Scanning Probe Microscopy - Assignment Example

Scanning Microscopy Honours module take home exam 2017 Student Name/Number: Date: Scanning probe microscopy section 1. Figure 1. The above plot shows the interatomic force versus distance curve an AFM tip experiences as it approaches a surface. a. At approximately what distance would an AFM tip sense the attractive interatomic forces? (2 marks) 10 nm b. At approximately what distance would an AFM tip sense the repulsive interatomic forces? (2 marks) 0.1 nm c. What is another name typically used for “interatomic forces” (1 mark) Van der Waals forces 2 a) What is a cantilever? (1 mark) A cantilever is a flexible spring that holds the probing tip. The interaction between the tip and the specimen causes the deflections in the cantilever. b. It is relatively easy to make a cantilever with a spring constant low enough to sense the forces between atoms, such as a cantilever made of aluminium foil that is 4 mm long and 1 mm wide. However AFM cantilever manufacturers do not make cantilevers that large. They make them much smaller, typically 100 to 200 microns long and 20 to 50 microns wide. What is the reason for this? (5 marks) Smaller cantilevers have two main advantages: Smaller cantilevers are more sensitive - they can sense interaction forces in high-speed AFM; and They can resonate at high frequencies (in the MHZ regime). 3. Describe how an AFM image is formed in constant force contact mode. (4 marks) In constant-force contact mode, the cantilever deflections are used as the input to a feedback loop that moves the scanner up and down at a constant probe-sample force. The output of the cantilever controls the distance along the -axis to keep a constant force during scanning and responds to the topography of the specimen by keeping a constant deflection. A proper feedback loop continuously adjusts the deflection of the cantilever during the scanning process. The scanner’s motion generates the data (feedback output) that is used to produce the specimen surface topography (AZONANO, 2012). 4. How is the force the AFM tip exerts on the sample surface related to its deflection or bending? (1 marks) From Hooke’s law; Where: – Force applied – Spring constant – Cantilever deflection If the force applied on the sample increases, the cantilever deflection also increases and when the force applied is reduced, deflection also reduces. 5. What are the advantages and disadvantages of contact mode compared to tapping mode? (4 marks) Advantages: High atomic resolution High scan rates Tapping mode can scan specimens that have extremely varying vertical topography. Disadvantages: High frictional and adhesive forces may damage the specimen – producing data with a distorted image. In ambient conditions, sample imaging using contact mode may experience capillary forces resulting from adsorbed fluid layer. This causes normal forces at the tip-sample interaction. A combination of both lateral and normal forces may cause reduced resolution. 6. What is kept constant during imaging in tapping mode? (1 mark) The oscillation amplitude of the cantilever 7.  Figure 2. Shows a typical resonance curve for an AFM tapping mode cantilever. a.Define what resonance frequency means in terms of an AFM cantilever (2 marks) Resonance frequency is the natural frequency at which the AFM cantilever vibrates as it scans the sample (Raman, et al., 2008). It is given by: = Where: – Spring constant – Mass of the atom b. Define what Q factor means in terms of an AFM cantilever resonance curve (2 marks) Q factor is a dimensionless parameter or the ratio of resonance frequency to the bandwidth. Higher Q factor is desired to optimize the sensitivity of the cantilever (Chen, et al., 2007). c. Determine the approximate Q factor for the resonance curve in figure 2 (The resonance curve is in an attached excel file called Figure 2) (5 marks) Q factor = = 320 kHz/ (2.99-2.98)102 kHz Approximate Q factor = 8. What advantages does tapping mode have in comparison to contact mode? (3 marks) i. High image resolution ii. Can be used to image soft and fragile samples without inducing destructive forces. Tapping mode generates low shear forces during scanning. iii. The tapping mode can be used to analyse the membrane components when phase imaging is incorporated (MyScope, 2017). 9. Why is the spring constant and resonant frequency for tapping mode probes much larger, compared to contact mode probes when operating in air? (Hint: capillary layer) (4 marks) The spring constant and resonance frequency for tapping mode probes is much larger (in the range of 2-50N/m for spring constant, and 50-400 kHz for resonance frequency) to prevent the sticking or adherence of the probing tip to the sample surface due to capillary forces (MikroMasch, 2017). 