"s state.An adiabatic process is one in which there is no heat transfer between the system and its surroundings, while a diabatic process involves heat transfer.In conclusion, thermodynamics is a fundamental science that helps us understand the behavior of systems.By studying the laws of thermodynamics, units of measurement, thermodynamic properties, and processes, we can gain a deeper understanding of how energy and heat are transformed and transferred.With this knowledge, we can apply thermodynamics to various fields, such as engineering, physics, andchemistry, to solve real-world problems and improve our lives.。
二硼化钛陶瓷在不同温度下的氧化行为黄飞，傅正义，王为民，王皓，王玉成，张金咏，张清杰(武汉理工大学，复合材料新技术国家重点实验室，武汉 430070)摘要：采用静态氧化法对不同温度下TiB2陶瓷的氧化行为进行研究，利用X射线衍射仪、扫描电镜、X射线光电子能谱仪对氧化前后的样品进行表征。
结果表明：低温下TiB2陶瓷氧化动力学满足抛物线规律，并在表面形成液相B2O3，阻止氧化反应的进一步进行，冷却后B2O3以玻璃态覆盖在表面。
高温下TiB2氧化反应在4h前满足抛物线规律，表面形成一层TiO2多孔结构；氧化4h后，随着氧扩散距离的延长，扩散阻力加大，从而使氧化速率降低，氧化反应不再满足抛物线规律。
关键词：二硼化钛；氧化动力学；微观结构中图分类号：TF123；TB332 文献标识码：A 文章编号：0454–5648(2008)05–0584–04OXIDATION BEHA VIOR OF TITANIUM DIBORIDE CERAMIC AT DIFFERENT TEMPERATURES HUANG Fei，FU Zhengyi，W ANG W eimin，W ANG Hao，W ANG Yucheng，ZHANG Jinyong，ZHANG Qinjie(State key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University ofTechnology, Wuhan 430070, China)Abstract: The oxidation behavior of TiB2 ceramics at different temperatures was investigated using the static oxidation kinetic method. The samples before and after oxidation have been characterized by X-ray diffractometer, scanning electron microscope and X-ray photoelectron spectrometer. The results show that the oxidation kinetics appear the parabolic law at low temperature. A liquid B2O3 coating on the surface of TiB2 ceramic could prevent from further oxidation. After the ceramic samples were cooled, their sur-faces were covered with glassy B2O3. At high temperature, the oxidation reaction of TiB2 ceramics showed the parabolic law only before 4h. Porous rutile TiO2 formed on the surface. But the oxidation behavior with the parabolic law for the TiB2 ceramics was not observed after oxidation for 4h because of the long path of diffusion, strong diffusion resistance and low reaction rate.Key words: titanium diboride; oxidation kinetics; microstructureTitanium diboride with P6/mmm structure is a uniquely stable compound of the boron element and tita-nium element.[1] TiB2 based materials have received wide attention because of their high hardness and elastic modulus, good abrasion resistance and superior thermal and electrical conductivity.[2–3] Potential applications in-clude high temperature structural materials, cutting tools, armor, electrodes in metal smelting and wear parts. De-spite its useful properties, the application of monolithic TiB2 is limited by poor sinterability, exaggerated grain growth at high temperature and poor oxidation resistance above 800.℃[4–5]The starting temperature to oxidize TiB2 ceramics is about 400℃ and oxidation kinetics is controlled by outward diffusion of interstitial titanium ions and inner diffusion of oxygen ions.[5–6] But there are conflicting viewpoints about the detailed oxidation process, for ex-ample, about the oxidation products and oxidation mechanism. Koh et al.[7] investigated the oxidation be-havior of dense TiB2 specimens with 2.5% in mass (the same below) Si3N4 and found that TiB2 exhibited two distinct oxidation behaviors depending on the tempera-ture. At temperatures below 1000℃, the oxidation layer comprised two layers: an inner layer of crystalline TiO2 and an outer layer mainly composed of B2O3. When the oxidation temperatures were higher than 1000℃, the收稿日期：2007–09–23。
异丙苯过氧化物的热解反应及联枯的生成汪 超，丁 琳，金国杰（中国石化 上海石油化工研究院，上海 201208）［摘要］在密闭隔氧环境下研究了异丙苯、过氧化氢异丙苯（CHP ）和过氧化二异丙苯（DCP ）体系的热分解行为，分析了体系热解产物，探讨了热解反应的机理及相关动力学，并考察了苯酚对DCP 热解反应的影响规律。
实验结果表明，异丙苯过氧化物的热解反应主要沿自由基路径进行，过氧化物受热产生异丙苯氧自由基，再进一步通过β碎裂、链转移和自由基结合等反应得到α，α-二甲基苄醇、苯乙酮及2，3-二甲基-2，3-二苯基丁烷（联枯）等产物；DCP 分解速率符合一级反应动力学特征，活化能为127 kJ/mol ；体系中苯酚的存在不会影响DCP 分解的速率，但会显著改变热解产物的组成，特别是抑制联枯的生成。
［关键词］过氧化氢异丙苯；过氧化二异丙苯；热解；自由基；联枯［文章编号］1000-8144（2020）01-0020-07 ［中图分类号］TQ 243.1 ［文献标志码］AThermal decomposition of cumene peroxides and formation of bicummylWang Chao ，Ding Lin ，Jin Guojie（Sinopec Shanghai Research Institute of Petrochemical Technology ，Shanghai 201208，China ）［Abstract ］The thermal decomposition in the system of cumene-cumene hydroperoxide(CHP)- dicumyl peroxide(DCP) was investigated in the closed and anoxic atmosphere. The formed products were analyzed ，the mechanism and the kinetics of the thermal decomposition were discussed ，and the effects on the thermal decomposition of DCP were investigated. The experimental results indicated that the thermal decomposition of CHP and DCP mainly proceeds in the free radical path. Theperoxides were heated and formed the cumyl-oxy radical ，then the products including α，α-dimethyl phenylcarbinol ，acetophenone and 2，3-dimethyl-2，3-diphenylbutane(bicummyl) were obtained through the reactions of β-scission ，chains transfer and recombination of radicals. The decomposition rate of DCP can be described as first-order kinetic with the active energy of 127 kJ/mol. The existence of phenol will not affect the decomposition of DCP ，but change the composition of products remarkably ，especially inhibit the formation of bicummyl.［Keywords ］cumene hydroperoxide ；dicumyl peroxide ；thermal decomposition ；free radicals ；bicummylDOI ：10.3969/j.issn.1000-8144.2020.01.004［收稿日期］2019-07-16；［修改稿日期］2019-10-29。
第24卷第7期高分子材料科学与工程Vo l.24,No.72008年7月POLYMER MATERIALS SCIENCE AND ENGINEERINGJul.2008阻燃SEBS 共混材料的热分解动力学徐建波1,2,周 涛1,郑红娟1,张爱民1(1.四川大学高分子研究所,高分子材料工程国家重点实验室,四川成都610065;2.巴陵石化有限公司技术中心,湖南岳阳414014)摘要:采用T G 分析测试阻燃SEBS 共混材料的热分解过程,并用Friedman 微分法和非线性回归进行动力学分析,探讨其热分解机理。
分析结果表明,膨胀型与金属氢氧化物阻燃的SEBS 共混材料的热分解过程为多步平行反应,极限氧指数随分解活化能的提高而提高。
极限氧指数L OI 测试表明,两体系能有效阻燃SEBS 共混材料。
关键词:热塑性弹性体SEBS;热分解;阻燃中图分类号:O631.3+1 文献标识码:A 文章编号:1000 7555(2008)07 0113 04收稿日期:2007 09 25基金项目:国家863资助项目(2003AA333020)联系人:张爱民,主要从事高分子材料高性能化研究,Email:amzhang215@vip.si SEBS 是由氢化苯乙烯、丁二烯嵌段聚合物(SBS)制得的一种热塑性弹性体,它不仅保持了热塑性弹性体的易加工性与力学性能,而且其耐候、耐热性能得到提高。
已广泛用于软接触材料、医用材料、密封材料、汽车制件、胶粘剂、塑料改性及电线电缆等领域[1]。
但SEBS 及其共混材料仍存在受热易分解、制品易燃等缺陷,因此研究其热分解过程、制备高性能阻燃制品已成为其应用领域的重要课题。
近年来虽有许多关于聚合物热分解与阻燃的研究[2,3],但却少有关于阻燃SEBS 及其共混材料热分解动力学的报道。
本文采用TG 和极限氧指数L OI 测试膨胀型和金属氢氧化物阻燃SEBS 共混材料的热分解过程,并通过非等温线性回归推导,进行其热分解动力学与阻燃效果的研究。
