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Articles 9901 - 9930 of 16767
Full-Text Articles in Engineering
Factors Affecting The Heat Transfer During The Dip Testing Of Potential Third Generation Advanced High Strength Steels, Kramer Michael Pursell
Factors Affecting The Heat Transfer During The Dip Testing Of Potential Third Generation Advanced High Strength Steels, Kramer Michael Pursell
Masters Theses
"A dip tester was designed and built at Missouri University of Science and Technology to test the effects of the primary alloying elements (Mn, Si, and Al) of Fe-Mn-Al-Si-C type 3rd generation advanced high strength steel (AHSS) alloys, dipping superheat, and dipping speed on the heat transfer during rapid solidification. The difficulties associated with casting 3rd generation AHSS were compiled as well to serve as a best-practices guide. An extensive list of potential 3rd generation AHSS alloys was developed and tested, and the effects of various dip testing parameters were examined.
Manganese was found to increase the heat flux by …
Determination Of Setting Times By Shear Wave Velocity Evolution In Fresh Mortar Using Bender Element Method, Jianfeng Zhu
Determination Of Setting Times By Shear Wave Velocity Evolution In Fresh Mortar Using Bender Element Method, Jianfeng Zhu
Masters Theses
This study aims at using modified bender element (BE) method to monitor the shear wave velocity (Vs) of mortar at early-age and determine initial and final setting times with the Vs method. Modifications of the traditional BE method have been made to overcome the aggressive cementitious environment and eliminate electromagnetic coupling. BE has been successfully employed in mortar samples with and without admixtures to evaluate the evolution of Vs during the early age (first 24 hrs) of hydration. An energy approach method of determining the first arrival time of S-wave has been proposed. Pulse wave velocity …
Understanding Impurities In Copper Electrometallurgy, Paul Laforest
Understanding Impurities In Copper Electrometallurgy, Paul Laforest
Masters Theses
"This work involves examining two industrial reports of methods to handle impurities in copper electrowinning and electrorefining. The first part evaluates the addition of Hydrostar, Cyquest N-900, DXG-F7, and Guartec EW to copper electrowinning electrolyte to affect MnO2 deposition on coated titanium anodes (CTAs). The second part examines the effects of anode chemistry and thiourea addition on the ductility of electrorefined copper starter sheet.
In part one, a laboratory cell was used to simulate a short cycle electrowinning cell via chronopotentiometric operation with an IrO2-Ta2O5 CTA at 40⁰C. A cyclic voltammetric sweep was applied …
Development Of Two Color Imaging Pyrometer For Studying Thermal History Of Laser Metal Deposition, Niroop Matta
Development Of Two Color Imaging Pyrometer For Studying Thermal History Of Laser Metal Deposition, Niroop Matta
Masters Theses
"The laser aided manufacturing process is a process in which parts are built by adding material into the melt pool created by a laser. This process involves a complex thermal history which is important in determining the quality of the parts built. The objective of this study is to develop a high resolution two color imaging pyrometer which can measure the temperature of an object without the dependence of spectral emissivity of the material at an economical price. An 8.8 MP CMOS sensor is used as an imaging sensor. The visible spectrum of light is used for temperature measurement. The …
Nanomechanical And Scaling Behavior Of Nanoporous Gold, Nicolas J. Briot
Nanomechanical And Scaling Behavior Of Nanoporous Gold, Nicolas J. Briot
Theses and Dissertations--Chemical and Materials Engineering
Nanoporous metals have recently been drawn significant interest in various fields of research. Their high surface-to-volume ratio present a strong potential for applications in sensing, catalysis, micro-electromechanical systems (MEMS) and even in the medical field. However, the mechanical properties of nanoporous metals have not yet been well determined, as conducting mechanical tests was found to be challenging. Scaling relations linking the mechanical properties of porous materials to those of their dense counterparts are successfully and widely used for many porous metals. However, their applicability to nanoporous metals have recently been questioned, as estimations from the classic scaling relations were found …
Nanoindentation Of A Zinc Metal Soap Mixture For Use In A Laser Printer, George A. Nimick
Nanoindentation Of A Zinc Metal Soap Mixture For Use In A Laser Printer, George A. Nimick
Theses and Dissertations--Chemical and Materials Engineering
