Apatite Fission Track Thermochronology of Granite from the Xiazhuang Uranium Ore Field,South China:Implications for Exhumation History and Ore Preservation

Xiazhuang uranium ore field,located in the southern part of the Nanling Metallogenic Belt,is considered one of the largest granite-related U regions in South China.In this paper,we contribute new apatite fission track data and thermal history modeling to constrain the exhumation history and evaluate preservation potential of the Xiazhuang Uranium ore field.Nine Triassic outcrop granite samples collected from different locations of Xiazhuang Uranium ore field yield AFT ages ranging from 43 to 24 Ma with similar mean confined fission track lengths ranging from 11.8±2.0 to 12.9±1.9μm and Dpar values between 1.01 and 1.51μm.The robustness time-temperature reconstructions of samples from the hanging wall of Huangpi fault show that the Xiazhuang Uranium ore field experienced a time of monotonous and slow cooling starting from middle Paleocene to middle Miocene(~60-10 Ma),followed by relatively rapid exhumation in the late Miocene(~10-5 Ma)and nearly thermal stability in the Pliocene-Quaternary(~5-0 Ma).The amount of exhumation after U mineralization since the Middle Paleogene was estimated as~4.3±1.8 km according to the integrated thermal history model.Previous studies indicate that the ore-forming ages of U deposits in the Xiazhuang ore field are mainly before Middle Paleocene and the mineralization depths are more than 4.4±1.2 km.Therefore,the exhumation history since middle Paleocene plays important roles in the preservation of the Xiazhuang Uranium ore field.

Bulk geochemistry,Rb-Sr,Sm-Nd,and stable O-H isotope systematics of the Metzimevin high-grade iron ore deposit,Mbalam iron ore district,southern Cameroon

Bulk geochemistry,Sr,Nd,and O-H isotope systematics are reported for the first time on banded iron formation(BIF)-hosted high-grade iron ore at the northwestern segment of Congo Craton(CC).Located in Mbalam iron ore district,Southern Cameroon,Metzimevin iron ore deposit is a hematite-magnetite BIF system,dominated by SiO_(2)+Fe_(2)O_(3)(97.1 to 99.84 wt%),with low concentrations of clastic elements e.g.,Al_(2)O_(3),TiO_(2),and HFSE,depicting a nearly pure chemical precipitate.The REE+Y signature of the iron deposit displays strong positive Eu anomaly,strong negative Ce anomaly,and chondritic to superchondritic Y/Ho ratios,suggestive of formation by mixed seawater-high temperature hydrothermal fluids in oxidising environment.The^(87)Sr/^(86)Sr ratios of the BIF are higher than the maximum^(87)Sr/^(86)Sr evolution curves for all Archean reservoirs(bulk silicate earth,Archean crust and Archean seawater),indicating involvement of continentally-derived components during BIF formation and alteration.TheƐ_(Nd)(t)(+2.26 to+3.77)and Nd model age indicate that chemical constituents for the BIF were derived from undifferentiated crustal source,between 3.002 and 2.88 Ga.The variable and diverse O and H isotope data(−1.9‰to 17.3‰and−57‰to 136‰respectively)indicate that the Metzimevin iron ore formed initially from magmatic plumes and later enriched by magmatic-metamorphic-modified meteoric fluids.Mass balance calculations indicate mineralisation by combined leaching and precipitation,with an average iron enrichment factor of>2.67 and SiO_(2)depletion factor of>0.99.This is associated with an overall volume reduction of 28.27%,reflecting net leaching and volume collapse of the BIF protholith.

Diffusion and reaction mechanism of limestone and quartz in fluxed iron ore pellet roasting process