我的发现之热胀冷缩原理英语作文Thermal Expansion and Contraction: A Fundamental Principle of Physics.Thermal expansion and contraction are fundamental physical phenomena that describe the change in size and shape of materials due to variations in temperature. This phenomenon is observed in solids, liquids, and gases and plays a crucial role in various scientific and engineering applications.Microscopic Origin of Thermal Expansion.At the microscopic level, thermal expansion and contraction can be attributed to the vibrations of atoms or molecules within a material. As the temperature of a material increases, the average kinetic energy of its individual particles increases. This leads to an increase in the amplitude of their vibrations, causing the particles to occupy a larger average volume. Consequently, thematerial expands. Conversely, when the temperature decreases, the average kinetic energy of the particles decreases, and the particles move closer together,resulting in contraction.Linear, Area, and Volume Expansion.Thermal expansion can occur in one dimension (linear expansion), two dimensions (area expansion), or three dimensions (volume expansion). Linear expansion refers to the change in length of an object along a specific direction. Area expansion pertains to the change in the surface area of an object, while volume expansion describes the change in the total volume of an object. The extent of expansion or contraction depends on the material's coefficient of thermal expansion, which quantifies the amount of expansion or contraction per unit temperature change.Types of Thermal Expansion.There are two main types of thermal expansion:isotropic and anisotropic. Isotropic expansion occurs whena material expands or contracts uniformly in all directions. This behavior is observed in amorphous solids and liquids. Anisotropic expansion, on the other hand, occurs when a material expands or contracts differently in different directions. This phenomenon is common in crystals, wherethe arrangement of atoms or molecules can lead to varying degrees of expansion along different axes.Applications of Thermal Expansion.Thermal expansion has numerous practical applicationsin various fields. In engineering, it is crucial for designing structures that can withstand temperature variations without catastrophic failure. For example, bridges, buildings, and pipelines are designed to accommodate thermal expansion and contraction to prevent cracking or buckling.In metrology, thermal expansion must be taken into account when measuring the dimensions of objects with high precision. Precision instruments like calipers andmicrometers are often calibrated at specific temperatures to ensure accurate measurements regardless of temperature fluctuations.Additionally, thermal expansion is utilized in various temperature-sensing devices, such as thermostats and bimetallic strips. In a thermostat, a bimetallic strip composed of two metals with different coefficients of thermal expansion is used to detect temperature changes. As the temperature varies, the strip bends due to the differential expansion of the two metals, actuating a switch to control heating or cooling systems.Conclusion.Thermal expansion and contraction are fundamental physical principles that describe the change in size and shape of materials due to temperature variations. Understanding this phenomenon is essential for a wide range of scientific and engineering applications, from the design of structures to the development of temperature-sensing devices. By harnessing the effects of thermal expansion,engineers can create innovative solutions that improve our lives and enhance technological advancements.。
Evaluation of reliability of Coats-Redfern method forkinetic analysis of non-isothermal TGAR. Ebrahimi-Kahrizsangi1, 2, M. H. Abbasi21. Department of Engineering, Islamic Azad University, Najafabad branch, Isfahan, Iran;2. Department of Materials Engineering, Isfahan University of Technology, Isfahan, IranReceived 18 April 2007; accepted 31 July 2007Abstract: A critical examination was made on the reliability of kinetic parameters of nonisothermal thermoanalytical rate measurement by the widely applied Coats-Redfern(CR) equation. For this purpose, simulated TGA curves were made for reactions with different kinetic models, including chemical, diffusion (Janders) and mixed mechanism at different heating rates. The results show that, for reactions controlled kinetically by one mechanism, all solid state reaction models show linear trends by use of CR method and this method can not distinct the correct reaction model. For reactions with mixed mechanism, the CR method shows nonlinear trends and the reaction models and kinetic parameters can not be extracted from CR curves. The overall conclusion from this comparative appraisal of the characteristics of the CR approach to kinetic analysis of TGA data is that the CR approach is generally unsuitable for determination of kinetic parameters.Key words: kinetic analysis; Coats-Redfern equation; nonisothermal TGA; rate equation; Arrhenius parameters1 IntroductionKinetic analysis of thermal decomposition processes has been the subject interest for many investigators all along the modern history of thermal decomposition. The interest is fully justified. On one side, kinetic data are essential for designing any kind of device, in which the thermal decomposition takes place; on the other side, kinetics is intrinsically related with the decomposition mechanisms. The knowledge of the mechanism allows the postulation of kinetic equations or vice versa, and kinetics is the starting point to postulate mechanisms for the thermal decomposition[1].Although kinetic studies can be performed in different devices, thermogravimetry(TG) is, by large, the mostly used technique. This technique consists of preheating the sample to a given temperature (T0) and then starting the experiment with a fixed nominal heating rate (β). So, theoretically it is possible to writeT=T0+β·t(1) So in a TG experiment, a modern equipment typically registers hundreds or thousands of experimental points that can be used for kinetic analysis of the reaction. It is clear that the selection of correct model is a critical point in kinetic analysis. Knowing how a model can justify experimental data has been evaluated by many researchers[1−3]. There are different methods to study the kinetics of non-isothermal processes. These include statistical methods[4−8], predictions of activated complex theory for the value of the pre-exponential factor[9], methods based on the fact that, for different reaction models, the extent of reaction at maximum reaction rate a max falls into a narrow specific range[10], Coats-Redfern (CR) method[11] and iso-conversional model free methods[12].2 Rate equationsUsually the change in extent of reaction (α) is used to study the solid state reactions kinetics:∞−−=mmmm tα(1)where m0, m t and m∞ are initial sample mass, sample mass at time t and sample mass at the end of reaction, respectively.Using extent of reaction, the rate of a solid state reaction can be generally described byCorresponding author: Reza Ebrahimi-Kahrizangi; E-mail: rezaebrahimi@iaun.ac.irReza Ebrahimi-Kahrizangi, et al/Trans. Nonferrous Met. Soc. China 18(2008)218)()(d d ααf T k t= (3)Integration of the above equation gives the integral rate law:g (α)=kt (4)Several reaction models[13] using f (α) or g (α) are listed in Table 1.The explicit temperature dependence of the rate constant is introduced by replacing k (T ) with the Arrhenius equation which gives)(exp(d d a ααf RT E A t −= (5) Andt RTEA g )exp()(a −=α (6)where A (the pre-exponential factor) and E a (activation energy) are the Arrhenius parameters. These parameters together with the reaction model are sometimes called the kinetics triplet. Under non-isothermal conditions, in which a sample is heated at a constant rate, the explicit temporal in Eqn.