At the start of this project, the possible choices of metal soaps had already been narrowed to include some of the zinc soaps used in this project. These zinc soaps are mixtures of zinc stearate and zinc palmitate of varying ratios purchased from a supplier. Zinc soap was chosen as result of its common use in various industries as a lubricant and mold release, which implied potential benefits in an electrophotographic printing system. These potential benefits include, but are not limited to, a more efficient transfer from a photoconductive drum and protection of the drum from mechanical and chemical degradation. …
Fundamental Studies Of Surfactant Templated Metal Oxide Materials Synthesis And Transformation For Adsorption And Energy Applications, Saikat Das
Theses and Dissertations--Chemical and Materials Engineering
This work addresses fundamental aspects of designing templates and curing conditions for the synthesis of mesoporous metal oxide thin films. The first section addresses selection of cationic-carbohydrate surfactant mixtures to synthesize templated silica thin films for selective adsorption of simple carbohydrates based on molecular imprinting. Nuclear magnetic resonance and fluorescence spectroscopy results suggest a novel structure for mixtures of alkyl glucopyranosides or xylopyranosides with cationic (trimethylammonium) surfactants. Despite thermodynamically favorable mixing, the carbohydrate headgroups in the mixed micelle adopt an inverted configuration with their headgroups in the micelle core, and therefore are inaccessible for molecular imprinting. This orientation occurs even …
Engineered Surface Properties Of Porous Tungsten From Cryogenic Machining, Julius M. Schoop
Engineered Surface Properties Of Porous Tungsten From Cryogenic Machining, Julius M. Schoop
Theses and Dissertations--Chemical and Materials Engineering
Porous tungsten is used to manufacture dispenser cathodes due to it refractory properties. Surface porosity is critical to functional performance of dispenser cathodes because it allows for an impregnated ceramic compound to migrate to the emitting surface, lowering its work function. Likewise, surface roughness is important because it is necessary to ensure uniform wetting of the molten impregnate during high temperature service. Current industry practice to achieve surface roughness and surface porosity requirements involves the use of a plastic infiltrant during machining. After machining, the infiltrant is baked and the cathode pellet is impregnated. In this context, cryogenic machining is …
Microindentation Of Bi57in26sn17 Lead-Free Alloy, Ruiting Zhao
Microindentation Of Bi57in26sn17 Lead-Free Alloy, Ruiting Zhao
Theses and Dissertations--Chemical and Materials Engineering
There is great need to understand the mechanical properties of lead-free alloys—an alternative of lead-based alloys—to address the environmental problems associated with the use of lead-based materials in microelectronics. In this work, the microstructures of Bi57In26Sn17 lead-free alloy were examined using Optical Microscopy and Energy Dispersive X-ray Spectroscopy analysis. The micro-indentation technique was used to study the mechanical properties of Bi57In26Sn17 lead-free alloy. The experimental results of the hardness and contact modulus were presented and discussed. Local creep during the indentation was observed from the load-displacement curves. The Vickers hardness (HV) increases with the decrease of the indentation depth, suggesting …
Synthesis, Structure, Properties And Applications Of Nanoporous Silicon And Palladium, Xu Jiang
Synthesis, Structure, Properties And Applications Of Nanoporous Silicon And Palladium, Xu Jiang
Theses and Dissertations--Chemical and Materials Engineering
Nanoporous (np) materials with pore size below 100 nano-meters exist naturally in biological and mineral structures, and synthetic np materials have been used industrially for centuries. Np materials have attracted significant research interest in recent decades, as the development of new characterization techniques and nanotechnology allow the observation and design of np materials at a new level. This study focuses on two np materials: nanoporous silicon (np-Si) and nanoporous palladium (np-Pd).
Silicon (Si), because of its high capacity to store lithium (Li), is increasingly becoming an attractive candidate as anode material for Li ion batteries (LIB). One significant problem with …
Evaporation-Induced Formation Of Well-Ordered Surface Patterns On Polymer Films, Wei Sun
Evaporation-Induced Formation Of Well-Ordered Surface Patterns On Polymer Films, Wei Sun
Theses and Dissertations--Chemical and Materials Engineering
Various techniques of fabricating surface patterns of small scales have been widely studied due to the potential applications of surface patterns in a variety of areas. It is a challenge to fabricate well-ordered surface area efficiently and economically. Evaporation-induced surface patterning is a promising approach to fabricate well-ordered surface patterns over a large area at low cost. In this study, the evaporation-induced surface patterns with controllable geometrical characteristics have been constructed. The dewetting kinetics on deformable substrate is also investigated.
