Corrosion Resistance – Zirconium Metal

Zirconium Grades: Zr 702, Zr 704, and Zr 705

Introduction

Zirconium alloys are known for their exceptional corrosion resistance, mechanical strength, and thermal stability, making them suitable for a variety of demanding applications. Among the most widely used zirconium alloys are Zr 702, Zr 704, and Zr 705. Each grade has distinct properties and applications, tailored to meet specific industrial needs.

1. Zr 702: Commercially Pure Zirconium

Zr 702 is considered a commercially pure grade of zirconium, with a zirconium content of at least 99.2%. It contains very low levels of alloying elements such as iron, oxygen, and hafnium.

Key Properties

Corrosion Resistance: Exceptional resistance to most acids, alkalis, and seawater, making it highly effective in harsh chemical environments.
Ductility: Excellent ductility allows for easy forming, machining, and welding.
Thermal Stability: High melting point and stability in elevated temperatures.

Applications

Chemical Processing: Used for equipment like heat exchangers, reactors, and storage tanks in chemical industries.
Nuclear Reactors: Utilized as cladding for fuel rods due to its low neutron absorption.
Medical Applications: Used in medical implants and devices due to its biocompatibility.
Marine Applications: Suitable for seawater systems and marine hardware because of its resistance to saltwater corrosion.

2. Zr 704: Zirconium Alloy with Improved Strength

Zr 704 is an alloyed grade of zirconium that includes small amounts of niobium (0.5%-2.5%), iron (0.2%-0.4%), and oxygen. The added elements enhance its strength while maintaining excellent corrosion resistance.

Key Properties

Higher Strength: Enhanced mechanical strength compared to Zr 702 due to the alloying elements.
Corrosion Resistance: Excellent resistance to oxidizing and reducing environments, particularly in acidic solutions.
Good Fabricability: Retains good ductility for forming and welding.

Applications

Chemical and Petrochemical Industries: Commonly used for vessels, piping, and heat exchangers handling strong acids and other corrosive substances.
Aerospace Components: Ideal for components requiring high strength-to-weight ratios and resistance to high-temperature oxidation.
Hydrogen Storage: Utilized in hydrogen storage systems due to its stability and ability to resist hydrogen embrittlement.

3. Zr 705: Zirconium-Niobium Alloy

Zr 705 is a high-strength zirconium alloy containing 2%-3% niobium, along with small amounts of iron and oxygen. The addition of niobium significantly increases its strength and enhances its resistance to mechanical stress.

Key Properties

Exceptional Strength: Significantly stronger than Zr 702 and Zr 704, making it suitable for applications requiring high mechanical performance.
Corrosion Resistance: Maintains excellent corrosion resistance in most acidic and alkaline environments.
Fatigue Resistance: High resistance to cyclic stresses, making it ideal for dynamic or high-stress environments.

Applications

Nuclear Applications: Commonly used in advanced reactor designs where strength and corrosion resistance are critical.
Aerospace and Defense: Ideal for high-performance components in aerospace and defense systems.
Chemical Processing: Used for high-pressure vessels and piping in extreme chemical environments.
Medical Implants: Applied in high-load orthopedic implants due to its strength and biocompatibility.

Choosing the Right Grade

Property

Zr 702

Zr 704

Zr 705

Composi

-tion

Commercially

pure

zirconium

(>99.2%)

Zirconium

with Fe, Nb,

and O

additives

Zirconium

with 2%-3%

Nb, Fe, and O

Strength

Moderate

Higher than

Zr 702

Significantly

higher than

Zr 702/704

Corrosion

Resistance

Excellent

Ductility

High

Moderate

to high

Lower than

Zr 702,

higher than

many alloys

Applica

-tions

Chemical,

nuclear,

and

medical

Chemical,

petrochemical

aerospace

Nuclear,

aerospace,

chemical,

medical

(Note: For more zirconium grades information, please check Advanced Refractory Metals (ARM).)

Zr 702: Best for applications where corrosion resistance and ductility are priorities, such as chemical processing, marine systems, and medical implants.
Zr 704: Ideal for environments requiring a balance of strength and corrosion resistance, such as high-temperature or acidic chemical processes.
Zr 705: Suitable for high-stress and high-performance applications, including aerospace, defense, and advanced nuclear reactors.