(5) is eliminated through the trivial transformation:)()exp(d d a αβαf RT E AT −= (7)Upon integration, Eqn.(7) givesT TE Ag d )exp()(Ta∫=βα (8)If E a /(RT ) is replaced by x and integration limitstransformed, Eqn.(8) becomesx x x RT AE g x d )exp()( 2a ∫∞−=α (9)Eqn.(9) can be written as)()(ax p RTAE g =α (10)p (x ) has no analytical solution but has many approximations[14−16], with one of the most popular being the Coats-Redfern method[11]. This method utilizes the asymptotic series expansion for approximating the exponential integral in Eqn.(10), givingRT E E TR E AR Tg a a a 221(ln[)(ln −−=βα (11)Plotting the left hand side of Eqn.(11), which includes g (α) versus 1/T , gives E a and A from the slope and intercept respectively. The model that gives the best linear fit is selected as the chosen model.Despite the inability of this approach in kinetic analysis of non-isothermal process, many papers have been published based on this method in recent years [17−25] and conclusions based on this method continue to be published. In this study the reliability and accuracyTable 1 Solid state rate equationsReaction Modelf (α)g (α) Nucleation Models1 Power Law 4α3/4 α1/42 Power Law 3α2/3 α1/3 3 Power Law 2α1/2 α1/24 Avrami-Erofeev 4(1−α)[−ln(1−α)]3/4 [−ln(1−α)]1/45 Avrami-Erofeev 3(1−α)[−ln(1−α)]2/3 [−ln(1−α)]1/36 Avrami-Erofeev 2(1−α)[−ln(1−α)]1/2[−ln(1−α)]1/2Diffusion Models 7 One dimensional Diffusion (1/2)α−1 α28 Diffusion control (Janders) 2(1−α)2/3[1− (1−α)1/3] −1 [1−(1−α) 1/3]29Diffusion control (Crank)(3/2)[(1−α)−1/3−1]−11−(2/3)α–(1−α)2/3Reaction order and geometrical contraction models 10Mampel (first order)1−α −ln(1−α) 11 Second Order (1−α)2 (1−α)−1−112 Contracting cylinder 2(1−α)1/2 1−(1−α)1/2 13 Contracting Sphere3(1−α)2/31−(1−α)1/3Reza Ebrahimi-Kahrizangi, et al/Trans. Nonferrous Met. Soc. China 18(2008) 219of CR method to determine the kinetic model and kinetic parameters from non-isothermal data is evaluated using known simulated data.3 SimulationTo study the reliability of CR method, three TGA curves were simulated. One curve was simulated using the contracting sphere (model 13), the second curve with three dimensional diffusion model (model 8, Janders Eqn.) and third curve with mixed control mechanism (models 8 and 13). In the mixed regime for the reaction extent less than 0.25, the reaction is chemical reaction controlled; at the reaction extent greater than 0.8, the reaction is controlled by three dimensional diffusion and at the reaction extent 0.25−0.8, both chemical reaction and diffusion are involved. Table 2 lists the kinetic parameters used for TGA curves simulation. These values of A and E a are selected based on the experimental data reported in Refs.[23−25]. TGA curves were simulated at linear heating rates of 5, 7.5, 10 and 12.5 K/min. For all the curves, the initial temperature (T0) was considered to be 300 K. In the CR method a single TGA curve was used to determine kinetic parameters, so the data reported were extracted from TGA curves with heating rate of 10 K/min. Then by using the CR method, kinetic parameters were determined from simulated TGA curves and compared with original data.Table 2 Values of A and E a used for TGA curves simulationModel E a/(4.2 kJ·mol−1) A/min−1 Three-dimensional diffusion(Model 8) 68.33 1×1029 Contracting volume(Model 13) 64.46 1×1015 Mixed-controlled mechanism(Model 8) 60 1×1026 Mixed-controlled mechanism(Model 13) 40 1×10164 Results and discussionSimulated TGA curves for reactions with contracting sphere mechanism, three dimensional diffusion mechanism and mixed mechanism are shown in Figs.1−3 respectively. Also the initial temperature for all curves was considered to be same, but the reaction starts at different temperatures in simulated TGA curves. The range of reaction temperature for simulated TGA curves is in agreement with that of experimental works[23−25].Fig.4 shows the plot of ln[g(α)/T2] versus 1/T for different models using values of a extracted from Fig.1. According to CR equation, if a correct model is selected for the reaction, the plot of ln[g(α)/T2] versus 1/Twill be Fig.1 Simulated TGA curves for reaction with contracting sphere mechanism at different heating ratesFig.2 Simulated TGA curves for reaction with three- dimensional diffusion mechanism at different heating ratesFig.3 Simulated TGA curves for reaction with mixed-controlled mechanism at heating rate of 10 K/minlinear with high-correlation coefficient. Fig.4 reveals that all models show linear trend with correlation coefficient greater than 0.99. Table 3 lists the calculated kinetic parameters for different models with a from TGA simulated curves with contracting sphere mechanism by the CR method.Reza Ebrahimi-Kahrizangi, et al/Trans. Nonferrous Met. Soc. China 18(2008) 220Fig.4 Plots of ln[g(α)/T2] versus 1/T for different models using values of α from Fig.1Table 3 Kinetic parameters extracted from Fig.4 using CR methodModel E a/(4.2 kJ·mol−1) A/min−1|r|13 85.391.16×1021 0.99812 82.222.36×1020 0.99710 92.603.31×1023 0.9998 174.103.11×1043 0.9986 44.658.91×1010 0.999If model 13 in Table 3 is considered as reaction model, the activation energy calculated with CR method is 25% greater than real value and similarly pre-exponential factor (1.16×1021) is quite far from the assumed value (1×1015). These results show that the CR method reliability is not enough and cannot be used to kinetics assessment of reactions. The results of Fig.4 and Table 3 show that several chemical mechanisms (models 10, 12 and 13) are sufficiently similar in shape and calculated values of E a and A are very close to each other. This indicates that calculated values of E a are not directly proportional to reaction order because of the contribution from the term 2ln T in CR equation, which becomes relatively greater for the larger values of the reaction order[26].Fig.5 shows the plot of ln[g(α)/T2] versus 1/T for different models using values of α extracted from Fig.2.Fig.5 shows all models have linear trend with correlation coefficient greater than 0.99. Table 4 lists the calculated kinetic parameters for different models with αvalues from TGA simulated curve with three- dimensional