Neutron Reflectometry
Encyclopedia
Neutron reflectometry is a neutron diffraction
technique for measuring the structure of thin films, similar to the often complementary techniques of X-ray reflectivity
and ellipsometry
. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, polymer
and surfactant
adsorption
, structure of thin film magnetic systems, biological membranes, etc.
beam of neutrons onto an extremely flat surface and measuring the intensity of reflected radiation as a function of angle or neutron wavelength. The exact shape of the reflectivity profile provides detailed information about the structure of the surface, including the thickness, density, and roughness of any thin films layered on the substrate.
Neutron reflectometry is a specular reflection
technique, where the angle of the incident beam is equal to the angle of the reflected beam. The reflection is usually described in terms of a momentum
transfer vector, denoted
, which describes the change in momentum of a neutron after reflecting from the material. Conventionally the 
direction is defined to be the film normal direction, and for specular reflection, the scattering vector has only a 
-component. A typical neutron reflectometry plot displays the reflected intensity (relative to the incident beam) as a function of the scattering vector:
where
is the neutron wavelength
, and
is the angle of incidence. The Abeles matrix formalism or the Parratt recursion can be used to describe the specular signal arising from the interface.
The wavelength of the neutrons used for reflectivity are typically on the order of 0.2 to 1 nm (2 to 10 Å
). This technique requires a neutron source
, which may be either a research reactor
or a spallation
source (based on a particle accelerator
). Like all neutron scattering
techniques, neutron reflectometry is sensitive to contrast arising from different nuclei (as compared to electron density, which is measured in x-ray scattering). This allows the technique to differentiate between various isotopes of elements
. Neutron reflectometry measures the neutron scattering length density (SLD) and can be used to accurately calculate material density
if the atomic composition is known.
, carbon
, nitrogen
, oxygen
, etc.). Sensitivity to isotopes also allows contrast to be greatly (and selectively) enhanced for some systems of interest using isotopic substitution, and multiple experiments that differ only by isotopic substitution can be used to resolve the phase problem
that is general to scattering techniques. Finally, neutrons are highly penetrating and typically non-perturbing: which allows for great flexibility in sample environments, and the use of delicate sample materials (e.g., biological specimens). By contrast x-ray exposure may damage some materials, and laser
light can modify some materials (e.g. photoresist
s). Also, optical techniques may include ambiguity due to optical anisotropy
(birefringence
), which complementary neutron measurements can resolve. Dual polarisation interferometry
is one optical method which provides analogous results to neutron reflectometry at comparable resolution although the underpinning mathematical model is somewhat simpler, i.e. it can only derive a thickness (or birefringence
) for a uniform layer density.
Disadvantages of neutron reflectometry include the higher cost of the required infrastructure, the fact that some materials may become radioactive upon exposure to the beam, and insensitivity to the chemical state of constituent atoms. Moreover, the relatively lower flux and higher background of the technique (when compared to x-ray reflectivity) limit the maximum value of
that can be probed (and hence the measurement resolution).
Neutron diffraction
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material: A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of...
technique for measuring the structure of thin films, similar to the often complementary techniques of X-ray reflectivity
X-ray reflectivity
X-ray reflectivity sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR, is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers...
and ellipsometry
Ellipsometry
Ellipsometry is an optical technique for the investigation of the dielectric properties of thin films....
. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
and surfactant
Surfactant
Surfactants are compounds that lower the surface tension of a liquid, the interfacial tension between two liquids, or that between a liquid and a solid...
adsorption
Adsorption
Adsorption is the adhesion of atoms, ions, biomolecules or molecules of gas, liquid, or dissolved solids to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid...
, structure of thin film magnetic systems, biological membranes, etc.
Technical details
The technique involves shining a highly collimatedCollimator
A collimator is a device that narrows a beam of particles or waves. To "narrow" can mean either to cause the directions of motion to become more aligned in a specific direction or to cause the spatial cross section of the beam to become smaller.- Optical collimators :In optics, a collimator may...
beam of neutrons onto an extremely flat surface and measuring the intensity of reflected radiation as a function of angle or neutron wavelength. The exact shape of the reflectivity profile provides detailed information about the structure of the surface, including the thickness, density, and roughness of any thin films layered on the substrate.