10. What information about the sample surface can force distance curves potentially give? (2 marks) Sample elasticity Degree of hydrophobicity Density of the surface charges 11. The company called Bruker Corporation have developed an imaging mode called PeakForce tapping a. Describe how this imaging mode works (5 marks) The probe taps the specimen periodically. The pN-level interaction force during the taping is measured using the cantilever deflection. The feedback loop maintains a constant peak force to about 10 pN, which is significantly lower compared to other modes. This technique works in both fluid and air (BRUKER, 2017). b. What are the advantages of this imaging mode compared to other imaging modes? (3 marks) Provides the highest resolution in AFM Ease of use Protects the sample and probe from damage The technique is rapid because it operates at high frequencies 12 What does calibration mean? Why is calibration such an important part of any experiment? (3 marks) Calibration is a process of checking the accuracy of an instrument used in measurement by comparing with a standard. Calibration is important in maintaining the accuracy of an instrument, ensuring that the readings obtained are consistent with other measurements, and also establish instrument reliability. 13. What is quantitative data? (1 mark) Quantitative data is a measurement of values or counts and expressing them using numbers. 14. In order to accurately measure quantitative forces using AFM what components of the microscope must be calibrated? (4 marks) The probing tip Cantilever deflection 15. Describe a technique to calibrate the cantilever deflection of an AFM cantilever. Give advantages and disadvantages of the technique. (4 marks) Thermal Noise Method – This technique appeals to the equipartition theorem. If a cantilever is assumed to be an ideal spring, with a spring constant, measurement of its thermal noise allows the determination of the spring constant using the following equation: Where: – Spring constant - Boltzmann's constant  T - Absolute temperature (Kelvin) – Measurement of thermal noise Advantage: Ease of use Disadvantages: Assumes dumping effect. Requires a cantilever to be compressed against a hard surface (Burnham, et al., 2003). 16. Read the following paper carefully and answer the following questions 16a to 16e Paper citation information Title: A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy Journal: Review of Scientific Instruments Volume: 64 Year: 1993 Page or article number: 403 to 405 Authors: J. P. Cleveland, S. Manne, D. Bocek and P. K. Hansma DOI: 10.1063/1.1144209 a. What are the advantages and disadvantages of the method described in the paper? (4 marks) Advantages: The method provides a non-destructive way of determining the spring constant as well as the effective mass of a cantilever. By using the method described in the paper, it is possible to determine the spring constant for applications that do not require high precision by measuring the unloaded resonance frequency. Disadvantage: The assumption in the method that all cantilevers are identical in all aspects, except for their thickness is not real. b. Describe the sources of error for this method? (4 marks) There are two sources of errors for this method: i. Measurement of the diameters of the tungsten spheres; and ii. The micro-positioning of the tungsten spheres relative to the probing tip where forces are applied during the sample scanning process. Minimization of the above errors can be achieved by using pre-calibrated masses and taking a lot of care when positioning the spheres. c. What happens to the resonant frequency and Q factor of a cantilevers resonance curve when mass is added to the cantilever? (3 marks) The resonant frequency increases with addition of masses to the cantilever. This is also the same case with the Q factor – it increases with the added mass. d. Why is it best to use Tungsten or gold spheres as the added mass? (2 marks) Tungsten and gold provide several isolated spheres. This is because of their appropriate size distribution (ranging from 15 μm to 20 μm). The interactions that occur between the spheres and the glass are strong enough to ensure that the spheres are well secured on the cantilever. e. A sphere made of pure gold with a diameter of 10 microns is attached to the end of an AFM cantilever. The cantilever has an initial resonant frequency of 10 kHz and a resonant frequency of 8 kHz after the sphere is attached. What is the spring constant of the cantilever? Do not just write down the answer also describe how you calculated the answer. (Big hint: Use the first of the equations marked as (5) in the paper) (4 marks) Solution: Mass of gold (M) = Density of pure gold volume = 19320 [4/3 (5.0E -6)3] = 1.0116 10-11 Kg = 1.0116 10-10 Newtons Using the equation: , Where: – Spring constant – Mass of the sphere (Newtons) – Resonance frequency after the sphere is attached – Initial resonance frequency Substituting all the terms; 17. When imaging a carbon nanotube sample using AFM the measured height of the nanotubes is typically much smaller than the measured width. Why? (3 marks) This is caused by the finite tip width. The measured width is obtained by adding the tip width to the actual line. When this two measurements are combined, they can be used to calibrate the probing tip (DeBorde, et al., 2008). 