Using simple templates to control the geometry and the evaporation behavior of a droplet of volatile solvent, various gradient surface …
Processing And Property Evaluation Of Tungsten-Based Mixed Oxides For Photovoltaics And Optoelectronics, Mirella Vargas
Processing And Property Evaluation Of Tungsten-Based Mixed Oxides For Photovoltaics And Optoelectronics, Mirella Vargas
Open Access Theses & Dissertations
Tungsten Oxide (WO3) films and low-dimensional structures have proven to be promising candidates in the fields of photonics and electronics. WO3 is a well-established n-type semiconductor characterized by unique electrochromic behavior, an ideal optical band gap that permits transparency over a wide spectral range, and high chemical integrity. The plethora of diverse properties endow WO3 to be highly effective in applications related to electrochromism, gas sensing, and deriving economical energy. Compared to the bulk films, a materials system involving WO3 and a related species (elements or metal oxides) offer the opportunity to tailor the electrochromic response, and an overall enhancement …
An Improved Sin-Hyperbolic Constitutive Model For Creep Deformation And Damage, Mohammad Shafinul Haque
An Improved Sin-Hyperbolic Constitutive Model For Creep Deformation And Damage, Mohammad Shafinul Haque
Open Access Theses & Dissertations
Inspection and maintenance of industrial gas turbines (IGTs) cost millions of dollars. Growing demand of obtaining higher IGT efficiency leads to higher temperature and pressure operating conditions. Long exposure of turbine components at elevated temperature and pressure
makes creep damage critically important to consider during planning, designing and operating conditions. Effective and economic maintenance requires accurate creep deformation, damage
evolution and rupture life prediction information. Creep prediction models are used to determine the state of the turbine components and to schedule the inspection, maintenance and replacement time periods. The more accurate the prediction model, the less is the overall cost …
Transition Metal Carbide (Tmc) Novel Materials For Novel Catalytic Applications, Svetlana Lagoykina
Transition Metal Carbide (Tmc) Novel Materials For Novel Catalytic Applications, Svetlana Lagoykina
Open Access Theses & Dissertations
Transition metal carbides (TMC) constitute a diverse class of materials and traditionally have many technological applications. TMC became a subject of extensive research since 1973, when their platinum -like properties were discovered. They demonstrated high catalytical activity and selectivity in a variety of chemical reaction and have potential for some novel catalytic application.
This research is an effort to design new high effective, selective and stable bimetal or alkali promoted TMC catalyst. After extensive theoretical research a wide range of TMC, including bimetal and alkali promoted carbides, were synthesized by different methods. All solids were characterized by XRD and microscopy. …
Reaction Of Liquid Aluminium- Samarium Alloys With B4c At Ultra High Temperatures, Sanjay Shantha-Kumar
Reaction Of Liquid Aluminium- Samarium Alloys With B4c At Ultra High Temperatures, Sanjay Shantha-Kumar
Open Access Theses & Dissertations
Reactive studies between a packed bed of B4C and Al-Sm-Me (Me = Ti, Zr, Hf) alloy melts were carried out under a pseudo-isopiestic thermodynamic system. A graphite enclosure isolated the system under a temperature gradient with one end reaching temperatures greater than 1800 K and the opposite end of the graphite enclosure contains liquid Al with temperatures approximating 950 K. The liquid Al establishes an oxygen potential to control oxidation of very reactive elements (i.e., Al, Sm and Ti). The Al-Sm-Me alloy infuses into a packed bed of B4C reacting exothermically to form borides and carbides depending on the thermodynamic …
Hybrid Nano-Structure For Enhanced Energy Storage Devices, Mohammad Arif Ishtiaque Shuvo