Neutron reflectometry is a specular reflection
Specular reflection
Specular reflection is the mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction...
technique, where the angle of the incident beam is equal to the angle of the reflected beam. The reflection is usually described in terms of a momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
transfer vector, denoted
, which describes the change in momentum of a neutron after reflecting from the material. Conventionally the direction is defined to be the film normal direction, and for specular reflection, the scattering vector has only a -component. A typical neutron reflectometry plot displays the reflected intensity (relative to the incident beam) as a function of the scattering vector:where
is the neutron wavelengthWavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
, and
is the angle of incidence. The Abeles matrix formalism or the Parratt recursion can be used to describe the specular signal arising from the interface.The wavelength of the neutrons used for reflectivity are typically on the order of 0.2 to 1 nm (2 to 10 Å
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
). This technique requires a neutron source
Neutron source
A Neutron source is a device that emits neutrons. There is a wide variety of different sources, ranging from hand-held radioactive sources to neutron research facilities operating research reactors and spallation sources...
, which may be either a research reactor
Research reactor
Research reactors are nuclear reactors that serve primarily as a neutron source. They are also called non-power reactors, in contrast to power reactors that are used for electricity production, heat generation, or maritime propulsion.-Purpose:...
or a spallation
Spallation
In general, spallation is a process in which fragments of material are ejected from a body due to impact or stress. In the context of impact mechanics it describes ejection or vaporization of material from a target during impact by a projectile...
source (based on a particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
). Like all neutron scattering
Neutron scattering
Neutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
techniques, neutron reflectometry is sensitive to contrast arising from different nuclei (as compared to electron density, which is measured in x-ray scattering). This allows the technique to differentiate between various isotopes of elements
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...
. Neutron reflectometry measures the neutron scattering length density (SLD) and can be used to accurately calculate material density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
if the atomic composition is known.
Comparison to other reflectometry techniques
Although other reflectivity techniques (in particular optical reflectivity, x-ray reflectometry) operate using the same general principles, neutron measurements are advantageous in a few significant ways. Most notably, since the technique probes nuclear contrast, rather than electron density, it is more sensitive for measuring some elements, especially lighter elements (hydrogenHydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
, carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
, nitrogen
Nitrogen
Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
, oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
, etc.). Sensitivity to isotopes also allows contrast to be greatly (and selectively) enhanced for some systems of interest using isotopic substitution, and multiple experiments that differ only by isotopic substitution can be used to resolve the phase problem
Phase problem
In physics the phase problem is the name given to the problem of loss of information concerning the phase that can occur when making a physical measurement. The name itself comes from the field of x-ray crystallography, where the phase problem has to be solved for the determination of a structure...
that is general to scattering techniques. Finally, neutrons are highly penetrating and typically non-perturbing: which allows for great flexibility in sample environments, and the use of delicate sample materials (e.g., biological specimens). By contrast x-ray exposure may damage some materials, and laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
light can modify some materials (e.g. photoresist
Photoresist
A photoresist is a light-sensitive material used in several industrial processes, such as photolithography and photoengraving to form a patterned coating on a surface.-Tone:Photoresists are classified into two groups: positive resists and negative resists....
s). Also, optical techniques may include ambiguity due to optical anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
(birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
), which complementary neutron measurements can resolve. Dual polarisation interferometry
Dual Polarisation Interferometry
Dual polarization interferometry is an analytical technique that can probe molecular scale layers adsorbed to the surface of a waveguide by using the evanescent wave of a laser beam confined to the waveguide...
is one optical method which provides analogous results to neutron reflectometry at comparable resolution although the underpinning mathematical model is somewhat simpler, i.e. it can only derive a thickness (or birefringence
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
) for a uniform layer density.
Disadvantages of neutron reflectometry include the higher cost of the required infrastructure, the fact that some materials may become radioactive upon exposure to the beam, and insensitivity to the chemical state of constituent atoms. Moreover, the relatively lower flux and higher background of the technique (when compared to x-ray reflectivity) limit the maximum value of
that can be probed (and hence the measurement resolution).Partial list of neutron reflectometers
- ASTERIX at the Los Alamos Neutron Science CenterLos Alamos Neutron Science CenterThe Los Alamos Neutron Science Center , formerly known as the Los Alamos Meson Physics Facility is one of the world's most powerful linear accelerators. It is located in Los Alamos National Laboratory in New Mexico in Technical Area 53 . It was the most powerful linear accelerator in the world...