diffusion mechanism by the CR method.In this case if model 8 in Table 3 is considered as reaction model, the activation energy calculated with CR method is 1.4% greater than the real value and similarly pre-exponential factor (7.74×1030) is close to theFig.5 Plots of ln[g(α)/T2] versus 1/T for different models using values ofα extracted from Fig.2Table 4 Kinetic parameters extracted from Fig.5 using CR methodModel E a/(4.2 kJ·mol−1) A/min−1|r|13 33.766.81×1014 112 33.014.12×1014 0.99910 35.461.57×1016 0.9988 69.317.74×1030 16 16.842.21×107 0.998assumed value (1×1029). Also the calculated values of A and E a for three-dimensional diffusion mechanism are very close to the real values. However, in the first stage the correct model must be selected, which is impossible with CR method.Comparison of Tables 3 and 4 shows that the magnitude of E a calculated using diffusion model is nearly twice the values for chemical models (10, 12 and 13) and is ascribed to the dominant influence of characteristic diffusion exponent, n=0.5.Fig.6 shows the plots of ln[g(α)/T2] versus 1/T forFig.6 Plots of ln[g(α)/T2] versus 1/T for different models using values of α extracted from Fig.3Reza Ebrahimi-Kahrizangi, et al/Trans. Nonferrous Met. Soc. China 18(2008) 221different models using the values of αextracted from Fig.3.It is clear from Fig.6 that for extents of reaction less than 0.3 that reaction is a single mechanism, the plot of ln[g(α)/T2] versus 1/T is linear. However, for extents of reaction greater than 0.3 that reaction has multi model mechanisms, the plot of ln[g(α)/T2] versus 1/T shows nonlinear trend. This means that the CR method can not be used to determine the reaction model. Therefore the kinetics of complex reactions, where the reaction model changes with the extent of reaction, cannot be analyzed with CR method. In most of solid state reactions (especially solid-gas reactions), a layer of products forms on the surface of un-reacted core. This layer may be porous or dense and this causes a change in the reaction mechanism by the increase in extent of reaction. Thus the CR method is ineffectual method in kinetic analysis of solid state reactions.5 ConclusionsThe CR method for the kinetic analysis of nonisothermal TGA data is shown to be unsuitable and inconsistencies exist in published kinetic results obtained using this approach. The results of this investigation show that for the reactions with simple mechanisms, the plot of ln[g(α)/T2] versus 1/T will be linear for all reaction kinetic models and the reaction mechanism can not be recognized with CR method. However, for reactions having complex mechanisms, the plot of ln[g(α)/T2] versus 1/T will not be linear and the CR method is not valid for kinetic analysis to find the reaction model and kinetic parameters.References[1]CONESA J A, MARCILLA A, CABALLERO J A, FONT R.Comments on the validity and utility of the different methods forkinetic analysis of thermogravimetric data [J]. J Anal Appl Pyrol,2001, 58/59: 617−633.[2]VYAZOVKIN S V, LESNIKOVICH A I. Error in determiningactivation energy caused by the wrong choice of process model [J].Thermochim Acta, 1990, 165: 11−15.[3]KOGA N, SESTAK J, MALEK J. Distortion of the Arrheniusparameters by the inappropriate kinetic model function [J].Thermochim Acta, 1991, 188: 333−336.[4]SUN T, ZHAO Y, JIN J, WANG D. J Therm Anal, 1995, 45:1105−1109.[5]HU Q P, CUI X G, YANG Z H. Studies on the non-isothermalkinetics of thermal decomposition of the mixed ligand complex [J]. JTherm Anal, 1997, 48: 1379−1384.[6]CARP O, SEGAL E. 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Study on kinetics of thermal decomposition of low LOI goethetic hematite iron oreBeuria P.C.a,⇑,Biswal S.K.a ,Mishra B.K.a ,Roy G.G.ba Mineral Processing Department,CSIR –Institute of Minerals and Materials Technology,Bhubaneswar 751013,India bIndian Institute of Technology,Kharagpur 721302,Indiaa r t i c l e i n f o Article history:Received 29October 2016Received in revised form 26December 2016Accepted 26January 2017Available online 18July 2017Keywords:Loss on ignition Goethite Kaolinite Gibbsite Roasting Pellet feedKinetic analysisa b s t r a c tIn the present study,the kinetics of thermal decomposition of hydrated minerals associated in natural hematite iron ores has been investigated in a fixed bed system using isothermal methods of kinetic anal-ysis.Hydrated minerals in these hematite iron ores are kaolinite,gibbsite and goethite,which contribute to the loss on ignition (LOI)during thermal decomposition.Experiments in fixed bed have been carried out at variable bed depth (16,32,48and 64mm),temperature (400–1200°C)and residence time (30,45,60and 75min)for iron ore samples.It is observed that beyond a certain critical bed depth (16mm),100%removal of LOI is not found possible even at higher temperature and higher residence time.Most of the solid-state reactions of isothermal kinetic analysis have been used to analyze the reac-tion mechanism.The raw data are modified to yield fraction reacted ‘‘a ”versus time and used for devel-oping various forms of ‘‘a ”functions.f (a )is the inverse of first derivative of g (a )with respect to a .The study demonstrates that decomposition of hydrated mineral in hematite follows the chemical kinetics.The estimated activation energy values in all the experimental situations are found to high,of the order of 60kJ/mol,reinstating that the reactions are indeed controlled by moving phase boundary and random nucleation.Ó2017Published by Elsevier B.V.on behalf of China University of Mining &Technology.This is an openaccess article under the CC BY-NC-ND license (/licenses/by-nc-nd/4.0/).1.IntroductionIndian iron ore resources are mostly hematite.High grade hematite iron ore is depleting very fast.The low grade resource has become the major resources to produce iron and steel in India.The majority of low grade hematite iron ore resource at present is fragile in nature because of its association with good amount of goethite,kaolinite,and gibbsite.As per iron ore formation,goethite generates from hematite due to weathering.The goethite associ-ated with hematite is called vitreous goethite which is hard and crystalline.The goethite associated with clayey materials i.e.,kaolinite and gibbsite is called ochreous goethite [1].The liberation of iron phase minerals in this type of ore is at finer sizes.During the beneficiation of these low grade hematite iron ores,vitreous goethite comes with hematite and partly ocherous goethite along with kaolinite and gibbsite which contribute to the loss on ignition (LOI)in iron ore concentrate.The generation of fines is more during size reduction because of its fragile nature that leads to high Blaine number of the concentrate [2].The utilization of low grade iron ore is need of the hour