Hybrid Nano-Structure For Enhanced Energy Storage Devices, Mohammad Arif Ishtiaque Shuvo
Open Access Theses & Dissertations
The goal of this research is to develop electrode materials using various nano-structure hybrids for improved energy storage devices. Enhancing the performance of energy storage device has been gaining tremendous attention since it holds the key solution to advance renewable energy usage thus reduce the consumption of fossil fuels. The application of energy storage devices such as super-capacitor and Li-ion-battery has seen significant growth; however, it is still limited mainly by charge/discharge rate and energy density. One of the solutions is to use nano-structure materials, which offer higher power at high energy density and improved stability during the charge discharge …
High Temperature Oxidation Of Nb-Cr-Mo-Si-B Alloys, Kathryn S. Thomas
High Temperature Oxidation Of Nb-Cr-Mo-Si-B Alloys, Kathryn S. Thomas
Open Access Theses & Dissertations
It has been the trend to use nickel based superalloys in high temperature applications, however higher temperatures are required in the effort to enhance the efficiency of such components as jet turbine engines. The melting temperature of the nickel based superalloy limits the extent to which temperature can be raised as these materials are typically used at temperatures within 200 degrees of their melting point. Refractory metal based systems are attractive due to their high melting points, low densities, and good high temperature strength. However, in such cases as niobium, poor oxidation resistance limits the widespread use of such alloys. …
Defeating Anisotropy In Material Extrusion 3d Printing Via Materials Development, Ángel Ramón Torrado Pérez
Defeating Anisotropy In Material Extrusion 3d Printing Via Materials Development, Ángel Ramón Torrado Pérez
Open Access Theses & Dissertations
Additive Manufacturing technologies has been in continuous development for more than 35 years. Specifically, the later denominated Material Extrusion Additive Manufacturing (MEAM), was first developed by S. Scott Crump around 1988 and trademarked later as Fused Deposition Modeling (FDM). Although all of these technologies have been around for a while, it was not until recently that they have been more accessible to everyone. Today, the market of 3D printers covers all ranges of price, from very specialized, heavy and expensive machines, to desktop printers of only a few cubic inches in volume. Until recently, FDM technology had remained somewhat stagnant …
Multi-Platform Arabinoxylan Scaffolds As Potential Wound Dressing Materials, Donald C. Aduba Jr
Multi-Platform Arabinoxylan Scaffolds As Potential Wound Dressing Materials, Donald C. Aduba Jr
Theses and Dissertations
Biopolymers are becoming more attractive as advanced wound dressings because of their naturally derived origin, abundance, low cost and high compatibility with the wound environment. Arabinoxylan (AX) is a class of polysaccharide polymers derived from cereal grains that are primarily used in food products and cosmetic additives. Its application as a wound dressing material has yet to be realized. In this two-pronged project, arabinoxylan ferulate (AXF) was fabricated into electrospun fibers and gel foams to be evaluated as platforms for wound dressing materials. In the first study, AXF was electrospun with varying amounts of gelatin. In the second study, AXF …
A Study To Evaluate Non-Uniform Phase Maps In Shape Memory Alloys Using Finite Element Method, Naren Motte
A Study To Evaluate Non-Uniform Phase Maps In Shape Memory Alloys Using Finite Element Method, Naren Motte
Theses and Dissertations
The unique thermo-mechanical behavior of Shape Memory Alloys (SMAs), such as their ability to recover the original shape upon heating or being able to tolerate large deformations without undergoing plastic transformations, makes them a good choice for actuators.