The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron ore powder and the mineralization mechanism of fluxed iron ore pellet in the roasting process were investigated through diffusion couple experiments.Scanning electron microscopy with energy dispersive spectroscopy was used to study the elements’diffusion and phase transformation during the roasting process.The results indicated that limestone decomposed into calcium oxide,and magnetite was oxidized to hematite at the early stage of preheating.With the increase in roasting temperature,the diffusion rate of Fe and Ca was obviously accelerated,while the diffusion rate of Si was relatively slow.The order of magnitude of interdiffusion coefficient of Fe_(2)O_(3)-CaO diffusion couple was 10^(−10) m^(2)·s^(−1) at a roasting temperature of 1200℃for 9 h.Ca_(2)Fe_(2)O_(5) was the initial product in the Fe_(2)O_(3)-CaO-SiO_(2) diffusion interface,and then Ca_(2)Fe_(2)O_(5) continued to react with Fe_(2)O_(3) to form CaFe_(2)O_(4).With the expansion of the diffusion region,the sillico-ferrite of calcium liquid phase was produced due to the melting of SiO_(2) into CaFe_(2)O_(4),which can strengthen the consolidation of fluxed pellets.Furthermore,andradite would be formed around a small part of quartz particles,which is also conducive to the consolidation of fluxed pellets.In addition,the principle diagram of limestone and quartz diffusion reaction in the process of fluxed pellet roasting was discussed.

Bioleaching of vanadium from stone coal vanadium ore by Bacillus mucilaginosus:Influencing factors and mechanism

Vanadium and its derivatives are used in various industries,including steel,metallurgy,pharmaceuticals,and aerospace engineering.Although China has massive reserves of stone coal resources,these resources have low grades.Therefore,the effective extraction and recovery of metallic vanadium from stone coal is an important way to realize the efficient resource utilization of stone coal vanadium ore.Herein,Bacillus mucilaginosus was selected as the leaching strain.The vanadium leaching rate reached 35.5%after 20 d of bioleaching under optimal operating conditions.The cumulative vanadium leaching rate in the contact group reached 35.5%,which was higher than that in the noncontact group(9.3%).The metabolites of B.mucilaginosus,such as oxalic,tartaric,citric,and malic acids,dominated in bioleaching,accounting for 73.8%of the vanadium leaching rate.Interestingly,during leaching,the presence of stone coal stimulated the expression of carbonic anhydrase in bacterial cells,and enzyme activity increased by 1.335-1.905 U.Enzyme activity positively promoted the production of metabolite organic acids,and total organic acid content increased by 39.31 mg·L^(-1),resulting in a reduction of 2.51 in the pH of the leaching system with stone coal.This effect favored the leaching of vanadium from stone coal.Atomic force microscopy illustrated that bacterial leaching exacerbated corrosion on the surface of stone coal beyond 10 nm.Our study provides a clear and promising strategy for exploring the bioleaching mechanism from the perspective of microbial enzyme activity and metabolites.

Geochemistry, mineral paragenesis and geothermal conditions of oreforming fluids from the Ain El Bey Cu–Fe deposit: potential occurrence of native gold and precious metal traces (North African orogenic belt, Northern Tunisia)

The Ain El Bey abandoned mine, in North-West Tunisia, fits into the geodynamic context of the European and African plate boundary. Ore deposit corresponds to veins and breccia of multiphase Cu–Fe-rich mineralization related to various hydrothermal fluid circulations. Petromineralogical studies indicate a rich mineral paragenesis with a minimum of seven mineralization phases and, at least, six pyrite generations. As is also the case for galena and native silver, native gold is observed for the first time as inclusion in quartz which opens up, thus, new perspectives for prospecting and evaluating the potential for noble metals associated with the mineralization. Scanning Electron Microscope--Energy Dispersive Spectroscopy and Transmission electron microscopy analyses show, in addition, a large incorporation of trace elements, including Ag and Au, in mineral structures such as fahlores(tetrahedrite-tennantite) and chalcopyrite ones. The mineral/mineral associations, used as geothermometers, gave estimated temperatures for the mineralizing fluids varying from 254 to 330 ℃ for phase Ⅲ, from 254 to 350 ℃ for phase Ⅳ, and from 200 to 300 ℃ for phases Ⅴ and Ⅵ. The seventh and last identified mineralization phase, marked by a deposit of native gold, reflects a drop in the mineralizing fluid’s temperature(< 200 ℃) compatible with boiling conditions. Such results open up perspectives for the development of precious metal research and the revaluation of the Cu–Fe ore deposit at the Ain El Bey abandoned mine, as well as at the surrounding areas fitting in the geodynamic framework of the Africa-Europe plate boundary.