18. Describe 2 techniques you could use to determine the diameter of an AFM tip. What advantages and disadvantages do they have? (6 marks) Using Spheres – These technique is uses spheres to measure the diameter of the tip. Calculation of the radius of the tip is obtained provided that only the apex of the probing tip is used. Advantages: Require little de-convolution Can be used for all sizes Disadvantage: Easy to make a measurement error Circular Posts and Depressions – This method employs the use of fabricated structures such as posts and round holes to measure the diameter of the probing tip. Advantage: Provides calibration for X-Y axis Disadvantages: Only measures limited sizes of tip diameters Consumes a lot of time 19. What advantages do carbon nanotube tips have in comparison to standard silicon or silicon nitride tips? (3 marks) Mechanical robustness They have a large Young’s Modulus They have a smaller diameter Unique chemical properties High aspect ratio They have a well-defined structure (Schwarz, et al., 2004). 20. Describe three methods to attach carbon nanotubes to AFM tips (12 marks) i. Focus Ion Beam (FIB) Technology – In this method, a FIB tool is used to create a slot in the cantilever tip in which the carbon nanotube is to be inserted. The inserted carbon nanotube is welded to the probing tip using a FIB tool to deposit atoms of the metal (Shapiro, et al., 2004). ii. Electric field induced attachment – In this technique, an electric field is used to align the carbon nanotube along the axis of the probing tip. iii. Magnetic field induced attachment – This technique is similar to the electric field induced attachment, but a magnetic field is used in this case, as opposed to an electric field (Chow & Chai, 2010). The advantage of electric and magnetic field is that these two methods provide for adjustment of the nanotube orientation. Raman microscopy section 1. What is the selection rule for a molecule or material to be Raman active? (3 marks) Raman selection rule for a molecule or material is that there must be some change in polarizability during the process of transition from one state to another. What this means is that Raman transition will only occur if there will be a change in polarizability of a material from one transition to another. 2. What is Stokes scattering? (3 marks) This is a Raman scattering in which the material absorbs energy and the absorbed photon has higher energy compared to the emitted photon. 3. Why are most Raman microscopes based on Stokes scattering? (2 marks) The Stokes peaks and lines are stronger and more intense compared to the anti-Stokes lines and peaks. Stokes scattering is a more probable event than anti-Stokes scattering. 4. What information about a sample can Raman scattering potentially give? (5 marks) Chemical structure (molecular orientation and shape) and sample identity Vibrational symmetry Phase and polymorphism Sample contamination Intrinsic strain and stress 5. What is Rayleigh scattering? What problem does it pose for Raman scattering? How can it be counteracted? (6 marks) Rayleigh scattering refers to the elastic scattering of light by particles that are much smaller compared to the wavelength of the electromagnetic radiation. The problem posed by Rayleigh scattering is that it is stronger than Raman scattering and this can be counteracted by using a filter that is specific to the incident wavelength or the excitation source. 6. Why is it an advantage to have a Raman microscope with a range of excitation wavelengths (e.g. 532 nm, 633 nm and 785 nm) (5 marks) Having a range of excitation wavelengths increases sensitivity, high spatial resolution, and optimization of the results based on the behaviour of the sample (Bokobza, et al., 2015). 7. Figure 3. Raman spectrum of carbon nanotubes on silicon. a. For peaks 1 to 7 assign which ones are for elastic scattering and which are for silicon and carbon nanotubes. (7 marks) #Peak What It Represents 1 Carbon nanotube 2 Silicon nanotube 3 Carbon nanotube 4 Elastic scattering 5 Silicon 6 Silicon nanotube 7 Silicon nanotube b. What are the typical names given for peaks 2, 5, 6 and 7? What information do they give about the associated material? (6 marks) 8. Figure 4. Raman spectrum of Graphene on silicon. What information can peak 2 in figure 4 (at ~2680 wavenumbers and is known as either the 2D band) give about the Graphene sample? (6 marks) The 2D band can provide information about the number of layers present in the graphene - whether it is a single layer or a multilayer. This band is a single Lorentzian for single layer graphene, while for bilayer graphene, the 2D band splits into multiple peaks (Dresselhaus, et al., 2002). 