Each grade of zirconium is engineered to meet specific industrial challenges, ensuring optimal performance, safety, and durability. Selecting the right grade depends on the application’s mechanical, environmental, and operational demands.

Metal Products: Chemical Properties and Physical Properties

What is Metal?

Metals are a distinct category of elements known for their conductive properties, malleability, ductility, and generally high density. With the exception of mercury, metals are typically solid at room temperature and exhibit a lustrous appearance. These materials are integral to numerous industries, including construction, manufacturing, and electronics, due to their unique characteristics. A comprehensive understanding of both the physical and chemical properties of metals is essential for selecting the appropriate material for specific applications.

Physical Properties

Electrical and Thermal Conductivity: Metals are excellent conductors of electricity and heat, attributed to the presence of delocalized electrons within their atomic structure. For example, copper has an electrical conductivity of approximately 59.6 × 10^6 S/m, making it a preferred choice for electrical wiring, while aluminum, with a conductivity of around 37.7 × 10^6 S/m, is widely used in various thermal applications.
Malleability: This property refers to the ability of metals to deform under compressive stress without fracture. Metals such as gold and silver are highly malleable, enabling them to be shaped into thin sheets, which is advantageous in electronics and jewelry manufacturing.
Ductility: Ductility is the capacity of a metal to be drawn into wires. For instance, copper and aluminum can be extruded into long, thin wires without breaking, making them suitable for applications requiring high tensile strength, such as power transmission lines.
Density: Metals generally possess high density, a measure of mass per unit volume. For example, lead has a density of approximately 11.34 g/cm³, while aluminum has a density of 2.70 g/cm³. This property is crucial in industries where weight considerations are paramount, such as aerospace.
Hardness: Hardness indicates a material’s resistance to deformation and scratching. Hard metals, such as tungsten (hardness around 8.5 on the Mohs scale) and chromium, are utilized in cutting tools and machinery due to their durability.
Luster: The reflective quality of metals, or luster, is a result of their ability to reflect light. This characteristic not only enhances aesthetic appeal but also contributes to applications in decorative elements and surface coatings.
Melting and Boiling Points: Metals typically exhibit high melting and boiling points. Tungsten, for instance, has an exceptional melting point of approximately 3,422°C, making it ideal for high-temperature applications, such as aerospace components.

Chemical Properties

Reactivity: Metals display varying reactivities with other substances. For example, alkali metals, such as sodium and potassium, are highly reactive with water, while noble metals like gold and platinum exhibit minimal reactivity, making them suitable for use in corrosive environments.
Oxidation: Metals are prone to oxidation when exposed to air and moisture. Iron, for instance, oxidizes in the presence of oxygen and water, forming iron oxide (rust). Understanding oxidation rates is essential for selecting metals for outdoor applications or environments prone to corrosion.
Corrosion Resistance: Certain metals, such as stainless steel and aluminum, possess inherent corrosion resistance due to the formation of a protective oxide layer. This property is crucial for applications in construction, marine, and chemical processing industries where exposure to harsh conditions is common.
Alloy Formation: Metals can form alloys, which are mixtures of two or more elements that retain metallic properties. For example, steel, an alloy of iron and carbon, exhibits significantly enhanced strength compared to pure iron, making it suitable for structural applications.
Acid-Base Behavior: Metals can react with acids, producing hydrogen gas and corresponding metal salts. For instance, zinc reacts with hydrochloric acid to yield zinc chloride and hydrogen. This property is significant in chemical processing and waste management applications.

Property Values of Common Metals

Understanding the specific properties of common metals aids in material selection for various applications. Here are some key property values:

– Aluminum:

– Density: 2.70 g/cm³

– Electrical Conductivity: 37.7 × 10^6 S/m

– Melting Point: 660°C

– Corrosion Resistance: High due to oxide layer

– Copper:

– Density: 8.96 g/cm³

– Electrical Conductivity: 59.6 × 10^6 S/m

– Melting Point: 1,085°C

– Malleability: Excellent

– Iron:

– Density: 7.87 g/cm³

– Electrical Conductivity: 10.0 × 10^6 S/m

– Melting Point: 1,538°C

– Reactivity: Prone to oxidation

– Stainless Steel (an alloy):

– Density: 8.00 g/cm³

– Electrical Conductivity: 1.4 × 10^6 S/m

– Melting Point: 1,400-1,500°C

– Corrosion Resistance: Very high

– Titanium:

– Density: 4.51 g/cm³

– Electrical Conductivity: 2.4 × 10^6 S/m

– Melting Point: 1,668°C

– Corrosion Resistance: Excellent in acidic environments

– Lead:

– Density: 11.34 g/cm³

– Electrical Conductivity: 4.5 × 10^6 S/m

– Melting Point: 327.5°C

– Hardness: Relatively soft

Conclusion

Metals are fundamental materials with a diverse array of applications due to their distinctive physical and chemical properties. Understanding these properties—such as conductivity, malleability, and corrosion resistance—enables engineers and manufacturers to select the most suitable metal for specific applications. The ability to create alloys further enhances the versatility of metals, making them indispensable across various industries. As technological advancements continue, the exploration of metal properties will drive innovation and improve material performance in an ever-evolving landscape. For more information, please visit Advanced Refractory Metals (ARM).

Niobium in Aerospace: A Key Material

Introduction

Niobium is a metal with special properties that make it important in aerospace. It is strong, resists heat, and does not rust easily. These features make niobium perfect for the harsh conditions in airplanes and spacecraft.

What Makes Niobium Special?

Niobium has several key traits that make it useful in aerospace:

High Heat Resistance: Niobium can handle very high temperatures. It melts at 2,468°C (4,474°F), so it works well in places like jet engines that get extremely hot.
Corrosion Resistance: Niobium does not rust or break down easily, even when exposed to tough environments. This is crucial for parts that need to last a long time, such as those in space or at high altitudes.
Strength: When mixed with other metals, niobium makes them stronger. This means parts made from niobium alloys can endure a lot of stress without breaking or losing shape.
Lightweight: Niobium has a good strength-to-weight ratio, meaning it can help make strong but lightweight parts for aircraft and spacecraft.

Related reading: 10 Important Uses of Niobium

Niobium in Jet Engines

Jet engines are incredibly hot and put parts under extreme stress. Niobium alloys are often used in engine components like turbine blades. These blades must stay strong while spinning at high speeds and facing high temperatures.

Niobium makes sure the blades do not melt or break under these tough conditions. By using niobium, engineers can make engines more efficient and longer-lasting.

Niobium in Rockets

Rockets face even more heat and pressure than jet engines. When rockets launch, their engines burn fuel at extreme temperatures to create thrust. Niobium alloys are often used in the rocket nozzles, which direct the hot gases out of the engine. Since niobium can handle these extreme conditions, it helps prevent the rocket parts from melting or warping.

In addition, niobium resists “thermal creep,” which is when materials slowly deform from constant high heat. This is critical for long space missions, where parts need to maintain their shape over time.

Niobium in Spacecraft

Spacecraft are exposed to very harsh environments. Temperatures can swing from freezing cold to boiling hot. Spacecraft also face radiation and lack the protection that Earth’s atmosphere provides. Niobium alloys are used in the structural parts of spacecraft because they are strong, lightweight, and resistant to both heat and corrosion.

Niobium’s strength and resistance help ensure that spacecraft can survive the extreme conditions of space without breaking down. Its lightweight nature also helps reduce the overall weight of the spacecraft, which is crucial for successful launches.

Superconductivity in Aerospace

Niobium also has the ability to become “superconductive.” This means it can carry electricity without any resistance when it is cooled to very low temperatures. In aerospace, superconductivity could lead to advances in power systems, propulsion, and even magnetic levitation technology. Although this is still a developing area, niobium’s role in superconductivity makes it important for future technologies in space travel.

Future Uses of Niobium in Aerospace

As aerospace technology advances, the need for materials like niobium will grow. The industry is constantly pushing for lighter, stronger, and more heat-resistant materials. Niobium will continue to be used in aircraft and spacecraft because of its unique properties.

In the future, niobium could also be used in new types of power systems, advanced engines, and lighter spacecraft. Its ability to work in extreme conditions makes it an ideal material for the next generation of aerospace technologies.

Conclusion

Niobium is a key material in aerospace because it is strong, heat-resistant, and lightweight. It plays an important role in jet engines, rockets, and spacecraft, ensuring that these machines can operate under extreme conditions. As aerospace technology continues to evolve, niobium will remain a vital material in the industry. Its ability to handle heat and stress while staying strong makes it perfect for the future of flight and space exploration. For more metal products, please check Advanced Refractory Metals (ARM).