Determination of critical state line(CSL)for silty-sandy iron ore tailings subjected to low-high confining pressures

The disposal of filtered tailings in high dry stacks can induce particle breakage,changing the material's behaviour during the structure's lifetime.The grading changes influence material properties at the critical state,and this is not mature for intermediate artificial soils(tailings)in a broad range of confining pressures.In this paper,it aims to describe the behaviour of iron ore tailings in a spectrum of confining pressures broader than the reported in previous studies.A series of consolidated drained(CD)triaxial tests was carried out with confining pressures ranging from 0.075 MPa to 120 MPa.These results show that the amount of breakage plays an essential role in the response of iron ore tailings.The existence of curved critical state line(CSL)in both specific volume(ν)-logarithm of mean effective stress(p′)and deviatoric stress(q)-mean effective stress(p′)planes,and different responses in the deviatoric stress-axial strain-volumetric strain curves were verified.An inverse S-shaped equation was proposed to represent the silty-sandy tailings'behaviour up to high pressures onν-lnp′plane.The proposed equation provides a basis for enhancing constitutive models and considers the evolution of the grading up to severe loading conditions.The adjustment considered three regions with different responses associated with particle breakage at different pressure levels.

Enhancing XRF sensor-based sorting of porphyritic copper ore using particle swarm optimization-support vector machine(PSO-SVM)algorithm

X-ray fluorescence(XRF)sensor-based ore sorting enables efficient beneficiation of heterogeneous ores,while intraparticle heterogeneity can cause significant grade detection errors,leading to misclassifications and hindering widespread technology adoption.Accurate classification models are crucial to determine if actual grade exceeds the sorting threshold using localized XRF signals.Previous studies mainly used linear regression(LR)algorithms including simple linear regression(SLR),multivariable linear regression(MLR),and multivariable linear regression with interaction(MLRI)but often fell short attaining satisfactory results.This study employed the particle swarm optimization support vector machine(PSO-SVM)algorithm for sorting porphyritic copper ore pebble.Lab-scale results showed PSO-SVM out-performed LR and raw data(RD)models and the significant interaction effects among input features was observed.Despite poor input data quality,PSO-SVM demonstrated exceptional capabilities.Lab-scale sorting achieved 93.0%accuracy,0.24%grade increase,84.94%recovery rate,57.02%discard rate,and a remarkable 39.62 yuan/t net smelter return(NSR)increase compared to no sorting.These improvements were achieved by the PSO-SVM model with optimized input combinations and highest data quality(T=10,T is XRF testing times).The unsuitability of LR methods for XRF sensor-based sorting of investigated sample is illustrated.Input element selection and mineral association analysis elucidate element importance and influence mechanisms.

Study of Iron Ore Processing Technology of Tamir Gol Deposit in Mongolia

Iron ore processing for steel production is crucial to the development and economy of Mongolia. Regardless of having abundant natural resources and raw materials, Mongolia almost doesn’t produce final products. So far, most mining and mineral beneficiation plants export raw materials only subjected to beneficiation process. Out of more than 200 deposits in Mongolia, 91 deposits had been explored with different methods and stages, and estimated the resource of 33 reserves. Without processing the iron ore, it is impossible to use it for steelmaking due to its high sulfur and phosphorus impurities. Therefore, to study the processing of iron ore deposits in Mongolia, we did a preliminary investigation of iron ore deposits and took samples from the Tamir Gol deposit with high silica and phosphorus content that is difficult to process. Then, conducted mineral analysis and determined the grain structure and beneficiation characteristics of Tamir Gol iron deposit. .

Applicability of Gravity Separation Method on the Ashashire Gold Ore Deposit from Benishangul Gumuz Region, Western Ethiopia

The study was conducted to determine the applicability of gravity separation method on the Ashashire gold ore deposit Benishangul gumuz region, western Ethiopia. The Ashashire composite was produced to provide sufficient mass for this study and experiment, including sample preparation, mineralogical analysis of gold and associated elements, gravity concentration, and data interpretation and analysis. During the study, a grind optimization was conducted on the composites sample with varying grind size to evaluate the effect of grind size on gold recovery. The ore was moderately ground to the standard grind size of 80%, passing 106 µm, 75 µm, 53 µm and this nominal size was selected for the preliminary assessment for concentration optimization for this deposit. The gravity testing comprised three-stage concentration using Knelson concentrator. High recovery of gold from the gravity concentrates was achieved from the second gravity concentration. Based on the laboratory experimental result analysis, a grind size of P80 75 µm is selected as optimal size for the Ashashire gold deposit. Increasing the grind size from P80 of 75 µm to 106 µm decreases the recovery rate from 75% to 54%, or decreasing the grind size from P80 of 75 µm to 53 µm decreases the gold recovery rate to 37%. The native gold grain in the ores is mostly associated with quartz and fine gold is closely associated with pyrite. According to analysis of the fire assay, chemical, and mineralogical data, only gold and telluride is commercially valuable elements in the ores. Predominantly gold was occurred in the native form of Au-Te. The sample subjected to gravity separation assayed about 2.6 g/t Au.