11. Will the resolution of a Raman image using a 513 nm laser be better or worse than using a 785 nm laser, assuming the same objective is being used? (2 mark) In Raman imaging, spatial resolution is higher for lower wavelength than in higher wavelength. Thus, using a 513 nm laser will produce a better image than a 785 nm laser. 12. Why is the tip used in Tip enhanced Raman spectroscopy (TERS) coated with a metal or metal nanoparticle such as gold or silver? (3 marks) TERS is used for analysis of nanoscale surfaces for their high spatial resolution and single molecule sensitivity. Gold and silver are the preferred coating materials used to fabricate TERS tips due to their strong LSPR effect and high free electron density (Kumar, et al., 2015). 13. What is the main advantage of TERS imaging over conventional Raman imaging? (2 marks) TERS imaging can overcome the diffraction limit of conventional Raman imaging. Electron microscopy section 1. What advantage does using electrons as the excitation source in a microscope have in comparison with using optical light? (2 marks) i. Electrons act as both waves and particles ii. It is possible to manipulate electrons using electromagnetic and electrostatic fields, hence no need of glass lenses. 2. Can the Numerical Aperture (NA) of an electron microscope be superior to than in an optical microscope? Why? (5 marks) The NA of an electron microscope is superior to that of an optical microscope. This is because electron microscope produce shorter wavelength that increase the resolving power and provide better resolution. 3. What limitations does TEM have in comparison to SEM? (3 marks) TEM has a limited field of view Produce 2-D black and white images, SEM produces 3-D images Only a small sample can be analysed at a time Energy losses as the electrons pass through the sample 4. What factors determine the resolution of an SEM image? (3 marks) The cross-over diameter Accelerating voltage 5. What information can SEM give about a sample? (5 marks) SEM provides the following information: Crystalline structure of the sample Topography (texture)/ morphology Chemical composition of the sample Orientation of the elements present in a sample 6. What are the advantages and disadvantage SEM has in comparison to AFM? (8 marks) Advantages: A large depth of field Provide more sample details Provide different types of information about sample composition There are many analytical modes used in sample imaging Disadvantages: SEM requires a vacuum environment, while AFM can be carried out in gas or liquid, ambient or vacuum environment. SEM has insufficient resolving compared to AFM and therefore, cannot produce a greater level of detail about a sample surface. 7. What is depth of field in a microscope image? How does the depth of field of an SEM compare to an optical microscope (6 marks) Depth of field refers to the distance from the closest object plane in focus to the furthest object plane in focus. SEM has a greater depth of field compared to optical microscope. Is a specimen has millimetre high details, the penetration of a beam of electrons used in SEM provide the capability to image smaller details. 8. Why is there no colour in an SEM image? (4 marks) SEM imaging produces a single value per pixel. Each of these values is represented by a grey level which forms an image characterized by black and white parts. The use of a scattered electron beam only reveals the details of the specimen sample. 9. Name and describe two imaging modes used in SEM? (6 marks) High current mode – In this mode, large beam currents are used to provide better image visibility and quality. Resolution mode – In this mode, the spot size should be as small as possible. There must also be sufficient current to surpass the visibility threshold for the highest image resolution. 10. What disadvantages does SEM have in comparison to Raman microscopy? (4 marks) SEM is limited to solid and inorganic specimens Artefacts may result from sample preparation 11. Why must scanning electron microscopes operate under vacuum? (Choose a,b,c or d) (1 mark) a. To prevent samples from degrading b. To stop the scattering of high energy electrons of the beam c. To prevent the electromagnetic lenses from heating up d. All of the above Answer: b. 12. What coating type is preferred for carrying out compositional imaging on a conductive specimen? (Choose a,b,c or d) (1 mark) a. Gold coating b. No coating c. Carbon coating d. Platinum coating Answer: b 13. What is astigmatism in an SEM image? How can it be corrected? (5 marks) Astigmatism is a form of distortion of the probe cross section caused by various factors including the level of machining accuracy and the pole-piece material, imperfections in casted iron magnets and windings etc. This kind of distortion causes difficulties in focusing the image. 