in respect to meet the high quantity of production of steel in India as per the steel policy of government of India.In order to meet the future demand of steel,low grade iron ore fines need to be ben-eficiated to provide raw materials for steel plants in form of pellet.The presence of goethite,gibbsite,and kaolinite leads to high LOI and high Blaine number of the iron ore concentrate after benefici-ation.The presence of high LOI in the final concentrate deteriorates the quality of pellets [3].Due to the presence of chemically bound water in the matrix of goethite,kaolinite and gibbsite,high pres-sure steam is released at high temperature during induration pro-cess resulting in cracks inside the pellets thereby reducing the strength.The production of pellets and its use in blast furnace has increased largely over the past decade and hence there is con-siderable amount of research interest to remove LOI from the iron ore sample before making the pellet.Gibbsite and goethite release their water molecules within the temperature of 300–400°C whereas kaolinite releases its water molecule after the tempera-ture of 850°C.The kinetics of many solid-state reactions can be represented by Eq.(1):f ða Þ¼ktð1Þ/10.1016/j.ijmst.2017.06.0182095-2686/Ó2017Published by Elsevier B.V.on behalf of China University of Mining &Technology.This is an open access article under the CC BY-NC-ND license (/licenses/by-nc-nd/4.0/).⇑Corresponding author.E-mail address:pcbeuria@immt.res.in (P.C.Beuria).International Journal of Mining Science and Technology 27(2017)1031–1036Contents lists available at ScienceDirectInternational Journal of Mining Science and Technologyjournal homepage:www.else v i e r.c o m /l o c a t e /i j m stwhere a is the conversion factor(fraction of LOI removed)in time t, and the function f(a)depends on the thermal decomposition mech-anism of the iron ore with respect to temperature and pressure and the physical properties of the particle,i.e.,grain size,shape,and crystallinity.The activation energy during the transformation of goethite to hematite has been well documented by many researchers.Lima-de-Faria found that the activation energy for a crushed single crys-tal goethite is82.8kJ/mol[4].Pollack et al.quoted121±13kJ/mol activation energy of two natural limonite(amorphous goethite) [5].Thrierr-Sorel et al.reported activation energy of88kJ/mol for afibrous goethite[6].Keller also gave activation energies in the range of96–167kJ/mol for different variety of goethite types[7]. Goss reported the activation energy of154±15kJ/mol for the sed-imentary goethite[8].Prasad et al.examined the in-situ FTIR study on dehydration of natural graphite and reported that activation energy for pure goethite is85kJ/mol[9].In this paper,the most commonly methods for isothermal kinetic analysis are used in order to determine the mechanism of decomposition of hydrated minerals associated in hematite iron ore using heating cycle process in muffle furnace and thermo-gravimetric analyzer and evaluate the activation energy.The ther-mal decomposition of goethite,gibbsite and kaolinite has given in Eqs.(2)–(4)respectively:2FeOOH¼Fe2O3þH2Oð2Þ2AlðOHÞ3¼Al2O3þ3H2Oð3ÞAl2Si2O5ðOHÞ4¼Al2O3þ2SiO2þ2H2Oð4Þ2.Materials and methodsThe iron ore sample collected from Barbil region of Odisha, India is selected for the study,which contain LOI of5.46%.Miner-alogical characteristic are analyzed through quantitative X-ray diffraction(XRD).The XRD study was carried out by X-ray diffrac-tometer(PANalytical,X’pert)and quantitative analysis was done through high score plus software.The mineralogical characteristic of the sample is given in Table1.The chemical analysis of the sam-ple was carried out through wet chemical and XRF analysis tech-niques.The detailed chemical analysis of the sample is given in Table2.The particle size distribution is given in Table3.Initially,the iron ore samples are subjected to thermo gravimet-ric analysis to determine the rate of weight loss with increase in temperature by TGA(Thermo gravimetric Analysis)/SDTA(Simula-tion of Differential Thermal Analysis)supplied by Mettler,USA.In order to calculate the cumulative weight loss for high mass(250–1000g)samples infixed bed with temperature,the sample with different bed depths are taken after removal of surface moisture and kept inside the furnace for afixed time of30min at a particu-lar temperature from200°C to1200°C with an incremental increase of50°C to compare the TGA data.Further,the iron ore samples are dried at about120°C for 2hours for complete removal of surface moisture.Then the samples are put in four different crucibles of identical size having 96mm internal diameter and91mm height.All the experiments are made in batch mode in afixed bed system.The crucibles are made of high alumina refractory to withstand high temperature. The different weights i.e.250,500,750and1000g of samples are taken for the experiments.The depth of the ore bed varies from 16mm to64mm depending on the weight of the sample.The top of the crucibles is kept open.The samples are decomposed in the muffle furnace isothermally at different temperatures(ranging from400°C to1200°C)for a particular residence time.The heating rate of the furnace is maintained at15°C per minute.The temper-ature of the furnace is maintained precisely by PID controller.After removal from the furnace,final weight of each sample is measured to calculate the percentage of weight loss.The experiments are car-ried out for different residence time from30min to75min.For dif-ferent experiments,fresh samples are used.In overall,the heating cycle is conducted in the muffle furnace at different temperatures (400–1200°C)at incremental increase of50°C each,residence time(30–75min)and bed heights(16–64mm).Changes in the iron ore phases with increase in temperature were supplemented through XRD analysis.3.Results and discussion3.1.Non-isothermal conditionInitially a few experiments are carried out non-isothermally to understand the effect of increasing temperature on the LOI removal.Firstly,some low mass SDTA analysis is done tofind out the temperature when the chemical water starts releasing the hydrated hematite ore.The change in LOI of iron ore sample is observed through the loss of weight at different temperatures using SDTA/TGA as shown in Fig.1.Fig.1shows that the removal of LOI starts at a temperature of 200°C and loses around77%and86%at350°C and500°C,respec-tively.Following this some non-isothermal experiments are car-ried out for high mass system infixed bed.Here,temperature is increased in step wise fashion and the sample is soaked for 30min at each temperature.Fig.2shows the cumulative loss with increase in temperature taken with different bed depths.In this case the sample is contin-uously roasted at temperatures ranging