Roasting and chlorine leaching of gold-bearing refractory concentrate:Experimental and process analysis

This paper deals with gold extraction from a refractory concentrate by chlorine leaching.The process considers a pre-treatment of refractory materials by low temperature oxidation carried out with low oxygen concentration.The oxidized material is treated by leaching with brine.After gold adsorption/reduction onto activated carbon,iron and base metals can be precipitated by NaOH.Roasting tests show the necessity to carry out a thermal pre-treatment at least at 550°C to obtain a reduction of sulfur and mercury in the material(50%and 90%,respectively).Highest gold extraction yield(around 93%)is obtained in the leaching test performed with material sample treated at 650°C.This result confrms the necessity to optimize the thermal pre-treatment to improve Au recovery and to reduce chlorine consumption.A comparison with conventional cyanidation confrms that chlorination could be an useful alternative:in fact,gold extraction yield is quite low:57%in non-pre-treated material and 25%in pre-treatment material.

Ultrafine milling for the processing of gold-bearing sulphides

Ultrafine Milling technology is used to treat gold-bearingsulphides and to investigate the effects of minerals size, millingtime, liquid/solid ratio, NaCN consumption and leaching aid onleaching rate of gold. The results indicate that shorter treatingtime, decrease of NaCN consumption of 60/100 and increase of goldleaching rate of 15/100 can be ob- tained by the ultrafine millingtechnology compared with traditional cyanide leaching. Potentialexists for the new pro- cess to form the basis for an economicallyprocess for treatment of gold-bearing sulphides.

Pretreatment and thiosulfate leaching of refractory gold-bearing arsenosulfide concentrates

A hydrometallurgical process for refractory gold-bearing arsenosulfide concentrates at ambient temperature and pressure was presented, including fine grinding with intensified alkali-leaching （FGIAL）, enhanced agitation alkali-leaching （EAAL）, thiosulfate leaching and displacement. Experimental results on a refractory gold concentrate showed that the total consumption of NaOH in alkaline leaching is only 41% of those theoretically calculated under the conditions of full oxidization for the same amount of arse- nides and sulfides transformed into arsenates and sulfates, and 72.3% of gold is synchro-dissoluted by thiosulfate self-generated during alkaline leaching. After alkaline leaching, thiosulfate leaching was carried out for 24 h. The dissolution of gold is increased to 91.9% from 4.6% by cyanide without the pretreatment. The displacement of gold by zinc powder in the solution gets to 99.2%. Due to an amount of thiosulfate self-generated during alkaline leaching, the reagent addition in thiosulfate leaching afterwards is lower than the normal.

Amur Gold-Bearing Belt: Geotectonic Position and Perspectives for Revealing New Deposits of Precious Metals

The ore-bearing belts, specialized for precious metals, are substantia ted to exist in the south Far East of Russia. The longest of which is the Amursk y gold-bearing belt extended from the Amur River mouth to the Ussuri River lowe r course and further to the southwest on China territory, probably, to the Sungar i River head. The fact that we have distinguished the Amursky and other gold-be a ring belts, make it possible to reevaluate the perspectives of the South Far Eas t of Russia and North-East China for new deposits of precious metals.