14. What is scanned across the surface in each of the following microscopes to generate an image (3 marks). a. AFM – solids b. SEM - solids c. Raman imaging – solids, liquids and gases 15. Out of the following techniques, AFM, Raman, SEM and TEM, which have the capability to determine the diameter of carbon nanotubes? (4 marks) Answer: Raman scattering Additional questions 1. Questions 1a to 1i are based on the information from the following paper Paper citation information Title: Accurate thickness measurement of graphene Journal: Nanotechnology Volume: 27 Year: 2016 Page or article number: 125704 Authors: CJ Shearer, AD Slattery, AJ Stapleton, JG Shapter, CT Gibson DOI: 10.1088/0957-4484/27/12/125704 a. What is the main purpose of the article and what are its conclusions? (8 marks) The main purpose was to establish a protocol that can help users to determine the thickness of graphene films using standard and carbon nanotube-modified AFM probes with an imaging mode known as PeakForce tapping. The authors concluded that the new imaging mode reduces the measurement error from 0.1–1.3 nm to 0.1–0.3 nm. Accurate measurement of graphene films depend on components such as the imaging force and the adsorbate layer formed by graphene and substrate (Shearer, et al., 2016). b. What important information is the Raman data giving about the sample in this article? (3 marks) Raman data provides the information about the number of layers of graphene in the sample. c. Raman scanning of the sample also serves another useful purpose. What is it? (4 marks) Raman scanning also shows the intensities of G-band and 2D band of the sample area investigated. d. What limitation does Raman have in terms of analysing graphene samples? (3 marks) Power lasers cause heating of graphene samples which may alter its physical properties. e. What information is the SEM data giving in this article? (3 marks) SEM data indicates that the SWCNT probe has a smaller diameter compared to the standard tip (Shearer, et al., 2016). f. What is the reason the author’s give for analysing the surface with a carbon nanotube tip? (5 marks) A carbon nanotube tip was used to analyse the sample because it does not exert a lot of pressure when measuring graphene thickness. g. What reason is given for the change in diameter of the standard AFM tip before and after imaging? (2 marks) This is due to the increased force that is applied, which causes the tip to adjust to a stable condition during imaging. h. What was the NA and working distance of the objective used to collect the Raman data? (2 marks) NA = 0.9, objective = 100x Working distance = 0.23 mm i. According to the article what range of thickness values have been reported for single layer graphene using AFM? (1 mark) 0.4 – 1.8 nm 2 From the article in the previous question look up citation 20 in the Reference list. The following questions are based on information from citation 20. a. What is the purpose of the Raman data in this article? (3 marks) Raman data was used as a comparative measurement of thickness of FLG flakes to the measurements obtained in tapping mode AFM. b. What reason or reasons do the authors give for the apparent anomalies in heights or thickness for graphene measured using tapping mode AFM? (5 marks) Inappropriate range of free amplitude values and set point of the AFM cantilever. Unreliability of tapping mode AFM measurements in the attractive regime c. The authors use contact mode AFM to analyse a sample of graphene. What problem do they discover when using contact mode to measure the thickness of the graphene sample? (3marks) Different lateral forces on the FLG flake and support can result in deviations in the measured thickness when contact mode is used (Nemes-Incze, et al., 2008).   2. Figure 5a is a Raman image of a flake of Graphene oxide on silicon. The yellow/brown/orange coloured region is the flake of Graphene oxide and the Raman peak intensity plotted is the G-band peak located at approximately 1600 wavenumbers. Remember in a Raman image each point or pixel effectively represents a Raman spectra. The Raman spectra displayed in Figure 5c is an average of all the Raman spectra located only on the Graphene oxide flake which is defined as the spectra located within the white outlined region in Figure 5b. If the number of pixels in this image is 100 x 100 = 10,000 approximately how many pixels or Raman spectra is the average Raman spectra in figure 5c composed of? Show your working to the problem. (10 marks) Solution: Spectral range () = wavenumbers Number of pixels in the detector = Maximum intensity = 1.5 units Estimated number of pixels in figure C = Max. Intensity x spectral range x Number of pixels in the detector = = 9 million pixels 3. Euler beam equations can be used to determine the spring constant of AFM cantilevers with a variety of geometries. Figure 6a and 6b show the top-down view of two typical shapes for AFM cantilevers with the different dimensions of the cantilevers defined. Figure 6a is a rectangular or beam shaped cantilever and figure 6b is a trapezoidal shaped cantilever. The Euler beam