from200°C to1200°C with incremental increase of50°C at different bed depths(16–64mm)for a residence time of30min at each temperature.In these experiments the sample is loaded once in the beginning and not changed after each observed temperature to know the cumulative removal of LOI.Similar experiments are carried out for different bed depths.It is observed that LOI removal follows S-shaped curve.Initially up to300°C,the LOI removal is insignifi-cant and thereafter there is a steep rise in LOI removal to around 90%at temperature of700°C for all depths of bed.Subsequently, the LOI removal almost comes to standstill with increasing tem-perature in irrespective of depth.In respect to bed depth,initial percentage of removal of LOI shifts towards higher temperature with increase of bed depth in the range of400°C to700°C.This is in contrast to observe in low mass TGA experiments where LOI is removed at low temperature between250°C and350°C.The shift in temperature range between low(around36mg in TGA) and high(1000g in experiment)mass experiments may be attrib-uted to decrease in specific reaction surface area for large mass sample.In fact,the reaction surface area(cross section of the bed)remains the same irrespective of the mass in the bed.There-fore,higher temperature is required to enhance the surface reac-tion rate to compensate for the reduction in reaction rate due to lower specific surface area for larger mass infixed bed.While theTable1Mineralogical constituents of thesample.Details Sample(wt.%)Hematite44.96Goethite47.41Kaolinite 6.5Gibbsite0.9Quartzite0.11032P.C.Beuria et al./International Journal of Mining Science and Technology27(2017)1031–1036TGA experiments indicate the actual range of temperatures for LOI removal for low mass,the fixed bed experiments indicate the actual furnace temperature required for larger mass experiments in fixed bed.Moreover,LOI of the iron ore sample is 5.46%and as the sample contains around 6.5%kaolinite,total LOI cannot be removed at lower temperature,because kaolinite needs more time to release its water molecule from its matrix after 850°C.The LOI released by this process at lower temperature is mostly from goethite and gibbsite minerals.3.2.Isothermal conditionIn these experiments fresh samples are taken for each temper-ature and roasted isothermally from 400°C to 1200°C in 50°C interval with a variation of bed depth from 16mm to 64mm and residence time from 30min to 75min.In this condition the removal of LOI with respect bed depth and residence time were studied and analyzed.3.2.1.Mineralogy at different temperaturesQuantitative mineralogy by XRD analysis have been carried out on the bulk sample and after thermal decomposition at 400°C and700°C.The results are shown in Fig.3a–c.As per the mineralogical analysis,major minerals in the bulk sample are hematite,goethite,gibbisite,kaolinite and quartzite.It is also observed that hydrated minerals (gibbsite,goethite and kaolinite)peak gradually vanishes by increasing the temperature.Most of the LOI removal takes place within 700°C.Goethite converts to hematite [10],which is indi-cated by increase in hematite peaks at the expense of goethite peaks with increase in temperature,gibbsite changes over to alu-mina and kaolinite matrix breaks into silica and alumina after releasing the hydrated molecule,gibbsite and kaolinite goes to amorphous phase and they do not appear in the XRD analysis after conversion [11].3.2.2.Effect of bed depthFig.4shows the effect of bed depth on the removal of LOI with for 45min residence time.Rate of LOI removal depends on the bed depth in fixed bed system.Bed depth reduces the kinetic of LOI removal because of lower specific reaction surface area for deeper bed.For the lowest bed depth (16mm)removal of almost all LOI is found to be possible at 1050°C;whereas for highest bed depth (64mm)it is only 81%with a minimum residence time of 30min.At temperature of 900°C,80%of LOI could be removed;whereas at 1200°C,more than 90%LOI can be removed even at higher bed depth of 64mm.Finally it is observed that beyond a certain critical bed depth (16mm),100%removal of LOI is not found possible even at higher temperature and higher residence time.3.2.3.Effect of residence timeThe pattern of variations of LOI reduction with temperature at different residence times is shown in Fig.5.Four residence times viz.30,45,60and 75min are considered in fixed bed system in a bed depth of 16mm over the temperature range of 400–1200°C.It is observed that the percentage of removal of LOI is more with higher residence time at particular bed depth and tem-perature.For example,at 400°C,while the removal of LOI is less than 20%for residence time of 30min,it is around 70%for 75min residence.However,the effect of residence time diminishes at higher temperature.For example,at 900°C,variation of resi-dence time between 30min and 75min,only enhance the LOI removal from 91%to 96%.The study further indicates that since maximum LOI in the sample is contributed by goethite,which releases its water molecule from its matrix from 300°C onwards,maximum LOI gets removed prior to 850°C,beyond which kaolin-ite start releasing its water content.3.3.Kinetic analysisThe rate determining step in any solid-phase reaction can be evaluated either diffusion or chemical reaction process [4,12].In these two fundamental processes,surface diffusion rapidly coats the surface of the reacting particle with a continuous product layer.Another approach is also to consider that there is nucleation of products active sites [13,14].According to the above statements,kinetic functions f (a )have been classified into three groups:the diffusion,the chemical reaction,and the nucleation model.Several mechanisms of the solid state transformation of goethite to hema-tite have been reported.It has been reported that thermal decom-position of goethite directly converts to hematite without any intermediate phase during transformation [15,8].Wolska hasTable 2Chemical analysis of the sample (%).Details Fe Al 2O 3SiO 2CaO K 2O MgO MnO 2P 2O 5TiO 2Na 2O LOI Sample61.272.953.130.0540.0230.0710.0630.2130.1140.0845.46Table 3Size analysis of the sample.Size (l m)Sample (wt.