in Los Alamos National LaboratoryLos Alamos National LaboratoryLos Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico... - SPEAR at the Los Alamos Neutron Science CenterLos Alamos Neutron Science CenterThe Los Alamos Neutron Science Center , formerly known as the Los Alamos Meson Physics Facility is one of the world's most powerful linear accelerators. It is located in Los Alamos National Laboratory in New Mexico in Technical Area 53 . It was the most powerful linear accelerator in the world...
in Los Alamos National LaboratoryLos Alamos National LaboratoryLos Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico... - Platypus at ANSTO in SydneySydneySydney is the most populous city in Australia and the state capital of New South Wales. Sydney is located on Australia's south-east coast of the Tasman Sea. As of June 2010, the greater metropolitan area had an approximate population of 4.6 million people...
, AustraliaAustraliaAustralia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area... - C5 spectrometer at NRC CanadaNational Research Council of CanadaThe National Research Council is an agency of the Government of Canada which conducts scientific research and development.- History :...
Chalk River LabsChalk River LaboratoriesThe Chalk River Laboratories is a Canadian nuclear research facility located near Chalk River, about north-west of Ottawa in the province of Ontario.CRL is a site of major research and development to support and advance nuclear technology, in particular CANDU reactor...
in Chalk RiverChalk River, OntarioChalk River is a Canadian rural community part of the Laurentian Hills municipality in Renfrew County, Ontario. It is located in the Upper Ottawa Valley along Highway 17 , 10 km inland from the Ottawa River, approximately 21 km northwest of Petawawa, and 182 km northwest of Ottawa...
, CanadaCanadaCanada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
. Note: a new dedicated reflectometer (D3) was commissioned in 2006. - D3 reflectometer at NRC CanadaNational Research Council of CanadaThe National Research Council is an agency of the Government of Canada which conducts scientific research and development.- History :...
Chalk River LabsChalk River LaboratoriesThe Chalk River Laboratories is a Canadian nuclear research facility located near Chalk River, about north-west of Ottawa in the province of Ontario.CRL is a site of major research and development to support and advance nuclear technology, in particular CANDU reactor...
in Chalk RiverChalk River, OntarioChalk River is a Canadian rural community part of the Laurentian Hills municipality in Renfrew County, Ontario. It is located in the Upper Ottawa Valley along Highway 17 , 10 km inland from the Ottawa River, approximately 21 km northwest of Petawawa, and 182 km northwest of Ottawa...
, CanadaCanadaCanada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
. - D17, SuperADAM and Figaro at the Institut Laue-LangevinInstitut Laue-LangevinThe Institut Laue–Langevin, or ILL, is an internationally-financed scientific facility, situated in Grenoble, France. It is one of the world centres for research using neutrons...
(ILL) in GrenobleGrenobleGrenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...
, FranceFranceThe French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France... - EROS and PRISM (alternate) at CEACommissariat à l'Énergie AtomiqueThe Commissariat à l'énergie atomique et aux énergies alternatives or CEA, is a French “public establishment related to industrial and commercial activities” whose mission is to develop all applications of nuclear power, both civilian and military...
Laboratoire Léon Brillouin (LLB) in SaclaySaclaySaclay is a commune in the southwestern suburbs of Paris, France. It is located from the center of Paris.It is best known for the large scientific facility CEA Saclay, mostly dealing with nuclear and particle physics....
, FranceFranceThe French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France... - N-REX+, MIRA, TREFF@NoSpec, REFSANS and MARIA at the Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II) in Garching, GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
- NeRo and PNR at the GKSS Research Centre (GKSS) in GeesthachtGeesthachtGeesthacht is the largest city in the District of the Duchy of Lauenburg in Schleswig-Holstein in Northern Germany, 34 km southeast of Hamburg on the right bank of the river Elbe.-History:*Around 800: A church is documented....
, GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate... - V6 reflectometer at Hahn-Meitner-Institut (HMI) in BerlinBerlinBerlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
, GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate... - HADAS at Forschungszentrum Jülich in JülichJülichJülich is a town in the district of Düren, in the federal state of North Rhine-Westphalia, Germany. Jülich is well known as location of a world-famous research centre, the Forschungszentrum Jülich and as shortwave transmission site of Deutsche Welle...
, GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
- PNR at the Dhruva reactorDhruva reactorThe Dhruva reactor is India's largest nuclear research reactor. Located in the Mumbai suburb of Trombay at the Bhabha Atomic Research Centre , it is India's primary generator of weapons-grade plutonium-bearing spent fuel for its nuclear weapons program. Originally named the R-5, this pool-type...
, Bhabha Atomic Research CentreBhabha Atomic Research CentreThe Bhabha Atomic Research Centre is India's primary nuclear research facility based in Mumbai. It has a number of nuclear reactors, all of which are used for India's nuclear power and research programme.- History :...
in MumbaiMumbaiMumbai , formerly known as Bombay in English, is the capital of the Indian state of Maharashtra. It is the most populous city in India, and the fourth most populous city in the world, with a total metropolitan area population of approximately 20.5 million...
, IndiaIndiaIndia , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world... - REFLEX and REMUR at Joint Institute for Nuclear ResearchJoint Institute for Nuclear ResearchThe Joint Institute for Nuclear Research, JINR , in Dubna, Moscow Oblast , Russia, is an international research centre for nuclear sciences, with 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow...
IBR-2 in DubnaDubnaDubna is a town in Moscow Oblast, Russia. It has a status of naukograd , being home to the Joint Institute for Nuclear Research, an international nuclear physics research centre and one of the largest scientific foundations in the country. It is also home to MKB Raduga, a defence aerospace company...
, RussiaRussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects... - AMOR at the Paul Scherrer InstitutePaul Scherrer InstituteThe Paul Scherrer Institute is a multi-disciplinary research institute which belongs to the Swiss ETH-Komplex covering also the ETH Zurich and EPFL...
(PSI) in VilligenVilligenVilligen is a municipality in the district of Brugg in the canton of Aargau in Switzerland. In January 2006, Villigen incorporated the former municipality of Stilli....
, SwitzerlandSwitzerlandSwitzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition.... - SURF, CRISP, INTER, Offspec and polREF at the ISIS neutron sourceISIS neutron sourceISIS is a pulsed neutron and muon source. It is situated at the Rutherford Appleton Laboratory on the Harwell Science and Innovation Campus in Oxfordshire, United Kingdom and is part of the Science and Technology Facilities Council...
(ISIS) in OxfordshireOxfordshireOxfordshire is a county in the South East region of England, bordering on Warwickshire and Northamptonshire , Buckinghamshire , Berkshire , Wiltshire and Gloucestershire ....
, United KingdomUnited KingdomThe United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages... - NG1, NG7 and AND/R at the NIST Center for Neutron Research (NCNR) in Gaithersburg, MarylandGaithersburg, MarylandGaithersburg is a city in Montgomery County, Maryland, United States. The city had a population of 59,933 at the 2010 census, making it the fourth largest incorporated city in the state, behind Baltimore, Frederick, and Rockville...
, United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district... - Liquids and Magnetic at the Spallation Neutron SourceSpallation Neutron SourceThe Spallation Neutron Source is an accelerator-based neutron source facility that provides the most intense pulsed neutron beams in the world for scientific research and industrial development...
(ORNL) in Oak Ridge, TennesseeOak Ridge, TennesseeOak Ridge is a city in Anderson and Roane counties in the eastern part of the U.S. state of Tennessee, about west of Knoxville. Oak Ridge's population was 27,387 at the 2000 census...
, United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district... - Neutron Reflectometer at the University of Missouri Research Reactor, in Columbia, MissouriColumbia, MissouriColumbia is the fifth-largest city in Missouri, and the largest city in Mid-Missouri. With a population of 108,500 as of the 2010 Census, it is the principal municipality of the Columbia Metropolitan Area, a region of 164,283 residents. The city serves as the county seat of Boone County and as the...
Partial list of neutron reflectometry software
- Reflred and reflfit (NIST Center for Neutron Research)
- Motofit
- Parratt32 (HMI)
- Yanera (Brock UniversityBrock UniversityBrock University is a comprehensive university located in St. Catharines, Ontario, Canada. Brock offers undergraduate, graduate and doctoral degree programs that include co-op and other experiential learning opportunities to an enrolment of over 17,000 full-time students.The enabling legislation is...
) - StochFit
- FitSuite
- GenX