equation for a rectangular cantilever is given in equation 1 (1) Where k is the spring constant of the cantilever, t is the thickness, w0 is the width, L is the length and E is the Young’s modulus of the cantilever material The Euler beam equation for a trapezoidal shaped cantilever is given by equation 2 (2) Where C is determined using Figure 7 and depends on the ratio of the top width of the trapezoidal cantilever (w) to the base width (w0). Given equation 2 and Figure 7 what would be the Euler beam equation for a cantilever with a triangular geometry? Show your working to the problem. (10 marks) Using figure 7 for a triangle; = 0/ ( = 0 The value of C at = 0 from figure 7; = 1.5 Substituting the value of C in equation 2; Hence, the Euler beam equation for a cantilever with a triangular geometry will be given by the equation: References Read More

6. What is kept constant during imaging in tapping mode? (1 mark) The oscillation amplitude of the cantilever 7.  Figure 2. Shows a typical resonance curve for an AFM tapping mode cantilever. a.Define what resonance frequency means in terms of an AFM cantilever (2 marks) Resonance frequency is the natural frequency at which the AFM cantilever vibrates as it scans the sample (Raman, et al., 2008). It is given by: = Where: – Spring constant – Mass of the atom b. Define what Q factor means in terms of an AFM cantilever resonance curve (2 marks) Q factor is a dimensionless parameter or the ratio of resonance frequency to the bandwidth.

Higher Q factor is desired to optimize the sensitivity of the cantilever (Chen, et al., 2007). c. Determine the approximate Q factor for the resonance curve in figure 2 (The resonance curve is in an attached excel file called Figure 2) (5 marks) Q factor = = 320 kHz/ (2.99-2.98)102 kHz Approximate Q factor = 8. What advantages does tapping mode have in comparison to contact mode? (3 marks) i. High image resolution ii. Can be used to image soft and fragile samples without inducing destructive forces.

Tapping mode generates low shear forces during scanning. iii. The tapping mode can be used to analyse the membrane components when phase imaging is incorporated (MyScope, 2017). 9. Why is the spring constant and resonant frequency for tapping mode probes much larger, compared to contact mode probes when operating in air? (Hint: capillary layer) (4 marks) The spring constant and resonance frequency for tapping mode probes is much larger (in the range of 2-50N/m for spring constant, and 50-400 kHz for resonance frequency) to prevent the sticking or adherence of the probing tip to the sample surface due to capillary forces (MikroMasch, 2017). 10. What information about the sample surface can force distance curves potentially give? (2 marks) Sample elasticity Degree of hydrophobicity Density of the surface charges 11.

The company called Bruker Corporation have developed an imaging mode called PeakForce tapping a. Describe how this imaging mode works (5 marks) The probe taps the specimen periodically. The pN-level interaction force during the taping is measured using the cantilever deflection. The feedback loop maintains a constant peak force to about 10 pN, which is significantly lower compared to other modes. This technique works in both fluid and air (BRUKER, 2017). b. What are the advantages of this imaging mode compared to other imaging modes? (3 marks) Provides the highest resolution in AFM Ease of use Protects the sample and probe from damage The technique is rapid because it operates at high frequencies 12 What does calibration mean?

Why is calibration such an important part of any experiment? (3 marks) Calibration is a process of checking the accuracy of an instrument used in measurement by comparing with a standard. Calibration is important in maintaining the accuracy of an instrument, ensuring that the readings obtained are consistent with other measurements, and also establish instrument reliability. 13. What is quantitative data? (1 mark) Quantitative data is a measurement of values or counts and expressing them using numbers. 14. In order to accurately measure quantitative forces using AFM what components of the microscope must be calibrated? (4 marks) The probing tip Cantilever deflection 15.

Describe a technique to calibrate the cantilever deflection of an AFM cantilever. Give advantages and disadvantages of the technique. (4 marks) Thermal Noise Method – This technique appeals to the equipartition theorem. If a cantilever is assumed to be an ideal spring, with a spring constant, measurement of its thermal noise allows the determination of the spring constant using the following equation: Where: – Spring constant - Boltzmann's constant  T - Absolute temperature (Kelvin) – Measurement of thermal noise Advantage: Ease of use Disadvantages: Assumes dumping effect.

Requires a cantilever to be compressed against a hard surface (Burnham, et al., 2003). 16.

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