Hafnium Wire: Specifications and Diverse Applications

Introduction

Hafnium, a transition metal known for its remarkable properties, is commonly used in the form of wire for various high-tech and industrial applications. This article explores the key specifications of hafnium wire and its diverse applications across multiple industries.

Key Specifications of Hafnium Wire

Hafnium wire specifications vary depending on the intended application. However, some general specifications include:

Purity: Hafnium wire is typically available in purity levels of 99.5%, 99.9%, and 99.95%, with higher purity levels being used in applications requiring exceptional corrosion resistance and neutron absorption.
Diameter: The wire is available in various diameters, commonly ranging from 0.1 mm to 3.0 mm. Custom diameters can be produced based on specific application needs. Send us an inquiry if you are interested.
Tensile Strength: Hafnium wire can achieve tensile strengths of up to 300 MPa, particularly when cold-drawn.
Density: 13.31 g/cm³, a relatively high density, contributing to its strength and durability in demanding applications.
Melting Point: 2,233°C, making it suitable for high-temperature environments.
Coating: Some hafnium wires may be coated with materials like platinum to enhance oxidation resistance.

Applications of Hafnium Wire

Hafnium wire is utilized across a broad range of industries due to its unique properties. Here are some of the key applications:

1. Nuclear Industry

Control Rods in Nuclear Reactors: Hafnium’s exceptional ability to absorb neutrons without forming long-lived radioactive isotopes makes it an ideal material for control rods in nuclear reactors. These rods are critical for controlling the fission process and maintaining reactor safety. The high melting point and corrosion resistance of hafnium wire further ensure its reliability in the harsh environment of a nuclear reactor.

2. Aerospace Industry

Jet Engine Components: In aerospace applications, hafnium wire, particularly in alloyed form (e.g., Hafnium-Zirconium alloy), is used in jet engine components that operate at temperatures exceeding 1,000°C. The wire’s oxidation resistance and strength at high temperatures make it suitable for these critical applications, where failure is not an option.

3. Industrial Heating Elements

Furnace Heating Elements: Oxide-dispersion strengthened (ODS) hafnium wire is used in industrial furnaces that operate at extremely high temperatures, often above 1,800°C. The fine oxide particles in the wire enhance its resistance to thermal creep, ensuring that the heating elements maintain their structural integrity over prolonged periods of use.

4. Automotive Industry

Catalytic Converters: Hafnium wire coated with platinum is used in automotive catalytic converters. The platinum coating enhances the wire’s resistance to oxidation and chemical attack from the corrosive gases in exhaust systems. This application is crucial for reducing harmful emissions from vehicles, contributing to environmental sustainability.

5. Medical Field

Surgical Implants and Clips: Annealed hafnium wire is employed in the production of surgical clips and other medical implants. The annealing process improves the wire’s ductility, allowing it to be easily shaped and manipulated during surgical procedures. Additionally, hafnium’s biocompatibility makes it safe for use within the human body.

6. Electronics and Semiconductor Industry

Gate Electrodes in Semiconductors: Hafnium wire is used in the semiconductor industry for gate electrodes in field-effect transistors (FETs). Its high dielectric constant helps reduce leakage currents, improving the performance and efficiency of electronic devices. The use of hafnium in semiconductor applications is vital for the advancement of microelectronics.

7. Scientific Research

High-Temperature Thermocouples: In scientific research, hafnium wire is used in thermocouples for measuring extremely high temperatures. The wire’s stability at high temperatures ensures accurate and reliable temperature measurements, which are critical in experiments and industrial processes.

Industry	Application	Key Benefits
Nuclear Industry	Control Rods in Nuclear Reactors	Absorbs neutrons, high melting point, corrosion resistance
Aerospace Industry	Jet Engine Components	Oxidation resistance, high-temperature strength
Industrial Heating Elements	Furnace Heating Elements	Resistance to thermal creep, structural integrity at high temperatures
Automotive Industry	Catalytic Converters	Oxidation resistance, reduces harmful emissions
Medical Field	Surgical Implants and Clips	Ductility, biocompatibility
Electronics & Semiconductor Industry	Gate Electrodes in Semiconductors	High dielectric constant, improves electronic performance
Scientific Research	High-Temperature Thermocouples	Stability at high temperatures, accurate temperature measurements

Advanced Refractory Metals (ARM) provides an extensive selection of high-quality refractory metal products and heat-resistant materials. ARM offers low pricing and great lead times on all our metals and alloys, and we’re capable of supplying custom materials per any specs/drawings you provide us with.