Lithium extraction from hard rock lithium ores(spodumene,lepidolite,zinnwaldite,petalite):Technology,resources,environment and cost

Lithium production in China mainly depends on hard rock lithium ores,which has a defect in resources,environment,and economy compared with extracting lithium from brine.This paper focuses on the research progress of extracting lithium from spodumene,lepidolite,petalite,and zinnwaldite by acid,alkali,salt roasting,and chlorination methods,and analyzes the resource intensity,environmental impact,and production cost of industrial lithium extraction from spodumene and lepidolite.It is found that the sulfuric acid method has a high lithium recovery rate,but with a complicated process and high energy consumption;alkali and chlorination methods can directly react with lithium ores,reducing energy consumption,but need to optimize reaction conditions and safety of equipment and operation;the salt roasting method has large material flux and high energy consumption,so require adjustment of sulfate ratio to increase the lithium yield and reduce production cost.Compared with extracting lithium from brine,extracting lithium from ores,calcination,roasting,purity,and other processes consume more resources and energy;and its environmental impact mainly comes from the pollutants discharged by fossil energy,9.3-60.4 times that of lithium extracted from brine.The processing cost of lithium extraction from lepidolite by sulfate roasting method is higher than that from spodumene by sulfuric acid due to the consumption of high-value sulfate.However,the production costs of both are mainly affected by the price of lithium ores,which is less competitive than that of extracting lithium from brine.Thus,the process of extracting lithium from ores should develop appropriate technology,shorten the process flow,save resources and energy,and increase the recovery rate of related elements to reduce environmental impact and improve the added value of by-products and the economy of the process.

THIOUREA LEACHING OF GOLD FROM A CALCINE OF GOLD-BEARING ARSENICAL PYRITE CONCENTRATE

The thiourea leaching of gold from the calcine of gold-bearing arsenical pyrite concentrate of Kangjiawan mine was studied.The effects of the leaching time,the concentrations of thiourea,hydrochloric acid and initial ferric ion on the leaching recovery of gold were investigated,and a regressive model has been established,which showed that the concentrations of thiourea and hydrochloric acid were the most important factors,leaching time the second,and concentration of the initial ferric ion the least・Under the optimal conditions,that is,temperature 50℃,the ratio of liquid to solid 4:1,thiourea 12g/L,hydrochloric acid 1 mol/L,and initial ferric ion 1 g/L,the leaching recoveries of gold and silver were more than 81%and 73%,respectively.The increase of silver recovery and the reduction of thiourea consumption could be attained when sodium sulphite was added.

Genesis and metallogenic characteristic of Dongnan Cu–Mo deposit associated granitoids:LA-ICP-MS zircon U–Pb dating and isotope constraint from Zijinshan ore field in southeastern China

The Dongnan Cu–Mo deposit,located in the southeast of the Zijinshan ore field(the largest porphyry–epithermal system in Southeast China),represents the complex magmatic and metallogenesis events in the region.The petrogenesis and metallogenesis of granitoids from the deposit are not determined,especially the interactions between ore-bearing(granodiorite porphyry)and barren samples(granodiorite and diorite).In the paper,the whole rock geochemical features shared a similar affinity to the middle-lower content and revealed that they derived from partial melting of the Cathaysian basement with the contribution of mantle materials,even represented that they generated in the plate subduction;LA-ICP-MS zircon U–Pb ages show that these granodiorites,granodioritic porphyry and diorite,were generated during 114–103 Ma.The ore-bearing samples mostly presented ε_(Hf)(t)of negative values(peak value is-4 to-3)with old two-stage Hf model ages(t_(DM)^(2))(peak value is 1.10–1.15 Ga),while the barren sample showed slightly negative ε_(Hf)(t)(peak value is-1 to 0)values with young t_(DM)^(2)(peak value is 1.00–1.05 Ga).The value of zircon Ce^(4+)/Ce^(3+)ratio mostly higher than 450 was first verified for the ore-bearing samples in the Dongnan Cu–Mo deposit,and the values of ore-bearing were found to be higher than those from the barren,which suggests that the ore-bearing formed in more oxidized parental magma with higher oxygen fugacity.Based on the geochemical characteristic of the element and isotope,we concluded that the Early Cretaceous multiphases magmatic activities,low melting temperature and low pressure of pluton,and high oxygen fugacity of zircon,were the favorable conditions for metallogenesis of Dongnan Cu–Mo deposit.