This work studies their application in the aerospace and defense industries where SMA components can serve as release mechanisms for gates of enclosures that have to be deployed remotely. This work provides a novel approach in evaluating the stress and heat induced change of phase in a SMA, in terms of the transformation strain tensor. In particular, the FEA tool
ANSYS has …
Peracetic Acid Sterilization Of Electrospun Polycaprolactone Scaffolds, Suyog Yoganarasimha
Peracetic Acid Sterilization Of Electrospun Polycaprolactone Scaffolds, Suyog Yoganarasimha
Theses and Dissertations
Sterilization of tissue engineered scaffolds is an important regulatory issue and is at the heart of patient safety. With the introduction of new biomaterials and micro/nano structured scaffolds, it is critical that the mode of sterilization preserve these built-in features. Conventional sterilization methods are not optimal for engineered polymeric systems and hence alternate systems need to be identified and validated. PCL is polyester with a low melting point (heat labile), susceptible to hydrolysis and is popular in tissue engineering. Electrospinning generates some nanoscale features within the scaffold, the integrity of which can be affected by sterilization method. Chapter 1 explores …
Simulation Study Of Hemt Structures With Hfo2 Cap Layer For Mitigating Inverse Piezoelectric Effect Related Device Failures, Deepthi Nagulapally, Ravi P. Joshi, Aswini Pradhan
Simulation Study Of Hemt Structures With Hfo2 Cap Layer For Mitigating Inverse Piezoelectric Effect Related Device Failures, Deepthi Nagulapally, Ravi P. Joshi, Aswini Pradhan
Electrical & Computer Engineering Faculty Publications
The Inverse Piezoelectric Effect (IPE) is thought to contribute to possible device failure of GaN High Electron Mobility Transistors (HEMTs). Here we focus on a simulation study to probe the possible mitigation of the IPE by reducing the internal electric fields and related elastic energy through the use of high-k materials. Inclusion of a HfO2 "cap layer" above the AlGaN barrier particularly with a partial mesa structure is shown to have potential advantages. Simulations reveal even greater reductions in the internal electric fields by using "field plates" in concert with high-k oxides
The Influence Of Particle Content On The Equi-Biaxial Fatigue Behaviour Of Magnetorheological Elastomers, Yanfen Zhou, Stephen Jerrams, Tony Betts, Gerald Farrell, Lin Chen
The Influence Of Particle Content On The Equi-Biaxial Fatigue Behaviour Of Magnetorheological Elastomers, Yanfen Zhou, Stephen Jerrams, Tony Betts, Gerald Farrell, Lin Chen
Articles
The equi-biaxial fatigue behaviour of silicone based magnetorheological elastomers (MREs) with various volume fractions of carbonyl iron particles ranging between 15% and 35% was studied. Wöhler curves for each material were derived by cycling test samples to failure over a range of stress amplitudes. Changes in complex modulus (E*) and dynamic stored energy during the fatigue process were observed. As for other elastic solids, fatigue resistance of MREs with different particle contents was shown to be dependent on the stress amplitudes applied. MREs with low particle content showed the highest fatigue life at high stress amplitudes while MREs with high …
Quantitative Modeling Of The Equilibration Of Two-Phase Solid-Liquid Fe By Atomistic Simulations On Diffusive Time Scales, Ebrahim Asadi, Mohsen Asle Zaeem, Sasan Nouranian, Michael I. Baskes
Quantitative Modeling Of The Equilibration Of Two-Phase Solid-Liquid Fe By Atomistic Simulations On Diffusive Time Scales, Ebrahim Asadi, Mohsen Asle Zaeem, Sasan Nouranian, Michael I. Baskes
Materials Science and Engineering Faculty Research & Creative Works
In this paper, molecular dynamics (MD) simulations based on the modified-embedded atom method (MEAM) and a phase-field crystal (PFC) model are utilized to quantitatively investigate the solid-liquid properties of Fe. A set of second nearest-neighbor MEAM parameters for higherature applications are developed for Fe, and the solid-liquid coexisting approach is utilized in MD simulations to accurately calculate the melting point, expansion in melting, latent heat, and solid-liquid interface free energy, and surface anisotropy. The required input properties to determine the PFC model parameters, such as liquid structure factor and fluctuations of atoms in the solid, are also calculated from MD …
Dynamic Phases, Pinning, And Pattern Formation For Driven Dislocation Assemblies, Caizhi Zhou, Charles Reichhardt, Cynthia Olson Reichhardt, Irene J. Beyerlein
Dynamic Phases, Pinning, And Pattern Formation For Driven Dislocation Assemblies, Caizhi Zhou, Charles Reichhardt, Cynthia Olson Reichhardt, Irene J. Beyerlein
Materials Science and Engineering Faculty Research & Creative Works