Conclusion

With a high melting point, corrosion resistance, and neutron absorption capability, Hafnium Wire has become essential in nuclear reactors, aerospace engines, industrial furnaces, automotive components, medical implants, and advanced electronics. Its specifications can be tailored to suit specific requirements, ensuring that it continues to play a vital role in modern technology and industry.

How Is Zirconium Wire Used in Marine Environments?

Introduction

Zirconium wire has emerged as a vital material in marine environments due to its high corrosion resistance, excellent thermal stability, and robust mechanical strength. This article will discuss the advantages of Zr wire in marine settings, exploring its properties, applications, and the reasons behind its growing adoption.

Properties of Zirconium Wire

Zirconium is a transition metal known for several key properties:

Corrosion Resistance: Zirconium exhibits superior resistance to corrosion by seawater, including both chloride and sulfate ions. This property is critical for materials exposed to marine environments, where corrosion is a primary concern.
Mechanical Strength: The metal maintains its strength and integrity under mechanical stress, making it ideal for structural applications in marine settings.
Thermal Stability: Zirconium can withstand high temperatures without degrading, which is essential for components exposed to varying thermal conditions in marine environments.
Biocompatibility: The non-toxic nature of zirconium makes it safe for use in environments where it may come into contact with marine life.

Applications of Zirconium Wire in Marine Environments

Zirconium wire is used in various marine applications, where its unique properties contribute to enhanced performance and longevity:

1. Seawater Pumps and Valves

Seawater pumps and valves are essential components in marine vessels and offshore platforms. Zirconium wire is used in these applications to ensure the longevity and reliability of the equipment. The corrosion resistance of zirconium prevents the deterioration of pumps and valves, reducing maintenance costs and downtime.

2. Heat Exchangers

Heat exchangers in marine environments often deal with the transfer of heat between seawater and other fluids. Zirconium wire is utilized in the construction of heat exchanger components due to its thermal stability and resistance to seawater corrosion. This ensures efficient heat transfer and extends the lifespan of the equipment.

3. Underwater Sensors and Instrumentation

Underwater sensors and instrumentation are critical for various marine activities, including navigation, research, and resource exploration. Zirconium wire is used in these devices to enhance their durability and performance. Its resistance to corrosion and biofouling ensures accurate and reliable operation over extended periods.

4. Marine Fasteners and Connectors

Marine fasteners and connectors made from zirconium wire offer superior strength and corrosion resistance. These components are crucial in securing structures and equipment in marine environments. The use of zirconium wire ensures that fasteners and connectors can withstand harsh conditions without failing.

5. Fishing and Aquaculture Equipment

Zirconium wire is also used in the construction of fishing and aquaculture equipment, such as nets, cages, and hooks. Its biocompatibility and resistance to seawater corrosion make it ideal for prolonged use in marine environments, ensuring the safety and health of marine life.

Advantages of Zirconium Wire in Marine Applications

The use of zirconium wire in marine environments offers several significant advantages:

Longevity: Zirconium wire’s resistance to corrosion and wear extends the lifespan of marine components, reducing the need for frequent replacements and repairs.
Reliability: The mechanical strength and thermal stability of zirconium ensure the consistent performance of marine equipment under challenging conditions.
Cost-Effectiveness: Although zirconium wire may have a higher initial cost compared to other materials, its durability and low maintenance requirements lead to overall cost savings in the long run.
Environmental Safety: The biocompatibility of zirconium makes it safe for marine life, supporting sustainable marine operations and reducing environmental impact.

Conclusion

Zirconium wire is a superior material for marine environments, offering unmatched corrosion resistance, mechanical strength, and thermal stability. Its applications in seawater pumps, heat exchangers, underwater sensors, fasteners, and fishing equipment demonstrate its versatility and reliability.

As the demand for durable and efficient materials in marine environments continues to grow, zirconium wire is poised to play an increasingly important role in ensuring the success and sustainability of marine operations. For more information, please check Advanced Refractory Metals (ARM).