%)+1002.97À100+759.80À75+4522.97À4564.26Fig.1.SDTA analysis ofsample.Fig.2.Cumulative removal of LOI with temperature at different bed height.P.C.Beuria et al./International Journal of Mining Science and Technology 27(2017)1031–10361033reported that goethite transforms into protohematite,then into hydrohematite and finally into hematite with increasing of tem-perature during thermal decomposition [16].Even Ozdemir and Dunlop found that small amounts of magnetite were formed in intermediate phase during phase transform from goethite and hematite [17].Diamandescu et al.established that the solid state reaction of goethite to hematite as a first order reaction controlled by nucleation process in isothermal process [18].The thermal transformation mechanism was studied by Fan et al.,to evaluate maximum decomposition degree under non-isothermal conditions and supported by microstructural evidence [19].The fraction decomposed (a )versus time for different tempera-ture values are presented in Fig.6for 16mm bed depth.The curves show the characteristics of sigmoidal curve as generalized a -t plot,but since the data are collected after 5min interval,initial reaction and induction period covers within this time,especially at higher temperature;whereas acceleratory period,point of inflection,decelerator period and completion of the reaction are visible in Fig.6.The maximum decomposition of 67%(a =0.67)is possible at a temperature of 400°C for residence time of 75min;whereas at higher temperature of 800°C,thermal decomposition are 83%(a =0.83)and 89%(a =0.89)for residence time of 30min and 75min,respectively.Further,the rate of decomposition for different temperature as a function of time is calculated.A typical graphical representation of d a /d t versus time at different temperatures for 16mm bed depth is shown in Fig.7.It can be assessed that rate of decomposi-tion is more at high temperature and reduces with time.In case of low temperature,the rate decomposition remains almost constant throughout the residence time because of deficiency of required enthalpy during the decomposition.The above data are further kinetically treated and analyzed to determine the controlling mechanism and underlying equations.To study the kinetics on the rate of removal of LOI from hydrated iron ore,most of the isothermal kinetics for solid state reactions is analysed.The raw data are modified to give fractional decomposition of LOI (a ),and subsequently to obtain various func-tional forms of a ,and their plots against reduced time,t /t 0.5to determine the reaction kinetics.Various isothermal kinetics for solid state reduction considered in the present study are presented in Table 4.In Table 4,D 1(a )to D 4(a )represent the cases where rate is controlled by diffusion,while F 1(a ),R 2(a )and R 3(a )represent the situation where rate mechanism follows chemical kinetics.The A 2(a ),A 3(a )represents cases where fractional reaction follows a sigmoidal variation with time,which is controlled by nucleation and growth that is mixed controlled.Table 5makes a summary of kinetic equations that best fit the experimental data with corre-lation coefficients for various temperatures and depth of thebed.Fig.3.XRD analysis of sample with 16mm beddepth.Fig.4.LOI removal with temperature at different bed depth at 30min.residencetime.Fig. 5.LOI removal of with temperature with 16mm bed depth at different residencetimes.Fig.6.Variation of thermal decomposition with time and temperature for 16mm beddepth.Fig.7.Rate of thermal decomposition with time for 16mm bed height.1034P.C.Beuria et al./International Journal of Mining Science and Technology 27(2017)1031–1036Fig.8depicts a typical representation of the various bestfit lines through the data points when various functions of a(controlling process)is plotted against reduced time for depth of32mm and 500°C.Similarly,the data generated for other conditions of varying bed depths and temperatures are given in Table5.From Table5,it is observed that decomposition and removal of LOI mostly follows F1(a),R2(a)and R3(a)equations and in some cases at higher tem-peratures,A2(a)indicating decomposition of LOI is mostly gov-erned by chemical kinetics with random nucleation.Halikia et al.have studied thermal decomposition of various other minerals like magnesium hydroxide and calcium carbonate, and predicted the bestfit model for solid-state reaction utilizing thermo gravimetric data,are chemical kinetics,viz.F1(a)and R2(a)and R3(a)[12,13].Goss investigated the kinetics and reaction mechanism for conversion through TG,TEM and XRD analysis and estimated the range of activation energy of goethite and found that the reaction is controlled by R2(a),i.e.,chemical kinetics[8].Dia-mandescu et al.reported F1,i.e.,first order decay law bestfit the transformation of goethite to hematite[18].All the above experi-ments point to the fact that decomposition reactions follow the chemical kinetics,which is also observed in the present study.It may also be noted that all the investigations were made taking low mass and without varying the bed height in afixed bed for practical application in industries.The present experiments have been carried out for higher bed depth.However,up to64mm bed depth and even at high temperature of850°C,the reaction kinetics for LOI decomposition remains primarily controlled by chemical kinetics.Activation energy values are also estimated to confirm the influ-ence of chemical kinetics.These values are estimated using Arrhe-nius plots(Fig.9).Estimated activation energy values for different bed depths and are presented in Table6.The activation energy values estimated for all the bed depths are found to be around60kJ/mol.These higher activation energy values reinstates that the chemical kinetics indeed controls the dehydration reaction up to64mm bed depth and900°C.The acti-vation energy during the transformation of goethite to hematite has been well documented by many researchers.Lima-de-Faria found that the activation energy for a crushed single crystal goethite is82.8kJ/mol[20].Pollack et al.quoted121±13kJ/mol activation energies of two natural limonite(amorphous goethite) [5].Thrierr-Sorel et al.,reported an activation energy of88kJ/mol for afibrous goethite[6].Keller also gave activation energies in the range of96–167kJ/mol for different variety of goethite types[7].Table4a-functions for most commonly used solid-state reaction processes(a represents fractional reaction,and k,trepresent rate constant and time,respectively).Rate controlling process Kinetic equationDiffusion,one dimensional D1(a):a2=ktDiffusion,two dimensional D2(a):(1Àa)ln(1Àa)+a=ktDiffusion,three dimensional(spherical symmetry)D3(a):[1À(1Àa)1/3]2=ktDiffusion,three dimensional(contracting sphere model)D4(a):1À(2/3)a(1Àa)2/3=ktMoving phase boundary,two dimensional R2(a):1À(1Àa)1/2=ktMoving phase boundary,three dimensional R3(a):1À(1Àa)1/3=ktRandom nucleation,two dimensional A2(a):[Àln(1Àa)]1/2=ktRandom nucleation,three dimensional A3(a):[Àln(1Àa)]1/3=ktRandom nucleation,first order decay law F1(a):Àln(1Àa)=ktTable5Various a-functions thatfit the present experimental data for different bed depths and temperature.Temperature and bed depth16mm32mm48mm64mm400°C F1(a):(R2=0.9987)F1(a):(R2=0.9964)F1(a):(R2=0.9967)F1(a):(R2=0.9957)R2(a):(R2=0.9983)R2(a):(R2=0.9959)R2(a):(R2=0.9962)R2(a):(R2=0.995)R3(a):(R2=0.9985)R3(a):(R2=0.9962)R3(a):(R2=0.9964)R3(a):(R2=0.9953) 