Real-time ore sorting using color and texture analysis

Sensor-based ore sorting is a technology used to classify high-grade mineralized rocks from low-grade waste rocks to reduce operation costs.Many ore-sorting algorithms using color images have been proposed in the past,but only some validate their results using mineral grades or optimize the algorithms to classify rocks in real-time.This paper presents an ore-sorting algorithm based on image processing and machine learning that is able to classify rocks from a gold and silver mine based on their grade.The algorithm is composed of four main stages:(1)image segmentation and partition,(2)color and texture feature extraction,(3)sub-image classification using neural networks,and(4)a voting system to determine the overall class of the rock.The algorithm was trained using images of rocks that a geologist manually classified according to their mineral content and then was validated using a different set of rocks analyzed in a laboratory to determine their gold and silver grades.The proposed method achieved a Matthews correlation coefficient of 0.961 points,higher than other classification algorithms based on support vector machines and convolutional neural networks,and a processing time under 44 ms,promising for real-time ore sorting applications.

Mechanical behavior of iron ore tailings under standard compression and extension triaxial stress paths

The disposal of mining tailings has increasingly focused on the use of dry stacks.These structures offer more security since they use filtered and compacted material.Because of the construction method and the heights achieved,the material that compounds the structure can be subjected to different stress paths along the failure plane.The theoretical framework considered in the design of these structures generally is the critical state soil mechanics(CSSM).However,the data in the literature concerning the uniqueness of critical state line(CSL)is still controversial as the soil is subjected to different stress paths.With respect to tailings,this question is even more restricted.This paper studies two tailings with different gradings due to the beneficial processes over extension and compression paths.A series of drained and undrained triaxial tests was conducted over a range of initial densities and stress levels.In the q-p'plane,different critical stress ratio(M)values were obtained for compression and extension stress paths.However,the critical state friction angle is very similar with a slightly higher critical state friction angle for extension tests.Curved stress path dependent CSLs were obtained in the n-lnp0 plane with the extension tests below the CSL defined in compression.Regarding the fines content,the studied tailings presented very similar M and critical state friction angle values.However,the fines content af-fects the volumetric behavior of the studied tailings and the CSLs on the n-lnp0 plane shift downwards with the increasing fines content for compression and extension tests.In relation to dilatancy analysis,the fines content did not present an evident influence on the dilatancy of the materials.However,different values of mean stress ratio N were obtained between compression and extension tests and can corroborate the existence of non-unique CSLs for these materials.

An integrated and efficient process for borax preparation and magnetite recovery from soda-ash roasted ludwigite ore under CO–CO_(2)–N_(2) atmosphere

To realize the comprehensive utilization of ludwigite ore,an integrated and efficient route for the boron and iron separation was proposed in this work,which via soda-ash roasting under CO–CO_(2)–N_(2) atmosphere followed by grind-leaching,magnetic separation,and CO_(2) carbonation.The effects of roasting temperature,roasting time,CO/(CO+CO_(2))composition,and Na_(2)CO_(3) dosage on the boron and iron separation indices were primarily investigated.Under the optimized conditions of the roasting temperature of 850℃,roasting time of 60 min,soda ash dosage of 20 wt%,and CO/(CO+CO_(2)) of 10 vol%,92%of boron was leached during wet grinding,and 88.6%of iron was recovered during the magnetic separation and magnetic concentrate with a total iron content of 61.51 wt%.Raman spectra and^(11)B NMR results indicated that boron exists asB(OH)_(4)^(-) in the leachate,from which high-purity borax pentahydrate could be prepared by CO_(2) carbonation.

Gold-bearing formations and their evolution in central Inner Mongolia

In central Inner Mongolia, five gold bearing formations (Xiajining, Dongwufenzi, Wulashan, Baiyunebo and Bainaimiao Groups) belong either to volcano sedimentation or clasolite sedimentation. They formed in different tectonic environments such as an Archean rift zone (Xiajining and Dongwufenzi Groups), an Early Proterozoic stable basin (Wulashan Group), a Middle to Late Proterozoic continental rift zone (Baiyunebo Group), and a Paleozoic island arc environment (Bainaimiao Group). Gold contents in the gold bearing formations in the area are higher than those of other gold bearing formations in the North China Craton. However, as most gold bearing formations in the area are limited, there are a few big gold deposits in central Inner Mongolia. Gold contents in all formations were strongly influenced by migmatization and ductile shearing, the former process prompting mobilization, and the latter process resulting in gold enrichment in ductile shear zones. During the development of Archean to Proterozoic gold bearing formations, gold migrated from the mantle to the crust, then through the crust, finally deposited at the earth’s surface.