Corrosion Resistance of Zirconium Strip in Industrial Applications

Introduction

For centuries, the quest for substances that combine strength with exceptional resistance to corrosion has led to significant advancements. Among these materials, the zirconium strip stands out for its superior corrosion resistance. It marks a significant leap forward in extending the longevity and reliability of equipment across various industries.

This article delves into the corrosion resistance of zirconium strips. It also focuses on zirconium’s applications and the future outlook of this remarkable material.

Unveiling the Properties of Zirconium Strip

Zirconium is a lustrous, grey-white, strong transition metal. It is renowned for its corrosion resistance. When fashioned into strips, it offers a combination of durability, flexibility, and a formidable barrier against corrosive agents.

This resistance is primarily due to the formation of a thin, stable oxide layer on its surface when exposed to oxygen. That oxide layer effectively seals the metal from further attack by most acids and alkalis.

Industrial Applications: A Spectrum of Uses

The unique properties of the zirconium strip have led to its widespread adoption across multiple sectors. Here are some key areas where its impact is most pronounced:

–Chemical Processing Industry

In environments where exposure to harsh chemicals is a daily occurrence, equipment longevity is a constant challenge.

Zirconium strips are useful in the construction of pipes, valves, and reactors. Their resistance to corrosion significantly reduces maintenance costs and prevents contamination of sensitive reactions.

–Nuclear Reactors

Zirconium comes with a low neutron absorption cross-section. It has become ideal for nuclear reactors, where it is used in cladding fuel rods. The corrosion-resistant nature of the zirconium strip ensures the integrity of the reactor’s core components and enhances safety and efficiency.

–Medical Devices

The strip also stands out for its biocompatibility and corrosion resistance. It is suitable for various medical implants and devices. Its use in this field ensures that the implants remain safe and effective over time, without reacting adversely with bodily fluids.

–Aerospace and Defense

In aerospace and defense, Zr’s high strength-to-weight ratio and corrosion resistance are invaluable. Components made from zirconium strips can withstand the extreme conditions encountered in these applications. Such uses range from the corrosive nature of aviation fuels to the high-temperature environments of jet engines.

Advantages over Other Materials

Zirconium strip offers several advantages over traditional corrosion-resistant materials like stainless steel and titanium.

–Corrosion Resistance: Zirconium vs. Stainless Steel

Zirconium: It exhibits superior corrosion resistance in most acidic environments, particularly in hydrochloric acid, sulfuric acid, and other aggressive media where stainless steel would typically fail.
Stainless Steel: While stainless steel is known for its corrosion resistance, its performance heavily depends on the alloy composition and the environment it’s exposed to. In chloride-containing environments or highly acidic conditions, certain grades of stainless steel can suffer from pitting, crevice corrosion, or stress corrosion cracking.

–Corrosion Resistance: Zirconium vs. Titanium

Zirconium: Similar to titanium, zirconium’s corrosion resistance is attributed to a protective oxide layer that forms on the surface. However, zirconium’s layer is even more effective in certain acidic conditions. It offers better protection than titanium in environments where titanium might be prone to corrosion.
Titanium: Titanium’s excellent corrosion resistance comes from a passive oxide film that forms on its surface. It performs exceptionally well in seawater and chlorinated environments, as well as in the presence of most acids. However, at high temperatures or in the presence of certain acids (like hydrofluoric acid or concentrated sulfuric acid), titanium’s corrosion resistance can be compromised.

The Future of Zirconium Strip

The increasing demand for materials that can ensure the longevity and reliability of industrial equipment in corrosive environments is driving research into enhancing the properties of zirconium strips.

Innovations in alloying techniques aim at improving its strength and corrosion resistance even further.
Moreover, the development of cost-effective manufacturing processes is expected to make zirconium strips more accessible for a wider array of industries, from renewable energy to water treatment.

Conclusion

Zirconium strips offer industries a solution to one of their most persistent challenges. With impressive corrosion resistance, it gains applications in chemical processing, nuclear reactors, medical devices, and aerospace.

As research continues to unlock new potentials for this material, the Zr strip is set to become an even more integral component of industrial applications in the years to come. It promises a future where materials are not only stronger but also more resilient against the relentless forces of corrosion. For more information, please check Advanced Refractory Metals (ARM).