We examine driven dislocation assemblies and show that they can exhibit a set of dynamical phases remarkably similar to those of driven systems with quenched disorder such as vortices in superconductors, magnetic domain walls, and charge density wave materials. These phases include pinned-jammed, fluctuating, and dynamically ordered states, and each produces distinct dislocation patterns as well as specific features in the noise fluctuations and transport properties. Our work suggests that many of the results established for systems with quenched disorder undergoing plastic depinning transitions can be applied to dislocation systems, providing a new approach for understanding pattern formation and dynamics …
Nanoscale Mechanical Switching Of Ferroelectric Polarization Via Flexoelectricity, Yijia Gu, Zijian Hong, Jason Britson, Long-Qing Chen
Nanoscale Mechanical Switching Of Ferroelectric Polarization Via Flexoelectricity, Yijia Gu, Zijian Hong, Jason Britson, Long-Qing Chen
Materials Science and Engineering Faculty Research & Creative Works
Flexoelectric coefficient is a fourth-rank tensor arising from the coupling between strain gradient and electric polarization and thus exists in all crystals. It is generally ignored for macroscopic crystals due to its small magnitude. However, at the nanoscale, flexoelectric contributions may become significant and can potentially be utilized for device applications. Using the phase-field method, we study the mechanical switching of electric polarization in ferroelectric thin films by a strain gradient created via an atomic force microscope tip. Our simulation results show good agreement with existing experimental observations. We examine the competition between the piezoelectric and flexoelectric effects and provide …
Tunable Optical Nanocavity Of Iron-Garnet With A Buried Metal Layer, Alexey N. Kuz'michev, Lars E. Kreilkamp, Mohammed Nur-E-Alam, Evgeni Bezus, Mikhail Vasilev, Iliya A. Akimov, Kamal Alameh, Manfred Bayer, Vladimir I. Belotelov
Tunable Optical Nanocavity Of Iron-Garnet With A Buried Metal Layer, Alexey N. Kuz'michev, Lars E. Kreilkamp, Mohammed Nur-E-Alam, Evgeni Bezus, Mikhail Vasilev, Iliya A. Akimov, Kamal Alameh, Manfred Bayer, Vladimir I. Belotelov
Research outputs 2014 to 2021
We report on the fabrication and characterization of a novel magnetophotonic structure designed as iron garnet based magneto-optical nanoresonator cavity constrained by two noble metal mirrors. Since the iron garnet layer requires annealing at high temperatures, the fabrication process can be rather challenging. Special approaches for the protection of metal layers against oxidation and morphological changes along with a special plasma-assisted polishing of the iron garnet layer surface were used to achieve a 10-fold enhancement of the Faraday rotation angle (up to 10.8°=μm) within a special resonance peak of 12 nm (FWHM) linewidth at a wavelength of 772 nm, in …
Biocorrosion Rate And Mechanism Of Metallic Magnesium In Model Arterial Environments, Patrick Bowen
Biocorrosion Rate And Mechanism Of Metallic Magnesium In Model Arterial Environments, Patrick Bowen
Dissertations, Master's Theses and Master's Reports
A new paradigm in biomedical engineering calls for biologically active implants that are absorbed by the body over time. One popular application for this concept is in the engineering of endovascular stents that are delivered concurrently with balloon angioplasty. These devices enable the injured vessels to remain patent during healing, but are not needed for more than a few months after the procedure. Early studies of iron- and magnesium-based stents have concluded that magnesium is a potentially suitable base material for such a device; alloys can achieve acceptable mechanical properties and do not seem to harm the artery during degradation. …
Monolithic Optofluidic Ring Resonator Lasers Created By Femtosecond Laser Nanofabrication, Hengky Chandrahalim, Qiushu Chen, Ali A. Said, Mark Dugan, Xudong Fan
Monolithic Optofluidic Ring Resonator Lasers Created By Femtosecond Laser Nanofabrication, Hengky Chandrahalim, Qiushu Chen, Ali A. Said, Mark Dugan, Xudong Fan
Faculty Publications
We designed, fabricated, and characterized a monolithically integrated optofluidic ring resonator laser that is mechanically, thermally, and chemically robust. The entire device, including the ring resonator channel and sample delivery microfluidics, was created in a block of fused-silica glass using a 3-dimensional femtosecond laser writing process. The gain medium, composed of Rhodamine 6G (R6G) dissolved in quinoline, was flowed through the ring resonator. Lasing was achieved at a pump threshold of approximately 15 μJ/mm2. Detailed analysis shows that the Q-factor of the optofluidic ring resonator is 3.3 × 104, which is limited by both solvent …
Deforming Diamond, Ciprian Borcea, Ileana Streinu
Deforming Diamond, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
For materials science, diamond crystals are almost unrivaled for hardness and a range of other properties. Yet, when simply abstracting the carbon bonding structure as a geometric bar-and-joint periodic framework, it is far from rigid. We study the geometric deformations of this type of framework in arbitrary dimension d, with particular regard to the volume variation of a unit cell.