450°C F1(a):(R2=0.9988)F1(a):(R2=0.9987)F1(a):(R2=0.9987)F1(a):(R2=0.9978)R2(a):(R2=0.9992)R2(a):(R2=0.9994)R2(a):(R2=0.9983)R2(a):(R2=0.9978)R3(a):(R2=0.9993)R3(a):(R2=0.9993)R3(a):(R2=0.9985)R3(a):(R2=0.9978) 500°C F1(a):(R2=0.992)F1(a):(R2=0.9982)F1(a):(R2=0.995)F1(a):(R2=0.9873)R2(a):(R2=0.9984)R2(a):(R2=0.998)R2(a):(R2=0.9905)R2(a):(R2=0.9893)R3(a):(R2=0.9968)R3(a):(R2=0.9959)R3(a):(R2=0.9927)R3(a):(R2=0.99) 550°C F1(a):(R2=0.9925)F1(a):(R2=0.9882)F1(a):(R2=0.9946)F1(a):(R2=0.9762)R2(a):(R2=0.9991)R2(a):(R2=0.998)R2(a):(R2=0.9973)R2(a):(R2=0.9826)R3(a):(R2=0.9976)R3(a):(R2=0.9959)R3(a):(R2=0.9971)R3(a):(R2=0.9806) 600°C F1(a):(R2=0.9984)F1(a):(R2=0.9858)F1(a):(R2=0.989)F1(a):(R2=0.9926)R2(a):(R2=0.9976)R2(a):(R2=0.9813)R2(a):(R2=0.9886)R2(a):(R2=0.9983)R3(a):(R2=0.995)R3(a):(R2=0.9837)R3(a):(R2=0.9894)R3(a):(R2=0.9968)A2(a):(R2=0.9784)650°C F1(a):(R2=0.9786)F1(a):(R2=0.9829)F1(a):(R2=0.989)F1(a):(R2=0.9949)R2(a):(R2=0.9964)R2(a):(R2=0.9974)R2(a):(R2=0.9986)R2(a):(R2=0.9926)R3(a):(R2=0.992)R3(a):(R2=0.9939)R3(a):(R2=0.9964)R3(a):(R2=0.9944)A2(a):(R2=0.9602)700°C F1(a):(R2=0.974)F1(a):(R2=0.9785)F1(a):(R2=0.9825)F1(a):(R2=0.979)R2(a):(R2=0.9958)R2(a):(R2=0.9953)R2(a):(R2=0.9966)R2(a):(R2=0.9751)R3(a):(R2=0.9906)R3(a):(R2=0.9912)R3(a):(R2=0.9931)R3(a):(R2=0.9776)A2(a):(R2=0.9737)A2(a):(R2=0.9696)750°C F1(a):(R2=0.9649)F1(a):(R2=0.9606)F1(a):(R2=0.9772)F1(a):(R2=0.9663)R2(a):(R2=0.994)R2(a):(R2=0.9676)R2(a):(R2=0.995)R2(a):(R2=0.9869)R3(a):(R2=0.987)R3(a):(R2=0.9574)R3(a):(R2=0.9906)R3(a):(R2=0.9814)A2(a):(R2=0.9753)A2(a):(R2=0.9603) 800°C R2(a):(R2=0.995)R2(a):(R2=0.9932)F1(a):(R2=0.9741)F1(a):(R2=0.9776)R3(a):(R2=0.998)R3(a):(R2=0.9857)R2(a):(R2=0.9956)R2(a):(R2=0.9958)A2(a):(R2=0.978)A2(a):(R2=0.9761)R3(a):(R2=0.9904)R3(a):(R2=0.9908)A2(a):(R2=0.9695)A2(a):(R2=0.9709) P.C.Beuria et al./International Journal of Mining Science and Technology27(2017)1031–10361035Goss reported the activation energy of 154±15kJ/mol for the sedimentary goethite [8].Prasad et al.examined the in-situ FTIR study on dehydration of natural graphite and reported that activa-tion energies for natural goethite samples from Karnataka are 103kJ/mol and 85kJ/mol [9].Therefore,the present estimated activation energy values are found to be in tune with the literature data.Slightly lower value in the present study may be attributed naturally occurring ore having 47%of goethite is being considered in the present study in contrast to synthetic goethetic mostly reported in literature.Besides,the mass of the bed is also higher in the present study.4.Conclusions(1)The reduction of LOI from a fixed bed is prominent in thetemperature range of 300–700°C due to the release of water molecule by goethite and gibbsite from their matrix.(2)Since the kaolinite releases its matrix moisture at 850°C,more temperature and residence time is required for sample containing kaolinite along with goethite and gibbsite for maximum removal of LOI.(3)The extent of LOI removal decreases with increase in beddepth and decrease in residence time.Effect of residence time is found to be prominent at comparatively lower tem-perature.Beyond a certain critical bed depth (16mm),100%removal of LOI is not found to be possible even at higher temperature and higher residence time.(4)The rate of thermal decomposition of hydrated iron ore ismore for initial stages and reduces thereafter for tempera-tures more than 500°C,whereas it remains more or less con-stant for temperature below 500°C.(5)Kinetics of thermal decomposition of hydrated minerals inhematite has been studied through various a functions against reduced time plot.Thermal decomposition at all bed depths up to 64mm and temperatures up to 900°C,fol-lowed a -functions for chemical kinetics.The activation energy values calculated for all cases for various bed depths and temperatures in the present study are found to be more than 60kJ/mol,reinstating the role of chemical kinetics.(6)It is found that temperature required to remove LOIincreases with increase in mass in the fixed bed,which is attributed to the lower specific surface area for high mass fixed bed samples,where surface reaction controls the over-all reaction.AcknowledgmentsThe authors are very much thankful to Ministry of Steel –India,New Delhi for sponsoring the program to carry out the research work.References[1]Das SK,Das B,Saktivel R,Mishra BK.Mineralogy,microstructure,and chemicalcompositions of goethites in some iron ore deposits of Orissa,India.Miner Process Extr Metall Rev 2010;31(2):7–110.[2]Mishra BK,Das B,Prakash S,Das SK,Biswal SK,Reddy PSR.Issues relatingcharacterization and beneficiation of low grade iron ore.Steel World 2007:34–7.[3]Biswal SK.Utilization of low grade iron ore fines,slimes and tailings byphysical beneficiation to minimize the waste generation.J Sustain Planet 2010:46–58.[4]Bamford CH,Tipper CFH,prehensive chemical kinetics.TheNetherlands:Elsevier Scientific Publishing Corporation;1980.[5]Pollack JB,Pitman D,Khare N,Sagan C.Goethite on Mars:a laboratory study ofphysically and chemically bound water in 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carbonate by isothermal method of analysis.Eur J Miner Process Environ Prot 2001;1(2):89–102.[13]Halikia I,Neou-Syngouna P,Kolitsa D.Isothermal kinetic analysis of thethermal decomposition of magnesium hydroxide using thermo gravimetric data.Thermochim Acta 1998;320(1–2):75–88.[14]Garner WE,editor.Chemistry of the solid state.London:ButterworthsScientific Publications;1955.[15]Watari F,Delavignette P,Amelinckx S.Electron microscopic study ofdehydration transformation.II.The formation of ‘‘superstructures”on dehydration of goethite and diaspora.J Solid State Chem 1979;29(3):417–27.[16]Wolska E.Relation between the existence of hydroxyl ions in the anionicsubstance of hematite and its infrared and X-ray characteristics.Solid State Ionics 1988;28–30:1349–51.[17]Ozdemir O,Dunlop DJ.Intermediate magnetite formation during dehydrationof goethite.Earth Planetary Sci Lett 2000;177:59–67.[18]Diamandescu L,Mihaila-Tarabasanu D,Calogero S.Mossbauer study of thesolid phase transformation a -FeOOH ?Fe 2O 3.Mater Chem Phys 1997;48(2):170–3.[19]Fan H,Song B,Li Q.Thermal behaviour of goethite during transformation tohematite.Mater Chem Phys 2006;98:148–53.[20]Lima-de-Faria J.Dehydration of goethite and diaspore.Zeitschrift furKristallographie1963;119:176–203.Fig.8.Best fit lines for various a -functions at 500°C and 32mm beddepth.Fig.9.Arrhenius plot for 16mm bed depth.Table 6Activation energy values estimated for various bed depths using Arrhenius plot.Bed depth (mm)Slope =ÀEa /R Ea =Activation energy (kJ/mol)16À7.907565.7432À7.790264.7748À7.343661.0564À7.065058.741036P.C.Beuria et al./International Journal of Mining Science and Technology 27(2017)1031–1036。
